Journal of Experimental Psychology:Human Perception and Performance1977, Vol. 3, No, 3, 473-483

Perceived Shape at a Slant as a Function of Processing Timeand Processing Load

William Epstein, Gary Hatfield, and Gerard MuiseUniversity of Wisconsin—Madison

Shape and slant judgments of rotated or frontoparallel ellipses were elicitedfrom three groups of 10 subjects. A masking stimulus was introduced tocontrol processing time. Backward masking trials were presented with inter-stimulus intervals of 0, 25, and 50 msec, Reduction of processing time alteredshape judgments in the direction of projective shape and slant judgments inthe direction of frontoparallelness. This finding is consistent with the shape-slant invariance hypothesis. In order to study the effects of processing load,one group of subjects was given prior knowledge of the kind of judgmentto be made on each trial, one group had no prior knowledge, and a thirdgroup made both judgments on each trial. The effects of the processing loadmanipulation were interpreted in terms of the role of attention in perceptualencoding. Consistent with previous findings, allocation of attention did notaffect perceptual encoding.

Leibowitz and Bourne (1956) found thatexposure duration affected the shape judg-ment of a circle rotated in depth. Reductionof exposure duration was accompanied bydeviations from shape constancy, shapematches that were in closer agreement withprojective shape than with objective shape.For exposure durations of 100 msec andless, the matches conformed perfectly to pro-jective shape, that is, the subject selected asa match an elliptical shape equal to thefrontoparallel projection of the rotatedcircle.

The effect of exposure duration is analo-gous to the effect of reduction of depth in-formation in a variety of perceptual con-stancy experiments (Epstein, 1973, 1977;Epstein & Park, 1963; Epstein, Park, &Casey, 1961). In fact, Leibowitz andBourne (1956) suggested that the effect ofexposure duration on shape judgment mayhave been mediated by perceived orienta-tion. The shape-slant invariance hypothesis(Epstein, 1973; Epstein & Park, 1963) pro-

Requests for reprints should be sent to WilliamEpstein, Department of Psychology, University ofWisconsin, Madison, Wisconsin 53706.

vides a context for elaboration of Leibowitzand Bourne's speculation. According to thishypothesis, projective shape determines an in-variant relationship between perceived shapeand perceived slant. Since only a single ob-jective shape-objective orientation combina-tion was used in the Leibowitz and Bourneexperiment, projective shape was the sameon all trials. Consequently, to be consistentwith the shape-slant hypothesis, the reduc-tions of exposure duration should have beenaccompanied by underestimations of per-ceived slant. For the 100-msec exposure,which yielded a perfect projective shapematch, the circle should have been perceivedas frontoparallel, although objectively it wasrotated 30°. One aim of the present experi-ment was to evaluate this interpretation bysecuring slant judgments as well as shapejudgments.

The procedure we employed differed inthree essential respects from Leibowitz andBourne's (1956) procedure, (a) Ratherthan presenting a single standard shape re-peatedly at a single orientation, we presentedtwo families of shape-slant combinations.Within each family, all shape-slant combi-nations produced the same projective shape.This arrangement allowed a more satisfac-

473

474 W. EPSTEIN, G. HATFIELD, AND G. MUISE

tory evaluation of the effect of exposureduration on perceived shape at a slant bytesting discrimination of differences in ob-jective shape in the presence of projectiveequivalence, (b) In four unreported experi-ments in which we followed Leibowitz andBourne's procedure of varying exposuretime, we consistently found significant ef-fects of exposure time: At very brief dura-tions, judged shape tended toward projec-tive shape; while for longer durations, forexample, 500 msec, constancy was nearlyperfect. Although these findings were in gen-eral agreement with Leibowitz and Bourne,we were unable to secure perfect projectiveshape matches even with an exposure du-ration as low as 10 msec. Our lack of suc-cess in this respect led us to question theadequacy of the exposure duration manipu-lation, A simple manipulation of exposuretime provides no control of processing in theperiod immediately following stimulus off-set. For this reason, exposure time and pro-cessing time probably are not synchronous.Accordingly, in the present study, insteadof varying exposure time we varied pro-cessing time. Exposure time was constanton all trials for an individual subject; pro-cessing time was varied by varying thestimulus onset asynchrony in a backwardmasking paradigm, (c) In Leibowitz andBourne's procedure, all of the shapes thatconstituted the comparison series from whichsubjects selected the match to the standardhad the same vertical-linear dimension asthe standard. Consequently, the possibilitycannot be dismissed that subjects based theirresponses on a match between the projectedhorizontal extents rather than shape match.In our comparison series, the shapes werescale reductions, so that subjects were in-duced to make shape judgments.

The second aim of our study was to de-termine whether perception of shape at aslant is affected by attentional control andtemporal capacity limitations. Our concernmay be explained by comparing Leibowitzand Bourne's (1956) procedure with thepresent procedure. In the former case, thesubjects were tested only for shape; whilein the present case, both shape and slant

perception were tested. Consider the firstprocedure. Are we justified in drawing con-clusions about perceiving shape at a slantwhen a subject has been directed to reportonly shape? It may be contended that sinceshape and slant normally are packaged as asingle perceptual unit, emphasis on only oneof these elements alters the task of percep-tual processing. Despite the fact that ques-tions of this sort often are adumbrated inthe literature on perceptual constancies,there has been no direct empirical investi-gation of the matter.

The question was evaluated in the presentstudy by varying the specificity and timingof the tests. On only tests, the subject wasinformed in advance that only a single at-tribute, shape or slant, would be tested. Onboth tests, the subject was informed in ad-vance that both shape and slant would betested. On either tests, the subject was in-formed that either shape or slant would beprobed, but that the attribute would be des-ignated after presentation of the standard.We looked at two aspects of the perform-ance under these three conditions: (a) theeffect on shape judgments and slant judg-ments and (b) the effect on the relationshipbetween perceived shape and perceived slant.If testing a single property, shape or slant,alters the nature of the process, then per-formance should not be the same on onlyand both tests. The either tests were equiva-lent to both tests in respect to processingload and equivalent to only tests in termsof demands on retrieval. In the event thata difference between only and both tests isobtained, the either tests should help to de-termine whether the difference is in initialprocessing or in retrieval. The rationale isreminiscent of the logic underlying the anal-ysis of selective attention in the experimentsof Massaro (1975), Shiffrin, Gardner, andAlltneyer (1973), and Shiffrin, McKay, andShaffer (1976).

The variations of test type also bear ona methodological problem in experimentalassessments of the various algorithms forspace perception (Epstein, 1973), for ex-ample, the size-distance invariance hypoth-esis and the shape-slant invariance hypothe-

PERCEIVED SHAPE AND PROCESSING DEMANDS 475

sis. When the algorithms are assessed byexamining the correlations between two per-ceptual variables, for example, perceivedsize and perceived distance or perceivedshape and perceived slant, in what sequenceshould the to-be-correlated judgments besecured? When the judgments of the sametest object are secured in immediate suc-cession, first one and then the other, thereis the risk of inflating the correlation due toinduction of a response set that favors pack-aging the two judgments in a reasonableway. In order to avoid this potential artifact,the judgments of the same object often areseparated by intervening judgments of othertargets. However, this procedure entails therisk that the intervening experience hasmodified the perceptual or response system,so that the obtained correlation does notaccurately reflect the relationship that pre-vailed at either the occasion of the firstprobe or the second. Examination of thecorrelations between perceived shape andperceived slant across the three trial typesin the present experiment will show whetherthese methodological concerns are in factwarranted.

MethodSubjects

Thirty-four undergraduates participated in theexperiment for course credit, money ($2.50 persession), or a combination of the two at theiroption.

Stimuli

The standard stimuli were eight ellipses cutfrom 1/16 in. (.159 cm) white posterboard andaffixed to 2% in. (6.35 cm) high black stalks. Theedges of the stimuli were beveled to minimize edgecues. The length of the vertical axis in each stan-dard was 5.3 cm. The horizontal axes varied from3.29 to 15.64 cm. The stimuli were partitioned intotwo sets, Set 1 consisting of four stimuli havinghorizontal-vertical axis ratios of .62, .79, 1.00, and1.46; and Set 2 consisting of four stimuli havinghorizontal-vertical axis ratios of 1.25, 1.61, 2.03,and 2.95. Within each set, one shape was presentedat only one orientation, 0° (frontoparallel), 39°,52", or 65°. For half of the subjects, the stimuliin Set 1 were rotated clockwise, and those in Set2 were rotated counterclockwise; for the otherhalf, the converse obtained. The objective shape-objective orientation pairs were such that all

shapes in Set 1 projected a horizontal-verticalratio of .62 (vertical subtense of 4.5°, horizontalsubtense of 2.8°), and all shapes in Set 2 pro-jected a horizontal-vertical ratio of 1.25 (verticalsubtense of 4.5°, horizontal subtense of 5.50).1

The masking stimulus consisted of randomlyshaped and randomly arranged pieces of whitepaper, each less than 1 square centimeter in size,attached to black matte construction paper.

The comparison stimuli for shape were 11scaled-down drawings, each with a vertical axisof 2.2 cm. The horizontal axes varied to produceshapes with horizontal-vertical axis ratios rangingfrom .45 to 3.8. The shapes were arranged onsingle sheets of paper in a single column, eitherin ascending or descending order. Embedded withinthe 11 comparison shapes were the 8 shapes cor-responding to the horizontal-vertical axis ratiosof the stimuli, one shape narrower than any ofthe stimuli (ratio of .45), one wider (ratio of3.8), and two that served as interpolations be-tween the shapes of the first and second stimuliin each set (ratios of .70 and 1.46, the latter actingboth as an intermediate and as a match to Set 1).

The comparison stimuli for orientation were 13circles (2.2 cm in diameter), each containing asingle line drawn along a diameter. Each drawingrepresented a top view of the stimulus at one ori-entation relative to the observer. The representedorientations ranged from 78° counterclockwisethrough 0 through 78° clockwise in 13° incre-ments. The stimuli were arranged on a single sheetof paper in either ascending or descending order.

lindividual sheets of comparison stimuli wereprepared for each trial and placed in a predeter-mined random order in a loose-leaf binder, so thatonly the current trial information was available tothe subject. Each comparison stimulus was num-bered, and the subject recorded the response bywriting its number on a new index card for eachtrial.

Apparatus

The apparatus was a modified two-field tachisto-scope controlled by an Automated Data System1248 timer. Each arm of the tachistoscope was 54cm long, 23.5 cm wide, and 25 cm high. A light-proof extension of the direct-view channel of thetachistoscope provided access to a calibrated diskinto which the stimuli could be inserted. The mask-ing stimulus was in the reflected arm of the tach-istoscope at a distance of 59 cm from the viewer'seyes. The standard stimuli were located 67 cm

lThe shapes within each set were equivalentwhen projected orthogonally onto the frontoparal-lel plane. The projection of the shapes onto theretina was subject to perspective distortions (forrotated stimuli) and binocular disparity, so thatthe retinal projections of the shapes within eachset were not precisely equivalent.

476 W. EPSTEIN, G. HATFIELD, AND G. MUISE

Table 1Mean Shape Judgment Averaged for all EightStandards as a Function of Masking Conditionand Test Type

Masking condition

Group

OnlyEitherBoth (shape first)Both (slant first)

Inter*

0

1.1741.2981.2421.246

stimulus interval(in msec)

25

1.2331.3631.2681.280

SO

1.2781.3961.3031.306

No mask

1.5221.5471.4111.475

from the subject and were viewed binocularlythrough a 10 X 4 cm window framed by a viewinghood that excluded ambient light and restrictedhead movement. The viewing field was restrictedto the standard and the masking stimulus by oc-cluders appropriately placed in each channel of thetachistoscope. Illumination was provided by afluorescent light in each arm, located in front ofand below the stimuli. The luminance level in eachdisplay field was 3.0 cd/m2.

Exposure DurationsOn all trials calling for a mask, the mask was

exposed for 400 msec. The interstimulus intervalwas 0, 25, or SO msec. When no mask was pre-sented, offset of the standard was followed by anempty dark field. Exposure durations for the stan-dards were determined for each subject individu-ally in the manner explained below.

ProcedureA subject served in three 1-hour-long sessions,

each separated by 24 hours. The instructions em-phasized phenomenal (apparent) shape and orien-tation judgments (Carlson & Tassone, 1967; Ep-stein, 1963; Epstein, Bontrager, & Park, 1962).The subject was directed to base the response onan immediate impression of shape or orientation.The first session was devoted to determining theappropriate exposure duration for each subjectindividually. We searched for an exposure dura-tion that satisfied two criteria: (a) approximationof the minimum duration that allowed a high de-gree of constancy (defined as a Brunswik ratioa

of .70 or higher) and (b) a duration that wouldbe compatible with a significant masking effect(defined as a mask-induced reduction of the Bruns-wik ratio of at least .20 from the no-mask level).These criteria could not be satisfied for all sub-jects. Three subjects were dismissed for failure toexhibit a Brunswik ratio of at least .70, and onewas dismissed for failure to exhibit a reliablemasking effect.

The following routine was used to establish thedesired exposure duration. First there were eight

trials, one for each standard, at a 500-msec ex-posure with no mask. Responses to both shape andorientation were elicited on each of these trials.A Brunswik ratio was calculated for the six stan-dards that were rotated from the frontal plane.Another series of eight trials at 200 msec with nomask followed, and another Brunswik ratio wascalculated. These trials familiarized the subjectwith the procedure and the class of stimuli andhelped the experimenter narrow the range of du-rations to be considered. Two practice trials withthe mask, followed by three blocks of 16 trials(eight mask and eight no-mask trials randomlyinterspersed) were then administered. The expo-sure duration for the first block was selected onthe basis of the performance on the previous trialsat 500 and 200 msec. A duration of 150 msec wasmost often chosen. The interstimulus interval(ISI) on mask trials was always zero. Shapejudgments were elicited on all of the trials andorientation judgments on three trials in each blockof 16 to ensure that the subject would not adopt ashape-only set. At the end of each block, a Bruns-wik ratio was calculated, and the next stimulusduration was adjusted recursively to converge tothe above-mentioned criteria. Whenever ambiguityarose about which stimulus duration to use, thelower exposure duration was selected.

At the conclusion of the first session, the sub-jects were randomly assigned to three groups of10 according to the type of test they would receiveon the second and third days. The mean exposuredurations for the three groups did not differ (70,87, and 82 msec for only, both, and either, respec-tively). The only group had to report either shapeor slant on each trial and knew beforehand whetherit was to be shape or slant. The either group alsomade only one judgment per trial but did notknow until stimulation had been terminated whethershape or slant would be tested. The both groupjudged both shape and slant on each trial but werenot informed beforehand which they were to re-port first.

Eight practice trials were presented on eachday, followed by 64 test trials. For the only andeither groups, the test trials on each day con-sisted of the eight standards presented at each ofthe three ISIs and with no mask, once for shapejudgment and once for slant judgment. The bothgroup received the eight standards at the fourmasking conditions presented once on each day forjudgment of shape and then slant, once for judg-ment of slant and then shape. All subjects receiveddifferent permutations of the test trials for allsessions.

2 A Brunswik ratio (Hochberg, 1971) is com-puted according to the formula (a — p ) / ( o — p ) ,where a is judged or perceived shape, p is projec-tive shape, and o is objective shape (shape is de-fined in terms of the width-height ratio).

PERCEIVED SHAPE AND PROCESSING DEMANDS 477

1.46

;iLU

'fLLJ itr I

.79

.62

OBJECTIVEMATCH

SET I

295

PSi,012.03

1.61

1.25

® NO MASKD 50 MSEC ISI

O 25 MSEC ISI

A 0 MSEC ISIOBJECTIVE/MATCH

x/SET 2

.62 79 1.00 1.46 1.25 1.61 2.03OBJECTIVE SHAPE (WIDTH-HEIGHT RATIOS)

2.95

1.46 2.95r

.62(0°)

.79(39°)

1.00(52°)

1.46 1.25 1.61 2.03(65°) (0°) (39°) (52°)

TRANSFORMED OBJECTIVE ORIENTATION

2.95(65°)

Figure 1. Mean shape scores and transformed mean orientation scores under each maskingcondition for all subjects across test type. (Sets 1 and 2 are projectively equivalent families ofshapes. ISI = interstimulus interval.)

Results

Separate analyses of variance (Test TypeX Stimulus Set X Standard X MaskingCondition) of shape and orientation judg-ments yielded no significant main effect orinteraction of test type. The conclusion thattest type did not influence the processing ofshape at a slant is confirmed by the meanshape matches (expressed as width-heightratios) presented in Table 1. Since test typewas not a significant variable, the resultspresented henceforth pertain to mean scoresacross test type.

Shape Judgments

The upper half of Figure 1 shows the ef-fect of the masking variable on judged

shape. In the absence of a mask, the fourshapes within each set were discriminated.The line labeled objective match and hav-ing a slope of 1.0 represents the set of judg-ments that would exhibit perfect constancy.The slopes of the best-fitting line for thejudgments in the absence of the mask were.80 and .79 for Sets 1 and 2, respectively.The Brunswik ratio provides another sum-mary of these results. A ratio of 1,0 repre-sents perfect constancy. The obtained ratiosin the absence of the mask were 1.03 and.90 for Sets 1 and 2, respectively.

It is also plain from Figure 1 that intro-duction of the mask drastically reduced con-stancy (the masking variable was significantat p < .001). For the ISI of zero, the Bruns-

478 W. EPSTEIN, G. HATFIELD, AND G. MUISE

Table 2Standard Deviation of Shape Judgments for Each Stimulus Under Each Masking Condition

Masking condition

Interstimulus interval (in msec)

of standard

.62

.791.001.46

1.251.612.032.9S

of standard

0°39°52°65°

0°39°52°65°

0

Setl

.190

.404

.289

.296

Set 2

.223

.258

.364

.440

25

.209

.252

.219

.400

.283

.279

.414

.555

50

.152

.187

.226

.362

.216

.404

.424

.525

No mask

.195

.203

.282

.575

.321

.372

.480

.572

wik ratios for Sets 1 and 2 were reduced to.58 and .46, respectively. The slopes for thiscondition were .19 and .29, respectively. Aslope of zero would result from projectivematching. The obtained slopes for the ISIof zero indicate that subjects only minimallydiscriminated among the projectively equiva-lent rotated and frontoparallel shapes withinSets 1 and 2. Figure 1 suggests that the ef-fectiveness of the mask tended to diminishfor longer ISIs, although even the ISI of 50msec had a pronounced effect. The mask af-fected the judgment of rotated shapes only,which is reflected in a significant (p < .001)Masking X Shape Withn Set interaction.Since for frontoparallel standards, objectiveand projective axis ratios do not differ, nomasking effect was expected.

Examination of the SDs reported inTable 2 shows a clear tendency for thevariability of the shape judgments of therotated shapes to be greater in the no-maskcondition than in the masking conditions.Variability also increased in most condi-tions as the standards increased in widthand degree of rotation, as can be seen byexamination of the columns in Table 2.

Orientation Judgments

Table 3 shows the mean orientation judg-ments. Without exception the shapes in Set

2 were judged to be less rotated than theshapes in Set 1 (the effect of set was sig-nificant, p < .001). With the exception ofthe frontoparallel orientation, the orienta-tions for Set 2 were greatly underestimated.As a rule, orientation judgments of the ro-tated shapes when the mask was presentwere smaller than when the mask was ab-sent (the masking variable was significant,/><.001). The slopes of the best-fittinglines shown in Table 3 increase regularlyfrom ISIs of zero through the longer ISIsand are steepest when no mask was present,as is consistent with the significant (p <.001) Masking X Slant Within Set inter-action. Variabilities were not affected bymasking or orientation.

In the lower half of Figure 1, the orienta-tion judgments have been transformed sothat the orientation and shape judgmentsare represented in a common metric. Thetransformed orientation values (TO) resultfrom a nonlinear rescaling of the mean ori-entation values across subjects. The numeri-cal value of a transformed score representsthe shape (width-height ratio) that wouldbe compatible with the actual projectiveshape of the standard involved and the ob-tained judged orientation in degrees. Thus,for the standard having a horizontal-verticalratio of .62 and presented in the frontal

PERCEIVED SHAPE AND PROCESSING DEMANDS 479

plane, the transformation is as follows: TO= .62/cos ®, where .62 is the projectiveshape of the standard, and ® is the obtainedorientation score in degrees. As orientationincreases from 0°, the denominator in theabove formula diminishes at a positively accel-erated rate. Consequently, the transforma-tion has the effect of compressing the scalefor orientation between 0° and about 35°,so that incremental changes in orientationwithin this range produce relatively smallchanges in TO.

Examination of the upper and lowerhalves of Figure 1 permits comparison ofthe effects of the mask on shape judgmentswith the effects on orientation judgments.Introduction of the mask and decreases inISI moved the shape judgments away fromobjective matching. Consistent with theshape-slant invariance hypothesis, these de-viations from shape constancy were accom-panied by increasing underestimations oforientation as processing time was reduced.However, as is apparent from Figure 1, the

effects of the mask on shape and orientationjudgments were not precisely equivalent. Inparticular, the masking conditions produceda greater spread among the shape scoresthan among the slant scores. The relevanceof these findings for the invariance hypothe-sis will be considered in the Discussionsection.

Since exposure duration of the standardwas determined independently for each sub-ject, the durations (stimulus onset asyn-chronies, in the case of the masking trials)varied considerably among subjects. To de-termine the effect of this methodologicallyintroduced variable, the subjects weregrouped into five classes according to thefollowing exposure durations: 25, 50, 75,100-125, and 150-200 msec. Analysis ofvariance for unequal Ns using Henderson'sMethod I failed to yield a significant maineffect or interaction of exposure durationfor either shape or orientation judgments.Other features of this analysis were consist-ent .with the findings reported earlier.

Table 3Mean Orientation Scores in Degrees for Each Standard Under Each Masking Condition

Masking condition

Orientationof standard

Interstimulus interval (in msec)

25 SO No mask

0395265

Regression*SlopeIntercept

19.2 (25.3)30.7 (22.3)41.0 (23.3)45.5 (23.4)

Set!

17.5 (24.12)28.3 (23.1)41.5 (20.4)48.3 (22.3)

17.7 (22.9)34.4 (24.1)42.5 (20.8)55.5 (17.4)

.332.7

.411.8

.53-1.3

13.4 (20.0)33.4 (20.3)45.7 (18.8)56.3 (17.2)

Regression*SlopeIntercept

0395265

.4018.3

3.4 (10.7)14.3 (16.6)19.3 (13.8)25.8 (16.1)

.4115.6

Set 2

3.3 (6.7)14.2 (13.4)22.9 (16.0)30.9 (15.8)

.5511.8

3.2 (9.7)16.0 (12.7)23.7 (13.2)34.6 (13.0)

.5711.9

1.5 (4.0)21.6 (14.3)28.3 (12.69)38.5 (14.2)

.55

Note. First entry is the mean; second entry (shown in parentheses) is the standard deviation.8 The regression analysis was performed for judged slant on objective slant.

480 W. EPSTEIN, G. HATFIELD, AND G. MUISE

Table 4Regression (r) Analysis of Judged Shape (Y) and Transformed Judged Slant (X) Basedon Group Averages

Masking condition

Interstimulus interval (in msec)

Statistic 0

rxy .934Y .75* + ,X 1.17F-

rxy .974Y 3.60* -

X .26F +

,27.22

.31,87

25

Set 1

.955.95X + .13.96 Y - .06

Set 2

.9962.19* - .12.45 Y + .57

50

.995MX +1.18F-

.9951.97* -.50 K +

.17.19

.90.47

No mask

.976.76* +

1.25F -

.9982.80* -.36K + .

.29

.32

.2070

Correlation Between Judged Shape andJudged Orientation

Table 4 shows that the correlations be-tween judged shape and transformed orien-tation were high. This indicates that "thefunction relating judged shape to judgedorientation was nearly linear, as is predictedby the shape-slant invariance hypothesis.Since the transformed orientation scores arein the same metric as the shape scores, per-fect congruence between orientation andshape judgments would result in a regres-sion line slope of 1.0. This would occur ifthe masking conditions had precisely equiva-lent effects upon shape and orientation judg-ments. Inspection of Table 4 reveals thatthis was much more nearly the case forjudgments of the standards in Set 1 thanfor Set 2. The extreme slopes in Set 2 re-flect the previously mentioned fact thatthe masking conditions produced a greaterspread among shape scores than amongslant scores. Nonetheless, from inspectionof Figure 1, it is apparent that for both sets,if shape scores are adjusted downwards,taking the scores obtained for the fronto-parallel standards (the standard with shape.62 in Set 1 and 1.25 in Set 2) as a basefor projective shape matching, judged shapeand judged slant become nearly congruentfor the three masking conditions, while slant

judgments still fall below shape judgmentsfor the no-mask condition.

In order to further assess the effects oftest type, a regression analysis was per-formed on the mean judged shape and trans-formed judged orientation scores withineach instructional group. Comparison of thecoefficients and regression line slopes re-vealed no consistent differences among thetest types. However, an isolated exceptionbears mentioning. For Set 2 at the 0- and25-msec ISIs, the subjects who judged bothshape and slant on the same trial exhibitedhigher correlation coefficients (range: .80 to.98; mean: .92) than those who judgedshape and slant on separate trials (range:.07 to .98; mean: .48). Furthermore, thefact that the regression line slopes for theboth group for Set 2, 0 msec and 25 msec,were closer to 1.00 (range of deviation from1.00: .09 to .43) than the slopes for theother groups (range of deviation from 1.00:.45 to .93) indicates that the effects of themask on shape and slant judgments weremore nearly equivalent for the both groupthan for the other groups under these con-ditions. These isolated findings provide lim-ited justification for the methodological con-cern, expressed in the introduction, that eli-citation of both types of judgment on asingle trial may influence the results in favorof the invariance hypothesis (high correla-

PERCEIVED SHAPE AND PROCESSING DEMANDS 481

tion and more nearly congruent shape andslant scores).

Discussion

The masking stimulus was utilized to con-trol processing time. Introduction of themask did not disrupt formation of the sen-sory icon, that is, contour formation, sincefor all of the ISIs the reports were withinthe range of values expected given intactprojective shape information. Nor did themask increase variability. In fact, as wasnoted, variability of the shape judgmentswas decreased by the introduction of themask. The principal effect of the mask onperceived shape was to induce deviationsfrom shape constancy, so that the inferredfunction relating judged shape to the ob-jective shape of the standards was in betteragreement with projective than with objec-tive shape matching. The greatest effect wasobtained with the ISI of zero. The 25- and50-msec ISIs yielded shape judgments in-termediate between the near projective matchof the zero ISI and the near objectivematch of the no-mask condition.

In the introduction, we derived an inter-pretation of Leibowitz and Bourne's (1956)data from the general hypothesis that per-ceived shape is the result of combining pro-jective shape information and perceivedorientation. This account was intended toapply also to the effect of masking on per-ceived shape. Two expectations were gen-erated by this account: (a) Introduction ofa mask should lead to underestimation oforientation relative to judged orientation inthe absence of a mask, (b) The effect of themask on perceived orientation should beproportional to the effect on perceivedshape. The obtained effect of the mask onjudged orientation and the high correlationsbetween shape and slant judgments satisfyboth of these expectations. We concludethat the effect upon judged shape of themask in our experiment and of exposureduration in Leibowitz and Bourne's studywas mediated by an i effect upon the dis-crimination of orientation, in accordancewith the shape-slant invariance hypothesis.

The two expectations just mentioned areconsistent with a weak form of the shape-slant invariance hypothesis, which requiresonly that the effects of the mask on shapeand slant perception be proportional. Astronger form of the invariance hypothesiswould require perceived shape and perceivedorientation to be in strict congruence withthe shape-slant algorithm. For our data, thisrequirement would be satisfied only if thelines representing judged shape and trans-formed judged orientation in Figure 1 werecongruent under each masking condition.While our data does not support thestronger form of the hypothesis, neither doesit provide falsifying evidence. For our datato be sufficient as falsifying evidence, itwould have to be assumed that reported orjudged orientation is an accurate measureof orientation information as registered bythe perceptual system and as combined withshape information to yield perceived shape.Since a distinction between registered andreported stimulus features has been pro-posed for other constancies, such as for size(Epstein, 1973, 1977, Chap. 13), the aboveassumption is unwarranted. Our data istherefore mute with respect to the strongform of the invariance hypothesis.

Early studies of shape constancy summa-rized by Koffka (1935, pp. 233-235) re-ported that constancy decreases as the de-gree of rotation from the frontal plane in-creases. This finding has been replicated bysubsequent investigations (summarized byEpstein & Park, 1963) and is buttressed bythe observation of a similar falling off forsize constancy with increasing viewing dis-tances. However, reexamination of the re-sults for the no-mask condition depicted inthe top panels of Figure 1 shows that, inthe present experiment, shape constancyvaried little for rotations from frontoparallelup to 65°.

The discrepancy between the present andearlier results may be due to differences be-tween our stimuli and those used previ-ously: We varied objective shape as a func-tion of orientation, keeping projective shapeconstant; whereas in the earlier studies,objective shape was held constant at all

482 W. EPSTEIN, G. HATFIELD, AND G. MUISE

orientations. Since under our procedure ob-ject width increased with orientation, dis-parity and convergence cues were not de-graded at extreme orientations as theywould have been under the earlier proce-dure. Orientation was therefore less likelyto be underestimated at extreme orien-tations, which is consistent with our find-ing that under the full-cue (no-mask) con-dition, the underestimation of orientationwas proportionally equivalent at all orien-tations. The conventional explanation ofthe earlier finding that shape constancydiminishes as orientation increases at-tributes the diminution to poorer discrimi-nation of extreme orientations, specificallyto underestimation that increases as objec-tive orientation increases. If the earlier re-sults did reflect an underestimation of ori-entation, a comparison with our results sug-gests that it was because orientation cueswere degraded at extreme orientations.

The earlier practice of holding objectiveshape constant at all orientations has an-other consequence that bears on the findingof underconstancy. As degree of stimulusrotation increases, variations of constantmagnitude in orientation or projective shapeare associated with relatively larger andlarger changes in objective shape. This factcoupled with the shape-slant invariance al-gorithm has specific consequences for per-ceived shape. Strict application of the algo-rithm predicts that for a given objectiveshape, a constant deviation from the veri-dical in the registration of either orientationor projective shape will have a greater ef-fect at more extreme orientations. Thus, ifobjective shape is held constant as degree ofrotation increases, a slight under-registra-tion of either orientation or projective shapewill have a greater effect on perceived shape(by affecting perceived width for horizon-tally rotated stimuli) at larger orientationsthan at smaller ones. Consistent with theearlier findings, a larger degree of under-constancy is predicted at greater orientationsthan smaller ones. This consideration doesnot apply with our procedure. For our stim-uli, objective width was larger for moreextremely rotated stimuli, so that the ef-fects of small perturbations in the registra-

tion of shape and slant information wouldhave a relatively small impact upon per-ceived shape at any orientation when com-pared to objective stimulus dimensions.

Variability of the shape judgments forrotated standards increased as inferred pro-cessing time increased and also as objectiveorientation increased. In the process under-lying the perception of shape at a slant,which is summarized by the shape-slant in-variance hypothesis, there are three possibleloci of variability: (a) discrimination of ori-entation, (b) discrimination of projectiveshape, and (c) the stage that combinesorientation and projective shape. The requi-site pattern of variability was not obtainedfor orientation judgments nor for the fronto-parallel stimuli (which provide a gauge forprojective shape) ; therefore, the combina-torial stage is implicated. One account ofthe pattern of variability attributes it to cog-nitive factors present during the combina-torial stage. When the mask occurs imme-diately after onset of the standard, the com-binatorial process may occur spontaneouslywithout any accompanying cognitive adjust-ments. However, as processing time is in-creased, the opportunity for cognitive com-pensation for rotation increases. The like-lihood of such cognitive intervention isexpected to be greater at more extreme per-ceived rotations. The pattern of variabilityin the shape judgments may reflect differ-ences in this hypothesized cognitive involve-ment. When the ISI is zero, there is nocognitive involvement and perceived shapeis specified by the shape-slant invariancealgorithm. Variability is low. At longerISIs and especially at larger perceived ro-tations, individual differences in cognitivecompensation lead to higher variability ofreported shape. Although we have no syste-matic observations to bring to bear on thisthesis, unsolicited remarks by our subjectswere consistent with the thesis, particularlywith respect to the effect of orientation onthe intrusion of cognitive considerations.

Another account of the obtained patternof variability follows from consideration ofthe shape-slant algorithm. As was discussedabove, the algorithm predicts that variationsin either orientation or projective shape

PERCEIVED SHAPE AND PROCESSING DEMANDS 483

have a greater effect upon perceived shapeat extreme rotations than at more moderaterotations. For example, for our stimulus Set1, a deviation in registered orientation of13° leads to a deviation in perceived shapeof 7.2% (expressed as percent of changein width-height ratio) when this deviationis computed for a stimulus with a meanregistered orientation of 26°. However, ifthe mean registered orientation is 52°, adeviation of the same magnitude produces a21% deviation in perceived shape. Thus, asregistered orientation increases, the effectupon perceived shape of a constant error inregistered orientation increases with posi-tive acceleration. Moreover, since our stim-uli were wider at greater orientations, thepredicted effect of constant variability inprojective shape is numerically larger varia-bility in perceived shape at larger values ofstimulus rotation. In conclusion, given thatthe effect upon perceived shape of a constanterror in registered shape or orientation in-creases as registered orientation increases,the pattern of variability in the present re-sults is predicted by straightforward appli-cation of the algorithm.

Variations in the allocation of attentionpresumably were associated with the differ-ent test types. Yet, test type had no con-sistent effect on perceived shape and orien-tation. In line with the claims of Shiffrinet al. (1973, 1976), it would appear thatvoluntary attentional control does not affectthe encoding stage of visual processing.Our concern, expressed earlier, that testingonly one of the attributes, for example,shape or slant, may alter the nature of theunderlying process was not substantiated. Itseems that whatever the emphasis of thetest, the percipient always processes a shapeat a slant. Probably for the same reason ourresults showed no consistent differences as-sociated with the arrangement of tests inthe degree of perceived shape - perceivedorientation correlation: The measured rela-tionship was the same when orientation andshape were tested separately on differenttrials as when orientation and shape weretested successively on the same trial, savefor the exception mentioned in the Resultssection.

In assessing the significance of these find-ings for the claim that all attentional effectsare postperceptual, it is worth noting thatthe possibility of selective allocation of atten-tion could depend on the degree to whichthe to-be-attended and the to-be-unattendedfeatures normally are treated separately inperception. Since shape and orientation typi-cally are packaged as a perceptual unit, ourfailure to show an effect of directed atten-tion ought not to be generalized for casesthat do not present the same degree ofintegration.

References

Carlson, V. R., & Tassone, E. P. Independent sizejudgments at different distances. Journal of Ex-perimental Psychology, 1967, 73, 491-497.

Epstein, W. Attitudes of judgment and the size-distance invariance hypothesis. Journal of Ex-perimental Psychology, 1963, 66, 78-83.

Epstein, W. The process of "taking-into-account"in visual perception. Perception, 1973, 2, 267-285.

Epstein, W. (Ed.). Stability and constancy in vis-ual perception: Mechanisms and processes.Wiley-Interscience: New York, 1977.

Epstein, W., Bontrager, H., & Park, J. The in-duction of nonveridical slant and the perceptionof shape. Journal of Experimental Psychology,1962, 63, 472-479.

Epstein, W., & Park, J. Shape constancy: Func-tional relationships and theoretical formulations.Psychological Bulletin, 1963, 60, 265-288.

Epstein, W., Park, J., & Casey, A. The currentstatus of the size-distance hypothesis. Psycho-logical Bulletin, 1961, 58, 491-514.

Hochberg, J. Perception: II. Space and movement.In J. W. Kling & L. A. Riggs (Eds.), Wood-worth and Schlosberg's experimental psychol-ogy. New York: Holt, Rinehart & Winston,1971.

Koffka, K. Principles of Gestalt psychology. NewYork: Harcourt Brace, 1935.

Leibowitz, H., & Bourne, L. Time and intensityas determiners of perceived shape. Journal ofExperimental Psychology, 1956, 51, 277-281.

Massaro, D. W. Backward recognition masking.Journal of the Acoustical Society of America,1975, 58, 1059-1065.

Shiffrin, R. M., Gardner, G. T., & Allmeyer, D. H.On the degree of attention and capacity limita-tions in visual processing. Perception & Psycho-physics, 1973, 14, 231-236.

Shiffrin, R. M., McKay, D. P., & Shaffer, W. O.Attending to forty-nine spatial positions at once.Journal of Experimental Psychology: HumanPerception and Performance, 1976, 2, 14-22.

Received November 2, 1976 •