Perception amp Psychophysics2002 64 (7) 1039-1054

A basic problem in object perception is segmenting reti-nal arrays into regions that are likely to have arisen fromcoherent objectsmdashin other words the formation of per-ceptual units Perceptual units exist at many levels how-ever The objects and surfaces we see are not unstructuredwholes they themselves have further part structure Whenwe look at a chair for example we see not only a coherentobject but also a spatial arrangement of clearly defined partsa back a seat and four legs Perceptual units thus exist atthe level of whole objects at the level of parts and possi-bly at the level of smaller parts nested hierarchically withinlarger ones (Marr amp Nishihara 1978 Palmer 1977)

In principle although any physical subset of an objectmay be considered to be its part only some of theseldquopartsrdquo are perceptually natural Parts like objects (Spelke1994) must be cohesive connected units1 The bottominch of a chairrsquos leg along with the top half of its back hardlyconstitutes a natural part Connectedness by itself is notsufficient however For instance the upper half of a leg alongwith a small adjoining portion of the seat is a connectedpiece But it seems rather contrived to consider it a part of

the chair What stimulus features then serve to charac-terize perceptually natural parts

Hoffman and Richards (1984) noted that whenever twoindependent parts connect or interpenetrate to form acomplete object (as occurs with manufactured objectsFigure 1A) or when a part grows out of a body (as occurswith biological objects Figure 1B see Leyton 1992) theboundaries between these parts typically lie in negativeminima of curvature2 Intuitively these are points of a high(locally maximal) magnitude of curvature that lie in con-cave regions of the shape Hoffman and Richards thus for-mulated the minima rule Human vision segments shapesby using negative minima of curvature as boundaries be-tween parts

A number of experimental studies have demonstratedthe perceptual reality of part-based representations (Bie-derman 1987 Biederman amp Cooper 1991 Driver amp Baylis1995) and in particular of the minima rule Indeed re-searchers have used the minima rule to explain a variety ofvisual phenomena including the perception of shape sim-ilarity (Attneave 1971 Hoffman 1983) short-term mem-ory for shapes (Braunstein Hoffman amp Saidpour 1989)the perception of symmetry and repetition (Baylis amp Dri-ver 1994 1995 Driver amp Baylis 1995 1996) the assign-ment of figure and ground (Hoffman amp Singh 1997) theperception of transparency (Singh amp Hoffman 1998) andvisual search (Hulleman te Winkel amp Boselie 2000Wolfe amp Bennett 1997)

In this paper we will address the question of whether pars-ing at negative minima of curvature occurs preattentivelymdashor at least rapidly and early in visual processing Tradi-tionally the processing of certain visual features has been

1039 Copyright 2002 Psychonomic Society Inc

YX is supported by a McDonnell-Pew Investigator Initiated Grantand MS by NSF BCS-0216944 For many useful discussions we thankBart Anderson Roland Fleming Don Hoffman and Mary C Potter Wealso thank Bart Anderson for his kind support at MIT Correspondenceconcerning this article may be addressed either to Y Xu Vision Sci-ences Laboratory Psychology Department Harvard University Cam-bridge MA 02138 (e-mail yaodawjhharvard edu) or to M SinghDepartment of Psychology Rutgers University New Brunswick Cam-pus 152 Frelinghuysen Road Piscataway NJ 08854-8020 (e-mail man-ishruccsrutgersedu)

Early computation of part structureEvidence from visual search

YAODA XUHarvard University Cambridge Massachusetts

and

MANISH SINGHRutgers University New Brunswick New Jersey

The visual system represents object shapes in terms of intermediate-level parts The minima ruleproposes that the visual system uses negative minima of curvature to define boundaries between partsWe used visual search to test whether part structures consistent with the minima rule are computedpreattentivelymdashor at least rapidly and early in visual processing The results of Experiments 1 and 2showed that whereas the search for a nonndashminima-segmented shape is fast and efficient among minima-segmented shapes the reverse search is slow and inefficient This asymmetry is expected if parsing atnegative minima occurs obligatorily The results of Experiments 3 and 4 showed that although bothminima- and nonndashminima-segmented shapes pop out among unsegmented shapes the search for minima-segmented shapes is significantly slower Together these results demonstrate that the visual systemsegments shapes into parts using negative minima of curvature and that it does so rapidly in early stagesof visual processing

1040 XU AND SINGH

considered to be completely free of attentional de-mandsmdashhence preattentive (Neisser 1967)mdashand asym-metry in visual search tasks has been taken to be an im-portant sign of such processing (Treisman amp Gormican1988 Treisman amp Souther 1985 Wolfe 1994) In partic-ular if visual search for a target with Feature X is fast andefficient among distractors that lack Feature X but the re-verse search is slow and inefficient Feature X is consid-ered to be computed preattentively3 Some recent work hasdisputed whether any visual task can really be consideredto be free from attentional demands (see eg JosephChun amp Nakayama 1997) On the other hand Wolfersquos(1994) guided search model suggests that there are a lim-ited number of preattentive features that can guide atten-tion toward likely targets Flat slopes (and pop-out) occurwhen the preattentive features can guide attention to thetarget on the first deployment of attention If a single fea-

ture defines the target that feature is a good candidate fora preattentive feature Despite these differing views on preat-tentive processing there is nevertheless a consensus thatpop-out and search asymmetry are indicative of featuresthat are computed rapidly and early in visual processing

Some evidence for the early computation of negativeminima has come from such visual search studies Wolfeand Bennett (1997) for example found that a target witha sharp negative minimum of curvature (Figure 2A) popsout among a set of distractors with no such negative min-imum (Figure 2B) but not vice versamdashhence suggestingthat negative minima are computed early and in parallelacross the visual field Using stimuli like those in Fig-ure 3 however Elder and Zucker (1993) found that thesearch for their target shape with a negative minimum(Figure 3A) did not quite reach the criterion for parallelsearch There are two possible interpretations of this ap-parent inconsistency (Hulleman et al 2000) First it maybe that negative minima have no special status in visualsearch and that the results of Wolfe and Bennett (1997)simply reflected the fact that the shape in Figure 2A has apoint of high curvature whereas the shape in Figure 2Bdoes not (Curvature has indeed been shown previously tobe a basic feature see Wolfe Yee amp Friedman-Hill 1992)Second it may be that negative minima do have a specialstatus but that the results of Elder and Zucker did not revealthis because their curvature extrema had a low turningangle and hence low visual salience4 (see eg Hoffmanamp Singh 1997)

To distinguish between these two possibilities Hulle-man et al (2000) conducted visual search experimentsusing shapes such as those shown in Figure 4 The shapein Figure 4B has a sharp negative minimum of curvature

Figure 1 Demonstration of the motivation behind the minimarule Whenever two independent parts connect or interpenetrategenerically (A) or when a part grows out of a body (B) the bound-aries between parts lie in negative minima of curvature Intu-itively these are points of locally highest magnitude of curvaturethat lie in concave regions of the shape

Figure 2 Stimuli adapted from the study by Wolfe and Bennett(1997) Their experiment showed that whereas the shape with thesharp negative minimum (A) pops out among distractors thatlack a negative minimum (B) the reverse search is slow and inef-ficient

EARLY COMPUTATION OF PART STRUCTURE 1041

whereas the one in Figure 4A does not However theshape in Figure 4A does have an equally sharp point thatlies in a convex region of the shape (ie a positive maxi-mum of curvature) In a series of experiments Hullemanet al found that a shape with a negative minimum (suchas Figure 4B) pops out among distractors each with a pos-itive maximum (such as Figure 4A) but not vice versamdasheven though the magnitude of curvature is the same inboth extrema They thus argued that negative minima(and more generally salient concavities) are computedearly and in parallel across the visual field More evidencein support of this interpretation has come from experi-ments by Humphreys and Muumlller (2000) They not onlyfound a search asymmetry in favor of concave targets overconvex targets but also showed that this asymmetry canbe reversed by switching the assignment of figure andground

Granting that negative minima are computed early invisual processing does not in itself imply however thatpart structures themselves are computed early On a two-dimensional shape negative minima are simply pointsthat lie on the contour of the shape whereas the computa-tion of part structure requires computing part cuts thatsegment the shape into parts In this paper we will studythe simple case of two-part shapes that can be segmentedby joining two negative minima of curvature on the con-tour of the shape In addition to negative minima recentwork has also pointed to the role of more global region-based geometric factors in determining perceived shapein general (Burbeck amp Pizer 1995 Kimia Tannenbaumamp Zucker 1995) and part structure in particular (Siddiqiamp Kimia 1995 Siddiqi Tresness amp Kimia 1996 Singhamp Hoffman 2001 Singh Seyranian amp Hoffman 1999)The method developed in this paper will allow us to studymore complex cases as well We will return to this issue inthe General Discussion section

Some evidence for the early computation of parts comesfrom judgments of symmetry and repetition It has oftenbeen observed (at least as far back as Mach see Baylis ampDriver 1994 1995) that humans are more sensitive tosymmetry within a pattern than to repetition This obser-vation has been confirmed in many experiments (egBertamini Friedenberg amp Kubovy 1997 Bruce amp Mor-gan 1975 Corballis amp Roldan 1974 Friedenberg amp Ber-tamini 2000) More recently Baylis and Driver (1994)have argued that whereas symmetry within a shape can bedetected in parallel repetition seems to involve a serialprocess They had participants judge whether or not agiven shape was perfectly symmetric (see Figure 5A) orwhether or not it was perfectly repeated (see Figure 5B)They found that for symmetry judgments response times(RTs) were hardly affected by the number of steps addedto the sides of the shapes (RT slopes 6 msecstep) How-Figure 3 Stimuli adapted from the study by Elder and Zucker

(1993) In their study the search for the shape with the negativeminimum (A) did not quite reach the criterion for pop-out Thisindicates either that negative minima have no privileged status ofvisual search or that the curvature extrema on the shapes used inthis study were perceptually too weak

Figure 4 Stimuli adapted from the study by Hulleman teWinkel and Boselie (2000) Although each of the two shapes con-tains a sharp corner with the same turning angle the shape withthe negative minimum (B) popped out among distractors with thepositive maximum (A) but not vice versa This suggests that neg-ative minimamdashand salient concavities more generallymdashdo havea privileged status in visual search

1042 XU AND SINGH

ever for repetition judgments response times increasedsteadily with the number of steps (RT slopes 26 msecstep) Baylis and Driver (1994) argued that this occurs be-cause a symmetric shape has matching negative minimaof curvature on the two sidesmdashand hence matchingpartsmdashwhereas a repeated shape has mismatching parts(because concavities on one side correspond to convexi-ties on the other) If the visual system represents shapes interms of parts and compares them at the level of parts(rather than point by point) it would indeed make sensefor symmetry to be an easier judgment than repetitionMoreover if parts mediate the parallel detection of sym-metry they must themselves be computed in parallel

As further evidence for their claim Baylis and Driver(1995) demonstrated that the advantage for symmetry canbe reversed by reversing the figure and ground relation-ships on one of the two curves (see Figures 5C and 5D)For these modified stimuli they found that repetition be-came an easier judgment than symmetry consistent withthe fact that the repeated pattern (Figure 5D) now hasmatching parts whereas the symmetric pattern (Fig-ure 5C) has mismatching parts

The results of Baylis and Driver (1994 1995) thus pro-vide some evidence for the early computation of partsThese results do not demonstrate however that perceivedparts are necessarily delineated at negative minima of cur-vature The symmetric shape in Figure 5A for examplealso has matching positive maxima of curvature (pointsof locally highest magnitude of curvature that lie in con-vex regions) and matching inflection points (points of

transition from convex to concave and vice versa) and inprinciple these could also have been used to make thesymmetry judgments Similarly the repeated shape in Fig-ure 5D has matching negative minima as well as match-ing positive maxima Thus this methodology does not sin-gle out negative minima as the critical determiners ofperceived parts In addition the results were obtained inthe context of judgments of symmetry and repetition sothe experimental method does not allow one to test shapesthat are not near-symmetric or near-repeated It thereforeremains unclear to what extent these results generalize toarbitrary shapes Finally this experimental method doesnot allow one to compare the perceptual naturalness oftwo different ways of segmenting a shape (eg by com-paring part structures that are consistent with the minimarule with those that are not)

In the present study our goal was to test directly whetherpart structures consistent with the minima rule are com-puted preattentivelymdashor at least rapidly and early in visualprocessing In Experiments 1 and 2 we used visual searchasymmetry resulting from different parsings to assess theearly computation of part structure (Treisman amp Souther1985) In Experiments 3 and 4 we compared visual searchRTs for differently segmented shapes among unseg-mented shapes and obtained further evidence for the earlycomputation of perceived part structures All the experi-ments used the standard visual search paradigm howeverunlike previous visual search studies we used the sameshape for targets and distractors but segmented in two dif-ferent ways

Figure 5 Stimuli adapted from the study by Baylis and Driver (1994 1995) For thestimuli in the top row judgments of symmetry (A) were faster and more accurate thanjudgments of repetition (B) Baylis and Driver argued that this is because the shapein A has matching parts whereas the one in B has mismatching parts on the two sidesConsistent with this account they found that the advantage for symmetry could be re-versed if the symmetric contours resulted in mismatching parts (C) and the repeatedcontours resulted in matching parts (D)

EARLY COMPUTATION OF PART STRUCTURE 1043

EXPERIMENT 1

In Experiment 1 participants searched for either a shapesegmented at negative minima of curvature (Figure 6A)among distractor shapes parsed elsewhere (Figure 6C) orthe reverse Our logic was as follows If the visual systemsegments shapes at negative minima of curvature then thebottom ldquopartrdquo of the shape in Figure 6C would be seg-mented further into two parts yielding the effective pars-ing shown in Figure 6D As a result the shape in Fig-ure 6C would end up having an extra ldquofeaturerdquo that theshape in Figure 6A does not havemdashnamely the cut in therectangular part of the shape (or equivalently an addi-tional partmdashthree rather than two) Previous visual searchstudies have shown that when a target is defined by thepresence of a unique feature search is usually fast and ef-ficient whereas when the target is distinguished by the ab-sence of a feature search becomes slow and self-terminating(eg Treisman amp Gormican 1988 Treisman amp Souther1985) If the visual system in fact segments shapes at neg-ative minima we should expect the search for a nonndashminima-segmented shape among minima-segmentedshapes to be fast and efficient and the search for a minima-segmented shape among nonndashminima-segmented shapesto be slow and inefficient

In designing the stimuli we minimized differences alongother dimensions that might distinguish between the nat-ural and the unnatural parsings For example the lengths ofthe part cuts in the two parsings were equated because cutlength has previously been shown to be an important fac-tor in parsing shapes (Singh et al 1999) Moreover in thecontext of visual search the difference in the lengths ofthese line segments might itself provide a distinguishing

feature quite independently of the fact that these line seg-ments are part cuts Similarly the relative areas of the twoparts created by these cuts were also equated The area ofthe bottom part in Figure 6A is equal to the area of the toppart in Figure 6C Finally the part cuts in both parsingshad the same orientation (ie horizontal) so that any ob-served search asymmetry could not be attributed to a dif-ference in orientation

MethodParticipants Twelve participants 7 males and 5 females from

the Massachusetts Institute of Technology were recruited Theywere between 17 and 40 years of age all had normal or corrected-to-normal vision and they were paid for their participation

Materials and Design The shapes used in Experiment 1 are shownin Figures 6A and 6C They are naturally seen as a bar attached toan oval with either a cut in the middle of the bar (non-minima pars-ing) or a cut at the junction of the bar and the oval (minima parsing)The size of the (uncut) bar was 057ordm 3 183ordm and that of the ovalwas 057ordm 3 115ordm The thickness of the cut was 011ordm The area ofthe oval in the minima-parsed shape was equal to the area of the de-tached bar piece in the nonndashminima-parsed shape Hence the twoldquopartsrdquo in both the minima-parsed and the nonndashminima-parsedshapes had equal relative areas

Each display consisted of either 6 or 12 shapes distributed in a 5 33 grid (938ordm 3 972ordm) Each position was offset slightly from thegrid so that the shapes were not perfectly aligned with each otherThe experiment was run in two sessions In one session the partici-pants searched for a nonndashminima-parsed shape among minima-parsed shapes (Figure 7A) and in the other session they searchedfor a minima-parsed shape among nonndashminima-parsed shapes (Fig-ure 7B) The order of the two sessions was counterbalanced acrossparticipants Within each session displays with set size 6 and setsize 12 were intermixed randomly These resulted in a total of 96 tri-als for each set size 48 target-present trials and 48 target-absent tri-als Trials from different conditions were divided evenly into three64-trial blocks Thirty-two practice trials preceded the experimentaltrials in each session

Apparatus The displays were presented on the 15-in monitor ofa 350-MHz G3 iMac using the MacProbe experimental softwareThe participants were seated 50 cm away from the monitor

Procedure Each trial began with the presentation of a fixationdot for 500 msec which was then followed by the search displayThe search display remained on the screen until the participants hadpressed one of the two prespecified keys to indicate the presence orabsence of the target The participants were instructed to use eithertheir thumbs or their index fingers to press the response keys Theresponse keys were the Control key on the extreme left of the key-board and the Enter key on the extreme right of the keyboard Keyassignments were counterbalanced across participants and the as-signment was indicated by appropriately labeled stickers on thekeys Within a block the next trial began automatically 500 msecafter the participant had responded to the previous trial An incorrectresponse was indicated by a single short beep The participants wereallowed to take a break for as long as they wished between blocks

ResultsReaction time for correct trials Of the total data col-

lected 746 were removed owing to response errors Twofurther data points were removed because the RTs weregreater than 3000 msec The remaining data were ana-lyzed with a within-subjects analysis of variance (ANOVA)The mean RTs averaged across participants are plotted inFigure 8

Figure 6 Stimuli used in Experiment 1 (A) minima-parsedshape (B) no further parsing occurs for Shape A (C) nonndashminima-parsed shape and (D) the resulting shape if parsing atnegative minima occurs automatically for the shape presented inpanel C

1040 XU AND SINGH

considered to be completely free of attentional de-mandsmdashhence preattentive (Neisser 1967)mdashand asym-metry in visual search tasks has been taken to be an im-portant sign of such processing (Treisman amp Gormican1988 Treisman amp Souther 1985 Wolfe 1994) In partic-ular if visual search for a target with Feature X is fast andefficient among distractors that lack Feature X but the re-verse search is slow and inefficient Feature X is consid-ered to be computed preattentively3 Some recent work hasdisputed whether any visual task can really be consideredto be free from attentional demands (see eg JosephChun amp Nakayama 1997) On the other hand Wolfersquos(1994) guided search model suggests that there are a lim-ited number of preattentive features that can guide atten-tion toward likely targets Flat slopes (and pop-out) occurwhen the preattentive features can guide attention to thetarget on the first deployment of attention If a single fea-

ture defines the target that feature is a good candidate fora preattentive feature Despite these differing views on preat-tentive processing there is nevertheless a consensus thatpop-out and search asymmetry are indicative of featuresthat are computed rapidly and early in visual processing

Some evidence for the early computation of negativeminima has come from such visual search studies Wolfeand Bennett (1997) for example found that a target witha sharp negative minimum of curvature (Figure 2A) popsout among a set of distractors with no such negative min-imum (Figure 2B) but not vice versamdashhence suggestingthat negative minima are computed early and in parallelacross the visual field Using stimuli like those in Fig-ure 3 however Elder and Zucker (1993) found that thesearch for their target shape with a negative minimum(Figure 3A) did not quite reach the criterion for parallelsearch There are two possible interpretations of this ap-parent inconsistency (Hulleman et al 2000) First it maybe that negative minima have no special status in visualsearch and that the results of Wolfe and Bennett (1997)simply reflected the fact that the shape in Figure 2A has apoint of high curvature whereas the shape in Figure 2Bdoes not (Curvature has indeed been shown previously tobe a basic feature see Wolfe Yee amp Friedman-Hill 1992)Second it may be that negative minima do have a specialstatus but that the results of Elder and Zucker did not revealthis because their curvature extrema had a low turningangle and hence low visual salience4 (see eg Hoffmanamp Singh 1997)

To distinguish between these two possibilities Hulle-man et al (2000) conducted visual search experimentsusing shapes such as those shown in Figure 4 The shapein Figure 4B has a sharp negative minimum of curvature

Figure 1 Demonstration of the motivation behind the minimarule Whenever two independent parts connect or interpenetrategenerically (A) or when a part grows out of a body (B) the bound-aries between parts lie in negative minima of curvature Intu-itively these are points of locally highest magnitude of curvaturethat lie in concave regions of the shape

Figure 2 Stimuli adapted from the study by Wolfe and Bennett(1997) Their experiment showed that whereas the shape with thesharp negative minimum (A) pops out among distractors thatlack a negative minimum (B) the reverse search is slow and inef-ficient

EARLY COMPUTATION OF PART STRUCTURE 1041

whereas the one in Figure 4A does not However theshape in Figure 4A does have an equally sharp point thatlies in a convex region of the shape (ie a positive maxi-mum of curvature) In a series of experiments Hullemanet al found that a shape with a negative minimum (suchas Figure 4B) pops out among distractors each with a pos-itive maximum (such as Figure 4A) but not vice versamdasheven though the magnitude of curvature is the same inboth extrema They thus argued that negative minima(and more generally salient concavities) are computedearly and in parallel across the visual field More evidencein support of this interpretation has come from experi-ments by Humphreys and Muumlller (2000) They not onlyfound a search asymmetry in favor of concave targets overconvex targets but also showed that this asymmetry canbe reversed by switching the assignment of figure andground

Granting that negative minima are computed early invisual processing does not in itself imply however thatpart structures themselves are computed early On a two-dimensional shape negative minima are simply pointsthat lie on the contour of the shape whereas the computa-tion of part structure requires computing part cuts thatsegment the shape into parts In this paper we will studythe simple case of two-part shapes that can be segmentedby joining two negative minima of curvature on the con-tour of the shape In addition to negative minima recentwork has also pointed to the role of more global region-based geometric factors in determining perceived shapein general (Burbeck amp Pizer 1995 Kimia Tannenbaumamp Zucker 1995) and part structure in particular (Siddiqiamp Kimia 1995 Siddiqi Tresness amp Kimia 1996 Singhamp Hoffman 2001 Singh Seyranian amp Hoffman 1999)The method developed in this paper will allow us to studymore complex cases as well We will return to this issue inthe General Discussion section

Some evidence for the early computation of parts comesfrom judgments of symmetry and repetition It has oftenbeen observed (at least as far back as Mach see Baylis ampDriver 1994 1995) that humans are more sensitive tosymmetry within a pattern than to repetition This obser-vation has been confirmed in many experiments (egBertamini Friedenberg amp Kubovy 1997 Bruce amp Mor-gan 1975 Corballis amp Roldan 1974 Friedenberg amp Ber-tamini 2000) More recently Baylis and Driver (1994)have argued that whereas symmetry within a shape can bedetected in parallel repetition seems to involve a serialprocess They had participants judge whether or not agiven shape was perfectly symmetric (see Figure 5A) orwhether or not it was perfectly repeated (see Figure 5B)They found that for symmetry judgments response times(RTs) were hardly affected by the number of steps addedto the sides of the shapes (RT slopes 6 msecstep) How-Figure 3 Stimuli adapted from the study by Elder and Zucker

(1993) In their study the search for the shape with the negativeminimum (A) did not quite reach the criterion for pop-out Thisindicates either that negative minima have no privileged status ofvisual search or that the curvature extrema on the shapes used inthis study were perceptually too weak

Figure 4 Stimuli adapted from the study by Hulleman teWinkel and Boselie (2000) Although each of the two shapes con-tains a sharp corner with the same turning angle the shape withthe negative minimum (B) popped out among distractors with thepositive maximum (A) but not vice versa This suggests that neg-ative minimamdashand salient concavities more generallymdashdo havea privileged status in visual search

1042 XU AND SINGH

ever for repetition judgments response times increasedsteadily with the number of steps (RT slopes 26 msecstep) Baylis and Driver (1994) argued that this occurs be-cause a symmetric shape has matching negative minimaof curvature on the two sidesmdashand hence matchingpartsmdashwhereas a repeated shape has mismatching parts(because concavities on one side correspond to convexi-ties on the other) If the visual system represents shapes interms of parts and compares them at the level of parts(rather than point by point) it would indeed make sensefor symmetry to be an easier judgment than repetitionMoreover if parts mediate the parallel detection of sym-metry they must themselves be computed in parallel

As further evidence for their claim Baylis and Driver(1995) demonstrated that the advantage for symmetry canbe reversed by reversing the figure and ground relation-ships on one of the two curves (see Figures 5C and 5D)For these modified stimuli they found that repetition be-came an easier judgment than symmetry consistent withthe fact that the repeated pattern (Figure 5D) now hasmatching parts whereas the symmetric pattern (Fig-ure 5C) has mismatching parts

The results of Baylis and Driver (1994 1995) thus pro-vide some evidence for the early computation of partsThese results do not demonstrate however that perceivedparts are necessarily delineated at negative minima of cur-vature The symmetric shape in Figure 5A for examplealso has matching positive maxima of curvature (pointsof locally highest magnitude of curvature that lie in con-vex regions) and matching inflection points (points of

transition from convex to concave and vice versa) and inprinciple these could also have been used to make thesymmetry judgments Similarly the repeated shape in Fig-ure 5D has matching negative minima as well as match-ing positive maxima Thus this methodology does not sin-gle out negative minima as the critical determiners ofperceived parts In addition the results were obtained inthe context of judgments of symmetry and repetition sothe experimental method does not allow one to test shapesthat are not near-symmetric or near-repeated It thereforeremains unclear to what extent these results generalize toarbitrary shapes Finally this experimental method doesnot allow one to compare the perceptual naturalness oftwo different ways of segmenting a shape (eg by com-paring part structures that are consistent with the minimarule with those that are not)

In the present study our goal was to test directly whetherpart structures consistent with the minima rule are com-puted preattentivelymdashor at least rapidly and early in visualprocessing In Experiments 1 and 2 we used visual searchasymmetry resulting from different parsings to assess theearly computation of part structure (Treisman amp Souther1985) In Experiments 3 and 4 we compared visual searchRTs for differently segmented shapes among unseg-mented shapes and obtained further evidence for the earlycomputation of perceived part structures All the experi-ments used the standard visual search paradigm howeverunlike previous visual search studies we used the sameshape for targets and distractors but segmented in two dif-ferent ways

Figure 5 Stimuli adapted from the study by Baylis and Driver (1994 1995) For thestimuli in the top row judgments of symmetry (A) were faster and more accurate thanjudgments of repetition (B) Baylis and Driver argued that this is because the shapein A has matching parts whereas the one in B has mismatching parts on the two sidesConsistent with this account they found that the advantage for symmetry could be re-versed if the symmetric contours resulted in mismatching parts (C) and the repeatedcontours resulted in matching parts (D)

EARLY COMPUTATION OF PART STRUCTURE 1043

EXPERIMENT 1

In Experiment 1 participants searched for either a shapesegmented at negative minima of curvature (Figure 6A)among distractor shapes parsed elsewhere (Figure 6C) orthe reverse Our logic was as follows If the visual systemsegments shapes at negative minima of curvature then thebottom ldquopartrdquo of the shape in Figure 6C would be seg-mented further into two parts yielding the effective pars-ing shown in Figure 6D As a result the shape in Fig-ure 6C would end up having an extra ldquofeaturerdquo that theshape in Figure 6A does not havemdashnamely the cut in therectangular part of the shape (or equivalently an addi-tional partmdashthree rather than two) Previous visual searchstudies have shown that when a target is defined by thepresence of a unique feature search is usually fast and ef-ficient whereas when the target is distinguished by the ab-sence of a feature search becomes slow and self-terminating(eg Treisman amp Gormican 1988 Treisman amp Souther1985) If the visual system in fact segments shapes at neg-ative minima we should expect the search for a nonndashminima-segmented shape among minima-segmentedshapes to be fast and efficient and the search for a minima-segmented shape among nonndashminima-segmented shapesto be slow and inefficient

In designing the stimuli we minimized differences alongother dimensions that might distinguish between the nat-ural and the unnatural parsings For example the lengths ofthe part cuts in the two parsings were equated because cutlength has previously been shown to be an important fac-tor in parsing shapes (Singh et al 1999) Moreover in thecontext of visual search the difference in the lengths ofthese line segments might itself provide a distinguishing

feature quite independently of the fact that these line seg-ments are part cuts Similarly the relative areas of the twoparts created by these cuts were also equated The area ofthe bottom part in Figure 6A is equal to the area of the toppart in Figure 6C Finally the part cuts in both parsingshad the same orientation (ie horizontal) so that any ob-served search asymmetry could not be attributed to a dif-ference in orientation

MethodParticipants Twelve participants 7 males and 5 females from

the Massachusetts Institute of Technology were recruited Theywere between 17 and 40 years of age all had normal or corrected-to-normal vision and they were paid for their participation

Materials and Design The shapes used in Experiment 1 are shownin Figures 6A and 6C They are naturally seen as a bar attached toan oval with either a cut in the middle of the bar (non-minima pars-ing) or a cut at the junction of the bar and the oval (minima parsing)The size of the (uncut) bar was 057ordm 3 183ordm and that of the ovalwas 057ordm 3 115ordm The thickness of the cut was 011ordm The area ofthe oval in the minima-parsed shape was equal to the area of the de-tached bar piece in the nonndashminima-parsed shape Hence the twoldquopartsrdquo in both the minima-parsed and the nonndashminima-parsedshapes had equal relative areas

Each display consisted of either 6 or 12 shapes distributed in a 5 33 grid (938ordm 3 972ordm) Each position was offset slightly from thegrid so that the shapes were not perfectly aligned with each otherThe experiment was run in two sessions In one session the partici-pants searched for a nonndashminima-parsed shape among minima-parsed shapes (Figure 7A) and in the other session they searchedfor a minima-parsed shape among nonndashminima-parsed shapes (Fig-ure 7B) The order of the two sessions was counterbalanced acrossparticipants Within each session displays with set size 6 and setsize 12 were intermixed randomly These resulted in a total of 96 tri-als for each set size 48 target-present trials and 48 target-absent tri-als Trials from different conditions were divided evenly into three64-trial blocks Thirty-two practice trials preceded the experimentaltrials in each session

Apparatus The displays were presented on the 15-in monitor ofa 350-MHz G3 iMac using the MacProbe experimental softwareThe participants were seated 50 cm away from the monitor

Procedure Each trial began with the presentation of a fixationdot for 500 msec which was then followed by the search displayThe search display remained on the screen until the participants hadpressed one of the two prespecified keys to indicate the presence orabsence of the target The participants were instructed to use eithertheir thumbs or their index fingers to press the response keys Theresponse keys were the Control key on the extreme left of the key-board and the Enter key on the extreme right of the keyboard Keyassignments were counterbalanced across participants and the as-signment was indicated by appropriately labeled stickers on thekeys Within a block the next trial began automatically 500 msecafter the participant had responded to the previous trial An incorrectresponse was indicated by a single short beep The participants wereallowed to take a break for as long as they wished between blocks

ResultsReaction time for correct trials Of the total data col-

lected 746 were removed owing to response errors Twofurther data points were removed because the RTs weregreater than 3000 msec The remaining data were ana-lyzed with a within-subjects analysis of variance (ANOVA)The mean RTs averaged across participants are plotted inFigure 8

Figure 6 Stimuli used in Experiment 1 (A) minima-parsedshape (B) no further parsing occurs for Shape A (C) nonndashminima-parsed shape and (D) the resulting shape if parsing atnegative minima occurs automatically for the shape presented inpanel C

EARLY COMPUTATION OF PART STRUCTURE 1041

whereas the one in Figure 4A does not However theshape in Figure 4A does have an equally sharp point thatlies in a convex region of the shape (ie a positive maxi-mum of curvature) In a series of experiments Hullemanet al found that a shape with a negative minimum (suchas Figure 4B) pops out among distractors each with a pos-itive maximum (such as Figure 4A) but not vice versamdasheven though the magnitude of curvature is the same inboth extrema They thus argued that negative minima(and more generally salient concavities) are computedearly and in parallel across the visual field More evidencein support of this interpretation has come from experi-ments by Humphreys and Muumlller (2000) They not onlyfound a search asymmetry in favor of concave targets overconvex targets but also showed that this asymmetry canbe reversed by switching the assignment of figure andground

Granting that negative minima are computed early invisual processing does not in itself imply however thatpart structures themselves are computed early On a two-dimensional shape negative minima are simply pointsthat lie on the contour of the shape whereas the computa-tion of part structure requires computing part cuts thatsegment the shape into parts In this paper we will studythe simple case of two-part shapes that can be segmentedby joining two negative minima of curvature on the con-tour of the shape In addition to negative minima recentwork has also pointed to the role of more global region-based geometric factors in determining perceived shapein general (Burbeck amp Pizer 1995 Kimia Tannenbaumamp Zucker 1995) and part structure in particular (Siddiqiamp Kimia 1995 Siddiqi Tresness amp Kimia 1996 Singhamp Hoffman 2001 Singh Seyranian amp Hoffman 1999)The method developed in this paper will allow us to studymore complex cases as well We will return to this issue inthe General Discussion section

Some evidence for the early computation of parts comesfrom judgments of symmetry and repetition It has oftenbeen observed (at least as far back as Mach see Baylis ampDriver 1994 1995) that humans are more sensitive tosymmetry within a pattern than to repetition This obser-vation has been confirmed in many experiments (egBertamini Friedenberg amp Kubovy 1997 Bruce amp Mor-gan 1975 Corballis amp Roldan 1974 Friedenberg amp Ber-tamini 2000) More recently Baylis and Driver (1994)have argued that whereas symmetry within a shape can bedetected in parallel repetition seems to involve a serialprocess They had participants judge whether or not agiven shape was perfectly symmetric (see Figure 5A) orwhether or not it was perfectly repeated (see Figure 5B)They found that for symmetry judgments response times(RTs) were hardly affected by the number of steps addedto the sides of the shapes (RT slopes 6 msecstep) How-Figure 3 Stimuli adapted from the study by Elder and Zucker

(1993) In their study the search for the shape with the negativeminimum (A) did not quite reach the criterion for pop-out Thisindicates either that negative minima have no privileged status ofvisual search or that the curvature extrema on the shapes used inthis study were perceptually too weak

Figure 4 Stimuli adapted from the study by Hulleman teWinkel and Boselie (2000) Although each of the two shapes con-tains a sharp corner with the same turning angle the shape withthe negative minimum (B) popped out among distractors with thepositive maximum (A) but not vice versa This suggests that neg-ative minimamdashand salient concavities more generallymdashdo havea privileged status in visual search

1042 XU AND SINGH

ever for repetition judgments response times increasedsteadily with the number of steps (RT slopes 26 msecstep) Baylis and Driver (1994) argued that this occurs be-cause a symmetric shape has matching negative minimaof curvature on the two sidesmdashand hence matchingpartsmdashwhereas a repeated shape has mismatching parts(because concavities on one side correspond to convexi-ties on the other) If the visual system represents shapes interms of parts and compares them at the level of parts(rather than point by point) it would indeed make sensefor symmetry to be an easier judgment than repetitionMoreover if parts mediate the parallel detection of sym-metry they must themselves be computed in parallel

As further evidence for their claim Baylis and Driver(1995) demonstrated that the advantage for symmetry canbe reversed by reversing the figure and ground relation-ships on one of the two curves (see Figures 5C and 5D)For these modified stimuli they found that repetition be-came an easier judgment than symmetry consistent withthe fact that the repeated pattern (Figure 5D) now hasmatching parts whereas the symmetric pattern (Fig-ure 5C) has mismatching parts

The results of Baylis and Driver (1994 1995) thus pro-vide some evidence for the early computation of partsThese results do not demonstrate however that perceivedparts are necessarily delineated at negative minima of cur-vature The symmetric shape in Figure 5A for examplealso has matching positive maxima of curvature (pointsof locally highest magnitude of curvature that lie in con-vex regions) and matching inflection points (points of

transition from convex to concave and vice versa) and inprinciple these could also have been used to make thesymmetry judgments Similarly the repeated shape in Fig-ure 5D has matching negative minima as well as match-ing positive maxima Thus this methodology does not sin-gle out negative minima as the critical determiners ofperceived parts In addition the results were obtained inthe context of judgments of symmetry and repetition sothe experimental method does not allow one to test shapesthat are not near-symmetric or near-repeated It thereforeremains unclear to what extent these results generalize toarbitrary shapes Finally this experimental method doesnot allow one to compare the perceptual naturalness oftwo different ways of segmenting a shape (eg by com-paring part structures that are consistent with the minimarule with those that are not)

In the present study our goal was to test directly whetherpart structures consistent with the minima rule are com-puted preattentivelymdashor at least rapidly and early in visualprocessing In Experiments 1 and 2 we used visual searchasymmetry resulting from different parsings to assess theearly computation of part structure (Treisman amp Souther1985) In Experiments 3 and 4 we compared visual searchRTs for differently segmented shapes among unseg-mented shapes and obtained further evidence for the earlycomputation of perceived part structures All the experi-ments used the standard visual search paradigm howeverunlike previous visual search studies we used the sameshape for targets and distractors but segmented in two dif-ferent ways

Figure 5 Stimuli adapted from the study by Baylis and Driver (1994 1995) For thestimuli in the top row judgments of symmetry (A) were faster and more accurate thanjudgments of repetition (B) Baylis and Driver argued that this is because the shapein A has matching parts whereas the one in B has mismatching parts on the two sidesConsistent with this account they found that the advantage for symmetry could be re-versed if the symmetric contours resulted in mismatching parts (C) and the repeatedcontours resulted in matching parts (D)

EARLY COMPUTATION OF PART STRUCTURE 1043

EXPERIMENT 1

In Experiment 1 participants searched for either a shapesegmented at negative minima of curvature (Figure 6A)among distractor shapes parsed elsewhere (Figure 6C) orthe reverse Our logic was as follows If the visual systemsegments shapes at negative minima of curvature then thebottom ldquopartrdquo of the shape in Figure 6C would be seg-mented further into two parts yielding the effective pars-ing shown in Figure 6D As a result the shape in Fig-ure 6C would end up having an extra ldquofeaturerdquo that theshape in Figure 6A does not havemdashnamely the cut in therectangular part of the shape (or equivalently an addi-tional partmdashthree rather than two) Previous visual searchstudies have shown that when a target is defined by thepresence of a unique feature search is usually fast and ef-ficient whereas when the target is distinguished by the ab-sence of a feature search becomes slow and self-terminating(eg Treisman amp Gormican 1988 Treisman amp Souther1985) If the visual system in fact segments shapes at neg-ative minima we should expect the search for a nonndashminima-segmented shape among minima-segmentedshapes to be fast and efficient and the search for a minima-segmented shape among nonndashminima-segmented shapesto be slow and inefficient

In designing the stimuli we minimized differences alongother dimensions that might distinguish between the nat-ural and the unnatural parsings For example the lengths ofthe part cuts in the two parsings were equated because cutlength has previously been shown to be an important fac-tor in parsing shapes (Singh et al 1999) Moreover in thecontext of visual search the difference in the lengths ofthese line segments might itself provide a distinguishing

feature quite independently of the fact that these line seg-ments are part cuts Similarly the relative areas of the twoparts created by these cuts were also equated The area ofthe bottom part in Figure 6A is equal to the area of the toppart in Figure 6C Finally the part cuts in both parsingshad the same orientation (ie horizontal) so that any ob-served search asymmetry could not be attributed to a dif-ference in orientation

MethodParticipants Twelve participants 7 males and 5 females from

the Massachusetts Institute of Technology were recruited Theywere between 17 and 40 years of age all had normal or corrected-to-normal vision and they were paid for their participation

Materials and Design The shapes used in Experiment 1 are shownin Figures 6A and 6C They are naturally seen as a bar attached toan oval with either a cut in the middle of the bar (non-minima pars-ing) or a cut at the junction of the bar and the oval (minima parsing)The size of the (uncut) bar was 057ordm 3 183ordm and that of the ovalwas 057ordm 3 115ordm The thickness of the cut was 011ordm The area ofthe oval in the minima-parsed shape was equal to the area of the de-tached bar piece in the nonndashminima-parsed shape Hence the twoldquopartsrdquo in both the minima-parsed and the nonndashminima-parsedshapes had equal relative areas

Each display consisted of either 6 or 12 shapes distributed in a 5 33 grid (938ordm 3 972ordm) Each position was offset slightly from thegrid so that the shapes were not perfectly aligned with each otherThe experiment was run in two sessions In one session the partici-pants searched for a nonndashminima-parsed shape among minima-parsed shapes (Figure 7A) and in the other session they searchedfor a minima-parsed shape among nonndashminima-parsed shapes (Fig-ure 7B) The order of the two sessions was counterbalanced acrossparticipants Within each session displays with set size 6 and setsize 12 were intermixed randomly These resulted in a total of 96 tri-als for each set size 48 target-present trials and 48 target-absent tri-als Trials from different conditions were divided evenly into three64-trial blocks Thirty-two practice trials preceded the experimentaltrials in each session

Apparatus The displays were presented on the 15-in monitor ofa 350-MHz G3 iMac using the MacProbe experimental softwareThe participants were seated 50 cm away from the monitor

Procedure Each trial began with the presentation of a fixationdot for 500 msec which was then followed by the search displayThe search display remained on the screen until the participants hadpressed one of the two prespecified keys to indicate the presence orabsence of the target The participants were instructed to use eithertheir thumbs or their index fingers to press the response keys Theresponse keys were the Control key on the extreme left of the key-board and the Enter key on the extreme right of the keyboard Keyassignments were counterbalanced across participants and the as-signment was indicated by appropriately labeled stickers on thekeys Within a block the next trial began automatically 500 msecafter the participant had responded to the previous trial An incorrectresponse was indicated by a single short beep The participants wereallowed to take a break for as long as they wished between blocks

ResultsReaction time for correct trials Of the total data col-

lected 746 were removed owing to response errors Twofurther data points were removed because the RTs weregreater than 3000 msec The remaining data were ana-lyzed with a within-subjects analysis of variance (ANOVA)The mean RTs averaged across participants are plotted inFigure 8

Figure 6 Stimuli used in Experiment 1 (A) minima-parsedshape (B) no further parsing occurs for Shape A (C) nonndashminima-parsed shape and (D) the resulting shape if parsing atnegative minima occurs automatically for the shape presented inpanel C

1042 XU AND SINGH

ever for repetition judgments response times increasedsteadily with the number of steps (RT slopes 26 msecstep) Baylis and Driver (1994) argued that this occurs be-cause a symmetric shape has matching negative minimaof curvature on the two sidesmdashand hence matchingpartsmdashwhereas a repeated shape has mismatching parts(because concavities on one side correspond to convexi-ties on the other) If the visual system represents shapes interms of parts and compares them at the level of parts(rather than point by point) it would indeed make sensefor symmetry to be an easier judgment than repetitionMoreover if parts mediate the parallel detection of sym-metry they must themselves be computed in parallel

As further evidence for their claim Baylis and Driver(1995) demonstrated that the advantage for symmetry canbe reversed by reversing the figure and ground relation-ships on one of the two curves (see Figures 5C and 5D)For these modified stimuli they found that repetition be-came an easier judgment than symmetry consistent withthe fact that the repeated pattern (Figure 5D) now hasmatching parts whereas the symmetric pattern (Fig-ure 5C) has mismatching parts

The results of Baylis and Driver (1994 1995) thus pro-vide some evidence for the early computation of partsThese results do not demonstrate however that perceivedparts are necessarily delineated at negative minima of cur-vature The symmetric shape in Figure 5A for examplealso has matching positive maxima of curvature (pointsof locally highest magnitude of curvature that lie in con-vex regions) and matching inflection points (points of

transition from convex to concave and vice versa) and inprinciple these could also have been used to make thesymmetry judgments Similarly the repeated shape in Fig-ure 5D has matching negative minima as well as match-ing positive maxima Thus this methodology does not sin-gle out negative minima as the critical determiners ofperceived parts In addition the results were obtained inthe context of judgments of symmetry and repetition sothe experimental method does not allow one to test shapesthat are not near-symmetric or near-repeated It thereforeremains unclear to what extent these results generalize toarbitrary shapes Finally this experimental method doesnot allow one to compare the perceptual naturalness oftwo different ways of segmenting a shape (eg by com-paring part structures that are consistent with the minimarule with those that are not)

In the present study our goal was to test directly whetherpart structures consistent with the minima rule are com-puted preattentivelymdashor at least rapidly and early in visualprocessing In Experiments 1 and 2 we used visual searchasymmetry resulting from different parsings to assess theearly computation of part structure (Treisman amp Souther1985) In Experiments 3 and 4 we compared visual searchRTs for differently segmented shapes among unseg-mented shapes and obtained further evidence for the earlycomputation of perceived part structures All the experi-ments used the standard visual search paradigm howeverunlike previous visual search studies we used the sameshape for targets and distractors but segmented in two dif-ferent ways

Figure 5 Stimuli adapted from the study by Baylis and Driver (1994 1995) For thestimuli in the top row judgments of symmetry (A) were faster and more accurate thanjudgments of repetition (B) Baylis and Driver argued that this is because the shapein A has matching parts whereas the one in B has mismatching parts on the two sidesConsistent with this account they found that the advantage for symmetry could be re-versed if the symmetric contours resulted in mismatching parts (C) and the repeatedcontours resulted in matching parts (D)

EARLY COMPUTATION OF PART STRUCTURE 1043

EXPERIMENT 1

In Experiment 1 participants searched for either a shapesegmented at negative minima of curvature (Figure 6A)among distractor shapes parsed elsewhere (Figure 6C) orthe reverse Our logic was as follows If the visual systemsegments shapes at negative minima of curvature then thebottom ldquopartrdquo of the shape in Figure 6C would be seg-mented further into two parts yielding the effective pars-ing shown in Figure 6D As a result the shape in Fig-ure 6C would end up having an extra ldquofeaturerdquo that theshape in Figure 6A does not havemdashnamely the cut in therectangular part of the shape (or equivalently an addi-tional partmdashthree rather than two) Previous visual searchstudies have shown that when a target is defined by thepresence of a unique feature search is usually fast and ef-ficient whereas when the target is distinguished by the ab-sence of a feature search becomes slow and self-terminating(eg Treisman amp Gormican 1988 Treisman amp Souther1985) If the visual system in fact segments shapes at neg-ative minima we should expect the search for a nonndashminima-segmented shape among minima-segmentedshapes to be fast and efficient and the search for a minima-segmented shape among nonndashminima-segmented shapesto be slow and inefficient

In designing the stimuli we minimized differences alongother dimensions that might distinguish between the nat-ural and the unnatural parsings For example the lengths ofthe part cuts in the two parsings were equated because cutlength has previously been shown to be an important fac-tor in parsing shapes (Singh et al 1999) Moreover in thecontext of visual search the difference in the lengths ofthese line segments might itself provide a distinguishing

feature quite independently of the fact that these line seg-ments are part cuts Similarly the relative areas of the twoparts created by these cuts were also equated The area ofthe bottom part in Figure 6A is equal to the area of the toppart in Figure 6C Finally the part cuts in both parsingshad the same orientation (ie horizontal) so that any ob-served search asymmetry could not be attributed to a dif-ference in orientation

MethodParticipants Twelve participants 7 males and 5 females from

the Massachusetts Institute of Technology were recruited Theywere between 17 and 40 years of age all had normal or corrected-to-normal vision and they were paid for their participation

Materials and Design The shapes used in Experiment 1 are shownin Figures 6A and 6C They are naturally seen as a bar attached toan oval with either a cut in the middle of the bar (non-minima pars-ing) or a cut at the junction of the bar and the oval (minima parsing)The size of the (uncut) bar was 057ordm 3 183ordm and that of the ovalwas 057ordm 3 115ordm The thickness of the cut was 011ordm The area ofthe oval in the minima-parsed shape was equal to the area of the de-tached bar piece in the nonndashminima-parsed shape Hence the twoldquopartsrdquo in both the minima-parsed and the nonndashminima-parsedshapes had equal relative areas

Each display consisted of either 6 or 12 shapes distributed in a 5 33 grid (938ordm 3 972ordm) Each position was offset slightly from thegrid so that the shapes were not perfectly aligned with each otherThe experiment was run in two sessions In one session the partici-pants searched for a nonndashminima-parsed shape among minima-parsed shapes (Figure 7A) and in the other session they searchedfor a minima-parsed shape among nonndashminima-parsed shapes (Fig-ure 7B) The order of the two sessions was counterbalanced acrossparticipants Within each session displays with set size 6 and setsize 12 were intermixed randomly These resulted in a total of 96 tri-als for each set size 48 target-present trials and 48 target-absent tri-als Trials from different conditions were divided evenly into three64-trial blocks Thirty-two practice trials preceded the experimentaltrials in each session

Apparatus The displays were presented on the 15-in monitor ofa 350-MHz G3 iMac using the MacProbe experimental softwareThe participants were seated 50 cm away from the monitor

Procedure Each trial began with the presentation of a fixationdot for 500 msec which was then followed by the search displayThe search display remained on the screen until the participants hadpressed one of the two prespecified keys to indicate the presence orabsence of the target The participants were instructed to use eithertheir thumbs or their index fingers to press the response keys Theresponse keys were the Control key on the extreme left of the key-board and the Enter key on the extreme right of the keyboard Keyassignments were counterbalanced across participants and the as-signment was indicated by appropriately labeled stickers on thekeys Within a block the next trial began automatically 500 msecafter the participant had responded to the previous trial An incorrectresponse was indicated by a single short beep The participants wereallowed to take a break for as long as they wished between blocks

ResultsReaction time for correct trials Of the total data col-

lected 746 were removed owing to response errors Twofurther data points were removed because the RTs weregreater than 3000 msec The remaining data were ana-lyzed with a within-subjects analysis of variance (ANOVA)The mean RTs averaged across participants are plotted inFigure 8

Figure 6 Stimuli used in Experiment 1 (A) minima-parsedshape (B) no further parsing occurs for Shape A (C) nonndashminima-parsed shape and (D) the resulting shape if parsing atnegative minima occurs automatically for the shape presented inpanel C

EARLY COMPUTATION OF PART STRUCTURE 1043

EXPERIMENT 1

In Experiment 1 participants searched for either a shapesegmented at negative minima of curvature (Figure 6A)among distractor shapes parsed elsewhere (Figure 6C) orthe reverse Our logic was as follows If the visual systemsegments shapes at negative minima of curvature then thebottom ldquopartrdquo of the shape in Figure 6C would be seg-mented further into two parts yielding the effective pars-ing shown in Figure 6D As a result the shape in Fig-ure 6C would end up having an extra ldquofeaturerdquo that theshape in Figure 6A does not havemdashnamely the cut in therectangular part of the shape (or equivalently an addi-tional partmdashthree rather than two) Previous visual searchstudies have shown that when a target is defined by thepresence of a unique feature search is usually fast and ef-ficient whereas when the target is distinguished by the ab-sence of a feature search becomes slow and self-terminating(eg Treisman amp Gormican 1988 Treisman amp Souther1985) If the visual system in fact segments shapes at neg-ative minima we should expect the search for a nonndashminima-segmented shape among minima-segmentedshapes to be fast and efficient and the search for a minima-segmented shape among nonndashminima-segmented shapesto be slow and inefficient

In designing the stimuli we minimized differences alongother dimensions that might distinguish between the nat-ural and the unnatural parsings For example the lengths ofthe part cuts in the two parsings were equated because cutlength has previously been shown to be an important fac-tor in parsing shapes (Singh et al 1999) Moreover in thecontext of visual search the difference in the lengths ofthese line segments might itself provide a distinguishing

feature quite independently of the fact that these line seg-ments are part cuts Similarly the relative areas of the twoparts created by these cuts were also equated The area ofthe bottom part in Figure 6A is equal to the area of the toppart in Figure 6C Finally the part cuts in both parsingshad the same orientation (ie horizontal) so that any ob-served search asymmetry could not be attributed to a dif-ference in orientation

MethodParticipants Twelve participants 7 males and 5 females from

the Massachusetts Institute of Technology were recruited Theywere between 17 and 40 years of age all had normal or corrected-to-normal vision and they were paid for their participation

Materials and Design The shapes used in Experiment 1 are shownin Figures 6A and 6C They are naturally seen as a bar attached toan oval with either a cut in the middle of the bar (non-minima pars-ing) or a cut at the junction of the bar and the oval (minima parsing)The size of the (uncut) bar was 057ordm 3 183ordm and that of the ovalwas 057ordm 3 115ordm The thickness of the cut was 011ordm The area ofthe oval in the minima-parsed shape was equal to the area of the de-tached bar piece in the nonndashminima-parsed shape Hence the twoldquopartsrdquo in both the minima-parsed and the nonndashminima-parsedshapes had equal relative areas

Each display consisted of either 6 or 12 shapes distributed in a 5 33 grid (938ordm 3 972ordm) Each position was offset slightly from thegrid so that the shapes were not perfectly aligned with each otherThe experiment was run in two sessions In one session the partici-pants searched for a nonndashminima-parsed shape among minima-parsed shapes (Figure 7A) and in the other session they searchedfor a minima-parsed shape among nonndashminima-parsed shapes (Fig-ure 7B) The order of the two sessions was counterbalanced acrossparticipants Within each session displays with set size 6 and setsize 12 were intermixed randomly These resulted in a total of 96 tri-als for each set size 48 target-present trials and 48 target-absent tri-als Trials from different conditions were divided evenly into three64-trial blocks Thirty-two practice trials preceded the experimentaltrials in each session

Apparatus The displays were presented on the 15-in monitor ofa 350-MHz G3 iMac using the MacProbe experimental softwareThe participants were seated 50 cm away from the monitor

Procedure Each trial began with the presentation of a fixationdot for 500 msec which was then followed by the search displayThe search display remained on the screen until the participants hadpressed one of the two prespecified keys to indicate the presence orabsence of the target The participants were instructed to use eithertheir thumbs or their index fingers to press the response keys Theresponse keys were the Control key on the extreme left of the key-board and the Enter key on the extreme right of the keyboard Keyassignments were counterbalanced across participants and the as-signment was indicated by appropriately labeled stickers on thekeys Within a block the next trial began automatically 500 msecafter the participant had responded to the previous trial An incorrectresponse was indicated by a single short beep The participants wereallowed to take a break for as long as they wished between blocks

ResultsReaction time for correct trials Of the total data col-

lected 746 were removed owing to response errors Twofurther data points were removed because the RTs weregreater than 3000 msec The remaining data were ana-lyzed with a within-subjects analysis of variance (ANOVA)The mean RTs averaged across participants are plotted inFigure 8

Figure 6 Stimuli used in Experiment 1 (A) minima-parsedshape (B) no further parsing occurs for Shape A (C) nonndashminima-parsed shape and (D) the resulting shape if parsing atnegative minima occurs automatically for the shape presented inpanel C

1044 XU AND SINGH

Overall the two search types differed from each othersignificantly [F(111) 5 8224 p 001] such that par-ticipants were much faster at detecting the presence or ab-sence of a nonndashminima-parsed shape among minima-parsed shapes than they were at detecting a minima-parsedshape among nonndashminima-parsed shapes The effect ofset size was also significant [F(111) 5 5187 p 001]and it interacted significantly with search type [F(111) 53353 p 001] The participants were much faster at de-tecting the presence rather than the absence of a target

[F(111) 5 5196 p 001] and this effect interacted sig-nificantly with search type [F(111) 5 3113 p 001]In addition the interaction between set size and targetpresenceabsence as well as the three-way interaction(among search type set size and target presenceabsence)were both significant [F(111) 5 511 p 5 045 andF(111) 5 522 p 5 0043 respectively]

A separate ANOVA was also carried out for each search type When the participants searched for a nonndashminima-parsed shape among minima-parsed shapes themain effects of set size and target presenceabsence wereboth significant [F(111) 5 1121 p 5 006 and F(111) 51790 p 5 001 respectively] However the interaction ofthe two effects did not reach significance (F 1) Whenthe participants searched for a minima-parsed shapeamong nonndashminima-parsed shapes the effect of set sizethe effect of target presenceabsence and the interactionof the two were all significant [F(111) 5 5431 p 001F(111) 5 5144 p 001 and F(111) 5 743 p 5 020respectively] These results show that the two types ofsearch differed from each other qualitatively with thesearch for a nonndashminima-parsed shape among minima-parsed shapes being consistent with a feature search andthe reverse search being consistent with a serial self-terminating search (Wolfe 1998)

Error rates The mean error rates are presented inTable 1 The participants made more errors searching fora minima-parsed shape among nonndashminima-parsedshapes than they did in the reverse search [F(111) 5 673p 5 025] They also made more errors with larger setsizes [F(111) 5 1699 p 5002] and more errors whenthe target shape was present than when it was absent[F(111) 5 2848 p 001]

DiscussionWhen the participants searched for a nonndashminima-parsed

shape among minima-parsed shapes the search slopeswere very shallow for both target-present and target-absent trials (both were less than 10 msecitem 55 msecitem for target-present trials 67 msecitem for target-absent trials) Moreover the ratio between target-presentand target-absent slopes was significantly less than 20(F 1) These results thus fulfilled the criteria proposedby Wolfe (1998) for feature search and indicated thatwhen a part cut occurred at a nonndashnegative-minima loca-tion on the target shape it was considered as a unique fea-ture among distractors with part cuts at negative minimaThe parsing from Figure 6C to Figure 6D must thereforeoccur rapidly and early in visual processing

When the roles of the target and the distractors were re-versedmdashsuch that the participants searched for a minima-parsed shape among nonndashminima-parsed shapesmdashsearchbecame slow and inefficient (193 and 322 msecitem fortarget present and absent respectively) In this case theobligatory parsing at negative minima in the distractorshapes made the cut in the target shape much less promi-nent As a result the target was now defined by the ab-sence of a cut in the non-minima location As is well

Figure 7 Examples of search displays used in Experiment 1The participants searched either for a nonndashminima-parsed tar-get among minima-parsed distractors (A) or for a minima-parsed target among nonndashminima-parsed distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1045

known search becomes slow and inefficient when the tar-get is defined by the absence of a feature (eg Treismanamp Gormican 1988 Treisman amp Souther 1985)

It is worth noting that this search asymmetry cannot beattributed to the difference in the lengths of the top verti-cal bars because a search based on bar length would in fact

predict the oppositepattern of results Search experimentsinvolving differences in bar length have shown that longerbars pop out among shorter ones but not vice versa (Treis-man amp Gormican 1988) Since the minima-segmentedshapes have longer bars on top than the nonndashminima-segmented shapes a search based on the lengths of these

Figure 8 The mean reaction times for correct trials in Experiment 1 When the partici-pants searched for a nonndashminima-parsed shape among minima-parsed shapes the searchwas fast and efficient for both target-present and target-absent trials when the roles of thetarget and the distractors were reversed search became slow and inefficient These resultsindicated that parsing at negative minima of curvature occurs rapidly and early in visualprocessing

Table 1Error Rates for Experiments 1ndash4

Target

Experiment Cut Present Absent Present Absent

Size 6 Size 12

M SE M SE M SE M SE

1 minima parsed 09 02 04 01 15 02 06 01nonndashminima parsed 08 01 04 01 10 02 05 01

2 minima parsed 10 01 02 01 14 03 01 003nonndashminima parsed 08 01 03 01 13 02 02 01

Size 10 Size 20

M SE M SE M SE M SE

3 minima parsed 05 02 02 004 06 02 01 004nonndashminima parsed 04 01 02 01 04 01 02 01

4 minima parsed 04 01 01 005 06 01 02 01nonndashminima parsed 04 01 03 01 03 01 02 01

1046 XU AND SINGH

bars would make the search for minima-segmented shapeseasiermdashthe opposite of what we obtained

EXPERIMENT 2

In Experiment 2 we sought to test the generality of theresults obtained in Experiment 1 Note that the shape weused in Experiment 1 had the following two characteris-tics First each of its two parts had a symmetric and fa-miliar form (ie a rectangular bar and an oval) Hence inprinciple the parsing of this shape into parts could haveoccurred simply owing to the familiarity and symmetry ofits constituent parts Second the part boundaries on theshape used in Experiment 1 were both points of tangentdiscontinuitymdashthat is sharp cornersmdashwhereas in generalpart boundaries can be smooth as well In order to test thegenerality of our results in Experiment 2 we used a shapewhose parts were both unfamiliar and nonsymmetric andwhose part boundaries were smoothed rather than sharpcorners (see Figure 9) As is well known smoothed partboundaries are visually less salient than are correspondingconcave-corner boundaries and lead to a weaker part struc-ture (see eg Hoffman amp Singh 1997) Thus one might ex-pect a somewhat weaker effect with such part boundariesHowever it is still reasonable to ask whether an asymme-try will be obtained in visual search As in Experiment1 thepart cuts in the two parsings were equated in their lengthsorientations and the areas of the parts that they created

MethodParticipants The same 12 participants who took part in Exper-

iment 1 also participated in this experiment The order of the twoexperiments was counterbalanced across participants

Materials and Design The shapes used in Experiment 2 areshown in Figures 9A and 9C The size of the shape was 126ordm 3275ordm and that of the cut was 069ordm 3 011ordm For the parsing shownin Figure 9A the vertical length of the top part was 040ordm and thatof the bottom part was 088ordm As in Experiment 1 the relative areasof the parts created by the minima parsing and the nonndashminima pars-ing were equated

Figure 9 Stimuli used in Experiment 2 (A) minima-parsedshape (B) no further parsing occurs for Shape A (C) nonndashminima-parsed shape and (D) the resulting shape if parsing atnegative minima occurs automatically for the shape presented inpanel C

Figure 10 Examples of search displays used in Experiment 2The participants searched either for a nonndashminima-parsed tar-get among minima-parsed distractors (A) or for a minima-parsed target among nonndashminima-parsed distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1047

The experiment was run in two sessions In one session the par-ticipants searched for a nonndashminima-parsed shape among minima-parsed shapes (Figure 10A) and in the other session they searchedfor a minima-parsed shape among nonndashminima-parsed shapes (Fig-ure 10B) Other aspects of the design and procedure were identicalto those of Experiment 1

ResultsReaction time for correct trials Of the total data col-

lected 651 were removed owing to response errorsTwo further data points were removed because the RTswere longer than 3000 msec The remaining data were an-alyzed with a within-subjects ANOVA The mean RTs av-eraged across participants are plotted in Figure 11

Overall as in Experiment 1 the two search types dif-fered from each other significantly [F(111) 5 3827 p 001] such that the participants were much faster at de-tecting the presenceabsence of a nonndashminima-parsed tar-get among minima-parsed distractors than they were at de-tecting the presenceabsence of a minima-parsed targetamong nonndashminima-parsed distractors The effect of setsize was significant [F(111) 5 3844 p 001] and it in-teracted significantly with search type [F(111) 5 1342p 5 004] The participants were faster at detecting the

presence rather than the absence of the target [F(111) 55246 p 001] and this effect interacted significantlywith search type [F(111) 5 599 p 5 032] The interac-tion between set size and target presenceabsence was alsosignificant [F(111) 5 737 p 5 020] However the threeway interaction among search type set size and targetpresenceabsence was not significant (F 1)

A separate ANOVA was also carried out for each searchtype When the participants searched for a nonndashminima-parsed shape among minima-parsed shapes the effect ofset size and target presenceabsence and the interactionbetween the two were all significant [F(111) 5 2689p 001 F(111) 5 1544 p 5 002 and F(111) 5 689p 5 024 respectively] When the participants searchedfor a minima-parsed shape among nonndashminima-parsedshapes the effect of set size and the effect of target presenceabsence were both significant [F(111) 5 2840 p 001and F(111) 5 3581 p 001 respectively] The inter-action between set size and target presenceabsence wasmarginally significant [F(111) 5 376 p 5 079]

Error rates The mean error rates are presented in Ta-ble 1 Only the effect of target presenceabsence [F(111) 55200 p 001] and the interaction between target pres-

Figure 11 The mean reaction times for correct trials in Experiment 2 As in Experiment 1when the participants searched for a nonndashminima-parsed shape among minima-parsedshapes the search was fast and efficient when the roles of the target and the distractors werereversed search became slow and inefficient These results indicated that parsing at nega-tive minima of curvature occurs rapidly and early in visual processing even for shapes whoseparts are neither symmetric nor simple familiar shapes and whose part boundaries aresmoothed rather than concave corners

enceabsence and set size [F(111) 5 730 p 5 021] weresignificant

DiscussionAs in Experiment 1 there was a clear search asymme-

try between the search for a nonndashminima-parsed targetamong minima-parsed distractors and the search for aminima-parsed target among nonndashminima-parsed distrac-tors When the part cut was located at a nonndashminima lo-

cation on the target shape search was very fast and effi-cient (48 and 117 msecitem for target-present and target-absent trials respectively) However when the cut occurredat the negative minima on the target shape search becameslow and inefficient (195 and 290 msecitem for targetpresent and target absent respectively)

When the participants searched for the nonndashminima-parsed target among minima-parsed distractors althoughsearch was still very fast the ratio between target-presentand target-absent slopes was higher than 20 (recallWolfersquos 1998 criteria for a feature search) Note howeverthat there is an inherent difficulty in interpreting the sloperatios for these shallow slopes because the confidence inter-vals around the average slope ratios are quite wide (617)thus adding uncertainty to the estimate of the slope ratio

In sum although the magnitude of the effect wasslightly weaker than it was in Experiment 1 (reflecting thefact that smoothed part boundaries typically lead to per-ceptually weaker part structures) the asymmetry in visualsearch remained highly significant This indicates thatparsing at negative minima occurs rapidly and early in vi-sual processing even for shapes whose parts are neithersymmetric nor simple familiar shapes and whose partboundaries are smoothed rather than concave corners

EXPERIMENTS 3ndash4

In the next two experiments our goal was to get at theissue of early parsing of shapes at negative minima byusing a slightly different method Using the same basicshapes as in Experiments 1 and 2 we asked the partici-pants to search for a parsed shape among unparsed shapesA pilot study showed that a parsed shape pops out amongunparsed shapes largely irrespective of the location of thepart cut (since the target is defined by the presence of aunique feature the part cut that the distractors lack) Wepredicted however that if parsing at negative minima oc-curs obligatorily in early stages of visual processing a cutlocated at negative minima would be somewhat less effi-cacious as a feature that distinguishes the target from thedistractors As a result a cut located at negative minimashould be harder to detectmdashand therefore slower to searchfor (Figure 12B)mdashthan a cut located at a nonndashnegative-minima location (Figure 12A)

0basic shapes were used as those in Experiment 1 (Fig-ures 6A and 6C) The participants searched either for anonndashminima-parsed shape among uncut shapes (Fig-ure 12A) or for a minima-parsed shape among uncutshapes (Figure 12B)

MethodParticipants Twelve new participants 6 males and 6 females

from the same participant pool were recruited They were paid fortheir participation

Materials and Design The stimuli used were the shapes in Fig-ures 6A and 6C and the uncut shape There were either 10 or 20search items in a given display In one session of the experiment theparticipants searched for a nonndashminima-parsed shape among uncutshapes (Figure 12A) in the other they searched for a minima-parsed

1048 XU AND SINGH

Figure 12 Examples of search displays used in Experiment 3The participants searched either for a nonndashminima-parsed tar-get among uncut distractors (A) or for a minima-parsed targetamong uncut distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1049

shape among uncut shapes (Figure 12B) The order for these twosessions was counterbalanced across participants Other aspects ofthe design and procedure were identical to those in Experiment 1

ResultsReaction time for correct trials Of the total data col-

lected 310 were removed owing to response errorsTwo further data points were removed because the RTswere longer than 2000 msec5 The remaining data wereanalyzed with a within-subjects ANOVA The mean RTsaveraged across participants are plotted in Figure 13

Overall the two search types differed significantlyfrom each other such that it took participants 86 mseclonger on average to detect the presence or absence ofthe target shape when it was parsed with a minima cut thanwhen it was parsed with a non-minima cut [F(111) 52041 p 5 001] The effect of set size was significant[F(111) 5 855 p 5 014] and it interacted significantlywith search type [F(111) 5 527 p 5 042] The partici-pants were faster at detecting the presence rather than theabsence of the target [F(111) 5 1589 p 5 002] and thiseffect interacted significantly with search type [F(111) 5878 p 5 013] The interaction between set size and targetpresenceabsence was marginally significant [F(111) 5397 p 5 072] However the three-way interaction among

search type set size and target presence absence was notsignificant (F 1)

A separate ANOVA was also carried out for each searchtype When the participants searched for a nonndashminima-parsed shape among uncut shapes only the effect of tar-get presenceabsence was significant [F(111) 5 712p 5 022] When the participants searched for a minima-parsed shape among uncut shapes both the effect of setsize and the effect of target presenceabsence were signif-icant [F(111) 5 1206 p 5 005 and F(111) 5 1504p 5 003 respectively]

Error rates The mean error rates are presented inTable 1 The only significant effect was target presenceabsence [F(111)5 689 p 5 024] The interaction betweentarget presenceabsence and search type was marginallysignificant [F(111) 5 376 p 5 078]

DiscussionAs was expected the parsed target popped out among

uncut distractor shapes both when the target was parsedusing a minima cut and when it was parsed using a non-minima cut (The search slopes for the minima-parsed tar-get were 25 msecitem for target present and 37 msecitem for target absent The search slopes for the nonndash

Figure 13 The mean reaction times for correct trials in Experiment 3 The parsed targetpopped out among uncut distractor shapes both when the target was parsed using a minimacut and when it was parsed using a non-minima cut However the participants were signifi-cantly faster (on average by 86 msec) at detecting the presence or absence of the parsed tar-get when it was parsed with a non-minima cut than when it was parsed with a minima cut

1050 XU AND SINGH

minima-parsed target were 02 msecitem for target presentand 14 msecitem for target absent)

However participants were significantly faster (on av-erage by 86 msec) at detecting the presence or absence ofthe parsed target when it was segmented with a non-min-ima cut than when it was segmented with a minima cut Inother words a cut located at negative minima was moredifficult and slower to detect than a cut located elsewhereThus the presence of a perceptual part cut at that locationappears to have a masking influence on the detection of a

physically present cut This effect was most striking for tar-get-absent displays Even though the search displays wereidentical in both cases (consisting only of uncut shapes) ittook the participants 100 msec longer to determine the ab-sence of a part cut when they were looking for it at nega-tive minima The fact that parsing at negative minima in-fluenced visual search even when search was already fastand efficient provides further evidence for the claim thatsuch parsing occurs very early in visual processing

Experiment 4In this experiment our goal was to extend the results of

Experiment 3 to the shapes used in Experiment 2 (Fig-ure 9) Participants searched either for a nonndashminima-parsed shape among uncut shapes (Figure 14A) or for aminima-parsed target shape among uncut shapes (Fig-ure 14B) In all other respects the experimental designand procedure were identical to those of Experiment 3

MethodParticipants The same 12 participants who took part in Exper-

iment 3 also participated in this experiment The order of the twoexperiments was counterbalanced across participants

Materials and Design The stimuli shown in Figures 9A and 9Cand the uncut shape were used in the experiment In one session theparticipants searched for a nonndashminima-parsed shape among uncutshapes (Figure 14A) and in the other the participants searched fora minima-parsed shape among uncut shapes (Figure 14B) The orderfor the two sessions was counterbalanced across participants

ResultsReaction time for correct trials Of the total data col-

lected 310 were removed owing to response errorsOne further data point was removed because the RT waslonger than 2000 msec (see note 5) The remaining datawere analyzed with a within-subjects ANOVA The meanRTs averaged across participants are plotted in Figure 15

Overall the two search types differed from each othersignificantly such that it took participants significantlylonger (49 msec on average) to detect the presence or ab-sence of the target shape when it was parsed with a min-ima cut than when it was parsed with a non-minima cut[F(111) 5 1169 p 5 006] The effect of set size wasmarginally significant [F(111) 5 331 p 5 096] Theparticipants were faster at detecting the presence ratherthan the absence of the target [F(111) 5 1383 p 5003] and this effect interacted significantly with searchtype [F(111) 5 2272 p 5 001] As in Experiment 3 thethree-way interaction among search type set size and tar-get presenceabsence was not significant (F 1)

A separate ANOVA was also carried out for each searchtype When participants searched for a nonndashminima-parsed target among uncut distractors none of the effectsreached significance When participants searched for aminima-parsed target among uncut distractors only theeffect of target presenceabsence was significant [F(111) 52703 p 001]

Error rates The mean error rates are presented inTable 1 The effect of target presenceabsence was signifi-

Figure 14 Examples of search displays used in Experiment 3The participants searched either for a nonndashminima-parsed tar-get among uncut distractors (A) or for a minima-parsed targetamong uncut distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1051

cant [F(111) 5 2256 p 5 001] and this effect interactedsignificantly with search type [F(111) 5 1355 p 5 004]

DiscussionAs in Experiment 3 the search for a parsed target among

unparsed distractors was quite fast and efficient both forthe minima-parsed and the nonndashminima-parsed targets(The search slopes for the minima-parsed target were12 msecitem for target present and 11 msecitem for tar-get absent The search slopes for the nonndashminima-parsedtarget were 16 msecitem for target present and 206 msecitem for target absent)

However the participants were significantly faster (onaverage by 49 msec) at detecting the presence or absenceof the target shape when it was parsed with a non-minimacut than when it was parsed with a minima cut This repli-cates the results of Experiment 3 with shapes whose partswere neither symmetric nor simple familiar shapes andwhose part boundaries were smooth rather than tangentdiscontinuities As in Experiment 3 these results weremost striking for the target-absent trials It took the par-ticipants 70 msec longer on average to determine the ab-

sence of a part cut when they were looking for it at nega-tive minima than when they were looking for it elsewhereeven though the search displays were identical in bothcases (consisting simply of identical uncut shapes)

The magnitude of the effect was somewhat smaller thanit was in Experiment 3 As in Experiment 2 this differ-ence reflects the fact that the part boundaries in Figure 9are smooth with low curvature as compared with thesharp corners in Figure 6 a change that has been demon-strated to reduce the salience of perceived part structure(Hoffman amp Singh 1997)

GENERAL DISCUSSION

We set out to address the question of whether parsing atnegative minima occurs preattentivelymdashor at least rapidlyand early in visual processing In Experiment 1 we foundthat whereas the search for a nonndashminima-parsed targetamong minima-parsed distractors was fast and efficientthe search for a minima-parsed target among nonndashminima-parsed distractors was slow and inefficient This asymme-try demonstrates that parsing at negative minima occurs

Figure 15 The mean reaction times for correct trials in Experiment 4 As in Experiment 3the parsed target popped out among uncut distractor shapes both when the target wasparsed using a minima cut and when it was parsed using a non-minima cut However eventhough shapes are neither symmetric nor simple familiar shapes and their part boundariesare smoothed rather than concave corners the participants were significantly faster (on av-erage by 49 msec) at detecting the presence or absence of the parsed target when it wasparsed with a non-minima cut than when it was parsed with a minima cut

enceabsence and set size [F(111) 5 730 p 5 021] weresignificant

DiscussionAs in Experiment 1 there was a clear search asymme-

try between the search for a nonndashminima-parsed targetamong minima-parsed distractors and the search for aminima-parsed target among nonndashminima-parsed distrac-tors When the part cut was located at a nonndashminima lo-

cation on the target shape search was very fast and effi-cient (48 and 117 msecitem for target-present and target-absent trials respectively) However when the cut occurredat the negative minima on the target shape search becameslow and inefficient (195 and 290 msecitem for targetpresent and target absent respectively)

When the participants searched for the nonndashminima-parsed target among minima-parsed distractors althoughsearch was still very fast the ratio between target-presentand target-absent slopes was higher than 20 (recallWolfersquos 1998 criteria for a feature search) Note howeverthat there is an inherent difficulty in interpreting the sloperatios for these shallow slopes because the confidence inter-vals around the average slope ratios are quite wide (617)thus adding uncertainty to the estimate of the slope ratio

In sum although the magnitude of the effect wasslightly weaker than it was in Experiment 1 (reflecting thefact that smoothed part boundaries typically lead to per-ceptually weaker part structures) the asymmetry in visualsearch remained highly significant This indicates thatparsing at negative minima occurs rapidly and early in vi-sual processing even for shapes whose parts are neithersymmetric nor simple familiar shapes and whose partboundaries are smoothed rather than concave corners

EXPERIMENTS 3ndash4

In the next two experiments our goal was to get at theissue of early parsing of shapes at negative minima byusing a slightly different method Using the same basicshapes as in Experiments 1 and 2 we asked the partici-pants to search for a parsed shape among unparsed shapesA pilot study showed that a parsed shape pops out amongunparsed shapes largely irrespective of the location of thepart cut (since the target is defined by the presence of aunique feature the part cut that the distractors lack) Wepredicted however that if parsing at negative minima oc-curs obligatorily in early stages of visual processing a cutlocated at negative minima would be somewhat less effi-cacious as a feature that distinguishes the target from thedistractors As a result a cut located at negative minimashould be harder to detectmdashand therefore slower to searchfor (Figure 12B)mdashthan a cut located at a nonndashnegative-minima location (Figure 12A)

0basic shapes were used as those in Experiment 1 (Fig-ures 6A and 6C) The participants searched either for anonndashminima-parsed shape among uncut shapes (Fig-ure 12A) or for a minima-parsed shape among uncutshapes (Figure 12B)

MethodParticipants Twelve new participants 6 males and 6 females

from the same participant pool were recruited They were paid fortheir participation

Materials and Design The stimuli used were the shapes in Fig-ures 6A and 6C and the uncut shape There were either 10 or 20search items in a given display In one session of the experiment theparticipants searched for a nonndashminima-parsed shape among uncutshapes (Figure 12A) in the other they searched for a minima-parsed

1048 XU AND SINGH

Figure 12 Examples of search displays used in Experiment 3The participants searched either for a nonndashminima-parsed tar-get among uncut distractors (A) or for a minima-parsed targetamong uncut distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1049

shape among uncut shapes (Figure 12B) The order for these twosessions was counterbalanced across participants Other aspects ofthe design and procedure were identical to those in Experiment 1

ResultsReaction time for correct trials Of the total data col-

lected 310 were removed owing to response errorsTwo further data points were removed because the RTswere longer than 2000 msec5 The remaining data wereanalyzed with a within-subjects ANOVA The mean RTsaveraged across participants are plotted in Figure 13

Overall the two search types differed significantlyfrom each other such that it took participants 86 mseclonger on average to detect the presence or absence ofthe target shape when it was parsed with a minima cut thanwhen it was parsed with a non-minima cut [F(111) 52041 p 5 001] The effect of set size was significant[F(111) 5 855 p 5 014] and it interacted significantlywith search type [F(111) 5 527 p 5 042] The partici-pants were faster at detecting the presence rather than theabsence of the target [F(111) 5 1589 p 5 002] and thiseffect interacted significantly with search type [F(111) 5878 p 5 013] The interaction between set size and targetpresenceabsence was marginally significant [F(111) 5397 p 5 072] However the three-way interaction among

search type set size and target presence absence was notsignificant (F 1)

A separate ANOVA was also carried out for each searchtype When the participants searched for a nonndashminima-parsed shape among uncut shapes only the effect of tar-get presenceabsence was significant [F(111) 5 712p 5 022] When the participants searched for a minima-parsed shape among uncut shapes both the effect of setsize and the effect of target presenceabsence were signif-icant [F(111) 5 1206 p 5 005 and F(111) 5 1504p 5 003 respectively]

Error rates The mean error rates are presented inTable 1 The only significant effect was target presenceabsence [F(111)5 689 p 5 024] The interaction betweentarget presenceabsence and search type was marginallysignificant [F(111) 5 376 p 5 078]

DiscussionAs was expected the parsed target popped out among

uncut distractor shapes both when the target was parsedusing a minima cut and when it was parsed using a non-minima cut (The search slopes for the minima-parsed tar-get were 25 msecitem for target present and 37 msecitem for target absent The search slopes for the nonndash

Figure 13 The mean reaction times for correct trials in Experiment 3 The parsed targetpopped out among uncut distractor shapes both when the target was parsed using a minimacut and when it was parsed using a non-minima cut However the participants were signifi-cantly faster (on average by 86 msec) at detecting the presence or absence of the parsed tar-get when it was parsed with a non-minima cut than when it was parsed with a minima cut

1050 XU AND SINGH

minima-parsed target were 02 msecitem for target presentand 14 msecitem for target absent)

However participants were significantly faster (on av-erage by 86 msec) at detecting the presence or absence ofthe parsed target when it was segmented with a non-min-ima cut than when it was segmented with a minima cut Inother words a cut located at negative minima was moredifficult and slower to detect than a cut located elsewhereThus the presence of a perceptual part cut at that locationappears to have a masking influence on the detection of a

physically present cut This effect was most striking for tar-get-absent displays Even though the search displays wereidentical in both cases (consisting only of uncut shapes) ittook the participants 100 msec longer to determine the ab-sence of a part cut when they were looking for it at nega-tive minima The fact that parsing at negative minima in-fluenced visual search even when search was already fastand efficient provides further evidence for the claim thatsuch parsing occurs very early in visual processing

Experiment 4In this experiment our goal was to extend the results of

Experiment 3 to the shapes used in Experiment 2 (Fig-ure 9) Participants searched either for a nonndashminima-parsed shape among uncut shapes (Figure 14A) or for aminima-parsed target shape among uncut shapes (Fig-ure 14B) In all other respects the experimental designand procedure were identical to those of Experiment 3

MethodParticipants The same 12 participants who took part in Exper-

iment 3 also participated in this experiment The order of the twoexperiments was counterbalanced across participants

Materials and Design The stimuli shown in Figures 9A and 9Cand the uncut shape were used in the experiment In one session theparticipants searched for a nonndashminima-parsed shape among uncutshapes (Figure 14A) and in the other the participants searched fora minima-parsed shape among uncut shapes (Figure 14B) The orderfor the two sessions was counterbalanced across participants

ResultsReaction time for correct trials Of the total data col-

lected 310 were removed owing to response errorsOne further data point was removed because the RT waslonger than 2000 msec (see note 5) The remaining datawere analyzed with a within-subjects ANOVA The meanRTs averaged across participants are plotted in Figure 15

Overall the two search types differed from each othersignificantly such that it took participants significantlylonger (49 msec on average) to detect the presence or ab-sence of the target shape when it was parsed with a min-ima cut than when it was parsed with a non-minima cut[F(111) 5 1169 p 5 006] The effect of set size wasmarginally significant [F(111) 5 331 p 5 096] Theparticipants were faster at detecting the presence ratherthan the absence of the target [F(111) 5 1383 p 5003] and this effect interacted significantly with searchtype [F(111) 5 2272 p 5 001] As in Experiment 3 thethree-way interaction among search type set size and tar-get presenceabsence was not significant (F 1)

A separate ANOVA was also carried out for each searchtype When participants searched for a nonndashminima-parsed target among uncut distractors none of the effectsreached significance When participants searched for aminima-parsed target among uncut distractors only theeffect of target presenceabsence was significant [F(111) 52703 p 001]

Error rates The mean error rates are presented inTable 1 The effect of target presenceabsence was signifi-

Figure 14 Examples of search displays used in Experiment 3The participants searched either for a nonndashminima-parsed tar-get among uncut distractors (A) or for a minima-parsed targetamong uncut distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1051

cant [F(111) 5 2256 p 5 001] and this effect interactedsignificantly with search type [F(111) 5 1355 p 5 004]

DiscussionAs in Experiment 3 the search for a parsed target among

unparsed distractors was quite fast and efficient both forthe minima-parsed and the nonndashminima-parsed targets(The search slopes for the minima-parsed target were12 msecitem for target present and 11 msecitem for tar-get absent The search slopes for the nonndashminima-parsedtarget were 16 msecitem for target present and 206 msecitem for target absent)

However the participants were significantly faster (onaverage by 49 msec) at detecting the presence or absenceof the target shape when it was parsed with a non-minimacut than when it was parsed with a minima cut This repli-cates the results of Experiment 3 with shapes whose partswere neither symmetric nor simple familiar shapes andwhose part boundaries were smooth rather than tangentdiscontinuities As in Experiment 3 these results weremost striking for the target-absent trials It took the par-ticipants 70 msec longer on average to determine the ab-

sence of a part cut when they were looking for it at nega-tive minima than when they were looking for it elsewhereeven though the search displays were identical in bothcases (consisting simply of identical uncut shapes)

The magnitude of the effect was somewhat smaller thanit was in Experiment 3 As in Experiment 2 this differ-ence reflects the fact that the part boundaries in Figure 9are smooth with low curvature as compared with thesharp corners in Figure 6 a change that has been demon-strated to reduce the salience of perceived part structure(Hoffman amp Singh 1997)

GENERAL DISCUSSION

We set out to address the question of whether parsing atnegative minima occurs preattentivelymdashor at least rapidlyand early in visual processing In Experiment 1 we foundthat whereas the search for a nonndashminima-parsed targetamong minima-parsed distractors was fast and efficientthe search for a minima-parsed target among nonndashminima-parsed distractors was slow and inefficient This asymme-try demonstrates that parsing at negative minima occurs

Figure 15 The mean reaction times for correct trials in Experiment 4 As in Experiment 3the parsed target popped out among uncut distractor shapes both when the target wasparsed using a minima cut and when it was parsed using a non-minima cut However eventhough shapes are neither symmetric nor simple familiar shapes and their part boundariesare smoothed rather than concave corners the participants were significantly faster (on av-erage by 49 msec) at detecting the presence or absence of the parsed target when it wasparsed with a non-minima cut than when it was parsed with a minima cut

EARLY COMPUTATION OF PART STRUCTURE 1049

shape among uncut shapes (Figure 12B) The order for these twosessions was counterbalanced across participants Other aspects ofthe design and procedure were identical to those in Experiment 1

ResultsReaction time for correct trials Of the total data col-

lected 310 were removed owing to response errorsTwo further data points were removed because the RTswere longer than 2000 msec5 The remaining data wereanalyzed with a within-subjects ANOVA The mean RTsaveraged across participants are plotted in Figure 13

Overall the two search types differed significantlyfrom each other such that it took participants 86 mseclonger on average to detect the presence or absence ofthe target shape when it was parsed with a minima cut thanwhen it was parsed with a non-minima cut [F(111) 52041 p 5 001] The effect of set size was significant[F(111) 5 855 p 5 014] and it interacted significantlywith search type [F(111) 5 527 p 5 042] The partici-pants were faster at detecting the presence rather than theabsence of the target [F(111) 5 1589 p 5 002] and thiseffect interacted significantly with search type [F(111) 5878 p 5 013] The interaction between set size and targetpresenceabsence was marginally significant [F(111) 5397 p 5 072] However the three-way interaction among

search type set size and target presence absence was notsignificant (F 1)

A separate ANOVA was also carried out for each searchtype When the participants searched for a nonndashminima-parsed shape among uncut shapes only the effect of tar-get presenceabsence was significant [F(111) 5 712p 5 022] When the participants searched for a minima-parsed shape among uncut shapes both the effect of setsize and the effect of target presenceabsence were signif-icant [F(111) 5 1206 p 5 005 and F(111) 5 1504p 5 003 respectively]

Error rates The mean error rates are presented inTable 1 The only significant effect was target presenceabsence [F(111)5 689 p 5 024] The interaction betweentarget presenceabsence and search type was marginallysignificant [F(111) 5 376 p 5 078]

DiscussionAs was expected the parsed target popped out among

uncut distractor shapes both when the target was parsedusing a minima cut and when it was parsed using a non-minima cut (The search slopes for the minima-parsed tar-get were 25 msecitem for target present and 37 msecitem for target absent The search slopes for the nonndash

Figure 13 The mean reaction times for correct trials in Experiment 3 The parsed targetpopped out among uncut distractor shapes both when the target was parsed using a minimacut and when it was parsed using a non-minima cut However the participants were signifi-cantly faster (on average by 86 msec) at detecting the presence or absence of the parsed tar-get when it was parsed with a non-minima cut than when it was parsed with a minima cut

1050 XU AND SINGH

minima-parsed target were 02 msecitem for target presentand 14 msecitem for target absent)

However participants were significantly faster (on av-erage by 86 msec) at detecting the presence or absence ofthe parsed target when it was segmented with a non-min-ima cut than when it was segmented with a minima cut Inother words a cut located at negative minima was moredifficult and slower to detect than a cut located elsewhereThus the presence of a perceptual part cut at that locationappears to have a masking influence on the detection of a

physically present cut This effect was most striking for tar-get-absent displays Even though the search displays wereidentical in both cases (consisting only of uncut shapes) ittook the participants 100 msec longer to determine the ab-sence of a part cut when they were looking for it at nega-tive minima The fact that parsing at negative minima in-fluenced visual search even when search was already fastand efficient provides further evidence for the claim thatsuch parsing occurs very early in visual processing

Experiment 4In this experiment our goal was to extend the results of

Experiment 3 to the shapes used in Experiment 2 (Fig-ure 9) Participants searched either for a nonndashminima-parsed shape among uncut shapes (Figure 14A) or for aminima-parsed target shape among uncut shapes (Fig-ure 14B) In all other respects the experimental designand procedure were identical to those of Experiment 3

MethodParticipants The same 12 participants who took part in Exper-

iment 3 also participated in this experiment The order of the twoexperiments was counterbalanced across participants

Materials and Design The stimuli shown in Figures 9A and 9Cand the uncut shape were used in the experiment In one session theparticipants searched for a nonndashminima-parsed shape among uncutshapes (Figure 14A) and in the other the participants searched fora minima-parsed shape among uncut shapes (Figure 14B) The orderfor the two sessions was counterbalanced across participants

ResultsReaction time for correct trials Of the total data col-

lected 310 were removed owing to response errorsOne further data point was removed because the RT waslonger than 2000 msec (see note 5) The remaining datawere analyzed with a within-subjects ANOVA The meanRTs averaged across participants are plotted in Figure 15

Overall the two search types differed from each othersignificantly such that it took participants significantlylonger (49 msec on average) to detect the presence or ab-sence of the target shape when it was parsed with a min-ima cut than when it was parsed with a non-minima cut[F(111) 5 1169 p 5 006] The effect of set size wasmarginally significant [F(111) 5 331 p 5 096] Theparticipants were faster at detecting the presence ratherthan the absence of the target [F(111) 5 1383 p 5003] and this effect interacted significantly with searchtype [F(111) 5 2272 p 5 001] As in Experiment 3 thethree-way interaction among search type set size and tar-get presenceabsence was not significant (F 1)

A separate ANOVA was also carried out for each searchtype When participants searched for a nonndashminima-parsed target among uncut distractors none of the effectsreached significance When participants searched for aminima-parsed target among uncut distractors only theeffect of target presenceabsence was significant [F(111) 52703 p 001]

Error rates The mean error rates are presented inTable 1 The effect of target presenceabsence was signifi-

Figure 14 Examples of search displays used in Experiment 3The participants searched either for a nonndashminima-parsed tar-get among uncut distractors (A) or for a minima-parsed targetamong uncut distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1051

cant [F(111) 5 2256 p 5 001] and this effect interactedsignificantly with search type [F(111) 5 1355 p 5 004]

DiscussionAs in Experiment 3 the search for a parsed target among

unparsed distractors was quite fast and efficient both forthe minima-parsed and the nonndashminima-parsed targets(The search slopes for the minima-parsed target were12 msecitem for target present and 11 msecitem for tar-get absent The search slopes for the nonndashminima-parsedtarget were 16 msecitem for target present and 206 msecitem for target absent)

However the participants were significantly faster (onaverage by 49 msec) at detecting the presence or absenceof the target shape when it was parsed with a non-minimacut than when it was parsed with a minima cut This repli-cates the results of Experiment 3 with shapes whose partswere neither symmetric nor simple familiar shapes andwhose part boundaries were smooth rather than tangentdiscontinuities As in Experiment 3 these results weremost striking for the target-absent trials It took the par-ticipants 70 msec longer on average to determine the ab-

sence of a part cut when they were looking for it at nega-tive minima than when they were looking for it elsewhereeven though the search displays were identical in bothcases (consisting simply of identical uncut shapes)

The magnitude of the effect was somewhat smaller thanit was in Experiment 3 As in Experiment 2 this differ-ence reflects the fact that the part boundaries in Figure 9are smooth with low curvature as compared with thesharp corners in Figure 6 a change that has been demon-strated to reduce the salience of perceived part structure(Hoffman amp Singh 1997)

GENERAL DISCUSSION

We set out to address the question of whether parsing atnegative minima occurs preattentivelymdashor at least rapidlyand early in visual processing In Experiment 1 we foundthat whereas the search for a nonndashminima-parsed targetamong minima-parsed distractors was fast and efficientthe search for a minima-parsed target among nonndashminima-parsed distractors was slow and inefficient This asymme-try demonstrates that parsing at negative minima occurs

Figure 15 The mean reaction times for correct trials in Experiment 4 As in Experiment 3the parsed target popped out among uncut distractor shapes both when the target wasparsed using a minima cut and when it was parsed using a non-minima cut However eventhough shapes are neither symmetric nor simple familiar shapes and their part boundariesare smoothed rather than concave corners the participants were significantly faster (on av-erage by 49 msec) at detecting the presence or absence of the parsed target when it wasparsed with a non-minima cut than when it was parsed with a minima cut

1050 XU AND SINGH

minima-parsed target were 02 msecitem for target presentand 14 msecitem for target absent)

However participants were significantly faster (on av-erage by 86 msec) at detecting the presence or absence ofthe parsed target when it was segmented with a non-min-ima cut than when it was segmented with a minima cut Inother words a cut located at negative minima was moredifficult and slower to detect than a cut located elsewhereThus the presence of a perceptual part cut at that locationappears to have a masking influence on the detection of a

physically present cut This effect was most striking for tar-get-absent displays Even though the search displays wereidentical in both cases (consisting only of uncut shapes) ittook the participants 100 msec longer to determine the ab-sence of a part cut when they were looking for it at nega-tive minima The fact that parsing at negative minima in-fluenced visual search even when search was already fastand efficient provides further evidence for the claim thatsuch parsing occurs very early in visual processing

Experiment 4In this experiment our goal was to extend the results of

Experiment 3 to the shapes used in Experiment 2 (Fig-ure 9) Participants searched either for a nonndashminima-parsed shape among uncut shapes (Figure 14A) or for aminima-parsed target shape among uncut shapes (Fig-ure 14B) In all other respects the experimental designand procedure were identical to those of Experiment 3

MethodParticipants The same 12 participants who took part in Exper-

iment 3 also participated in this experiment The order of the twoexperiments was counterbalanced across participants

Materials and Design The stimuli shown in Figures 9A and 9Cand the uncut shape were used in the experiment In one session theparticipants searched for a nonndashminima-parsed shape among uncutshapes (Figure 14A) and in the other the participants searched fora minima-parsed shape among uncut shapes (Figure 14B) The orderfor the two sessions was counterbalanced across participants

ResultsReaction time for correct trials Of the total data col-

lected 310 were removed owing to response errorsOne further data point was removed because the RT waslonger than 2000 msec (see note 5) The remaining datawere analyzed with a within-subjects ANOVA The meanRTs averaged across participants are plotted in Figure 15

Overall the two search types differed from each othersignificantly such that it took participants significantlylonger (49 msec on average) to detect the presence or ab-sence of the target shape when it was parsed with a min-ima cut than when it was parsed with a non-minima cut[F(111) 5 1169 p 5 006] The effect of set size wasmarginally significant [F(111) 5 331 p 5 096] Theparticipants were faster at detecting the presence ratherthan the absence of the target [F(111) 5 1383 p 5003] and this effect interacted significantly with searchtype [F(111) 5 2272 p 5 001] As in Experiment 3 thethree-way interaction among search type set size and tar-get presenceabsence was not significant (F 1)

A separate ANOVA was also carried out for each searchtype When participants searched for a nonndashminima-parsed target among uncut distractors none of the effectsreached significance When participants searched for aminima-parsed target among uncut distractors only theeffect of target presenceabsence was significant [F(111) 52703 p 001]

Error rates The mean error rates are presented inTable 1 The effect of target presenceabsence was signifi-

Figure 14 Examples of search displays used in Experiment 3The participants searched either for a nonndashminima-parsed tar-get among uncut distractors (A) or for a minima-parsed targetamong uncut distractors (B)

EARLY COMPUTATION OF PART STRUCTURE 1051

cant [F(111) 5 2256 p 5 001] and this effect interactedsignificantly with search type [F(111) 5 1355 p 5 004]

DiscussionAs in Experiment 3 the search for a parsed target among

unparsed distractors was quite fast and efficient both forthe minima-parsed and the nonndashminima-parsed targets(The search slopes for the minima-parsed target were12 msecitem for target present and 11 msecitem for tar-get absent The search slopes for the nonndashminima-parsedtarget were 16 msecitem for target present and 206 msecitem for target absent)

However the participants were significantly faster (onaverage by 49 msec) at detecting the presence or absenceof the target shape when it was parsed with a non-minimacut than when it was parsed with a minima cut This repli-cates the results of Experiment 3 with shapes whose partswere neither symmetric nor simple familiar shapes andwhose part boundaries were smooth rather than tangentdiscontinuities As in Experiment 3 these results weremost striking for the target-absent trials It took the par-ticipants 70 msec longer on average to determine the ab-

sence of a part cut when they were looking for it at nega-tive minima than when they were looking for it elsewhereeven though the search displays were identical in bothcases (consisting simply of identical uncut shapes)

The magnitude of the effect was somewhat smaller thanit was in Experiment 3 As in Experiment 2 this differ-ence reflects the fact that the part boundaries in Figure 9are smooth with low curvature as compared with thesharp corners in Figure 6 a change that has been demon-strated to reduce the salience of perceived part structure(Hoffman amp Singh 1997)

GENERAL DISCUSSION

We set out to address the question of whether parsing atnegative minima occurs preattentivelymdashor at least rapidlyand early in visual processing In Experiment 1 we foundthat whereas the search for a nonndashminima-parsed targetamong minima-parsed distractors was fast and efficientthe search for a minima-parsed target among nonndashminima-parsed distractors was slow and inefficient This asymme-try demonstrates that parsing at negative minima occurs

Figure 15 The mean reaction times for correct trials in Experiment 4 As in Experiment 3the parsed target popped out among uncut distractor shapes both when the target wasparsed using a minima cut and when it was parsed using a non-minima cut However eventhough shapes are neither symmetric nor simple familiar shapes and their part boundariesare smoothed rather than concave corners the participants were significantly faster (on av-erage by 49 msec) at detecting the presence or absence of the parsed target when it wasparsed with a non-minima cut than when it was parsed with a minima cut

EARLY COMPUTATION OF PART STRUCTURE 1051

cant [F(111) 5 2256 p 5 001] and this effect interactedsignificantly with search type [F(111) 5 1355 p 5 004]

DiscussionAs in Experiment 3 the search for a parsed target among

unparsed distractors was quite fast and efficient both forthe minima-parsed and the nonndashminima-parsed targets(The search slopes for the minima-parsed target were12 msecitem for target present and 11 msecitem for tar-get absent The search slopes for the nonndashminima-parsedtarget were 16 msecitem for target present and 206 msecitem for target absent)

However the participants were significantly faster (onaverage by 49 msec) at detecting the presence or absenceof the target shape when it was parsed with a non-minimacut than when it was parsed with a minima cut This repli-cates the results of Experiment 3 with shapes whose partswere neither symmetric nor simple familiar shapes andwhose part boundaries were smooth rather than tangentdiscontinuities As in Experiment 3 these results weremost striking for the target-absent trials It took the par-ticipants 70 msec longer on average to determine the ab-

sence of a part cut when they were looking for it at nega-tive minima than when they were looking for it elsewhereeven though the search displays were identical in bothcases (consisting simply of identical uncut shapes)

The magnitude of the effect was somewhat smaller thanit was in Experiment 3 As in Experiment 2 this differ-ence reflects the fact that the part boundaries in Figure 9are smooth with low curvature as compared with thesharp corners in Figure 6 a change that has been demon-strated to reduce the salience of perceived part structure(Hoffman amp Singh 1997)

GENERAL DISCUSSION

We set out to address the question of whether parsing atnegative minima occurs preattentivelymdashor at least rapidlyand early in visual processing In Experiment 1 we foundthat whereas the search for a nonndashminima-parsed targetamong minima-parsed distractors was fast and efficientthe search for a minima-parsed target among nonndashminima-parsed distractors was slow and inefficient This asymme-try demonstrates that parsing at negative minima occurs

Figure 15 The mean reaction times for correct trials in Experiment 4 As in Experiment 3the parsed target popped out among uncut distractor shapes both when the target wasparsed using a minima cut and when it was parsed using a non-minima cut However eventhough shapes are neither symmetric nor simple familiar shapes and their part boundariesare smoothed rather than concave corners the participants were significantly faster (on av-erage by 49 msec) at detecting the presence or absence of the parsed target when it wasparsed with a non-minima cut than when it was parsed with a minima cut

1052 XU AND SINGH

rapidly and early in visual processing Experiment 2 repli-cated the search asymmetry of Experiment 1 with shapeswhose parts are neither symmetric nor simple familiargeometric shapes and whose part boundaries are smoothrather than sharp corners

In Experiments 3 and 4 we used the same shapes as inExperiments 1 and 2 respectively but asked the partici-pants to search either for a minima-parsed target amonguncut distractors or for a nonndashminima-parsed target amonguncut distractors We found that although the parsed shapepopped out in both cases participants were significantlyslower at detecting the presence or absence of the minima-parsed target than that of the nonndashminima-parsed target Itis interesting to note that an even larger difference was ob-tained for the target-absent trials even though the searchdisplays were identical in the two cases consisting only ofuncut distractor shapes The fact that a cut located at neg-ative minima was systematically harder to detect andslower to search for provides further evidence for theclaim that parsing at negative minima occurs obligatorilyMoreover parsing at negative minima influenced visual

search even when the search was already fast and effi-cient indicating that this parsing must occur rapidly andearly in visual processing

Our findings are also consistent with recent work on thepart-based nature of visual attention which has shownthat attention shifts more readily within a single part thanacross two parts of a single object (Barenholtz amp Feldman2002 Singh amp Scholl 2000 Vecera Behrmann amp Fi-lapek 2001 Vecera Behrmann amp McGoldrick 2000)The fact that parts of objects can act as units of attentionalselection also suggests that they are computed obligato-rily requiring few attentional resources for their compu-tation

One recent study (Donnelly Found amp Muumlller 2000)tentatively reached the opposite conclusion on the basis ofvisual search In particular Donnelly et al postulated thatit is easier for the visual system to search for convexshapes than to search for shapes with negative minima (orconcavities more generally) Although it is not entirelyclear why Donnelly et alrsquos conclusion differs from ours aswell as those of other researchers (recall the results ofElder amp Zucker 1993 Hulleman et al 2000 Humphreysamp Muumlller 2000 Wolfe amp Bennett 1997) it should benoted as Donnelly et al acknowledged that their analy-sis of concavities was post hoc The focus of their experi-ments was on the role of contour segments in distinguish-ing shapes preattentively and these experiments did notsystematically manipulate the presence of concavities ornegative minima

In addition to the specific findings of the present studyour experiments also provide a general method for study-ing how the visual system parses shapes into parts Ratherthan using two distinct shapes for targets and distractorsone uses the same shape but shown with two different pars-ings On the assumption that other local factors (such ascut orientation cut length etc) have been controlled forany asymmetry obtained in visual search is then indicativeof a difference in the perceived naturalness of the twoparsings

For the shapes we studied in this article the perceptu-ally natural part cuts were always obtained by joining thetwo negative minima on the shapes In general howeverthe minima rule is not by itself sufficient to define the partstructure of a shape The minima rule gives negative min-ima as boundaries between parts for two-dimensionalshapes these are points on the bounding contour of theshape It does not give part cuts that segment the shapehowever which are needed to determine part structure Forexample if a shape has more than two negative minimathey may be joined in more than one way to give part cuts(see Figures 16A and 16B Beusmans Hoffman amp Ben-nett 1987 Siddiqi amp Kimia 1995) In addition even if ashape has precisely two negative minima joining themmay not always give a natural parsing of the shape (seeFigures 16C and 16D Singh et al 1999) Geometric fac-tors other than negative minima have been shown to playan important role in determining part structures (eg cutlength boundary strength good continuation local sym-

Figure 16 Examples demonstrating that points of negativeminima are not by themselves sufficient to define part structuresIf a shape contains more than two negative minima these may bepaired in different ways to give part cuts (A and B) Even if ashape has only two negative minima joining them may not nec-essarily give perceptually natural part structures (C and D)

EARLY COMPUTATION OF PART STRUCTURE 1053

metry etc see Singh amp Hoffman 2001 Singh et al1999) The methodology described in this article willallow us to investigate in future studies whether parsingsdetermined by other geometric factors also occur rapidlyin early stages of visual processing

Because the shapes we used in this article were quitesimple and their part structures were unambiguous otherschemes of shape representation and parsing would alsopredict the same perceived part structures for our stimuliFor example Burbeck and Pizerrsquos (1995) model of objectrepresentation by cores and Siddiqi and Kimiarsquos (1995)parsing scheme involving limbs and necks would also pre-dict the perceptually natural parsings depicted in Figures6A and 9A Our goal in this article was simply to testwhether such perceptually natural parsings are computedrapidly and early in visual processing for which we foundample evidence In future work the visual search method-ology can be used to compare directly the relative meritsof these alternative parsing schemes

Finally our data speak to a broader issue in the visualcomputation of parts Historically two main approacheshave been taken toward the problem of the computing ofparts According to the primitive-shapes approach toparts the visual system parses shapes by looking for a pre-defined set of basic shapes in images (eg Biederman1987 Marr amp Nishihara 1978 Winston 1975) Essen-tially it finds parts by fitting these basic shapes to imagesOn the other hand according to the geometric-constraintsapproach the visual system does not store any such set ofprimitive shapes but rather uses general geometric con-straintsmdashbased on intrinsic shape geometry alonemdashto de-f ine boundaries and cuts between parts (Hoffman ampRichards 1984 Hoffman amp Singh 1997 Singh amp Hoff-man 2001 Singh et al 1999) One problem faced by thebasic-shapes approach is that it can find only those partsthat belong to the prespecified set of basic shapes For thegeometric-constraints approach however parts do notneed to belong to a prespecified set of shape primitives6In the present set of experiments visual search asymme-try and feature search differences resulting from parsingat negative minima were observed for shapes regardlessof whether the resulting parts were simple familiar shapesor notmdashhence providing empirical evidence in favor ofthe geometric-constraints approach to shape parsing

REFERENCES

Attneave F (1971 December) Multistability in perception ScientificAmerican 225 63-71

Barenholtz E amp Feldman J (2002) Visual comparisons within andbetween object-parts Evidence for a single-part superiority effectManuscript submitted for publication

Baylis G C amp Driver J (1994) Parallel computation of symmetrybut not repetition in single visual objects Visual Cognition 1 377-400

Baylis G C amp Driver J (1995) Obligatory edge assignment in vi-sion The role of figure and part segmentation in symmetry detectionJournal of Experimental Psychology Human Perception amp Perfor-mance 21 1323-1342

Bertamini M Friedenberg J D amp Kubovy M (1997) Detectionof symmetry and perceptual organization The way a lock-and-keyprocess works Acta Psychologica 95 119ndash140

Beusmans J Hoffman D D amp Bennett B M (1987) Descriptionof solid shape and its inference from occluding contours Journal ofthe Optical Society of America A 4 1155-1167

Biederman I (1987) Recognition-by-components A theory of humanimage understanding Psychological Review 94 115-147

Biederman I amp Cooper E E (1991) Priming contour-deleted im-ages Evidence for intermediate representations in visual object recog-nition Cognitive Psychology 23 393-419

Braunstein M L Hoffmann D D amp Saidpour A (1989) Partsof visual objects An experimental test of the minima rule Perception18 817-826

Bruce V amp Morgan M J (1975) Violations of symmetry and repe-titions in visual patterns Perception 4 239-249

Burbeck C A amp Pizer S M (1995) Object representation by coresIdentifying and representing primitive spatial regions Vision Re-search 35 1917ndash1930

Corballis M C amp Roldan C E (1974) On the perception of sym-metrical and repeated patterns Perception amp Psychophysics 16 136-142

Donnelly N Found A amp Muumlller H J (2000) Are shape differ-ences detected in early vision Visual Cognition 7 719-741

Driver J amp Baylis G C (1995) One-sided edge assignment in vi-sion 2 Part decomposition shape description and attention to ob-jects Current Directions in Psychological Science 4 201-206

Driver J amp Baylis G C (1996) Edge-assignment and figurendashground segmentation in short-term visual matching Cognitive Psy-chology 31 248-306

Elder J amp Zucker S (1993) The effect of contour closure on therapid discrimination of two-dimensional shapes Vision Research 33981-991

Friedenberg J amp Bertamini M (2000) Contour symmetry detec-tion The influence of axis orientation and number of objects ActaPsychologica 105 107-118

Hoffman D D (1983 December) The interpretation of visual illu-sions Scientific American 249 154-162

Hoffman D D amp Richards W A (1984) Parts of recognition Cog-nition 18 65-96

Hoffman D D amp Singh M (1997) Salience of visual parts Cogni-tion 63 29-78

Hulleman J te Winkel W amp Boselie F (2000) Concavities asbasic features in visual search Evidence from search asymmetriesPerception amp Psychophysics 62 162-174

Humphreys G amp Muumlller H (2000) A search asymmetry reversedby figurendashground assignment Psychological Science 11 196ndash201

Joseph J S Chun M M amp Nakayama K (1997) Attentional re-quirements in a ldquopreattentiverdquo feature search task Nature 387 805-807

Kimia B B Tannenbaum A amp Zucker S W (1995) Shapeshocks and deformations I The components of two-dimensionalshape and the reaction-diffusion space International Journal of Com-puter Vision 15 189ndash224

Leyton M (1992) Symmetry causality mind Cambridge MA MITPress

Marr D amp Nishihara H K (1978) Representation and recognitionof three-dimensional shapes Proceedings of the Royal Society of Lon-don Series B 200 269-294

Neisser U (1967) Cognitive psychology New York Appleton-Century-Crofts

Palmer S E (1977) Hierarchical structure in perceptual representa-tion Cognitive Psychology 9 441-474

Rensink R amp Enns J (1998) Early completion of occluded objectsVision Research 38 2489-2505

Siddiqi K amp Kimia B B (1995) Parts of visual form Computationalaspects IEEE Transactions on Pattern Analysis amp Machine Intelli-gence 17 239-251

Siddiqi K Tresness K amp Kimia B B (1996) Parts of visual formPsychophysical aspects Perception 25 399-424

Singh M amp Hoffman D D (1998) Part boundaries alter the per-ception of transparency Psychological Science 9 370-378

Singh M amp Hoffman D D (2001) Part-based representations of vi-sual shape and implications for visual cognition In T Shipley ampP Kellman (Eds) From fragments to objects Segmentation and

1054 XU AND SINGH

grouping in vision (Advances in Psychology Vol 130 pp 401-459)New York Elsevier North-Holland

Singh M amp Scholl B (2000 November) Using attentional cueingto explore part structure Poster presented at the Annual Symposiumof Object Perception and Memory New Orleans

Singh M Seyranian G D amp Hoffman D D (1999) Parsing sil-houettes The short-cut rule Perception amp Psychophysics 61 636-660

Spelke E S (1994) Initial knowledge Six suggestions Cognition 50431-445

Treisman A amp Gormican S (1988) Feature analysis in early visionEvidence from search asymmetries Psychological Review 95 15-48

Treisman A amp Souther J (1985) Search asymmetry A diagnosticfor preattentive processing of separable features Journal of Experi-mental Psychology General 114 285-310

Vecera S P Behrmann M amp Filapek J C (2001) Attending to theparts of a single object Part-based attentional limitations Perceptionamp Psychophysics 63 308-321

Vecera S P Behrmann M amp McGoldrick J (2000) Selective at-tention to the parts of an object Psychonomic Bulletin amp Review 7301-308

Winston P A (1975) Learning structural descriptions from examplesIn P H Winston (Ed) The psychology of computer vision (pp 157-209) New York McGraw-Hill

Wolfe J M (1994) Guided Search 20 A revised model of visualsearch Psychonomic Bulletin amp Review 1 202-238

Wolfe J M (1998) What can 1 million trials tell us about visual searchPsychological Science 9 33-39

Wolfe J M amp Bennett S C (1997) Preattentive object files Shape-less bundles of basic features Vision Research 37 25-43

Wolfe J M Yee A amp Friedman-Hill S R (1992) Curvature is abasic feature for visual search tasks Perception 21 465-480

NOTES

1 Throughout our concern is with parts of objects bounded by con-tinuous surfaces rather than say with Gestalt groups (such as arrays of

dots or line segments) whose ldquopartsrdquo can of course consist of discon-nected elements

2 The differential-geometric principle of transversality ensures thatwhenever 2 three-dimensional shapes intersect generically the locus oftheir intersection lies with a probability of 1 in a concave creasemdashthatis a concave tangent discontinuity and smoothing such a concave creaseyields a locus of negative minima of curvature (see Hoffman amp Richards1984 and Hoffman amp Singh 1997 for details)

3 It should be noted that rapid computation can also be indicated bya slowdown in search performance owing to the preemption of featuresthat were previously easy to access (eg Rensink amp Enns 1998)

4 For any attribute that has preattentive status (say color or orienta-tion) it is clear that a pop-out will occur only if the target and the dis-tractors differ sufficiently along that dimension If they are too closealong that dimension (eg very similar hues or orientations) searchslopes will get large despite the featural status of the attribute In thecase of convex and concave corners lower turning angles simply trans-late into smaller differences between the two kinds of corners

5 A pilot study showed that both types of search (ie search for minima-parsed targets and for nonndashminima-parsed targets among uncut distrac-tors) were fast and efficient As a result we decided to use 2000 msec asthe cutoff threshold for RT truncation instead of the 3000 msec usedpreviously This change in cutoff threshold led to the elimination of onlytwo data points in Experiment 3 and of a single data point in Experi-ment 4 and did not significantly alter the results

6 It should be noted that the theories of Marr and Nishihara (1978)and Biederman (1987) have much broader scope than the minima rulesince they are general theories of shape representation and object recog-nition not just of shape segmentation Comparison of them with the min-ima rule is valid however insofar as these theories also make specificproposals regarding how the visual system segments objects into parts

(Manuscript received July 31 2001revision accepted for publication February 26 2002)