Pergamon

The DetectionLinear Motion

Vision Res., Vol. 36, No. 15, pp. 2271–2281, 1996Copyright 01996 Elsevier Science Ltd. AO rights reserved

0042-6989(95)00295-2 Printed in Great Britain0042-6989/96 $15.00 + 0.00

of Stimuli Rotating in Depth Amidand Rotating Distracters

J. TIMOTHY PETERSIK*

Received 14 December 1994; in revisedform 4 August 1995; in jinal jorm 23 October 1995

In three experiments, observers watched displays consisting of two or more areas that containedunidirectionally moving pixels. In half of the displays, ame area of pixels contained movement thatcorresponded to the projection of the front surface of a rotating cylinder. The total duration of thedisplays and the number of stimulus areas per displaly were varied. The subjects’ task was toindicate whether or not a given display contained rotatiam.When the display time required to reach75% accuracy was determined, it was found that the number of stimuli per display had no effect;nor did it interact with other variables. One control experiment eliminated “pixel crowding” at theedges of the rotating cylinders, with little effect on the results. Another control experiment foundthat the ability to discriminate rotating from linear motion declines with distance away fromfixation. A fourth experiment showed that under conditions similar to the first three, subjects canmake accurate shape discriminations, thereby suggesting that three-dimensional informationcontributed to the decisions made in the original experiments. On the basis of these results andprevious data, it is suggested that in the present experiments structure was recovered from motionby the short-range process, and that this recovery engages attention to a relatively constant extent,regardless of the number of stimuli contained in a display. Shape discrimination based on structurefrom motion may require a more effortful form of attention. Copyright @ 1996 Elsevier ScienceLtd.

Motion perception Structure from motion Visual attenticm Short-range process

INTRODUCTION

Dick et al. (1991)examinedconditionsthat facilitatedthedetection of a three-dimensional rotating stimulus. Arotating cylinder was simulated by pixels that moved inan orthographic projection; both front and back of thecylinderwere visible, and hence there were pixel motionsboth to the right and the left. While the pixels of thesimulated cylinder moved, there was also a backgroundof pixels, each of which moved linearlyeither to the rightor to the left with the same average velocity as thetarget’s pixels. Across several experiments, Dick et al.(1991) found that detection of the rotation amidst noisemotion was very high when the two-dimensional (2D)displacements of its pixels were within the spatialdisplacement limit of the short-range process (SRP),and that detection declined rapidly as more pixeldisplacements entered the range of the long-rangeprocess (LRP). Because the same authors had previouslyshown the SRP to be pre-attentive (i.e., reaction time toshort-range motion did not increase with the addition ofdistracters; Dick et al., 1987), their work makes the

*Department of Psychology, Ripon College, P. O. Box 248, Ripon, WI54971, U.S.A. IEmail petersikt@acad.ripen.edu].

implicitcase that the detectionof rotation,under optimaldisplacementconditions,is also pre-attentive.

The present experiments were conducted in order tofurther understand the attentionalrequirementsinvolvedin the detection of rotation produced by short-rangemotion. Like Dick et al. (1991), we asked subjects todetect the presence of a rotating stimulusin displaysthatcontained linearly movingpixels. However, a number ofchanges were made in the stimuli: first, whereas Dick etal. (1991)embeddedtheir rotatingcylinderin a relativelyhomogeneousbackground of linearly moving pixels, inthe currentdisplaystherewere discreteareasoccupiedbyeither linearly moving or rotating pixels. This made itpossible to examine the effect of set size (e.g., Palmer,1994), rather than pixel numerosity, on rotation detec-tion.Second,whereas the previousauthorsvaried angularvelocityof the rotatingstimulusin an effort to manipulateshort-range/long-rangeprocessing, in the present experi-ments angularvelocitywas held constant(along with theaverage, short-range, displacement of pixels), and theabsolluterotation (total duration) of the displays wasvaried.This permittedus to estimatethe time requiredforsubjects to reach a criterion level of decision-making.Third, whereas in the earlier study both left and right 2Dmotions of the pixels were visible, the present displays

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were unidirectional,showingeither leftwardor rightwardmotion only in a given display (only the “front” surfaceof a rotating cylinder was displayed and linear noisemotion was in the same direction). This separated anypotentialdirectionalartifacts from pure rotation informa-tion. In separate experiments, we also varied theeccentricity of the stimuli and examined the role of“edge-crowding” in rotation detection. Finally, todetermine the extent to which subjects actually use 3Dstructure from motion to make rapid discriminations,weembedded rotating targets (spheres) amidst rotatingdistracters (cylinders).

Along with the work of Dick et al. (1991) suggestingthat the most efficient detection of rotation is conductedby a “parallel” process (i.e., the SRP), Shulman (1991)has shown that rotationaftereffects(Petersiket al., 1984)can be modulated by selective attention to specificrotating adaptation stimuli. The former finding impliesthat rotation detection can be conductedby a rapid, low-level, relatively automatic process (i.e., the SRP); thelatter suggeststhat followingdetection, the perceptionofrotation can be, or is, maintained by a higher order,relativelyeffortful process.This could explain why Dicket al. (1991) were able to obtain some rotation detectionunder LRP conditions,although it was not very efficient.Currently, there is some issue in the literature as towhether visual attention is best considered in terms of aserial/parallel distinction (e.g., Treisman & Gelade,1980),a pre-attentivevs attentivedistinction(e.g., Julesz,1990), a decision integration approach (e.g., Palmer,1994), or by some not specifically attentional influencelike “discriminability” (e.g., Verghese & Nakayama,1994).Because the presentexperimentswere designedtobetter understand the processes underlying the detectionof rotating stimuli defined by the short-range motion ofpixels, and not as tests of any specific model of visualattention, there is an attempt to remain as theoreticallyneutral as possiblewith respect to theories of attention.

The goal of the present experimentswas to determinethe influenceof the stimulus set size on correct rotationdetection, and to determine whether set size influencesthe time required to make a decision about the presenceor absence of rotation. The influence of retinal eccen-tricity, the importance of edges, and the recovery ofstructure from brief motion in the detection of rotationare considered in separate control experiments.

GENERALMETHODS

Stimuli and apparatusGeneral construction of stimuli. All stimuli were

prepared on an Amiga 600 microcomputer.The overallstrategy was to prepare small area “micro-displays” ofcollections of pixels specifying the rotation of the nearsurface of a cylinder (i.e., the surface facing theobserver), along with micro-displays showing the sameset of pixels in linear motion with the same averagevelocity. First, 11 pairs of pixels (i.e., pixels adjacent toone another in either the vertical or horizontaldimension,

rando:mlydetermined) were randomly positioned in asmall area of the computer screen. From these, rotatingstimulliwere prepared using the techniques described inPetersik (1991b); i.e., the positions of pixel pairs in 29subsequent frames of the display were determined byconventional methods (e.g., Braunstein, 1976), and allframes were stored to create a 30 frame micro-displayshowing the pixels rotating through 180 deg (therebyproducing a rotational velocity of 6 deg per frame).Linear motionmicro-displayswere preparedby using thesame initialcollection of random pixel pairs in Frame 1.The fiinalhorizontal locations of the pixel pairs in therotation micro-displays was also determined. For thelinear motion micro-displays, the pixel-pairs weresubsequentlydisplaced in equal steps across the next 29frames so as to arrive at the same horizontal locationsastheir counterparts in the rotating micro-displays.In bothcases, the disappearanceof a pixel pair at one edge of adisplay occasioned the appearance of a new pixel pairrando]mlylocated (but the same in both types of micro-displays)at the oppositeedge in the subsequentframe ofthe di:splay.

For experimental conditions that required fewer than30 frames per micro-display, the unnecessary frameswere deletedfrom the beginningor end of the original,30frame, display. Thus, all micro-displaysmaintained thesame rotational or linear velocity and the spatialarrangement of pixels; only their total duration and theabsolute distance traversed by individual pixel pairsvaried from display to display.

Micro-displayswere stored on hard disk. They couldsubsequently be positioned anywhere on the computerscreenlin the preparation of “macro-displays”. Macro-displays were animations whose components were themicro-displays described above. The resulting macro-displaysthereby showeda variablenumberof collectionsof pixel pairs, each of which could either display rotationor linear motion.With the exceptionof Experiment4, nomore than one rotating micro-displaywas ever used in amacro-display.For the main experiment described here,pixel pairs in both rotation and linear motion micro-displaysalwaysmoved from left to right. For the rotationdirection control experiment described in the Resultssection, motion direction was randomly determined;direction could be varied by presenting the micro-displaysin either a forward or backward order of frames.

Details of stimuli.. Viewing distancewas set at 66 cm.The 200 pixel (vertical) x 320 pixel (horizontal)displayarea clfthe monitor screen (Commodore-Amiga,model1084S)therebysubtended13.5deg x 21 deg visual angle.Each micro-displaywas created within an approximatelysquare area subtending 2.78 deg (vertical) x 3.04 deg(horizontal); i.e., 41 pixels x 46 pixels. The backgroundof the display area, as well as the background of eachmicro-display,was kept dark (0.8 cd/m2).Each pixel in adisplay was white (25 cd/m2). The average horizontaldistance traversed between frames by pixels was 11.4’visual angle, well within the putative spatial limit of theSRP of 15’visual angle for small stimuli (cf. Petersik et

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al., 1983). Our measurements of the displacements ofpixels in the rotation simulationsshowed that four pixelsmade displacements greater than 15’ visual angle, thegreatest of these being 19’;we conclude therefore thatmost of the rotation information contained in thesedisplayswas limited to the spatial range of the SRP.

Micro-displaysthat simulatedthe rotationof a cylinderaround its longitudinal(i.e., vertical) axis were preparedin a polar projection with a perspective ratio (simulatedviewing distance divided by cylinder radius) of 3.0.

Macro-displayswere created that consisted of 5, 10,15, and 30 frames, each constructed from the parentdisplays described above. When macro-displays wereconstructed,micro-displayswere placed randomlywithinthe cells of an imaginary4 x 4 grid on the monitorscreen(except in Experiment 2); each cell subtended approxi-mately 3.38 deg (vertical) x 5.25 deg (horizontal).Eachmicro-display was confined to this area, but did notnecessarily occupy the exact center. Three different setsof micro-displays, and therefore macro-displays, wereconstructed in order to establish a population of stimulifrom which to sample for the subsequent experiments.Figure 1 shows diagrammaticallywhat a single frame ofthese displays looked like.

Stimuliwere presentedwith the monitoroperatingin anon-interlaced mode. Frame duration was 1/60 see;therefore, macro-displaysconsisting of only five framesof movementlasted slightlyover 83 msec,while displaysconsisting of 15 frames of movement lasted 250 msec.Only macro-displayscontaining30 frames of movement,lasting 500 msec, could have been expected to elicit eyemovementsthat would reliably lead to fixationsof targetmicro-displaysbefore their disappearance.Table 1 showsthe relationshipsbetween the variable number of framesused in displays, the duration of the movement in thedisplays,and the absoluteangularrotationof the cylindersimulations. Referral to this table will assist in theinterpretationof data shown in later sections.

TAEILE 1. Relationships between number of frames per display,dur:ition of subsequent movement and absolute angular rotation

Number of frames per display

Parameter 5 10 15 30

Duration of movement (msec) 83.35 166.67 250.01 500.01Absolute angular rotation (deg) 30 60 90 180

EXPERIMENT1: EFFECTSOF SET SIZE ANDNUMBEROF FRAMES

Subjects

Subjects consisted of two paid assistants, the author,and amunpaid volunteer. The assistants and volunteerwere female, aged 19–21yr. The author was male, aged41 yr. There was no visible difference in the data as afunction of age or gender. All subjects reported 20/20vision and good depth perception,either with or withoutcorrectivelenses.When correctivelenseswere indicated,they were worn throughouttesting.

Stimuli andprocedure

Micro-displayswere grouped randomlywithin the 4 x4 grid described above. There were three factors to theexperiment:numberof frames (that displayedmotion):5,10, 15, or 30; number of stimuli (or micro-displays)perdispla~y:2, 6, 9, 12, or 16; and presence or absence ofrotation.Stimuliwere factoriallycombinedand randomlydrawn from the larger populations described in theGeneral Methods section. The 40 possible conditions(4number of frames x 5 number of stimuli x 2 presence/absence) were run in blocks of trials 20 times for eachsubject. Within each block of trials, the stimuli werepresented in a randomizedorder. A singleblock of trialswas run in a single experimental session, successivesessicmstypically separated by no less than 24 hr, butoccasionallyby no less than 1 hr.

For each trial, the subject’s task was to stare at thecenter of the monitor screen, which was dark and blankfor 250 msec, and to maintainthat fixationthroughoutthetrial. Becauseof the grid-likearrangementof the stimuli,no stimuluswas ever presenteddirectly in fixation.Pixelsin motion appeared abruptly and ended with the screengoing;dark and blank, at which time the subject was tosay “:yes”or “no”, indicatingwhetheror not rotationhadbeen detected.

Results and discussion

Using the percentage of correct responses per condi-tion as the dependent variable, a 2 (rotation present vsrotation absent) x 4 (number of frames per display) x 5(numberof stimuliper frame) repeated measures analysisof variance was conducted. This analysis showed thatthere was no difference in the percentage of correctresponses as a function of whether a rotating stimuluswas or was not present in the display, F(1,3) = 5.72,P >0.05. Therefore, the stimuluspresentvs absent factorwas not considered in any further analyses.

2274 J. T. PETERSIK.

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FIGURE 2. Results of Experiment 1, expressed as the percentage ofcorrect rotation detection judgments as a function of the number offrames per display (each frame lasted 16.67 msec). Number of stimuli,or micro-displays, per display is the parameter. Error bars show largest

and smallest t 1 SE.

The overall percentages of correct responses as afunctionof the numberof framesper displayare showninFig. 2; the number of stimuli in each frame of the displayis the parameter. The smallest and largest standarderrorscorrespondingto the means are also shown in Fig. 2; thesmallest standard error (SE; 2.48%) occurred in thecondition that contained six micro-displays over 30frames, whereas the largest (10.2%) occurred in thecondition that contained nine micro-displays over fiveframes. As can be seen from the means, it was generallythe case that the more frames contained in a display, thegreater was the percentage of correct responses. Thiseffect was significant in the analysis of variance,F(3,9) = 29.07, P <0.05. However, the relationshipbetween the number of stimuli contained in a displayand the percentage of correct responses was non-monotonic: subjects were most accurate when displayscontained either 2 or 16 stimuli, and were somewhatlessaccurate when the displayscontainedsix, nine, or twelvestimuli. The effect of the number of stimuli per displaywas also significant, F(4,12) = 3.38, P c 0.05. Theinteraction between the “number of stimuli” and“number of frames” conditions was non-significant,F(12,36) = 1.50,P >0.05; thus, the effects of those twofactors appear to have been independentand additive.

Whereas subjects were significantlyinfluencedby thenumber of stimuli contained in the displays, it was clearthat the relationshipwas not so simpleas to concludethatthe addition of stimuli to a display increased theprocessingload required of the subjects in a proportionalmanner. In order to examine more specifically therelationship between the number of stimuli and proces-sing time, we examined each subject’s data separatelyand used linear interpolation to determine the overalldisplay time required to achieve 75% accuracy (referredto as the decision threshold)as a function of the numberof stimuli contained in a display. In most cases, this

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FIGURE 3. Results of Experiment 1, expressed as the 75% decisionthreshold (msec) as a function of the number of stimuli per display.Data are shown for individual subjects, along with the group average.

Error bars show typical standard deviations + 1 SD.

procedure was straightforward. However, of the 20functions considered, there was one that showednonmonotonicity; i.e., the function crossed the 75!Z0point twice. In this case, the secondcrossoverwas used toestimate the decision threshold. Also, there were threecases in which the functions never fell below 75V0correct; in these cases, we found the midpoint betweenthe percentage correct obtainedwith the 5 frame moviesand O$ZO(for Oframe movies).The resultingdata for eachof the subjects are shown in Fig. 3. The shortest 75Y0decisionthresholdswere obtainedfor displayscontaining16, 12,and 2 stimuli, respectively.Comparingthe 16 and2 stimuli displays, the short decision thresholds suggestthat f’orthese subjects there was no trade-off betweentime and accuracy in this experiment (i.e., subjectsrequiredroughlythe same amountof time to achieve75Y0accuracy for these displays).Using the logic of Treisman& Gelade (1980), we sought to determine whether therewas any significantchange in the 75’%0decisionthresholdas a :functionof the number of stimuli in a display. Arepeatedmeasuresanalysisof varianceon the data shownin Fig. 3 revealed that 7590decision thresholds did notchange significantly with the number of stimuli perdisplay F(4,12) = 1.34, P >0.05. Therefore, it wastentatively assumed that either (a) the detection ofrotating stimuli engages a relatively effortless, low-levelattentive process; or (b) the processing load engaged byrotating stimuli is relatively constant and does notfluctuate greatly as non-target stimuli are added to thebackground.

The macro-displaysused in Experiment 1 consistedofsets alfinitially identicallypositionedpixels, all of whichtraverseda small area of the screen in the same direction.The majorityof thesesetsof pixels (i.e., the linearmotion

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FIGURE 4. Results of a control experiment in which subjects identifiedthe rotation direction of a rotating target. The 75% decision threshold issbown as a function of the number of stimuli per display. Data are

sbown for two subjects and their average.

distracters) showed identicalmotion, and the movementsof the pixels contained in the rotating micro-displaysdiffered from those of the distracters only in smallvariations in velocity and displacements on the y-axis.Underany circumstance,the rapid detectionof the targetsshown in this experiment is impressive; however, itcannotbe guaranteedthat such detectionwas not due to adifference in the two-dimensional appearance of thetargets, relative to the general homogeneityexhibitedbythe distracters. Therefore, two subjects (the author andone of the paid assistants) replicated Experiment 1 withmacro-displaysthat consisted of micro-displayscontain-ing different randomly positioned sets of pixels, therebyeliminatingglobal homogeneity.The resultsof these twosubjects were remarkably consistent with those theyyielded in the main experiment:the percentageof correctresponsesnever differed by more than 10% (i.e., 2 of 20trials) for either subject in any condition.Therefore, it issuggested that the above results were not simply due tothe perceptual appearance of 2D variations among themicro-displays.Nonetheless,a further experiment invol-ving structure from motion shape discriminations wasconducted and is reported below as Experiment 4.

In an effort to clarify the processing requirements ofthe task employed in Experiment 1, a second, related,task was examined. It was assumed that the detection ofrotation (or linear translation) necessarily precedes itsidentification,and that identificationof rotation directionrequires a more effortful or advanced form of attentionthan detection. Therefore, it was thought that rotationdirection identificationwould be sensitiveto the numberof stimuli present in a display. Two subjects (onepreviously tested, and one naive) were exposed to therotating stimuli used in Experiment 1 under the sametestingconditionsdescribedabove. In this case, however,the subjects’ task was to determine the direction ofrotation (clockwise vs anticlockwise) of the targetstimuli. Displays containing only linear movements, in

the absence of a rotating stimulus, were not used. Eachsubjectwas tested on 30 trials in each condition.In orderto maintain good accuracy along with speedy responses,subjects were given five trials in each condition withfeedback prior to experimental testing (with two excep-tions, condition accuracy in this session was maintainedat 90-100’%).As with the original data, 7590 decisionthresholdsobtained during experimental trials (in whichno feedback was provided) were subsequently deter-minecl.The results are shown in Fig. 4. At least twodifferencesbetween the identificationdata shown in Fig.4 and the rotation direction data of Fig. 3 are apparent.First, the average decision thresholdshown in Fig. 3 was127.73msec, whereas for the data of Fig. 4 it was higher,191.71msec. Second, the data of Fig. 4 show consistentincreasesin decisionthresholdbetween displayscontain-ing two and twelve stimuli; the data of Fig. 3 tended tohoveraroundthe averagedecisiontime.Whereas the dataof Fig. 3 could not be fitted well by any function otherthan alhorizontal line, those of Fig. 4 show a significantlinear trend between 2 and 12 stimuli: the slope of thebest-tlttinglinewas almost 12msec/stimulus,and the lineaccountedfor 95Y0of the variation in the data.As was thecase in the original experiment, there was a decline indecisiontime for “filled” displayscontaining 16 stimuli.From the differences cited above, it seems reasonablysafe to conclude that, as shown by the initial data of thisexperiment, the addition of linear motion stimuli to adisplaycontaininga singlerotatingstimulusdoes not addto the processing load required for detection of therotating stimulus. Going beyond detection to a form ofidentification(i.e., naming rotation direction) appears toengage a more effortful form of attention. This generalprinciplewas also supportedby the resultsof Experiment4.

One comparisonbetween the data shown in Figs 3 and4 is consistent: in both cases, the estimated decisionthresholddeclinesbetween 12 and 16 stimuliper display.The reason for this decline is unclear, and discussionofthe appearanceof the displayswith subjectsdid not showa subjective difference between displays containing 12stimulliand thosecontaining16.A possiblereasonfor thisfinding is that as all positions of the 4 x 4 grid becomeoccupiedwith stimuli, the overall displayapproachesthedisplay used by Dick et al. (1991) in appearance;that is,the irrelevant stimuli take on the character of ahomogeneousbackground.

In lbothof the experiments reported thus far, whensubjectswere able to view the rotatingstimuluscentrally,or when a rotating stimulus in the peripherywas viewedfor a prolonged period of time, there was frequently astrong subjective impression of three-dimensionality,“objectless” and volume,alongwith rotation(this issuesfrom spontaneous reports of the subjects as well aspostexperiment questioning). Thus, to the extent thatsubjective reports are reliable, when display durationswere long enough to permit the micro-genesisof a clearpercept, observers appeared to have based their judg-ments on the gestalt of an object rotating in depth

2276 J. T. PETERSIK.

Nonetheless, it is possible that information secondary tothe perception of rotation (e.g., deviations from purelylinear translationsof the pixels involvedin rotation,pixelcrowding at the edges of the rotating stimuli) providedreliablecues that the subjectsmighthave used. In order toassess the extent to which such epiphenomenawere used,two separate control experimentswere conducted.

EXPERIMENT2: TARGET LOCATIONIN VISUALFIELD

Althoughno track was keptof subjectperformanceas afunction of target location in the visual field inExperiment 1, on several occasions subjects noted thatit seemed more difficultto be sure of judgmentswhen theapparently rotating stimuluswas in peripheral view. Anexamination of the displays showed that target stimuliappeared about equally in all locations in Experiment 1,so that the conclusionsdrawn above are not likely to beconfounded by a procedural bias with respect to targetlocation. Nonetheless, since the results of Experiment 1reflect an averaging of performance across all targetlocations within the visual field, Experiment 2 wasundertaken to determine the extent to which subjectscould judge the presence or absence of a rotating targetamidst a variable number of linear motion non-targetsasa function of increasing distance from fixation. Thenumber of stimuli per display was varied between twoand five to determine whether small changes in thisparameter would affect subject performance.

SubjectsFive subjects participated in this experiment. One

subject was male (the author) and four were femalesubjects, two of whom were paid assistants and two ofwhom were unpaid volunteers. The female subjectsranged in age between 19and 21 yr; the male was aged41yr. All subjects reported 20/20 vision and good depthperception, either with or without corrective lenses.When corrective lenses were indicated, they were wornthroughout testing.

Stimuli and procedure

The micro-displays used in the present experimentwere the same as those used in Experiment 1. However,the macro-displaysdiffered in the following ways: first,four concentric circles were drawn around the fixationcross at the center of the display area. These had radii of3.04, 5.47, 7.89 and 10.33 deg visual angle. In order toaccommodate the large diameter circle and stimuli, thedisplay area of the monitor was increased slightly.Second, in any macro-display, micro-displays wereplaced on one of the circles in random locations; theirorientations remained the same as in Experiment 1.Third, the number of micro-displays contained in themacro-displays was either 1, 2, 3, 4 or 5. In all otherrespects, the procedure and details of Experiment2 werethe same as in Experiment 1.

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FIGURE 5. Results of Experiment 2, showing percentage of correctrotation detection judgments as a function of the number of stimuli perdisplay. Distance of stimuli from fixation is the parameter. Separategraphs show the results from displays consisting of either 30 or 10

frames.

Resuits and discussion

As in Experiment1, the percentageof correctdecisionswas not dependenton the presencelabsenceof a rotatingstimulus. Therefore, the results are presented in Fig. 5,where the overall percentage of correct responses isshown as a functionof the numberof stimuliper display.Distanceof the stimulifrom fixation,in deg visual angle,is the:parameter. Separate frames of the figure show theresults obtained with displays that contained 10 and 30frames. Apparent in Fig. 5 is the finding that accuracywas indeedinfluencedby distancefrom fixation.The datafrom this experiment were subjected to a 2 (number offrames) x 3 (number of stimuli) x 4 (distance fromfixation) repeated measures analysis of variance. Dis-tance of the stimuliwas shown to have a significantmaineffect, F(3,12) = 26.25, P c 0.001. Similarly, as therelative elevations of corresponding curves in the twoframes of Fig. 5 suggest, the number of frames perdisplayalso had a significantmain effect,F’(1,4)= 15.43,P c 0.001, with the 30 frame displays resulting in a

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higher percentage of correct responses than 10 framedisplays.However, the number of stimuliper displaydidnot have a significant main effect, F(2,8) = 2.52,P >0.05, nor did it enter into a significant interactionwith number of frames, F(2,8) = 1.32,P >0.05, or withdistance from fixation, F(6,24) = 1.69, P >0.05. Thethree-wayinteractionwas not significant,F(6,24) = 0.24,P >0.05.

This pattern of results, along with those of Experiment1, suggests the following interpretation. Both experi-ments showthatwhen the percentageof correct responsesis the dependent variable, increases in the number offrames per display result in increases in correct respond-ing. However, the decision threshold data of Experiment1 show that the stimulus duration required to reach 75%accuracy does not fluctuate systematically across con-ditions. This, along with the failure to find a significantinteraction between number of frames and number ofstimuli in both experiments suggests that beyond someminimum, increases in the number of frames servemainly to provide opportunities for subjects to checkinitial impressionsand/or refine their judgments, therebyimproving the overall number of correct responses.Similarly, the failure of distance from fixationto interactwith number of stimuli in the present experimentsuggests that although the resolution of the rotationdetection perceptual apparatus decreases with distancefrom fixation,the influenceof competingstimulidoes notmake detection less efficient. The overall pictureobtained from the conclusions of these two studies isthat processing load (or attention required for detection)does not changewith the numberof linear motion stimulicontained in a display. Given that detection ability rarelyapproached 100% in the preceding two experiments,along with the fact that subjectsdid not find this to be aneffortless task, it seems unwise to characterize thedetection of rotation amidst linearly moving stimuli asinvolving a “pop-out” phenomenon. It is likely moreconsistent with both data and subjective experience tocharacterize the performance of this task as requiring arelatively constant degree of attention, regardless of thenumber of stimuli present.

EXPERIMENT3: REMOVALOF MICRO-DISPLAYEDGES

The present experimentwas conducted in order to ruleout the possibility that one, two-dimensionalartifactualcue had been used previously to discriminate rotatingfrom linearmotionstimuli.Since the polar projectionof arotating cylinderproducescrowdingof pixels at its edgesdue to foreshortening, it is possible that the subjects inexperiments 1 and 2 could have used the greater localdensity of pixels at the edges of the rotating cylinders tomake their judgments, rather than the perception ofrotation itself.To controlfor thispossibility,10volunteersubjects participated in a preliminary experiment inwhich vertical edges of various widths (in pixels) wereremoved from both the rotating stimuli and linear motionmicro-displays. Corresponding frames from pairs of

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FIGUR.E 6. Results of Experiment 3, a replication of Experiment 1with the exception that two columns of pixels were removed from theouter edges of the stimuli. Results show the percentage of correctrotation detection judgments as a function of the number of frames per

display. Number of stimuli per display is the parameter.

rotating and linear motion micro-displays were thenviewed for 3 sec each, with a 4 deg distance separatingthem (subjects stared at a fixation cross). On each trial,subjeetsrated the perceived similarityof the frames on ascale that ranged from 1 (identical) to 7 (extremelydifferent).Five pairs of such stimuli, in which either O,1,2, 3, 4, or 5 columns of pixels were removed from theouter (i.e., vertical) edges of the original micro-displays,were judged five times each by each subject. Averagejudgments applied to pairs’ frames were compared to theexpected value under the null hypothesis (i.e., 1) bysingle means t-tests.The results showed that the pairs offrames with O or 1 pixel columns removed were notperceived as significantly different; all others were.Therefore, in order to use stimuli in the presentexperiment that were as close as possible in detail tothose used in Experiments 1 and 2 but which werenonetheless undiscriminableon a frame-by-frame basis,micrcl-displayswith the outermosttwo columnsof pixelsremoved from the originalswere chosen.

The present experimentwas a replication of the mainExperiment 1, except that the micro-displays used tomake the stimuliwere modifiedas describedabove so asto make them undiscriminablewhen static. The goal ofthe experiment was to determine whether subjects stillwould be able to detect the rotating stimuli as well as inExperiment 1.

Subjects

Subjects were three of the participants who hadoriginally served in Experiment 2.

Stimuli and procedure

Stimuli, apparatus, and viewing conditions wereidentical to those noted for Experiment 1, except forthe fact that the micro-displays used to prepare themacro-displaysnow had two columnsof pixels removed

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A m

,

0 10 20

Number of Stimuli

FIGURE 7. Results of Experiment 3, expressed as the 75% decisionthreshold as a function of the number of stimuli per display. Data are

shown for individual subjects, along with their group average.

from the left and right edges of the cylinders andcorresponding linear motion stimuli. The perceptualeffect was the same as viewing the original micro-displays through an opaque mask hiding the outsideedges. The procedure of the experimentwas the same asin Experiment 1, except that the subjectsviewed stimuliin each condition 40 times instead of 20.

Results and discussionThe percentageof correct responsesas a functionof the

number of stimuliper display is shown in Fig. 6; numberof frames per display is the parameter. As can be seen,therewas a somewhatlower overallpercentageof correctresponses in the present experiment compared toExperiment 1. At the same time, the pattern of responsesis similarbetween the two experiments,except that in thepresent experiment the curve for 16 stimuli remains flat.The results were subjected to a 4 (number of stimuli perdisplay) x 5 (number of frames per display) repeatedmeasuresanalysisof variance. This revealed a significantmain effect for the number of frames, F’(3,6)= 6.61,P =0.025, but not for the number of stimuli,F(4,8) = 1.99, P >0.05. The interaction between thetwo effects was also non-significant,F(12,24) = 1.14,P >0.05.

As in Experiment 1, the 75%correct decisionthresholdwas determinedfor each subject, and is shown plotted asa function of number of stimuli in Fig. 7. The averagedecision times obtained in the present experiment werevery similar to those obtained in Experiment 1; that is,largely between 100 and 150 msec. As in Experiment 1,the function showing mean decision time showed nosignificantlinear trend,y = 151.41msec —(2.30 msec *x), R* =0.54. On the basis of this experiment incomparisonto the resultsof Experiment1, it is, therefore,concluded that the crowding caused by foreshorteninginthe original rotation micro-displayscontributed little, ifanything, to the discrimination of those displays from

others containing only linearly moving pixels. If any-thing, the crowding contributed to the developmentof amain effect of numberof stimuliin the percentagecorrectdata of Experiment 1. However, numberof stimulifailedto affect the 75% decision thresholds of either Experi-ment 1 or the present experiment. Both experimentssuggestthat the degreeof attentionor processingrequiredto detect rotating stimuli remains constant over thenumber of stimuli contained in a macro-display.

EXPERIMENT4: SHAPE DISCRIMINATIONINSTRUCTUREFROM MOTION

Do the results of Experiments 1–3 reflect thesensitivity of the human visual system to motion indepth.and 3D structure,or are they simply a reflectionofthe albilityof the SRP to detect small differences in the2D local motion of the pixels that constitute target anddistra.ctor micro-displays? It was reasoned that ifstructure from motion based on the SRP is rapid andrequires relatively little effortful attention to detect, thensubjects ought to be able to detect particular rotatingtarget shapesamidstrotatingdistracter shapeswith aboutthe same accuracy and speed that they detect rotatingshapes amidst linear motion distracters. Whether thespeed of such decisions varies with the number ofdistracters present ought to depend on the attentionalrequirementsfor the shape discriminationtask, after theshapes have in fact been detected.

Experiment4 was a replicationof Experiment 1, withthe exception that the target stimuli were rotatingspheres, whereas the distracters were rotating cylinders(all of which always rotated in the same direction andwith the same velocity).Atso, to ensure that performancewas not merely based on local 2D variations in motion,each micro-display had a different set of randomlypositionedpixels.

Subjects

Subjects consisted of the author, one paid femaleassistant (who had previously served in Experiments1–3), one unpaid male volunteer (age 19 yr), and oneunpaid female volunteer (age 20 yr).

Stimuli and procedure

Stimuli were prepared along the lines of thosedescribedin Experiment1with the followingexceptions:(a) instead of linear motion micro-displays, distractersnow (consistedof the same types of rotating cylindersused in Experiment 1; (b) these rotating cylinders,however, were not created from a single parent, butrather each was constructedwith a new set of randomlypositioned pixels; (c) target stimuli now consisted ofrotating spheres, each constructed with a new set ofrandomlypositionedpixels. The diameter of the sphereswas increasedrelativeto the cylindersby two pixels.Thiseffectively reduced the appearanceof “missing corners”without leading to the appearance of a noticeably largerfigure. In all other respects, the stimuliwere the same asdescribed in Experiment 1.

ROTATION DETECTtON 2279

100

90 -

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6

70

60

I

Z Stimli

6 Stimuli

9 Stimuli

12 Stimuli/

,. l-J_-&-0 10 30

Number of Frames

FIGURE 8. Results of Experiment 4, expressed as the percentage ofcorrect rotation detection judgments as a function of the number offrames per display. Number of stimuli, or micro-displays, per display is

the parameter. Error bars showed representative + 1 SE.

Subjectsparticipated in a procedure that was identicalto that describedfor Experiment 1, except now their taskwas to determinewhether a macro-displaydid or did notcontain a rotating sphere target.

Results and discussion

The overall percentages of correct responses as afunctionof the numberof framesper displayare showninFig. 8; the number of stimuli in each frame of the displayis the parameter. Representativestandard errors are alsoshown in Fig. 8. The smallest SE (O’%)occurred in thefollowing conditions:two stimuli/30frames, six stimuli/30 frames, and six stimuli/15 frames. The largest SE(10.1%) occurred in the condition consisting of sixstimuli/fiveframes. As was the case in Experiment 1, themore frames contained in a display, the greater was thepercentage of correct responses (three exceptionsoccurred in the transition between 10 and 15 framedisplays).The effect of the number of frames was againsignificant in a number of frames x number of stimulirepeated measures analysis of variance, F(3,9) = 26.64,P c 0.001. As in Experiment 1, the relationshipbetweenthe number of stimuli contained in a display and thepercentage of correct responses was non-monotonic:subjectswere more accurate when displayscontained 16stimuli than they were when displays contained 12stimuli, and in the 16 stimuli condition they were alsomore accurate with the 5 and 10 frame displays than inthe 9 stimuli condition. The effect of the number ofstimuli per display was also significant,F(4,12) = 20.12,P c 0.001.The interactionbetween the numberof stimuliand number of frames conditions was also significant,F(12,36) = 3.07, P c 0.01. Post-hoc analysis suggeststhat the significantinteractionwas due to a failureof the 2and 16 stimuli conditionsto be influencedby the numberof frames constitutingthe displays.

The percentage of correct responses per condition inExperiment4 ranged from about 12%lower to about5%

C0.-UI.-

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300

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100

1

Y = 27.65 + 13.36x RA2 = 0.93

● AS x

A CM.

x JP

.

m

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Number of Stimuli

FIGURE 9. Results of Experiment 4, expressed as the 75% decisionthreshold (msec) as a function of the number of stimuli per display.Data arc shown for individual subjects, along with the group average.Regression is shown for the first four average data points only. Notethat the decision threshold for subject AW in the condition containing

12 stimuli is beyond the limits of the graph.

higher than in Experiment 1,with the averagepercentageof correct responsesbeing somewhathigher.Thus, giventhat subjects in the present experimentneeded to rely onstructure from motion information to make their judg-ments, it seems reasonable to conclude that subjects inExperiment1 at leasthad structuralinformationavailablewith which to make their judgments.

As in Experiment 1, the next step was to estimate the75% decision threshold for each subject. Of the 20functions relating percentage of correct responses to thenumber of frames contained per display, two were non-monol:onicand eight never fell below 75’%.In thesecases, estimateswere made as describedin Experiment1.Figure 9 shows the resulting estimates of decisionthreshold as a function of the number of stimuli perdisplay. The first finding of this experiment is that thedecision thresholdsare in the same general range (about100-2:00 msec) as were the thresholds obtained inExperiment 1. This finding again suggests that thedecisions made in Experiment 1 could have been basedon structure from motion information.Additionally,Fig.9 shows that there is a generally linear increase indecision threshold with increasing numbers of micro-displaysfor displayscontaining2,6,9 and 12stimuli(theregression shown in Fig. 9 is based on the first fourconditions only). Once again a very low decisionthreshold was obtained when the screen was filled with16 stimuli. Considering that the decision thresholdobtainedwith the 16 stimulidisplaysmay be anomalous,perha]psowing to the perceptual influence of a filledscreen, these results suggest that the detection anddiscriminationof a target shape amidst similar distractershapes (when both are definedby motion) may require amoreeffortfulform of attentionthan the detectionof a 3Drotation amidst linearly moving 2D stimuli.

Why should stimuli whose detection on the basis of

2280 J. T. PETERSIK

rotation is relatively rapid, requiring little attentionalcontrol, be subject to an influence of the number ofdistracterswhen discriminationsare made on the basis ofshape? First, it has been known for some time that evenwhen stimuli are defined by simple primitives (e.g.,letters such as E, A and H which are defined by linesegments),discriminationrequiresa longer reaction timethe more similar the to-be-discriminateditems become(e.g., E and F; Neisser, 1967). Thus, the cylinders andspheresused in Experiment4, which were designedto bemaximally similar, may have required a more effortfulattentive processing to be discriminated because ofstructural similarity alone. Additionally,however, giventhat the cylinders and spheres used in this experimentwere difficult to discriminate at all when frames wereviewed statically, it is likely that the cylindrical andspherical forms themselves arose because of the activityof a “structure from rotation” process (suggesting thatthe detection of rotation in some sense precedes theformation of perceptual shape for these stimuli). It ispossiblethat an “intra-channel” discriminationof shapes(i.e., discriminationof shapesdefinedby the same type ofmotion) requires a more effortful form of attention thanan “inter-channel” discrimination(e.g., rotationvs linearmotion).

GENERALDISCUSSION

Insofar as possible, the stimuli used in the presentexperiments were designed to maximize the similaritybetween targetsand non-targets.Stimuliwere small areasthat showed unidirectionalmotion of approximately 11pixels. In Experiments 1–3, targets differed from non-targets only in the addition of path deviations thataccommodated the “cosine factor” responsible forproviding rotation information and the “perspectivefactor” responsible for providing rotation directioninformation (Braunstein, 1976). The only obvious non-motion-relatedcue that might have aided discrimination,edge crowding, was eliminated in Experiment 3 withlittle effect on the pattern of results or conclusions.Possible cues resulting from the identical positions ofpixels in all micro-displayswere eliminated in a small-scale control study associatedwith Experiment 1 and inExperiment4. Furthermore,the motionof all of the pixelswas nearly always short range. Under these conditions,when analyses were based on percentage of correctdiscriminations and the stimuli consisted of rotationamidst linearly moving distracters, the numberof stimulicontained in a display produced a significantmain effectonly in Experiment 1, and that effect accounted for nomore than a 15% absolute variation in correct discrimi-nations (see Fig. 2). When analyses were based on the75% decision time, the numberof stimuliper displayhadno significanteffects (except in Experiment4, where thenature of the perceptual task differed), nor did it enterinto any interactions.These resultsprovide evidencethatthe process responsible for producing structure frommotion operates very efficiently,perhaps pre-attentively,despite the extent of non-target linear motion. Addition-

ally, when 3D rotation of a target shape needs to bedetected and discriminated amidst other rotating 3Dshapes, rapid detection appears to be modulated by aslower discriminationprocess (Experiment4).

Although when the percentage of correct responseswas the basis for analysis, the number of framescontained in a displayhad a consistentmain effect, whenthis Iemporal factor was reduced to the time required toreach a 759%level of responding, the measure nevervaried significantlyin any experimentwhere the subject’stask was to detect rotation amidst 2D moving stimuli.This suggests that some minimum amount of processingtime is requiredto recoverstructurefrom motionand thatfurther viewing serves mainly to test the result, aconclusion that is consistentwith the results of Liter etal. (1993) and of Treue et al. (1991).

The results of Experiment 4, in which subjects usedstructure from motion information to detect and dis-criminate target shapes (spheres) from distracters (cylin-ders) showed that subjects could perform the taskaccurately and with decision times that were comparableto those obtained in the previous experiments. This inturn :]uggeststhat 3D rotation and shape informationwasavailable to guide the decisions made by subjects inExperiments 1–3. However, the results of Experiment 4also suggest that the time needed to make shape frommotionjudgments involvingthe detection/discriminationof a target shape amidst distracter shapes increaseswiththe numberof stimulicontainedin a display,at least up tothe point at which the screen becomesfilled.Consideringthe similarity in appearance of the rotating spheres andcylinders that were used, this findingwas not surprising:after (or perhaps concurrentwith) the determinationthat3D rotation was present in the displays, the taskamounted to a fine-graineddiscriminationof the shapesof candidate objects.

Consideredin total, the present results imply that whenseeking a rotating sphere amidst linearly movingdistralctors,the detection of three-dimensionalityaloneis sufficient to guide responses.This process appears tobe very rapid and to requirea relativelylow-levelform ofattention(i.e., one not seriouslyinfluencedby the numberof distracters). When seeking a rotating sphere amidstrotating cylinders, however, structure from motion mustgive :riseto perceptsof at least two different shapes.Thisprocess occurs within the same broad time frame as thedetection process itself, but decisions are influencedbythe number of distracters present, indicating a possiblyhigher degree of attention investment.

The present results also address the question of thenature of the process responsible for the recovery ofstructure from motion. Specifically, the present resultsand conclusionsare consistentwith the interpretationofDick et al. (1991), that under conditions of short-rangemotion, recovery of structure from 3D rotation simula-tions is a relatively low-level process that engagesattention to approximately the same degree, regardlessof the numberof competingnon-targetstimuli.While notruling out a role for the LRP, the work of Dick et al.

ROTATION DETECTION 2281

(1991), Mather (1989), Petersik (1991a), and Todd et al.(1988) suggeststhat the SRP makes a strongcontributionto the recovery of structure from motion.These findings,together with an accumulated body of evidence thatconcludes that the SRP is itself a low-level, high-capacity, process (e.g., Dick et al., 1987; Petersik,1989), allow for the advancementof the hypothesisthatthe efficiency of rotation detection in the presentexperiment is due to the contributionof the SRP.

If it is true that the detectability of rotation amidstlinearly moving non-targets is due to the activity of theSRP, then its efficiencymay be in part due to a globallyco-operative parallel-distributed type of processing.Previous results from this laboratory (Petersik, 1990)have demonstrated that the SRP behaves like a globallyco-operative perceptual process when a collection ofrandom dots is rotated about its center in the pictureplane. If the same global co-operativity applies to thecomputations underlying the detection of rotation, itmight explain the relative ease with which rotatingstimuli are detected amidst competing noise stimuli. Infact, Treue et al. (1991) propose that structure frommotion is the result of a globalperceptualconstructionofa surface representation from global velocity measure-ments of moving elements, presumably reflecting theoutputof the SRP. Given the earlier research establishingthat the SRP is co-operative in the processing of 2Ddisplays, it is reasonable to hypothesizethat the processresponsiblefor the recovery of structure from motion inour rotation simulationsis co-operativeas well.

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