Spatial Vision Vol 21 No 3ndash5 pp 201ndash227 (2008) Koninklijke Brill NV Leiden 2008Also available online - wwwbrillnlsv

How do painters represent motion in garmentsGraphic invariants across centuries

SIMONE GORI lowast RICCARDO PEDERSINI and ENRICO GIORADepartment of General Psychology University of Padua Italy

Received 25 June 2006 accepted 26 December 2006

AbstractmdashWestern visual art has radically changed throughout the centuries different techniquesinterest in the representation of reality and use of graphic signs Indeed only a few pictorial cueshave retained the same meaning and use These kinds of graphic invariants may play a key role notonly in a comparative study of art history but also for discovering underlying common perceptualmechanisms Here the aim is to show that western painters use the same graphic solutions torepresent motion in garments across countries and centuries A pilot experiment using 160 paintingsrepresentative of all main western European art movements from the thirteenth to the twentiethcentury shows that different artists represented the motion of garments with the same orientationcurvature and convergence of lines Experiment 1 demonstrates with a smaller sample of paintings(16 ie two per century) that the relationship between orientation curvature and convergence oflines is a good predictor of perceived motion Experiment 2 shows how the same garments isolatedfrom the context of the paintings still give different dynamic impressions according to the same rulesFinally Experiment 3 confirmed the same results whilst patterns previously used are simplified totheir geometrical structure These results call for an underlying perceptual mechanism that specificallyrecognizes orientation curvature and parallelism levels as cues of motion in a static pattern

Keywords Art depth graphic invariants motion perception static cues of motion

INTRODUCTION

The history of western visual art is characterised by radical changes in every aspectof the representation of reality depending on the historical setting of the painters(Gombrich 1972) Indeed when thinking about European western paintings itis easy to find conspicuous differences in the use of graphic signs especiallydepending on time and artistsrsquo tastes Hence if some graphic solutions employed torepresent reality are used constantly it may be deduced that our perceptual systemuses and recognises them unambiguously

lowastTo whom correspondence should be addressed E-mail goripsicounivtriesteit

202 S Gori et al

Representation of reality was not the first aim in any given period moreover eachsingle artist made very specific choices on how to depict it Even the so-calledlsquomirror of realityrsquo that some artists tried to achieve in their works especially beforethe invention of photography (Cutting 2002) was not an absolute priority for manyothers In other words sometimes paintings were an impressive attempt to createa realistic representation but at other times the artist wished to create somethingfar from the reality he was observing This happened for many different reasonsamong which was the symbolic value of some artworks This premise explains whyit is so rare for one graphic solution to stay unchanged through centuries Findinga few unadulterated graphic solutions could be interesting for both art history andvisual perception (Gombrich 1977) Furthermore their attestation in works lackinga primary interest for representing reality may mean that it was not only the artistrsquostaste that determined their choice

We decided to study motion in paintings Paintings are static patterns that a prioricannot change over time Nevertheless everybody has experienced an impression ofdynamism observing a painting in a museum or in an art book It is not an illusorymotion like that perceived for example in the Enigma figure (Leviant 1996) butit is still a clear perception of dynamism In viewing some paintings observerswill report that the scene is dynamic even if nobody would assert that there isany kind of physical motion in the paintings The objects of our investigation aregarments This choice was made for several reasons first the garments are alwaysrecognised as cues of motion in paintings furthermore they appear in variouslydated centuries Finally garments have no specific shape so that they can conveythe impression of motion in many ways unaffected by the constraints of anatomicmasses In his analysis of the phenomenon of perceived lsquodynamicsrsquo in art Arnheim(1954) describes how diagonal and convergent lines break the balance of a sceneThis suggestion reinforced our intention to test how lines composing garments couldbe a cue for motion

Summarising the aims of this article are to show the existence of a few specificgraphic invariants in paintings tied to the representation of motion in garments toshow how to predict the resulting perceived motion using these graphic invariants toshow how these predictors are effective also when the context surrounding garmentsis erased and finally how these graphic invariants alone in the absence of any othercue are compelling enough to elicit the perception of motion

PILOT EXPERIMENT

This experiment was conducted by Simone Gori and Caterina Borghini as partof her Laurea thesis directed by Professor Riccardo Luccio It was investigatedhow in different centuries painters used the same graphic solution in order togive an impression of motion The garmentsrsquo lines were counted and classifiedas belonging to three different categories straightcurved parallelconvergent andorthogonaldiagonal Afterwards the frequencies of specific line patterns were

Graphic invariants in visual art 203

checked for the garments respectively judged in motion and static According totheir initial hypothesis garments containing more diagonal curved and convergentlines should give an impression of motion on the other hand garments witha majority of orthogonal straight and parallel lines should convey the impressionof stativity It was expected to find this association of specific types of lines andmotion perception in works belonging to the centuries under examination

Methods

Subjects Ten naiumlve subjects (mean age 28 yrs SD = 51) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli 160 paintings were selected (Table 1) taking care to include the mostcited artists of every main artistic movement of the western European history ofart Twenty paintings per century were chosen from the thirteenth to the twentiethcentury All paintings were scanned with high definition and shown on a 28times21 cmmonitor Sony Trinitron Color E100P controlled by a PC Selecta Promo 600

The lines of the selected garments were manually counted and classified us-ing a superimposed grid in the following three categories straightcurved par-allelconvergent and orthogonaldiagonal (1) Lines were classified as straight andcurved according to agreement between two independent judges for each line Inthe few cases when an agreement was not reached the lines were assigned randomlyto one of the two categories (2) Lines were classified as parallel or convergent us-ing the following criterion all lines separating at an angle more than 20 deg fromeach other were defined as convergent the others were labelled parallel (3) Finallylines were classified as orthogonal and diagonal according to this criterion the linestilted more than 20 deg far from the vertical and horizontal axes of the painting wereclassified as diagonal the others as orthogonal Moreover all the lines perceived bythe three authors as distorted by objects (pins belts etc) or by joint articulations(elbows knees etc) were not counted because it was assumed that subjects did notuse them to assess the motion of the garments At the end a different subjective mo-tion index was also ascribed to each line Two judges decided what lines had moreimpact on the garments Only the lines cited by both judges as more relevant re-ceived a subjective motion index all the others were counted as a single unit Lineswere assigned a different value according to their strength For example a verylong and wide line cannot have the same subjective motion index as a really shortand thin line The judges assigned a subjective motion index for each more relevantline then the average of both indices was used When counting lines of differenttypes each line was counted many times as its subjective motion index (eg a linehaving a subjective motion index equal to 2 had the same weight of two lines havinga subjective motion index equal to 1)

204 S Gori et al

Table 1A pool of 160 works painted between the thirteenth and the twentieth century was selected Themain European movements and artists are represented in this list Each century is exemplified by20 paintings which according to the subjectsrsquo judgment (N = 10) are divided between static anddynamic scenes

Author Year Title LocationAnonymous 1246 The DonationAnonymous 1246 The SubmissionAnonymous 1248 Ars venandi Rome Vatican LibraryAnonymous 1248 Ars venandi Rome Vatican LibraryAnonymous 1248 Ars venandi Rome Vatican LibraryAnonymous 1250 Gauging God Wien Oumlsterreichische NationalbibliothekAnonymous 1250 PassionBacon 1952 Innocent X New York Carter Burden CollectionBeatoAngelico

1440 Deposition Florence San Marco Museum

Bembo 1440 The Star Magic CardBerlinghiero 1210ndash1220 Crucifix Lucca Picture GalleryBlacke 1795 Elohim creating Adam London Tate GalleryBoccioni 1909ndash1910 Three Women Milan Italian Commercial BankBonaventura 1235 Saint Francis Pescia Picture GalleryBosch 1504ndash1505 Santa Liberata Venice Dukersquos PalaceBotticelli 1483ndash1485 Birth of Venus Florence Uffizi GalleryBotticelli 1482 Spring (Primavera) Florence Uffizi GalleryBotticelli 1495 Calumny Florence Uffizi GalleryBronzino 1560ndash1565 Angel Florence Old PalaceCaravaggio 1594 Flight into Egypt Rome Doria Panphili GalleryCaravaggio 1602 Saint Matthew and the

AngelRome San Luigi dei Francesi Church

Carnach 1529 Princess Warsaw National MuseumCarpaccio 1520 Saint Paul Chioggia San Domenico ChurchCarracciAgostino

1587ndash1592 Battle of the Romansand the Sabines

Bologna Magnani Palace

Chagall 1917ndash1918 The Walk Saint Petersburg Russian MuseumCimabue 1275ndash1285 Crucifix Florence Santa Croce MuseumCimabue 1280ndash1285 Santa Trinita Madonna Florence Uffizi GalleryCimabue 1280ndash1285 Madonna Enthroned Paris Louvre MuseumCimabue 1278ndash1280 Saint Francis Assisi Inferior BasilicaCimabue 1280 Crucifixion (detail) Assisi Superior BasilicaCoppo diMarcovaldo

1261 Crucifix San Gemignano Civic Museum

Coppodi Marcovaldo

1261 Madonna of Bordone Sienna Dei Servi Church

Corot 1860 Girl with Comb inHair

Paris Louvre Museum

Courbet 1856 The Young Ladies onthe Banks of the Seine(Summer)

Parigi Petit Palais Museum

Graphic invariants in visual art 205

Table 1(Continued)

Author Year Title LocationDaligrave 1958ndash1959 Discovery of America Figueras Gala-Salvator Daligrave FoundationDaligrave 1930 Giraffe on Fire Basel KunstmuseumDaligrave 1950 Madonna of Lligat Tokyo Minami MuseumDaligrave 1950 Slaves Market Saint Petersburg Russian MuseumDavid 1784ndash1785 Oath of the Horatii Paris Louvre MuseumDavid 1781 Belisar asks for Alms Lilla Museum of Fine ArtsDavid 1783 Andromache mourning

HectorParis Ecole Nationale Supeacuterieure desBeaux-Arts

David 1789 The Lictors bring to Bru-tus the Bodies of his Sons

Paris Louvre Museum

David 1789 Oath of the Horatii (draw-ing)

Paris Louvre Museum

David 1799 The Sabine Women Paris Louvre MuseumDe Chirico 1918 Disquieting Muses Milan Mattioli CollectionDe Chirico 1954 Roger and Angelica Rome Isa and Giorgio De Chirico Foun-

dationdersquo Roberti 1466ndash1473 Stories of Saint Vincent

FerrerRome Vatican Picture Gallery

Degas 1886ndash1890 The Dancers New York Metropolitan MuseumDelCastagno

1447 Passion Florence Cenacolo SantrsquoApolloniaMonastery

Delacroix 1859ndash1861 Jacob wrestling with theAngel

Paris St Sulpice Church

Delacroix 1830 Freedom leading the Peo-ple

Paris Louvre Museum

Delacroix 1837 Jewish Bride Paris Louvre MuseumDellaFrancesca

1460 Resurrection Borgo San Sepolcro PinacotecaComunale

Dix 1929ndash1932 Trilogy of War Dresden National Museum of ArtDuccio daBuoninsegna

1285 Madonna Rucellai Florence Uffizi Gallery

Duccio daBuoninsegna

1308ndash1311 Crucifixion Florence Uffizi Gallery

Duumlrer 1500 Lamentation for the deadChrist

Munich Alte Pinakothek

El Greco 1586ndash1588 The Burial of Count Or-ganz

Toledo Santo Tomeacute Church

Ernst 1937 The Angel of the Hearthand Home

Chicago Art Istitute

Flinck 1655 Margaretha Amsterdam RiijksmuseumFragonard 1767 The Swing London Fallace CollectionFurini 1630 Agor and the Angel Florence Private CollectionFuumlssli 1781 Kriemhilde sees dead

Siegfried in DreamZuumlrich Kunsthaus

Fuumlssli 1781 Queen Katherinersquos Dream Lytham St Annes-Lancaster Town Hall

206 S Gori et al

Table 1(Continued)

Author Year Title LocationFuumlssli 1783 Lady Macbeth London Tate GalleryFuumlssli 1791 Nightmare Frankfurt upon Main Freies Deutsches

Hochstift Frankfurter Goethe MuseumFuumlssli 1798ndash1700 Lady of Esting Zolikon-Zuumlrich Martin Hurlimannrsquos

PropertyFuumlssli 1806ndash1807 Katersquos Madness Frankfurt upon Main Goethe MuseumFuumlssli 1812 Lady Macbeth Paris Louvre MuseumGentile da Fab-riano

1419 Saint Francis Malibu (Parma) P Getty MuseumMagnini Rocca Foundation

Gentileschi A 1620 Judith slaying Holofernes Florence Uffizi GalleryGericault 1818ndash1819 The Raft of the Medusa Paris Louvre MuseumGiotto 1290 Ognissanti Madonna Florence Uffizi GalleryGiotto 1304ndash1306 Noli me tangere Padua Scrovegni ChapelGiotto 1290 Saint Francis giving his

Mantle to a Poor ManAssisi Superior Basilica

Giotto 1290 Stories of Isaac Assisi Superior BasilicaGiotto 1320ndash1325 Ascension Padua Scrovegni ChapelGiotto 1304ndash1306 Lamentation (The mourn-

ing of Christ)Padua Scrovegni Chapel

Giotto 1304ndash1306 Meeting on the GoldenGate

Padua Scrovegni Chapel

Giotto 1303ndash1305 The Kiss of Judah Padua Scrovegni ChapelGiotto 1325 Saint Francis before the

Sultan (trial by fire)Florence Santa Croce Museum

Giottorsquos work-shop

1325ndash1330 Virgin Mary Montecarlo Private Collection Monaco

Girodette 1802 Apotheosis of the Heroes Paris MalmaisonGoya 1819 Oration in the Garden Madrid San Antograven SchoolGrunewald 1512ndash1516 Crucifixion Colmar Unterlinden MuseumReni 1621 Dawn Rome Casino dellrsquoAurora Rospigliosi

PalaceHogarth 1743 The Ladyrsquos Death London National GalleryHolben H Jr 1532ndash1533 Noli me tangere Hampton Court Royal CollectionIngres 1842 Muse of Lyric Paris Louvre MuseumKokoshka 1914 The Bride of the Wind Basel KunstmuseumLa Tour 1644 Job and his Wife Paris Louvre MuseumLeonardo daVinci

1480ndash1481 Study of Madonna with theCat

London National Gallery

Lippi F Sr 1452ndash1464 The Feast of Herod Prato CathedralLochner 1435 Last Judgement Koumlln Wallraff Richartz MuseumLonghi 1734 The Fall of the Giants Venice Carsquo SagredoLorenzetti P 1320ndash1322 Deposition Assisi Superior BasilicaLorenzetti A 1342 Presentation at the Temple Florence Uffizi GalleryLotto 1552 Saint Michael driving out

LuciferLoreto Apostolic Palace

Graphic invariants in visual art 207

Table 1(Continued)

Author Year Title LocationMagritte 1937 In memoriam Mack Sennet Private CollectionMantegna 1500 Cult of the Cybele London National GalleryMargaritone 1262 Saint Francis Arezzo Civic MuseumMartini 1312ndash1317 Miraculous Mass Assisi Inferior BasilicaMartini 1312ndash1317 Saint Martin renounces his

WeaponsAssisi Inferior Basilica

Martini 1300 The Road to Calvary Paris Louvre MuseumMartini 1330 Guidoriccio da Fogliano Sienna Public PalaceMartini 1312ndash1317 Saint Martin is knighted Assisi Cappella Basilica of St FrancisMasaccio 1425ndash1428 Adam and Eva banished

from ParadiseFlorence Brancacci Chapel

Masaccio 1426 Crucifixion Naples Capodimonte National GalleryMatisse 1907 The Music Saint Petersburg Hermitage GalleryMemling 1466ndash1473 Last Judgement Danzica PormoskieMemling 1485 Bathsheba Stuttgart StaatsgalerieMichelangelo 1508ndash1512 Sistina Chapel Vault

(detail)Rome Vatican Palaces

Michelangelo 1503ndash1504 Tondo Doni Florence Uffizi GalleryMichelino 1400 Ascension New York Metropolitan MuseumMonaco 1420ndash1422 Adoration of the Magi Florence Uffizi GalleryMonet 1876 Madame Monet in Japanese

CostumeBoston Museum of Fine Arts

Moreau 1876 Salomeacute Paris Gustave Moreau MuseumMoreau 1889 The Peacock complaining

to JunoParis Gustave Moreau Museum

Murillo 1646 The Angelsrsquo Kitchen Paris Louvre MuseumOrozco 1937 Hidalgo Guadalajara Jalisco State Government

PalaceParmigianino 1535 Madonna of the Long Neck Florence Uffizi GalleryPerugino 1496ndash1500 Venus Perugia Collegio del CambioPicasso 1915ndash1918 Crucifixion Paris Picasso MuseumPicasso 1899ndash1900 Woman with Mantilla Barcelona Picasso MuseumPicasso 1922 Women running on the

BeachParis Picasso Museum

Pissarro 1881 Young Peasant Girl witha Stick

Paris drsquoOrsay Museum

Pontormo 1526ndash1528 Deposition Florence Santa Felicita ChurchPontormo 1528 Visitation Carmignano (Florence) Pieve of San

MichelePoussin 1640ndash1650 Ecstasy of Saint Paul Paris Louvre MuseumPoussin 1628ndash1629 The Martyrdom of Saint

ErasmusRome Vatican Picture Gallery

Reni 1611 Massacre of the Innocents Bologna National Picture GalleryReni 1620 Atalanta and Hippomenes Naples Capodimonte National GalleryRenoir 1886 Dance at Bougival Paris drsquoOrsay Museum

208 S Gori et al

Table 1(Continued)

Author Year Title LocationRicci 1705 Madonna Venice San Marziale ChurchRossoFiorentino

1521 Deposition Volterra (Sienna) Picture Gallery

Rubens 1611 Deposition Anvers CathedralSchiele 1917 Reclined Woman Wien Private CollectionSchiele 1917 Sitting Woman Wien Graphische Sammlung AlbertinaLucca School XII century CrucifixionSeurat 1890ndash1891 The Circus Paris drsquoOrsay MuseumTaddeo Gaddi 1328 Stories of the Virgin Poppi (Arezzo) Count Guidi CastleTiepolo 1719 Repudiation of Agar Milan Rasini CollectionTiepolo 1749 Our Lady of Carmel

appearing to SaintSimon Stock

Venice Carmini School

Tiepolo 1750 The Martyrdom of SaintAgata

Milan Rasini Collection

Tintoretto 1558 Saint George and theDragon

London National Gallery

Tiziano 1514ndash1515 Sacred and Profane Love Rome Borghese GalleryToulouse-Loutrec

1892 Jane Avril Dancing Paris drsquoOrsay Museum

Uccello 1425 Stories of Genesis Florence Santa Maria Novella ChurchClaustrum

Van DerWeyden

1435 Deposition Madrid Prado Museum

Van Dyck 1625ndash1627 Genoan Lady with herDaughter

Paris Louvre Museum

Van Eyck 1422ndash1425 John the Baptist Paris Louvre MuseumVelasquez 1628 Immaculate Conception London National GalleryVermeer 1670 Allegory of Faith New York Metropolitan MuseumVitale daBologna

1350 Saint George and theDragon

Bologna National Picture Gallery

Volterrano 1670 Beauty Destroyed bythe Time

Florence Piccolini Palace

Von Mieris 1670 Lady on the Mirror Munich Alte PinakothekWatteau 1717 The Awkward Lover Paris Louvre MuseumZurbaran 1628 Saint Serapion Hartford Wadsworth AthenaeumZurbaran 1629 Christ Pantocrator Moscow Pushkin Museum

Procedure Subjects sat 60 cm away from the monitor Fixation was binocularSubjects saw all the 160 paintings in random order and in free vision Theyhad to decide in a binary classification task whether the garments indicated bythe experimenter were dynamic or static Each painting was shown once Theexperiment was conducted in a dark room

Graphic invariants in visual art 209

Results

The 10 subjects were in perfect agreement All the garments were classified asstatic or dynamic according to their answers Then for each century the numberof lines of different types in the two categories was compared to find out whetherany type of line was more represented in a category than the other The resultssummarized in Table 2 show that the presence of straight parallel and horizontallines characterises the static garments in paintings of almost every century whilecurved convergent and diagonal lines were significantly more when the garmentswere judged dynamic The only exceptions were the seventeenth and the eighteenth

Table 2For each century the frequencies of straight curved parallel convergent orthogonal and diagonallines are reported for dynamic and static garments Almost all the line types according to aχ2 statistic are statistically different for dynamic vs static garments in each century

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1200 Straight 729 134 70148 lt0001Curved 27 385Parallel 989 345 5524 lt0001Convergent 282 220Orthogonal 850 160 63692 lt0001Diagonal 62 372

1300 Straight 378 201 26332 lt0001Curved 25 281Parallel 490 350 7895 lt0001Convergent 57 170Orthogonal 352 139 27183 lt0001Diagonal 68 341

1400 Straight 160 310 22671 lt0001Curved 8 1116Parallel 210 714 16166 lt0001Convergent 11 732Orthogonal 178 293 44550 lt0001Diagonal 9 1133

1500 Straight 61 212 25029 lt0001Curved 20 1577Parallel 140 823 11218 lt0001Convergent 14 950Orthogonal 140 482 23910 lt0001Diagonal 15 1191

1600 Straight 43 144 044 NSCurved 280 1062Parallel 164 385 2437 lt0001Convergent 214 906Orthogonal 159 371 3647 lt0001Diagonal 182 895

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

204 S Gori et al

Table 1A pool of 160 works painted between the thirteenth and the twentieth century was selected Themain European movements and artists are represented in this list Each century is exemplified by20 paintings which according to the subjectsrsquo judgment (N = 10) are divided between static anddynamic scenes

Author Year Title LocationAnonymous 1246 The DonationAnonymous 1246 The SubmissionAnonymous 1248 Ars venandi Rome Vatican LibraryAnonymous 1248 Ars venandi Rome Vatican LibraryAnonymous 1248 Ars venandi Rome Vatican LibraryAnonymous 1250 Gauging God Wien Oumlsterreichische NationalbibliothekAnonymous 1250 PassionBacon 1952 Innocent X New York Carter Burden CollectionBeatoAngelico

1440 Deposition Florence San Marco Museum

Bembo 1440 The Star Magic CardBerlinghiero 1210ndash1220 Crucifix Lucca Picture GalleryBlacke 1795 Elohim creating Adam London Tate GalleryBoccioni 1909ndash1910 Three Women Milan Italian Commercial BankBonaventura 1235 Saint Francis Pescia Picture GalleryBosch 1504ndash1505 Santa Liberata Venice Dukersquos PalaceBotticelli 1483ndash1485 Birth of Venus Florence Uffizi GalleryBotticelli 1482 Spring (Primavera) Florence Uffizi GalleryBotticelli 1495 Calumny Florence Uffizi GalleryBronzino 1560ndash1565 Angel Florence Old PalaceCaravaggio 1594 Flight into Egypt Rome Doria Panphili GalleryCaravaggio 1602 Saint Matthew and the

AngelRome San Luigi dei Francesi Church

Carnach 1529 Princess Warsaw National MuseumCarpaccio 1520 Saint Paul Chioggia San Domenico ChurchCarracciAgostino

1587ndash1592 Battle of the Romansand the Sabines

Bologna Magnani Palace

Chagall 1917ndash1918 The Walk Saint Petersburg Russian MuseumCimabue 1275ndash1285 Crucifix Florence Santa Croce MuseumCimabue 1280ndash1285 Santa Trinita Madonna Florence Uffizi GalleryCimabue 1280ndash1285 Madonna Enthroned Paris Louvre MuseumCimabue 1278ndash1280 Saint Francis Assisi Inferior BasilicaCimabue 1280 Crucifixion (detail) Assisi Superior BasilicaCoppo diMarcovaldo

1261 Crucifix San Gemignano Civic Museum

Coppodi Marcovaldo

1261 Madonna of Bordone Sienna Dei Servi Church

Corot 1860 Girl with Comb inHair

Paris Louvre Museum

Courbet 1856 The Young Ladies onthe Banks of the Seine(Summer)

Parigi Petit Palais Museum

Graphic invariants in visual art 205

Table 1(Continued)

Author Year Title LocationDaligrave 1958ndash1959 Discovery of America Figueras Gala-Salvator Daligrave FoundationDaligrave 1930 Giraffe on Fire Basel KunstmuseumDaligrave 1950 Madonna of Lligat Tokyo Minami MuseumDaligrave 1950 Slaves Market Saint Petersburg Russian MuseumDavid 1784ndash1785 Oath of the Horatii Paris Louvre MuseumDavid 1781 Belisar asks for Alms Lilla Museum of Fine ArtsDavid 1783 Andromache mourning

HectorParis Ecole Nationale Supeacuterieure desBeaux-Arts

David 1789 The Lictors bring to Bru-tus the Bodies of his Sons

Paris Louvre Museum

David 1789 Oath of the Horatii (draw-ing)

Paris Louvre Museum

David 1799 The Sabine Women Paris Louvre MuseumDe Chirico 1918 Disquieting Muses Milan Mattioli CollectionDe Chirico 1954 Roger and Angelica Rome Isa and Giorgio De Chirico Foun-

dationdersquo Roberti 1466ndash1473 Stories of Saint Vincent

FerrerRome Vatican Picture Gallery

Degas 1886ndash1890 The Dancers New York Metropolitan MuseumDelCastagno

1447 Passion Florence Cenacolo SantrsquoApolloniaMonastery

Delacroix 1859ndash1861 Jacob wrestling with theAngel

Paris St Sulpice Church

Delacroix 1830 Freedom leading the Peo-ple

Paris Louvre Museum

Delacroix 1837 Jewish Bride Paris Louvre MuseumDellaFrancesca

1460 Resurrection Borgo San Sepolcro PinacotecaComunale

Dix 1929ndash1932 Trilogy of War Dresden National Museum of ArtDuccio daBuoninsegna

1285 Madonna Rucellai Florence Uffizi Gallery

Duccio daBuoninsegna

1308ndash1311 Crucifixion Florence Uffizi Gallery

Duumlrer 1500 Lamentation for the deadChrist

Munich Alte Pinakothek

El Greco 1586ndash1588 The Burial of Count Or-ganz

Toledo Santo Tomeacute Church

Ernst 1937 The Angel of the Hearthand Home

Chicago Art Istitute

Flinck 1655 Margaretha Amsterdam RiijksmuseumFragonard 1767 The Swing London Fallace CollectionFurini 1630 Agor and the Angel Florence Private CollectionFuumlssli 1781 Kriemhilde sees dead

Siegfried in DreamZuumlrich Kunsthaus

Fuumlssli 1781 Queen Katherinersquos Dream Lytham St Annes-Lancaster Town Hall

206 S Gori et al

Table 1(Continued)

Author Year Title LocationFuumlssli 1783 Lady Macbeth London Tate GalleryFuumlssli 1791 Nightmare Frankfurt upon Main Freies Deutsches

Hochstift Frankfurter Goethe MuseumFuumlssli 1798ndash1700 Lady of Esting Zolikon-Zuumlrich Martin Hurlimannrsquos

PropertyFuumlssli 1806ndash1807 Katersquos Madness Frankfurt upon Main Goethe MuseumFuumlssli 1812 Lady Macbeth Paris Louvre MuseumGentile da Fab-riano

1419 Saint Francis Malibu (Parma) P Getty MuseumMagnini Rocca Foundation

Gentileschi A 1620 Judith slaying Holofernes Florence Uffizi GalleryGericault 1818ndash1819 The Raft of the Medusa Paris Louvre MuseumGiotto 1290 Ognissanti Madonna Florence Uffizi GalleryGiotto 1304ndash1306 Noli me tangere Padua Scrovegni ChapelGiotto 1290 Saint Francis giving his

Mantle to a Poor ManAssisi Superior Basilica

Giotto 1290 Stories of Isaac Assisi Superior BasilicaGiotto 1320ndash1325 Ascension Padua Scrovegni ChapelGiotto 1304ndash1306 Lamentation (The mourn-

ing of Christ)Padua Scrovegni Chapel

Giotto 1304ndash1306 Meeting on the GoldenGate

Padua Scrovegni Chapel

Giotto 1303ndash1305 The Kiss of Judah Padua Scrovegni ChapelGiotto 1325 Saint Francis before the

Sultan (trial by fire)Florence Santa Croce Museum

Giottorsquos work-shop

1325ndash1330 Virgin Mary Montecarlo Private Collection Monaco

Girodette 1802 Apotheosis of the Heroes Paris MalmaisonGoya 1819 Oration in the Garden Madrid San Antograven SchoolGrunewald 1512ndash1516 Crucifixion Colmar Unterlinden MuseumReni 1621 Dawn Rome Casino dellrsquoAurora Rospigliosi

PalaceHogarth 1743 The Ladyrsquos Death London National GalleryHolben H Jr 1532ndash1533 Noli me tangere Hampton Court Royal CollectionIngres 1842 Muse of Lyric Paris Louvre MuseumKokoshka 1914 The Bride of the Wind Basel KunstmuseumLa Tour 1644 Job and his Wife Paris Louvre MuseumLeonardo daVinci

1480ndash1481 Study of Madonna with theCat

London National Gallery

Lippi F Sr 1452ndash1464 The Feast of Herod Prato CathedralLochner 1435 Last Judgement Koumlln Wallraff Richartz MuseumLonghi 1734 The Fall of the Giants Venice Carsquo SagredoLorenzetti P 1320ndash1322 Deposition Assisi Superior BasilicaLorenzetti A 1342 Presentation at the Temple Florence Uffizi GalleryLotto 1552 Saint Michael driving out

LuciferLoreto Apostolic Palace

Graphic invariants in visual art 207

Table 1(Continued)

Author Year Title LocationMagritte 1937 In memoriam Mack Sennet Private CollectionMantegna 1500 Cult of the Cybele London National GalleryMargaritone 1262 Saint Francis Arezzo Civic MuseumMartini 1312ndash1317 Miraculous Mass Assisi Inferior BasilicaMartini 1312ndash1317 Saint Martin renounces his

WeaponsAssisi Inferior Basilica

Martini 1300 The Road to Calvary Paris Louvre MuseumMartini 1330 Guidoriccio da Fogliano Sienna Public PalaceMartini 1312ndash1317 Saint Martin is knighted Assisi Cappella Basilica of St FrancisMasaccio 1425ndash1428 Adam and Eva banished

from ParadiseFlorence Brancacci Chapel

Masaccio 1426 Crucifixion Naples Capodimonte National GalleryMatisse 1907 The Music Saint Petersburg Hermitage GalleryMemling 1466ndash1473 Last Judgement Danzica PormoskieMemling 1485 Bathsheba Stuttgart StaatsgalerieMichelangelo 1508ndash1512 Sistina Chapel Vault

(detail)Rome Vatican Palaces

Michelangelo 1503ndash1504 Tondo Doni Florence Uffizi GalleryMichelino 1400 Ascension New York Metropolitan MuseumMonaco 1420ndash1422 Adoration of the Magi Florence Uffizi GalleryMonet 1876 Madame Monet in Japanese

CostumeBoston Museum of Fine Arts

Moreau 1876 Salomeacute Paris Gustave Moreau MuseumMoreau 1889 The Peacock complaining

to JunoParis Gustave Moreau Museum

Murillo 1646 The Angelsrsquo Kitchen Paris Louvre MuseumOrozco 1937 Hidalgo Guadalajara Jalisco State Government

PalaceParmigianino 1535 Madonna of the Long Neck Florence Uffizi GalleryPerugino 1496ndash1500 Venus Perugia Collegio del CambioPicasso 1915ndash1918 Crucifixion Paris Picasso MuseumPicasso 1899ndash1900 Woman with Mantilla Barcelona Picasso MuseumPicasso 1922 Women running on the

BeachParis Picasso Museum

Pissarro 1881 Young Peasant Girl witha Stick

Paris drsquoOrsay Museum

Pontormo 1526ndash1528 Deposition Florence Santa Felicita ChurchPontormo 1528 Visitation Carmignano (Florence) Pieve of San

MichelePoussin 1640ndash1650 Ecstasy of Saint Paul Paris Louvre MuseumPoussin 1628ndash1629 The Martyrdom of Saint

ErasmusRome Vatican Picture Gallery

Reni 1611 Massacre of the Innocents Bologna National Picture GalleryReni 1620 Atalanta and Hippomenes Naples Capodimonte National GalleryRenoir 1886 Dance at Bougival Paris drsquoOrsay Museum

208 S Gori et al

Table 1(Continued)

Author Year Title LocationRicci 1705 Madonna Venice San Marziale ChurchRossoFiorentino

1521 Deposition Volterra (Sienna) Picture Gallery

Rubens 1611 Deposition Anvers CathedralSchiele 1917 Reclined Woman Wien Private CollectionSchiele 1917 Sitting Woman Wien Graphische Sammlung AlbertinaLucca School XII century CrucifixionSeurat 1890ndash1891 The Circus Paris drsquoOrsay MuseumTaddeo Gaddi 1328 Stories of the Virgin Poppi (Arezzo) Count Guidi CastleTiepolo 1719 Repudiation of Agar Milan Rasini CollectionTiepolo 1749 Our Lady of Carmel

appearing to SaintSimon Stock

Venice Carmini School

Tiepolo 1750 The Martyrdom of SaintAgata

Milan Rasini Collection

Tintoretto 1558 Saint George and theDragon

London National Gallery

Tiziano 1514ndash1515 Sacred and Profane Love Rome Borghese GalleryToulouse-Loutrec

1892 Jane Avril Dancing Paris drsquoOrsay Museum

Uccello 1425 Stories of Genesis Florence Santa Maria Novella ChurchClaustrum

Van DerWeyden

1435 Deposition Madrid Prado Museum

Van Dyck 1625ndash1627 Genoan Lady with herDaughter

Paris Louvre Museum

Van Eyck 1422ndash1425 John the Baptist Paris Louvre MuseumVelasquez 1628 Immaculate Conception London National GalleryVermeer 1670 Allegory of Faith New York Metropolitan MuseumVitale daBologna

1350 Saint George and theDragon

Bologna National Picture Gallery

Volterrano 1670 Beauty Destroyed bythe Time

Florence Piccolini Palace

Von Mieris 1670 Lady on the Mirror Munich Alte PinakothekWatteau 1717 The Awkward Lover Paris Louvre MuseumZurbaran 1628 Saint Serapion Hartford Wadsworth AthenaeumZurbaran 1629 Christ Pantocrator Moscow Pushkin Museum

Procedure Subjects sat 60 cm away from the monitor Fixation was binocularSubjects saw all the 160 paintings in random order and in free vision Theyhad to decide in a binary classification task whether the garments indicated bythe experimenter were dynamic or static Each painting was shown once Theexperiment was conducted in a dark room

Graphic invariants in visual art 209

Results

The 10 subjects were in perfect agreement All the garments were classified asstatic or dynamic according to their answers Then for each century the numberof lines of different types in the two categories was compared to find out whetherany type of line was more represented in a category than the other The resultssummarized in Table 2 show that the presence of straight parallel and horizontallines characterises the static garments in paintings of almost every century whilecurved convergent and diagonal lines were significantly more when the garmentswere judged dynamic The only exceptions were the seventeenth and the eighteenth

Table 2For each century the frequencies of straight curved parallel convergent orthogonal and diagonallines are reported for dynamic and static garments Almost all the line types according to aχ2 statistic are statistically different for dynamic vs static garments in each century

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1200 Straight 729 134 70148 lt0001Curved 27 385Parallel 989 345 5524 lt0001Convergent 282 220Orthogonal 850 160 63692 lt0001Diagonal 62 372

1300 Straight 378 201 26332 lt0001Curved 25 281Parallel 490 350 7895 lt0001Convergent 57 170Orthogonal 352 139 27183 lt0001Diagonal 68 341

1400 Straight 160 310 22671 lt0001Curved 8 1116Parallel 210 714 16166 lt0001Convergent 11 732Orthogonal 178 293 44550 lt0001Diagonal 9 1133

1500 Straight 61 212 25029 lt0001Curved 20 1577Parallel 140 823 11218 lt0001Convergent 14 950Orthogonal 140 482 23910 lt0001Diagonal 15 1191

1600 Straight 43 144 044 NSCurved 280 1062Parallel 164 385 2437 lt0001Convergent 214 906Orthogonal 159 371 3647 lt0001Diagonal 182 895

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 205

Table 1(Continued)

Author Year Title LocationDaligrave 1958ndash1959 Discovery of America Figueras Gala-Salvator Daligrave FoundationDaligrave 1930 Giraffe on Fire Basel KunstmuseumDaligrave 1950 Madonna of Lligat Tokyo Minami MuseumDaligrave 1950 Slaves Market Saint Petersburg Russian MuseumDavid 1784ndash1785 Oath of the Horatii Paris Louvre MuseumDavid 1781 Belisar asks for Alms Lilla Museum of Fine ArtsDavid 1783 Andromache mourning

HectorParis Ecole Nationale Supeacuterieure desBeaux-Arts

David 1789 The Lictors bring to Bru-tus the Bodies of his Sons

Paris Louvre Museum

David 1789 Oath of the Horatii (draw-ing)

Paris Louvre Museum

David 1799 The Sabine Women Paris Louvre MuseumDe Chirico 1918 Disquieting Muses Milan Mattioli CollectionDe Chirico 1954 Roger and Angelica Rome Isa and Giorgio De Chirico Foun-

dationdersquo Roberti 1466ndash1473 Stories of Saint Vincent

FerrerRome Vatican Picture Gallery

Degas 1886ndash1890 The Dancers New York Metropolitan MuseumDelCastagno

1447 Passion Florence Cenacolo SantrsquoApolloniaMonastery

Delacroix 1859ndash1861 Jacob wrestling with theAngel

Paris St Sulpice Church

Delacroix 1830 Freedom leading the Peo-ple

Paris Louvre Museum

Delacroix 1837 Jewish Bride Paris Louvre MuseumDellaFrancesca

1460 Resurrection Borgo San Sepolcro PinacotecaComunale

Dix 1929ndash1932 Trilogy of War Dresden National Museum of ArtDuccio daBuoninsegna

1285 Madonna Rucellai Florence Uffizi Gallery

Duccio daBuoninsegna

1308ndash1311 Crucifixion Florence Uffizi Gallery

Duumlrer 1500 Lamentation for the deadChrist

Munich Alte Pinakothek

El Greco 1586ndash1588 The Burial of Count Or-ganz

Toledo Santo Tomeacute Church

Ernst 1937 The Angel of the Hearthand Home

Chicago Art Istitute

Flinck 1655 Margaretha Amsterdam RiijksmuseumFragonard 1767 The Swing London Fallace CollectionFurini 1630 Agor and the Angel Florence Private CollectionFuumlssli 1781 Kriemhilde sees dead

Siegfried in DreamZuumlrich Kunsthaus

Fuumlssli 1781 Queen Katherinersquos Dream Lytham St Annes-Lancaster Town Hall

206 S Gori et al

Table 1(Continued)

Author Year Title LocationFuumlssli 1783 Lady Macbeth London Tate GalleryFuumlssli 1791 Nightmare Frankfurt upon Main Freies Deutsches

Hochstift Frankfurter Goethe MuseumFuumlssli 1798ndash1700 Lady of Esting Zolikon-Zuumlrich Martin Hurlimannrsquos

PropertyFuumlssli 1806ndash1807 Katersquos Madness Frankfurt upon Main Goethe MuseumFuumlssli 1812 Lady Macbeth Paris Louvre MuseumGentile da Fab-riano

1419 Saint Francis Malibu (Parma) P Getty MuseumMagnini Rocca Foundation

Gentileschi A 1620 Judith slaying Holofernes Florence Uffizi GalleryGericault 1818ndash1819 The Raft of the Medusa Paris Louvre MuseumGiotto 1290 Ognissanti Madonna Florence Uffizi GalleryGiotto 1304ndash1306 Noli me tangere Padua Scrovegni ChapelGiotto 1290 Saint Francis giving his

Mantle to a Poor ManAssisi Superior Basilica

Giotto 1290 Stories of Isaac Assisi Superior BasilicaGiotto 1320ndash1325 Ascension Padua Scrovegni ChapelGiotto 1304ndash1306 Lamentation (The mourn-

ing of Christ)Padua Scrovegni Chapel

Giotto 1304ndash1306 Meeting on the GoldenGate

Padua Scrovegni Chapel

Giotto 1303ndash1305 The Kiss of Judah Padua Scrovegni ChapelGiotto 1325 Saint Francis before the

Sultan (trial by fire)Florence Santa Croce Museum

Giottorsquos work-shop

1325ndash1330 Virgin Mary Montecarlo Private Collection Monaco

Girodette 1802 Apotheosis of the Heroes Paris MalmaisonGoya 1819 Oration in the Garden Madrid San Antograven SchoolGrunewald 1512ndash1516 Crucifixion Colmar Unterlinden MuseumReni 1621 Dawn Rome Casino dellrsquoAurora Rospigliosi

PalaceHogarth 1743 The Ladyrsquos Death London National GalleryHolben H Jr 1532ndash1533 Noli me tangere Hampton Court Royal CollectionIngres 1842 Muse of Lyric Paris Louvre MuseumKokoshka 1914 The Bride of the Wind Basel KunstmuseumLa Tour 1644 Job and his Wife Paris Louvre MuseumLeonardo daVinci

1480ndash1481 Study of Madonna with theCat

London National Gallery

Lippi F Sr 1452ndash1464 The Feast of Herod Prato CathedralLochner 1435 Last Judgement Koumlln Wallraff Richartz MuseumLonghi 1734 The Fall of the Giants Venice Carsquo SagredoLorenzetti P 1320ndash1322 Deposition Assisi Superior BasilicaLorenzetti A 1342 Presentation at the Temple Florence Uffizi GalleryLotto 1552 Saint Michael driving out

LuciferLoreto Apostolic Palace

Graphic invariants in visual art 207

Table 1(Continued)

Author Year Title LocationMagritte 1937 In memoriam Mack Sennet Private CollectionMantegna 1500 Cult of the Cybele London National GalleryMargaritone 1262 Saint Francis Arezzo Civic MuseumMartini 1312ndash1317 Miraculous Mass Assisi Inferior BasilicaMartini 1312ndash1317 Saint Martin renounces his

WeaponsAssisi Inferior Basilica

Martini 1300 The Road to Calvary Paris Louvre MuseumMartini 1330 Guidoriccio da Fogliano Sienna Public PalaceMartini 1312ndash1317 Saint Martin is knighted Assisi Cappella Basilica of St FrancisMasaccio 1425ndash1428 Adam and Eva banished

from ParadiseFlorence Brancacci Chapel

Masaccio 1426 Crucifixion Naples Capodimonte National GalleryMatisse 1907 The Music Saint Petersburg Hermitage GalleryMemling 1466ndash1473 Last Judgement Danzica PormoskieMemling 1485 Bathsheba Stuttgart StaatsgalerieMichelangelo 1508ndash1512 Sistina Chapel Vault

(detail)Rome Vatican Palaces

Michelangelo 1503ndash1504 Tondo Doni Florence Uffizi GalleryMichelino 1400 Ascension New York Metropolitan MuseumMonaco 1420ndash1422 Adoration of the Magi Florence Uffizi GalleryMonet 1876 Madame Monet in Japanese

CostumeBoston Museum of Fine Arts

Moreau 1876 Salomeacute Paris Gustave Moreau MuseumMoreau 1889 The Peacock complaining

to JunoParis Gustave Moreau Museum

Murillo 1646 The Angelsrsquo Kitchen Paris Louvre MuseumOrozco 1937 Hidalgo Guadalajara Jalisco State Government

PalaceParmigianino 1535 Madonna of the Long Neck Florence Uffizi GalleryPerugino 1496ndash1500 Venus Perugia Collegio del CambioPicasso 1915ndash1918 Crucifixion Paris Picasso MuseumPicasso 1899ndash1900 Woman with Mantilla Barcelona Picasso MuseumPicasso 1922 Women running on the

BeachParis Picasso Museum

Pissarro 1881 Young Peasant Girl witha Stick

Paris drsquoOrsay Museum

Pontormo 1526ndash1528 Deposition Florence Santa Felicita ChurchPontormo 1528 Visitation Carmignano (Florence) Pieve of San

MichelePoussin 1640ndash1650 Ecstasy of Saint Paul Paris Louvre MuseumPoussin 1628ndash1629 The Martyrdom of Saint

ErasmusRome Vatican Picture Gallery

Reni 1611 Massacre of the Innocents Bologna National Picture GalleryReni 1620 Atalanta and Hippomenes Naples Capodimonte National GalleryRenoir 1886 Dance at Bougival Paris drsquoOrsay Museum

208 S Gori et al

Table 1(Continued)

Author Year Title LocationRicci 1705 Madonna Venice San Marziale ChurchRossoFiorentino

1521 Deposition Volterra (Sienna) Picture Gallery

Rubens 1611 Deposition Anvers CathedralSchiele 1917 Reclined Woman Wien Private CollectionSchiele 1917 Sitting Woman Wien Graphische Sammlung AlbertinaLucca School XII century CrucifixionSeurat 1890ndash1891 The Circus Paris drsquoOrsay MuseumTaddeo Gaddi 1328 Stories of the Virgin Poppi (Arezzo) Count Guidi CastleTiepolo 1719 Repudiation of Agar Milan Rasini CollectionTiepolo 1749 Our Lady of Carmel

appearing to SaintSimon Stock

Venice Carmini School

Tiepolo 1750 The Martyrdom of SaintAgata

Milan Rasini Collection

Tintoretto 1558 Saint George and theDragon

London National Gallery

Tiziano 1514ndash1515 Sacred and Profane Love Rome Borghese GalleryToulouse-Loutrec

1892 Jane Avril Dancing Paris drsquoOrsay Museum

Uccello 1425 Stories of Genesis Florence Santa Maria Novella ChurchClaustrum

Van DerWeyden

1435 Deposition Madrid Prado Museum

Van Dyck 1625ndash1627 Genoan Lady with herDaughter

Paris Louvre Museum

Van Eyck 1422ndash1425 John the Baptist Paris Louvre MuseumVelasquez 1628 Immaculate Conception London National GalleryVermeer 1670 Allegory of Faith New York Metropolitan MuseumVitale daBologna

1350 Saint George and theDragon

Bologna National Picture Gallery

Volterrano 1670 Beauty Destroyed bythe Time

Florence Piccolini Palace

Von Mieris 1670 Lady on the Mirror Munich Alte PinakothekWatteau 1717 The Awkward Lover Paris Louvre MuseumZurbaran 1628 Saint Serapion Hartford Wadsworth AthenaeumZurbaran 1629 Christ Pantocrator Moscow Pushkin Museum

Procedure Subjects sat 60 cm away from the monitor Fixation was binocularSubjects saw all the 160 paintings in random order and in free vision Theyhad to decide in a binary classification task whether the garments indicated bythe experimenter were dynamic or static Each painting was shown once Theexperiment was conducted in a dark room

Graphic invariants in visual art 209

Results

The 10 subjects were in perfect agreement All the garments were classified asstatic or dynamic according to their answers Then for each century the numberof lines of different types in the two categories was compared to find out whetherany type of line was more represented in a category than the other The resultssummarized in Table 2 show that the presence of straight parallel and horizontallines characterises the static garments in paintings of almost every century whilecurved convergent and diagonal lines were significantly more when the garmentswere judged dynamic The only exceptions were the seventeenth and the eighteenth

Table 2For each century the frequencies of straight curved parallel convergent orthogonal and diagonallines are reported for dynamic and static garments Almost all the line types according to aχ2 statistic are statistically different for dynamic vs static garments in each century

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1200 Straight 729 134 70148 lt0001Curved 27 385Parallel 989 345 5524 lt0001Convergent 282 220Orthogonal 850 160 63692 lt0001Diagonal 62 372

1300 Straight 378 201 26332 lt0001Curved 25 281Parallel 490 350 7895 lt0001Convergent 57 170Orthogonal 352 139 27183 lt0001Diagonal 68 341

1400 Straight 160 310 22671 lt0001Curved 8 1116Parallel 210 714 16166 lt0001Convergent 11 732Orthogonal 178 293 44550 lt0001Diagonal 9 1133

1500 Straight 61 212 25029 lt0001Curved 20 1577Parallel 140 823 11218 lt0001Convergent 14 950Orthogonal 140 482 23910 lt0001Diagonal 15 1191

1600 Straight 43 144 044 NSCurved 280 1062Parallel 164 385 2437 lt0001Convergent 214 906Orthogonal 159 371 3647 lt0001Diagonal 182 895

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

206 S Gori et al

Table 1(Continued)

Author Year Title LocationFuumlssli 1783 Lady Macbeth London Tate GalleryFuumlssli 1791 Nightmare Frankfurt upon Main Freies Deutsches

Hochstift Frankfurter Goethe MuseumFuumlssli 1798ndash1700 Lady of Esting Zolikon-Zuumlrich Martin Hurlimannrsquos

PropertyFuumlssli 1806ndash1807 Katersquos Madness Frankfurt upon Main Goethe MuseumFuumlssli 1812 Lady Macbeth Paris Louvre MuseumGentile da Fab-riano

1419 Saint Francis Malibu (Parma) P Getty MuseumMagnini Rocca Foundation

Gentileschi A 1620 Judith slaying Holofernes Florence Uffizi GalleryGericault 1818ndash1819 The Raft of the Medusa Paris Louvre MuseumGiotto 1290 Ognissanti Madonna Florence Uffizi GalleryGiotto 1304ndash1306 Noli me tangere Padua Scrovegni ChapelGiotto 1290 Saint Francis giving his

Mantle to a Poor ManAssisi Superior Basilica

Giotto 1290 Stories of Isaac Assisi Superior BasilicaGiotto 1320ndash1325 Ascension Padua Scrovegni ChapelGiotto 1304ndash1306 Lamentation (The mourn-

ing of Christ)Padua Scrovegni Chapel

Giotto 1304ndash1306 Meeting on the GoldenGate

Padua Scrovegni Chapel

Giotto 1303ndash1305 The Kiss of Judah Padua Scrovegni ChapelGiotto 1325 Saint Francis before the

Sultan (trial by fire)Florence Santa Croce Museum

Giottorsquos work-shop

1325ndash1330 Virgin Mary Montecarlo Private Collection Monaco

Girodette 1802 Apotheosis of the Heroes Paris MalmaisonGoya 1819 Oration in the Garden Madrid San Antograven SchoolGrunewald 1512ndash1516 Crucifixion Colmar Unterlinden MuseumReni 1621 Dawn Rome Casino dellrsquoAurora Rospigliosi

PalaceHogarth 1743 The Ladyrsquos Death London National GalleryHolben H Jr 1532ndash1533 Noli me tangere Hampton Court Royal CollectionIngres 1842 Muse of Lyric Paris Louvre MuseumKokoshka 1914 The Bride of the Wind Basel KunstmuseumLa Tour 1644 Job and his Wife Paris Louvre MuseumLeonardo daVinci

1480ndash1481 Study of Madonna with theCat

London National Gallery

Lippi F Sr 1452ndash1464 The Feast of Herod Prato CathedralLochner 1435 Last Judgement Koumlln Wallraff Richartz MuseumLonghi 1734 The Fall of the Giants Venice Carsquo SagredoLorenzetti P 1320ndash1322 Deposition Assisi Superior BasilicaLorenzetti A 1342 Presentation at the Temple Florence Uffizi GalleryLotto 1552 Saint Michael driving out

LuciferLoreto Apostolic Palace

Graphic invariants in visual art 207

Table 1(Continued)

Author Year Title LocationMagritte 1937 In memoriam Mack Sennet Private CollectionMantegna 1500 Cult of the Cybele London National GalleryMargaritone 1262 Saint Francis Arezzo Civic MuseumMartini 1312ndash1317 Miraculous Mass Assisi Inferior BasilicaMartini 1312ndash1317 Saint Martin renounces his

WeaponsAssisi Inferior Basilica

Martini 1300 The Road to Calvary Paris Louvre MuseumMartini 1330 Guidoriccio da Fogliano Sienna Public PalaceMartini 1312ndash1317 Saint Martin is knighted Assisi Cappella Basilica of St FrancisMasaccio 1425ndash1428 Adam and Eva banished

from ParadiseFlorence Brancacci Chapel

Masaccio 1426 Crucifixion Naples Capodimonte National GalleryMatisse 1907 The Music Saint Petersburg Hermitage GalleryMemling 1466ndash1473 Last Judgement Danzica PormoskieMemling 1485 Bathsheba Stuttgart StaatsgalerieMichelangelo 1508ndash1512 Sistina Chapel Vault

(detail)Rome Vatican Palaces

Michelangelo 1503ndash1504 Tondo Doni Florence Uffizi GalleryMichelino 1400 Ascension New York Metropolitan MuseumMonaco 1420ndash1422 Adoration of the Magi Florence Uffizi GalleryMonet 1876 Madame Monet in Japanese

CostumeBoston Museum of Fine Arts

Moreau 1876 Salomeacute Paris Gustave Moreau MuseumMoreau 1889 The Peacock complaining

to JunoParis Gustave Moreau Museum

Murillo 1646 The Angelsrsquo Kitchen Paris Louvre MuseumOrozco 1937 Hidalgo Guadalajara Jalisco State Government

PalaceParmigianino 1535 Madonna of the Long Neck Florence Uffizi GalleryPerugino 1496ndash1500 Venus Perugia Collegio del CambioPicasso 1915ndash1918 Crucifixion Paris Picasso MuseumPicasso 1899ndash1900 Woman with Mantilla Barcelona Picasso MuseumPicasso 1922 Women running on the

BeachParis Picasso Museum

Pissarro 1881 Young Peasant Girl witha Stick

Paris drsquoOrsay Museum

Pontormo 1526ndash1528 Deposition Florence Santa Felicita ChurchPontormo 1528 Visitation Carmignano (Florence) Pieve of San

MichelePoussin 1640ndash1650 Ecstasy of Saint Paul Paris Louvre MuseumPoussin 1628ndash1629 The Martyrdom of Saint

ErasmusRome Vatican Picture Gallery

Reni 1611 Massacre of the Innocents Bologna National Picture GalleryReni 1620 Atalanta and Hippomenes Naples Capodimonte National GalleryRenoir 1886 Dance at Bougival Paris drsquoOrsay Museum

208 S Gori et al

Table 1(Continued)

Author Year Title LocationRicci 1705 Madonna Venice San Marziale ChurchRossoFiorentino

1521 Deposition Volterra (Sienna) Picture Gallery

Rubens 1611 Deposition Anvers CathedralSchiele 1917 Reclined Woman Wien Private CollectionSchiele 1917 Sitting Woman Wien Graphische Sammlung AlbertinaLucca School XII century CrucifixionSeurat 1890ndash1891 The Circus Paris drsquoOrsay MuseumTaddeo Gaddi 1328 Stories of the Virgin Poppi (Arezzo) Count Guidi CastleTiepolo 1719 Repudiation of Agar Milan Rasini CollectionTiepolo 1749 Our Lady of Carmel

appearing to SaintSimon Stock

Venice Carmini School

Tiepolo 1750 The Martyrdom of SaintAgata

Milan Rasini Collection

Tintoretto 1558 Saint George and theDragon

London National Gallery

Tiziano 1514ndash1515 Sacred and Profane Love Rome Borghese GalleryToulouse-Loutrec

1892 Jane Avril Dancing Paris drsquoOrsay Museum

Uccello 1425 Stories of Genesis Florence Santa Maria Novella ChurchClaustrum

Van DerWeyden

1435 Deposition Madrid Prado Museum

Van Dyck 1625ndash1627 Genoan Lady with herDaughter

Paris Louvre Museum

Van Eyck 1422ndash1425 John the Baptist Paris Louvre MuseumVelasquez 1628 Immaculate Conception London National GalleryVermeer 1670 Allegory of Faith New York Metropolitan MuseumVitale daBologna

1350 Saint George and theDragon

Bologna National Picture Gallery

Volterrano 1670 Beauty Destroyed bythe Time

Florence Piccolini Palace

Von Mieris 1670 Lady on the Mirror Munich Alte PinakothekWatteau 1717 The Awkward Lover Paris Louvre MuseumZurbaran 1628 Saint Serapion Hartford Wadsworth AthenaeumZurbaran 1629 Christ Pantocrator Moscow Pushkin Museum

Procedure Subjects sat 60 cm away from the monitor Fixation was binocularSubjects saw all the 160 paintings in random order and in free vision Theyhad to decide in a binary classification task whether the garments indicated bythe experimenter were dynamic or static Each painting was shown once Theexperiment was conducted in a dark room

Graphic invariants in visual art 209

Results

The 10 subjects were in perfect agreement All the garments were classified asstatic or dynamic according to their answers Then for each century the numberof lines of different types in the two categories was compared to find out whetherany type of line was more represented in a category than the other The resultssummarized in Table 2 show that the presence of straight parallel and horizontallines characterises the static garments in paintings of almost every century whilecurved convergent and diagonal lines were significantly more when the garmentswere judged dynamic The only exceptions were the seventeenth and the eighteenth

Table 2For each century the frequencies of straight curved parallel convergent orthogonal and diagonallines are reported for dynamic and static garments Almost all the line types according to aχ2 statistic are statistically different for dynamic vs static garments in each century

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1200 Straight 729 134 70148 lt0001Curved 27 385Parallel 989 345 5524 lt0001Convergent 282 220Orthogonal 850 160 63692 lt0001Diagonal 62 372

1300 Straight 378 201 26332 lt0001Curved 25 281Parallel 490 350 7895 lt0001Convergent 57 170Orthogonal 352 139 27183 lt0001Diagonal 68 341

1400 Straight 160 310 22671 lt0001Curved 8 1116Parallel 210 714 16166 lt0001Convergent 11 732Orthogonal 178 293 44550 lt0001Diagonal 9 1133

1500 Straight 61 212 25029 lt0001Curved 20 1577Parallel 140 823 11218 lt0001Convergent 14 950Orthogonal 140 482 23910 lt0001Diagonal 15 1191

1600 Straight 43 144 044 NSCurved 280 1062Parallel 164 385 2437 lt0001Convergent 214 906Orthogonal 159 371 3647 lt0001Diagonal 182 895

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 207

Table 1(Continued)

Author Year Title LocationMagritte 1937 In memoriam Mack Sennet Private CollectionMantegna 1500 Cult of the Cybele London National GalleryMargaritone 1262 Saint Francis Arezzo Civic MuseumMartini 1312ndash1317 Miraculous Mass Assisi Inferior BasilicaMartini 1312ndash1317 Saint Martin renounces his

WeaponsAssisi Inferior Basilica

Martini 1300 The Road to Calvary Paris Louvre MuseumMartini 1330 Guidoriccio da Fogliano Sienna Public PalaceMartini 1312ndash1317 Saint Martin is knighted Assisi Cappella Basilica of St FrancisMasaccio 1425ndash1428 Adam and Eva banished

from ParadiseFlorence Brancacci Chapel

Masaccio 1426 Crucifixion Naples Capodimonte National GalleryMatisse 1907 The Music Saint Petersburg Hermitage GalleryMemling 1466ndash1473 Last Judgement Danzica PormoskieMemling 1485 Bathsheba Stuttgart StaatsgalerieMichelangelo 1508ndash1512 Sistina Chapel Vault

(detail)Rome Vatican Palaces

Michelangelo 1503ndash1504 Tondo Doni Florence Uffizi GalleryMichelino 1400 Ascension New York Metropolitan MuseumMonaco 1420ndash1422 Adoration of the Magi Florence Uffizi GalleryMonet 1876 Madame Monet in Japanese

CostumeBoston Museum of Fine Arts

Moreau 1876 Salomeacute Paris Gustave Moreau MuseumMoreau 1889 The Peacock complaining

to JunoParis Gustave Moreau Museum

Murillo 1646 The Angelsrsquo Kitchen Paris Louvre MuseumOrozco 1937 Hidalgo Guadalajara Jalisco State Government

PalaceParmigianino 1535 Madonna of the Long Neck Florence Uffizi GalleryPerugino 1496ndash1500 Venus Perugia Collegio del CambioPicasso 1915ndash1918 Crucifixion Paris Picasso MuseumPicasso 1899ndash1900 Woman with Mantilla Barcelona Picasso MuseumPicasso 1922 Women running on the

BeachParis Picasso Museum

Pissarro 1881 Young Peasant Girl witha Stick

Paris drsquoOrsay Museum

Pontormo 1526ndash1528 Deposition Florence Santa Felicita ChurchPontormo 1528 Visitation Carmignano (Florence) Pieve of San

MichelePoussin 1640ndash1650 Ecstasy of Saint Paul Paris Louvre MuseumPoussin 1628ndash1629 The Martyrdom of Saint

ErasmusRome Vatican Picture Gallery

Reni 1611 Massacre of the Innocents Bologna National Picture GalleryReni 1620 Atalanta and Hippomenes Naples Capodimonte National GalleryRenoir 1886 Dance at Bougival Paris drsquoOrsay Museum

208 S Gori et al

Table 1(Continued)

Author Year Title LocationRicci 1705 Madonna Venice San Marziale ChurchRossoFiorentino

1521 Deposition Volterra (Sienna) Picture Gallery

Rubens 1611 Deposition Anvers CathedralSchiele 1917 Reclined Woman Wien Private CollectionSchiele 1917 Sitting Woman Wien Graphische Sammlung AlbertinaLucca School XII century CrucifixionSeurat 1890ndash1891 The Circus Paris drsquoOrsay MuseumTaddeo Gaddi 1328 Stories of the Virgin Poppi (Arezzo) Count Guidi CastleTiepolo 1719 Repudiation of Agar Milan Rasini CollectionTiepolo 1749 Our Lady of Carmel

appearing to SaintSimon Stock

Venice Carmini School

Tiepolo 1750 The Martyrdom of SaintAgata

Milan Rasini Collection

Tintoretto 1558 Saint George and theDragon

London National Gallery

Tiziano 1514ndash1515 Sacred and Profane Love Rome Borghese GalleryToulouse-Loutrec

1892 Jane Avril Dancing Paris drsquoOrsay Museum

Uccello 1425 Stories of Genesis Florence Santa Maria Novella ChurchClaustrum

Van DerWeyden

1435 Deposition Madrid Prado Museum

Van Dyck 1625ndash1627 Genoan Lady with herDaughter

Paris Louvre Museum

Van Eyck 1422ndash1425 John the Baptist Paris Louvre MuseumVelasquez 1628 Immaculate Conception London National GalleryVermeer 1670 Allegory of Faith New York Metropolitan MuseumVitale daBologna

1350 Saint George and theDragon

Bologna National Picture Gallery

Volterrano 1670 Beauty Destroyed bythe Time

Florence Piccolini Palace

Von Mieris 1670 Lady on the Mirror Munich Alte PinakothekWatteau 1717 The Awkward Lover Paris Louvre MuseumZurbaran 1628 Saint Serapion Hartford Wadsworth AthenaeumZurbaran 1629 Christ Pantocrator Moscow Pushkin Museum

Procedure Subjects sat 60 cm away from the monitor Fixation was binocularSubjects saw all the 160 paintings in random order and in free vision Theyhad to decide in a binary classification task whether the garments indicated bythe experimenter were dynamic or static Each painting was shown once Theexperiment was conducted in a dark room

Graphic invariants in visual art 209

Results

The 10 subjects were in perfect agreement All the garments were classified asstatic or dynamic according to their answers Then for each century the numberof lines of different types in the two categories was compared to find out whetherany type of line was more represented in a category than the other The resultssummarized in Table 2 show that the presence of straight parallel and horizontallines characterises the static garments in paintings of almost every century whilecurved convergent and diagonal lines were significantly more when the garmentswere judged dynamic The only exceptions were the seventeenth and the eighteenth

Table 2For each century the frequencies of straight curved parallel convergent orthogonal and diagonallines are reported for dynamic and static garments Almost all the line types according to aχ2 statistic are statistically different for dynamic vs static garments in each century

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1200 Straight 729 134 70148 lt0001Curved 27 385Parallel 989 345 5524 lt0001Convergent 282 220Orthogonal 850 160 63692 lt0001Diagonal 62 372

1300 Straight 378 201 26332 lt0001Curved 25 281Parallel 490 350 7895 lt0001Convergent 57 170Orthogonal 352 139 27183 lt0001Diagonal 68 341

1400 Straight 160 310 22671 lt0001Curved 8 1116Parallel 210 714 16166 lt0001Convergent 11 732Orthogonal 178 293 44550 lt0001Diagonal 9 1133

1500 Straight 61 212 25029 lt0001Curved 20 1577Parallel 140 823 11218 lt0001Convergent 14 950Orthogonal 140 482 23910 lt0001Diagonal 15 1191

1600 Straight 43 144 044 NSCurved 280 1062Parallel 164 385 2437 lt0001Convergent 214 906Orthogonal 159 371 3647 lt0001Diagonal 182 895

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

208 S Gori et al

Table 1(Continued)

Author Year Title LocationRicci 1705 Madonna Venice San Marziale ChurchRossoFiorentino

1521 Deposition Volterra (Sienna) Picture Gallery

Rubens 1611 Deposition Anvers CathedralSchiele 1917 Reclined Woman Wien Private CollectionSchiele 1917 Sitting Woman Wien Graphische Sammlung AlbertinaLucca School XII century CrucifixionSeurat 1890ndash1891 The Circus Paris drsquoOrsay MuseumTaddeo Gaddi 1328 Stories of the Virgin Poppi (Arezzo) Count Guidi CastleTiepolo 1719 Repudiation of Agar Milan Rasini CollectionTiepolo 1749 Our Lady of Carmel

appearing to SaintSimon Stock

Venice Carmini School

Tiepolo 1750 The Martyrdom of SaintAgata

Milan Rasini Collection

Tintoretto 1558 Saint George and theDragon

London National Gallery

Tiziano 1514ndash1515 Sacred and Profane Love Rome Borghese GalleryToulouse-Loutrec

1892 Jane Avril Dancing Paris drsquoOrsay Museum

Uccello 1425 Stories of Genesis Florence Santa Maria Novella ChurchClaustrum

Van DerWeyden

1435 Deposition Madrid Prado Museum

Van Dyck 1625ndash1627 Genoan Lady with herDaughter

Paris Louvre Museum

Van Eyck 1422ndash1425 John the Baptist Paris Louvre MuseumVelasquez 1628 Immaculate Conception London National GalleryVermeer 1670 Allegory of Faith New York Metropolitan MuseumVitale daBologna

1350 Saint George and theDragon

Bologna National Picture Gallery

Volterrano 1670 Beauty Destroyed bythe Time

Florence Piccolini Palace

Von Mieris 1670 Lady on the Mirror Munich Alte PinakothekWatteau 1717 The Awkward Lover Paris Louvre MuseumZurbaran 1628 Saint Serapion Hartford Wadsworth AthenaeumZurbaran 1629 Christ Pantocrator Moscow Pushkin Museum

Procedure Subjects sat 60 cm away from the monitor Fixation was binocularSubjects saw all the 160 paintings in random order and in free vision Theyhad to decide in a binary classification task whether the garments indicated bythe experimenter were dynamic or static Each painting was shown once Theexperiment was conducted in a dark room

Graphic invariants in visual art 209

Results

The 10 subjects were in perfect agreement All the garments were classified asstatic or dynamic according to their answers Then for each century the numberof lines of different types in the two categories was compared to find out whetherany type of line was more represented in a category than the other The resultssummarized in Table 2 show that the presence of straight parallel and horizontallines characterises the static garments in paintings of almost every century whilecurved convergent and diagonal lines were significantly more when the garmentswere judged dynamic The only exceptions were the seventeenth and the eighteenth

Table 2For each century the frequencies of straight curved parallel convergent orthogonal and diagonallines are reported for dynamic and static garments Almost all the line types according to aχ2 statistic are statistically different for dynamic vs static garments in each century

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1200 Straight 729 134 70148 lt0001Curved 27 385Parallel 989 345 5524 lt0001Convergent 282 220Orthogonal 850 160 63692 lt0001Diagonal 62 372

1300 Straight 378 201 26332 lt0001Curved 25 281Parallel 490 350 7895 lt0001Convergent 57 170Orthogonal 352 139 27183 lt0001Diagonal 68 341

1400 Straight 160 310 22671 lt0001Curved 8 1116Parallel 210 714 16166 lt0001Convergent 11 732Orthogonal 178 293 44550 lt0001Diagonal 9 1133

1500 Straight 61 212 25029 lt0001Curved 20 1577Parallel 140 823 11218 lt0001Convergent 14 950Orthogonal 140 482 23910 lt0001Diagonal 15 1191

1600 Straight 43 144 044 NSCurved 280 1062Parallel 164 385 2437 lt0001Convergent 214 906Orthogonal 159 371 3647 lt0001Diagonal 182 895

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 209

Results

The 10 subjects were in perfect agreement All the garments were classified asstatic or dynamic according to their answers Then for each century the numberof lines of different types in the two categories was compared to find out whetherany type of line was more represented in a category than the other The resultssummarized in Table 2 show that the presence of straight parallel and horizontallines characterises the static garments in paintings of almost every century whilecurved convergent and diagonal lines were significantly more when the garmentswere judged dynamic The only exceptions were the seventeenth and the eighteenth

Table 2For each century the frequencies of straight curved parallel convergent orthogonal and diagonallines are reported for dynamic and static garments Almost all the line types according to aχ2 statistic are statistically different for dynamic vs static garments in each century

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1200 Straight 729 134 70148 lt0001Curved 27 385Parallel 989 345 5524 lt0001Convergent 282 220Orthogonal 850 160 63692 lt0001Diagonal 62 372

1300 Straight 378 201 26332 lt0001Curved 25 281Parallel 490 350 7895 lt0001Convergent 57 170Orthogonal 352 139 27183 lt0001Diagonal 68 341

1400 Straight 160 310 22671 lt0001Curved 8 1116Parallel 210 714 16166 lt0001Convergent 11 732Orthogonal 178 293 44550 lt0001Diagonal 9 1133

1500 Straight 61 212 25029 lt0001Curved 20 1577Parallel 140 823 11218 lt0001Convergent 14 950Orthogonal 140 482 23910 lt0001Diagonal 15 1191

1600 Straight 43 144 044 NSCurved 280 1062Parallel 164 385 2437 lt0001Convergent 214 906Orthogonal 159 371 3647 lt0001Diagonal 182 895

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

210 S Gori et al

Table 2(Continued)

Centuries Lines Static (freq) Dynamic (freq) χ21 p

1700 Straight 68 177 002 NSCurved 390 1040Parallel 212 565 1096 lt0001Convergent 299 558Orthogonal 153 143 6571 lt0001Diagonal 418 1090

1800 Straight 300 116 28644 lt0001Curved 176 620Parallel 409 325 21512 lt0001Convergent 71 428Orthogonal 333 176 20945 lt0001Diagonal 182 562

1900 Straight 355 58 46658 lt0001Curved 174 641Parallel 464 339 11640 lt0001Convergent 142 375Orthogonal 440 176 46450 lt0001Diagonal 66 544

centuries where in the static garments we observed a surprising amount of curvedconvergent and diagonal lines

Discussion

The results showed clearly that painters used almost constantly from the MiddleAges up to today the same graphic solution to give the observer the impressionof the garmentsrsquo motion As stated in the introduction in the history of art itis really hard to find a graphic invariant that remains the same despite the timeThe exception of the seventeenth and eighteenth centuries could be explained withthe triumph of motion in the representations of the pictorial works of these twocenturies This may mean that the subjects judged garments as static using differentcues mdash as body positions or the surrounding environment mdash whenever those cueswere in contrast with the appearance of the garments This happened often in theartworks of these two centuries

If these data support the existence of graphic invariants expressing motion somemethodological issues could be raised First the complete agreement of the subjectsin judging the presence or absence of motion in garments suggests that if thesubjects were given a Likert scale instead of a binary classification task moreprecise results would have been possible Moreover the calculation of the subjectivemotion index of the lines could be too arbitrary A more appropriate way to calculateit should be taken in account Also the assumption that functional lines (the linesdue to pins belts etc) are not used by the observers to judge motion perceptionof garments should be proven in some way It is not certain that the subjects do

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 211

not use other cues of motion from the other parts of the painting as suggested bythe unexpected results for the seventeenth and eighteenth centuries Finally to testwhether some orientations and shapes of the lines can give motion sensation to ourvisual system is probably necessary to simplify these complex stimuli Using thispilot experiment as a starting point the following three experiments were devisedin order to address all these issues

EXPERIMENT 1

The attempt here was to replicate the results of the pilot experiment using a moresophisticated methodology and a smaller sample of paintings However this is stillrepresentative of the centuries covered by the pilot According to our hypothesisalso with a smaller sample it can be inferred that the shape of lines (straightvs curved) their position respect to the other lines (parallel vs convergent) andtheir orientation (orthogonal vs diagonal) should all be excellent predictors for theperception of motion in the garments

Method

Subjects Ten naiumlve subjects (mean age 24 yrs SD = 47) participated in theexperiment All had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen of the 160 paintings of the pilot experiment were randomlyselected two for each century (Fig 1 and Table 3) Then only one garment foreach painting was chosen We used the following constraint for the same centuryone garment had been judged as dynamic and the other one as static during the pilotexperiment All paintings were shown on a 28 times 21 cm monitor Sony TrinitronColor E100P controlled by a PC Selecta Promo 600 All paintings were presentedat full screen size

For all garments used in the experiment all lines were counted and classified inthe same categories of the pilot experiment following the same criteria To gaugethe subjective motion index of the lines a more accurate method was used A gridwas applied on each painting and a line in the garments that was 00prime36primeprime longand 00prime23primeprime wide was used as unit This small line was assigned the value of 1All lines longer or wider were measured as a function of this unit For exampleeach line that was 01prime12primeprime long but still 00prime23primeprime wide was counted 2 if the linewas 01prime12primeprime long and 00prime46primeprime wide the line was counted 4 and so on In this waya more objective impact for each line was obtained as a function of their length andwidth We called this new index line weight Also in this experiment the functionallines mdash ie the lines distorted by objects or anatomic joints mdash were excluded fromthe general count but here they were separately counted and divided in the samecategories

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

212 S Gori et al

Figure 1 Set of stimuli used in Experiment 1 (achromatic version)

Procedure Subjects were seated 60 cm away from the monitor Fixation wasbinocular Subjects saw all 16 paintings in random order and in free vision Thetask was to value all the garments that the experimenter indicated as in motionor static The difference from the pilot experiment was that the subject used aLikert scale where 0 meant no motion and 4 meant very strong impression ofmotion Each painting was shown once The experiment was performed in a darkroom

Results

As summarised in the upper part of Table 4 movement perception judgments arehigher for paintings having a higher percentage of curved convergent and diagonallines As seen in Fig 2 those three variables predict judgments in a very similar

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 213

Figure 1 (Continued)

way showing that they constitute redundant cues indicating the same characteristic(motion) Single linear regressions for each category mdash such as shape (straight vscurved) position of lines in respect to the other lines (parallel vs convergent) andorientation (orthogonal vs diagonal) mdash show that each category of lines is a strongpredictor of perceived motion in garments The upper parts of Tables 5 and 6 showcorrelation coefficients parameters and significance levels for each linear regressionmodel curved lines seem to be the best predictor followed by diagonal lines andthen by convergent ones (Fig 2)

Single regressions were calculated also without including the functional lines Thethree categories are still very good predictors of the perceived motion in garmentsjust as in the results previously shown These results confirm those of the pilotexperiment

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

214 S Gori et al

Figure 1 (Continued)

Discussion

Results show that it is easy to predict the amount of perceived motion in thegarments using the number of curved convergent and diagonal lines Each categoryexhibits a considerable amount of variance thus indicating that the painters usedthese three categories together In other words a painter willing to give to theobserver a strong effect of motion in garments will use curved convergent anddiagonal lines all together On the other hand a painter who would like to give usthe impression of static garments will use a noteworthy amount of straight paralleland orthogonal lines Calculation of the regressions with the functional lines inthe count shows that their presence or absence does not change the value of thesethree predictors Still the amount of variance exhibited by the predictors without

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 215

Figure 1 (Continued)

functional lines is slightly better That suggests that subjects do not use these linesas cues of motion With this sharper methodology it is possible to confirm the pilotexperiment and show that the use of specific types of lines is the technique mainlyused from the Middle Ages to the twentieth century to give us the impression ofmotion in the garments

EXPERIMENT 2

To prevent other details of the paintings from influencing the perception of motionin the garments they were extracted from the backdrop and shown on a whitebackground The subjectsrsquo task was exactly the same as in the first experimentThe hypothesis was that the environment of the paintings does not influence in

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

216 S Gori et al

Table 3From the 160 paintings used in the pilot experiment 16 were selected There are two of them percentury According with the results of the pilot experiment the garments should be one static and theother one dynamic

Author Year Title Location(1) Berlinghiero 1210ndash1220 Crucifix Lucca Picture Gallery(2) Cimabue 1280 Crucifixion (detail) Assisi Superior Basilica(3) Giotto 1290 Saint Francis giving his Mantle to a

Poor ManAssisi Superior Basilica

(4) Martini 1330 Guidoriccio da Fogliano Sienna Public Palace(5) Botticelli 1483ndash1485 Birth of Venus Florence Uffizi Gallery(6) Masaccio 1426 Crucifixion Naples Capodimonte

National Gallery(7) Duumlrer 1500 Lamentation for the Dead Christ Munich Alte Pinakothek(8) Michelangelo 1508ndash1512 Sistina Chapel Vault (detail) Rome Vatican Palaces(9) Velasquez 1628 Immaculate Conception London National Gallery

(10) Caravaggio 1602 Saint Matthew and the Angel Rome San Luigi deiFrancesi Church

(11) David 1784ndash1785 Oath of the Horatii Paris Louvre Museum(12) Fragonard 1767 The Swing London Fallace Collection(13) Delacroix 1830 Freedom leading the People Paris Louvre Museum(14) Courbet 1856 The Young Ladies on the Banks of

the Seine (Summer)Paris Petit Palais Museum

(15) Chagall 1917ndash1918 The Walk Saint Petersburg RussianMuseum

(16) De Chirico 1918 Disquieting Muses Milan Mattioli Collection

a significant way the perception of dynamism in the garments In other words thethree categories of lines should still have been very good predictors just like beforeThe only difference expected was that the functional lines should be added to thecount to have a better prediction of the perceived motion only in the paintings wherefunctional lines are a major number This was expected because all the objects likepins or belts were removed from the garments The observer would then interpretthe lines as if they were not distorted by the removed objects

Methods

Subjects Ten naiumlve subjects (mean age 29 yrs SD = 67) participated in thestudy They all had normal or corrected-to-normal visual acuity and normal colourvision (tested with the Ishihara pseudo-isochromatic plates)

Stimuli Sixteen garments the same as those used in Experiment 1 were shownto the subjects on a white background To cut them from the paintings Jasc PaintShop Pro 8 was used All the details were removed from them except the garmentsthemselves All the lines were counted and classified as in Experiment 1 the

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 217

Table 4The percentage of curved diagonal and convergent lines as well as the mean judgment betweenall subjects (N = 10 for each experiment) is reported for each painting and each of the threeexperiments For Experiments 1 and 2 the same percentages are given also excluding from the countthe functional lines

Descriptive Statistics

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Paintings Berlinghiero 5128 000 6148 958 2130 522 050(Expt 1) Cimabue 7255 7063 8039 7810 7712 7107 210

Giotto 544 000 544 000 272 000 170Martini 8435 8435 9696 9696 6739 6739 170Botticelli 9249 9237 9289 9277 2964 2851 330Masaccio 1481 000 1667 000 370 000 020Duumlrer 2681 000 1495 000 352 000 070Michelagelo 9679 9641 8717 8659 7647 7647 270Velasquez 5749 1191 1930 530 2977 1779 180Caravaggio 9245 9192 9214 9175 1530 1494 360David 3438 392 1652 743 1830 1202 130Fragonard 8984 8899 8695 8631 8104 8006 360Delacroix 9665 9632 9139 9032 7225 6848 330Courbet 9041 000 3344 000 2315 000 170Chagall 9608 9608 10000 10000 5686 5686 230De Chirico 000 000 000 000 000 000 030

Garments Berlinghiero 5128 000 6148 958 2130 522 120(Expt 2) Cimabue 7255 7063 8039 7810 7712 7107 230

Giotto 544 000 544 000 272 000 140Martini 8435 8435 9696 9696 6739 6739 210Botticelli 9249 9237 9289 9277 2964 2851 390Masaccio 1481 000 1667 000 370 000 060Duumlrer 2681 000 1495 000 352 000 090Michelagelo 9679 9641 8717 8659 7647 7647 340Velasquez 5749 1191 1930 530 2977 1779 280Caravaggio 9245 9192 9214 9175 1530 1494 260David 3438 392 1652 743 1830 1202 140Fragonard 8984 8899 8695 8631 8104 8006 340Delacroix 9665 9632 9139 9032 7225 6848 210Courbet 9041 000 3344 000 2315 000 250Chagall 9608 9608 10000 10000 5686 5686 270De Chirico 000 000 000 000 000 000 000

line weight was also calculated in the same way All garments were shown ona 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600 The dimension of the garments was the same of Experiment 1 but allthe rest of the painting was now a white background

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

218 S Gori et al

Table 4(Continued)

Conditions Painting Curved lines Diagonal lines Convergent Meanjudg-ment

lines

All With- All With- All With-out F out F out F

Squares Berlinghiero 5542 5627 6720 320(Expt 3) Cimabue 7343 9230 1386 300

Giotto 531 383 531 070Martini 9758 9793 9832 360Botticelli 9663 9878 8751 320Masaccio 364 9831 486 140Duumlrer 318 398 407 160Michelagelo 9395 8930 8581 320Velasquez 5142 2015 7093 200Caravaggio 9938 8473 9532 340David 338 161 261 150Fragonard 9867 9863 9914 400Delacroix 219 9810 9556 330Courbet 260 454 8735 230Chagall 6278 9971 1010 280De Chirico 000 000 000 020

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same as in Experiment 1 Each garment was shown once Theexperiment was performed in a dark room

RESULTS

The middle part of Table 4 shows that as for Experiment 1 in Experiment 2garments characterised by more curved convergent and diagonal lines result inhigher rankings of perceived motion Single linear regressions were performedusing the three types of lines to predict subjectsrsquo judgments of dynamism Allthe three models work well in predicting judgements (see Fig 3 middle part ofTables 5(a) and 6(a) and lower part of Tables 5(b) and 6(b)) This is true also whenfunctional lines are taken off the count

In general the presence or absence of functional lines does not change in a sig-nificant way the values of R2 (middle part Table 5(a) and lower part of Table 6(b))But a tendency can be found suggesting that the functional lines could be countedby the observers to judge motion perception in the garments Moreover by lookingin detail into the data related to each garment it is possible to find some interest-ing examples of functional lines constituting a relevant difference between Experi-ments 1 and 2 Good examples of this are the paintings by Berlinghiero MasaccioVelasquez and Courbet Each of them contains a major proportion of functionallines In the first experiment the average value of perceived motion measured

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 219

Figure 2 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment in its pictorial context

on a scale from 0 to 4 was respectively Berlinghierorsquos garments = 05 Masac-ciorsquos garments = 02 Velasquezrsquos garments = 18 and Courbetrsquos garments = 17In the second experiment where only the garments are shown and all the func-tional lines no longer appear as functional the mean value of perceived motionbecomes respectively Berlinghierorsquos garments = 12 Masacciorsquos garments = 06Velasquezrsquos garments = 28 and Courbetrsquos garments = 25 These differences areattested only in the paintings where functional lines appear in high percentage asexpected For the majority of the paintings where the functional lines are not a ma-jor proportion their presence has no statistical effect

Discussion

Results show that the amounts of specific types of lines are very good predictors forthe perceived motion Also from this experiment it is clear that the artists use thethree categories always in the same way which justifies the conspicuous amount ofvariance that each category can exhibit Moreover the exclusive use of the garmentshelps to understand which cues of motions subjects used in the attempt to determine

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

220 S Gori et al

Table 5Correlations between subjectsrsquo judgements and the percentage of curved diagonal and convergentlines is rather high in all the experiments Table 5(a) shows the correlations obtained when all linesare included whereas Table 5(b) shows those obtained when all the lines but the functional ones areincluded

(a) Correlations (all lines included)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 626138 3561070 0849 0721 072343 16

Diagonal lines 559792 3866569 0741 0549 080026 16 Convergent lines 361600 3032691 0608 0370 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 626138 3561070 0782 0611 059533 16

Diagonal lines 559792 3866569 0705 0498 079932 16 Convergent lines 361600 3032691 0631 0398 087508 16

Squares Mean judgment 24625 111168 16(Expt 3) Curved lines 468469 4266657 0849 0721 071724 16

Diagonal lines 592600 4428391 0761 0579 074670 16 Convergent lines 517455 4276811 0777 0604 072391 16

(b) Correlations (functional lines excluded)

Condition Variable Mean Standard R R2 Std error of N

deviation the estimatePaintings Mean judgment 19250 115094 16(Expt 1) Curved lines 458060 4574739 0839 0704 064819 16

Diagonal lines 465696 4553861 0798 0637 071769 16 Convergent lines 311763 3239946 0631 0399 094577 16

Garments Mean judgment 20813 108948 16(Expt 2) Curved lines 458060 4574739 0728 0530 077299 16

Diagonal lines 465696 4553861 0695 0483 092383 16 Convergent lines 311763 3239946 0603 0364 089957 16

the dynamic or static nature of the garments The substantial increase of perceivedmotion from the first to the second experiment is seen only in garments wherefunctional lines are conspicuously attested Our hypothesis that the subjects usethese three categories of lines to decide if the garments are in motion is confirmedFurthermore it becomes also clear that the functional lines after removing everyelement that accounts for the reason for their distortion become a cue of motionexactly like the other lines

EXPERIMENT 3

The aim of this experiment is to answer the following question Are simple lineswith a specific shape relationship with the other lines and orientation enough toelicit an impression of motion in our visual system In other words was the artistsrsquochoice to use the same graphic solution giving an impression of motion unchanged

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 221

Table 6All the models are linear regressions using the mean judgment of subjects (N = 10) for each ofthe 16 paintings as dependent variable and the percentage of curved diagonal or convergent linesas independent variable Table 6(a) shows the parameters obtained when all lines are includedwhereas Table 6(b) shows those obtained when all the lines but the functional ones are includedAll independent variables explain a relevant proportion of variance

(a) Models (all lines included)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0317 0375(Expt 1) Curved lines 0026 0005 0795 23967 lt0001

(Constant) 0691 0360 Diagonal lines 0022 0005 0741 17027 0001(Constant) 1091 0375 Convergent lines 0023 0008 0608 8214 0012

Garments (Constant) 0454 0309(Expt 2) Curved lines 0026 0004 0849 36236 lt0001

(Constant) 0969 0359 Diagonal lines 0020 0005 0705 13866 0002(Constant) 1262 0347 Convergent lines 0023 0007 0631 9250 0009

Squares (Constant) 1508 0271(Expt 3) Curved lines 0020 0004 0782 22035 lt0001

(Constant) 1331 0318 Diagonal lines 0019 0004 0761 19247 0001(Constant) 1417 0290 Convergent lines 0020 0004 0777 21374 lt0001

(b) Models (functional lines excluded)

Condition Variable Unstandardised Standardisedcoefficients

F(114) p

coefficients

B Std error BPaintings (Constant) 0958 0233(Expt 1) Curved lines 0021 0004 0839 33292 lt0001

(Constant) 0986 0261 Diagonal lines 0020 0004 0798 24576 lt0001(Constant) 1226 0326 Convergent lines 0022 0007 0631 9282 0009

Garments (Constant) 1287 0278(Expt 2) Curved lines 0017 0004 0728 15797 0001

(Constant) 1307 0295 Diagonal lines 0017 0005 0695 13071 0003(Constant) 1449 0317 Convergent lines 0020 0007 0603 8002 0013

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

222 S Gori et al

Figure 3 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved diagonal and convergent lines attestedin a garment

because our visual system leads us to perceive dynamism in the presence of a simplelines pattern To understand whether this was true or not a new set of stimuli wascreated constituted by simplified patterns and the perceived motion was tested asa function of the type of lines The hypothesis was also that meaningless patternsthat differed only in the types of lines composing them are enough to elicit motionperception It was also hypothesised that it could happen only when specific typesof lines are attested The same results for the linear regressions found in the firstand in the second experiment were also expected

Methods

Subjects Ten naiumlve subjects (mean age 26 yrs SD = 51) participated in thestudy All had normal or corrected-to-normal visual acuity

Stimuli Sixteen patterns were created by a square cut out of each garment usedin Experiment 2 in a random position Every square had a dimension of 12 deg Allthe patterns were transformed in grey scale and the Michelson contrast was brought

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 223

Figure 4 This picture exemplifies how garments were extracted from a painting and then thecorresponding high contrast squared patterns from the garments

to 94 In this way every pattern was deprived of all details and it was impossibleto understand from which configuration it came (see Fig 4 for an example of theprocedure) All the patterns appeared like a square with different types of lines(Fig 5) This procedure was chosen instead of creating a completely new set ofstimuli to maintain the link with the original paintings To cut them from thepaintings Jasc Paint Shop Pro 8 was used The lines were counted and classifiedas in Experiments 1 and 2 also the line weight was calculated in the same wayUnlike the other experiments given the nature of the stimuli involved it would bemeaningless to use the concept of functional lines All these patterns were shownon a 28 times 21 cm monitor Sony Trinitron Color E100P controlled by a PC SelectaPromo 600

Procedure The subjects were seated 60 cm away from the stimulus The taskwas exactly the same of the Experiments 1 and 2 Each pattern was shown onceThe experiment was performed in a dark room

Results

Just as happened for the previous two experiments the lower part of Table 4 showsthat the squares with a higher percentage of curved diagonal and convergent lineselicit stronger impressions of movement Three single linear regressions (see lowerpart of Tables 5(a) and 6(a)) show that each of the three considered variables is initself a good enough predictor of the perceived level of movement (Fig 6) In thepresence of straight parallel and orthogonal lines the pattern was seen as static

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

224 S Gori et al

Figure 5 Set of stimuli used in Experiment 3

in the presence or higher percentage of curved convergent and diagonal lines thepattern elicited perceived motion

Discussion

The results of this experiment reveal that specific lines elicit motion perception instatic patterns It seems that garments in the paintings are only a specific case ofthis general phenomenon that was discovered by artists many centuries ago for itsstrong and clear motion impression and was used extensively by them At thispoint it is possible to speculate on our visual system How does it recognise motionin a specific static pattern and not in another one This phenomenon could berelated with the speed lines Cutting (2002) describes them like an array of linesattached to the object This method of conveying the impression of motion in a

Graphic invariants in visual art 225

Figure 6 Mean judgments of subjectsrsquo perception of motion (N = 16) used as the dependentvariable are equally well predicted by the percentage of curved convergent and diagonal lines attestedin a high contrast squared patterns

static pattern allows the artist to avoid deforming the object which still retains itsshape yet appears to be moving This kind of solution is well known because it isoften used in comics Burr (2000) has shown that behind their efficacy in producingan impression of motion there could be some neurophysiological mechanism

As a consequence it looks like the presence of lines on a static figure could beinterpreted by our visual system like a fast movement of the object that leaves tracesof the object itself where it was located just before If one accepts this interpretationthe reason why some lines evoked the motion perception remains unexplainedShowing which lines give a stronger effect of motion if located in a static squareframe does not give a real answer about the neurophysiological basis that could beinvolved in this mechanism We wish to stimulate new researches looking for thesubstrate of this interesting phenomenon of perception of dynamism when we arepresented with static patterns

We would like to highlight an interesting coincidence The most famous bi-dimensional static patterns that give illusory motion like MacKay Rays (MacKay1957) Enigma Illusion (Leviant 1996) PinnandashBrelstaff Illusion (Pinna and Brel-

226 S Gori et al

staff 2000) Rotating Snakes (Kitaoka and Ashida 2003) have also a commonglobal characteristic many three-dimensional cues We found that curved con-vergent and diagonal lines give the strongest dynamic impression All of themcould be interpreted by our visual system like a cue of three-dimensional spacethe opposite could happen when viewing straight parallel and orthogonal linesInterestingly Ramachandran (1988) argues that the brain needs first to computethree-dimensional shapes using depth cues in two-dimensional figures in order tobe able to perceive apparent motion Moreover Ramachandranrsquos study shows thata reduced depth impression leads to an almost complete loss of the apparent mo-tion effect These results seem to agree with the idea that three-dimensional indicesin a two-dimensional image can trigger the impression of movement A relation-ship between the neural processing of depth perception and the visual motor areasis perhaps worthy of consideration and can be an interesting challenge for furtherinvestigation

CONCLUSION

Our findings show an interesting graphic invariant in the history of art It wasdemonstrated that the representation of motion in garments follows the same ruleirrespective of its use by different painters and different centuries It was shownhow perceived motion in garments can be predicted using the presence or absence ofspecific types of lines It was demonstrated that lines inside garments are sufficientto elicit motion impression independent of the presence of other cues of motionin the paintings It was shown that some types of lines give an impression ofdynamism also in meaningless square patterns We would like to suggest thatthese results are indicative of a perceptual underlying mechanism that specificallyrecognizes curvature parallelism and orientation as cues of motion in a staticpattern Moreover we highlight the interesting possibility that the perception ofmotion in static bi-dimensional patterns is related to the presence of many three-dimensional cues

Acknowledgement

We would like to thank Caterina Borghini and Professor Riccardo Luccio for thecontribution given to the pilot experiment and the two anonymous reviewers forexcellent advice Dr Sara Saba kindly helped by commenting upon an earlierversion of the manuscript

REFERENCES

Arnheim R (1954) Art and Visual Perception A Psychology of the Creative Eye Regents of theUniversity of California California USA

Burr D (2000) Are lsquospeed linesrsquo used in human visual motion Curr Biol 10 R440ndashR443

Graphic invariants in visual art 227

Cutting J E (2002) Representing motion in a static image constraints and parallels in art scienceand culture Perception 31 1165ndash1193

Gombrich E H (1972) The Story of Art Phaidon Press Limited London UKGombrich E H (1977) Art and Illusion Phaidon Press Limited London UKKitaoka A and Ashida H (2003) Phenomenal characteristics of the peripheral drift illusion Vision

15 261ndash262Leviant I (1996) Does lsquobrain-powerrsquo make Enigma spin Proc Royal Soc London Ser B 263

997ndash1001MacKay D M (1957) Moving visual images produced by regular stationary patterns Nature 180

849ndash850Pinna B and Brelstaff G J (2000) A new visual illusion of relative motion Vision Research 40

2091ndash2096Ramachandran V S (1988) Perceiving shape from shading Sci Amer 259 58ndash65