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V R Vol.36No.20,pp.3281-32%1996CopyrightID1996ElswierScienceLtd.AI rightsmserwd

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A N S I I E aR oPBARD J. GEESAMAN,*~NING QIANT

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Using random dot stimuli well controlled for dot speed, we found that the moving features ie x p ap a ta pt m f at t i r op aThe i i wc o r rw it s t ro t g lm os iF e xi d iw t no m od i r ed e ft p ai r et m ao t i dS i m it s t ro t e fd i ma d d ei r eI p w ow e d g es e go t s ta I e xt d ii p es iw it a n gs o t w eS tp lr et t f ip h l eo t p e r so t p h e— e x pp aa t c e o gs pi n d eo s t ie c c eT r ea a ga l e xf tp e r ci l ls u gt t g lm op ao t s tp s i r eC o p y@ 1 9E l sS cL

Motion perception Human Speed Opticalillusions Psychophysics

INTRODUCTION

Visual motion perceptionhas been studiedextensivelyinprimates (for a review see Nakayama, 1985). Much ofthis work has revolved around the detection,discrimina-tion and representationof linear motion.Primate corticalarea MT has been implicated in the perception of linearmotion, based on neuron selectivity for homogeneousfields of translational motion (Maunsell & van Essen,1983a,b; Albright, 1984).

More complex motion patterns, such as expansion,contractionand rotation, are thoughtalso to be importantin visual information processing. The medial superiortemporal region (MSTd), a region of primate cortex withunits specific for these motion patterns, has beenidentified (Graziano et a 1994; Sakata et a 1985,1986; Saito e a l1986; Tanaka e a 1986, 1989;Tanaka & Saito, 1989). Such pattern selectivity may beimportant for the tasks of ego-motionrepresentationandthe analysis of object motion in the environment.However, the relationship between area MSTd and theperception of these patterns has yet to be established.

Whether the different types of complex motion areanalyzed in separate neuralprocessingchannelshas been

*Departmentof Brain and CognitiveSciences,MassachusettsInstituteof Technology,Cambridge,MA 02139,U.S.A.

TCenterfor Neurobiologyand Behavior,ColumbiaUniversity,722 W168thSt, New York, NY 10032,U.S.A.

*To whom correspondence should be addressed at: Quincy House#517,57 PlymptonStreet, Cambridge,MA02138,U.S.A. [Tel617493 1754;E mgeesaman@geesaman.student.har’vard.edu].

subject to much debate. Unlike translational motion,these patterns do not “pop out” in displays containingdistracters (Braddick & Holliday, 1991; Werkhoven &Koenderink, 1991), arguing against the parallel proces-sing of these stimuli. Experiments looking at speeddiscrimination thresholds for complex motion haveshown that the thresholds for looming, rotation andlinear motion are all similar (Sekuler, 1992), furtherarguing against separate processing channels for thesedifferent motion types. Consistent with the theory thatthese patterns have a distributed representation at thelevel of local detectors, thresholds for complex motionpatternscan be predicted based on the simple pooling oflocal, linear motion signals. Finally, superimposing atranslational velocity field over an expansion patternshifts the perceivedfocus of expansionin the directionoftranslation, arguing for a lack of separation betweenchannelsprocessingthese motion types (Duffy & Wurtz,1993).

On the other hand, data from adaptation experiments(Regan, 1986) suggests the presence of independentchannels tuned to linear motion, expansion and rotation.Regan developed stimuli which selectively increasedperception thresholds for one pattern type withoutaffecting the others. Consistent with a “low-level”processingof complex motion pattern, studies in infants(Spitze a 1993)have demonstratedthat the capacity tointegrate information contained within non-uniformvelocity fields into coherent motion patterns developsas early as 7 monthsof age. Maskingstudies(Freeman &Harris, 1992)indicatethat the detectionof expansionin a

3281

3282 B. J. GEESAMANand N. QIAN

stimulus is unaffected by the presence of rotation,suggesting independent channels for expansion androtation.

In this study, we take a different approach to thisproblem and compare perceived dot speeds in expandingand rotatingpatterns.If there is a significantdifferenceinperceivedspeed,thisprovidesevidencefor at leastpartialindependence of the channels processing these motiontypes.

GENERALMETHODS

The following conditions were adhered to unlessotherwise specified for a particular experiment. Stimuliwere generated and data collected on a Macintoshcomputerwith a 13inchcolorTrinitronmonitor.Subjectsviewed the stimuli 24 inches (61 cm) away from thedisplay in a moderately lit room. In many cases, thestimuluswas a circle of diameter 200 pixels (7.63 deg ofvisual angle). The random dots for each stimulus wereplotted into a virtual square with dimensions200x 200pixels and a circular mask was used to limit those dotsvisible.

Each dot was a squarepixel that extendedover a visualangle of 0.038 deg. Each “on” pixel was a small blacksquare against a white background. This arrangementeliminated persistence artifacts associated with brightmoving features over a dark background. The fixationpoint was a filled circle of diameter 5 pixels (0.2 deg atthe 24 inch viewing distance).

The refresh rate of the video card was 60.0 Hz, andeach refresh cycle generated a software interrupt signalthat caused the animated sequence of the stimulus, or“movie”, to advance one frame. Accordingly, a 1 secmovie consisted of 60 consecutive image frames. Toconservememory, if the stimuluslasted longerthan 1 see,it was started over from the first frame. The life-time ofthe dots was limited to 12 frames (0.2 see). Once a dothad persisted for this period of time, it was randomlyassigned a new starting position with its trajectory andspeed consistent with the global motion pattern of thestimulus (see below). For the first frame of a movie, arandom age was assigned to each dot, ranging from zeroto one frame short of being extinguished. This causeddots to “die” asynchronously and prevented a globalblinking of the pattern. If a dot left the virtual squaredefining the stimulus boundary, it was given a newrandom location within the stimulus, whether or not ithad completed its entire life cycle. This prevented anyfluctuationin dot densityacross the pattern from frame toframe.

Except for Experiment 6, where dot density wasspecifically manipulated, 100 dots in the 200x 200virtual stimulus square were “on” at a time (one out of400 pixels). Because various masks were used, not all ofthese pixels were visible. For example,when a 200 pixeldiameter circular window was applied, 78.5% (31,416out of a possible 40,000 pixels) were visible to theobserver. Under this condition, an average of -78 dotswere visible each frame.

In most of the stimuli, the speed of each dot wasproportionalto the distance of its starting point from thecenter of the pattern. The motion of individualdots hadno accelerationto theirmotion,i.e. velocitywas constant.This restriction is inconsistent with the movement offeatures on real objects expanding and rotating. Thisconstraint was necessary to allow matching of velocityvectors between stimuli with different motion patterns.For example, to convert a random dot display with localmotionvectors organized into a global expansion(i.e. allvelocity vectors pointed away from the center of thestimulus)into global rotation, all that needs to be done isto rotate each of these local vectors by 90 deg (Grazianoet a 1994).

If the paths of the individual dots in the rotationpatterns were updated every frame according to a truerotation, their paths would be curved, and consequentlytheirnet displacementwouldbe less than dotsof the samespeed in expansion patterns, where trajectories arestraight. Although curvature was eliminated from thelocal motionof the individualdots to avoid this problem,global rotation is perceived because the visual systemspatiallyintegratesthe signals.Becausedistortionswouldoccur if the dots were allowed to travel too far beforedisappearing,life-timesand speedswere kept well belowthe point where this effect became noticeable.

A two alternativeforced choice (2-AFC)paradigmwasused in all experiments. Subjects initiated each trial bypressing the space bar on a computer keyboard. Theywere told not to press this key until they were looking atthe fixation point. Although subjects were instructed tolook straightahead at a fixationpoint for the durationofthe trial, head and eye positionwere not monitored,as theperception seemed largely independentof how well theobserver fixated. Although we insisted that the partici-pants maintain a fixed viewing distance (24 inches), inpilot studies this variable had little effect on the data.

Followingtrial initiation,the first stimulusappearedatthe center of the display, marked by the fixation point.The first movie was followed by a 1 sec gap, duringwhich time only the fixation point remained on thescreen. This gap was followed by the second stimulus,which was presented in the same manner as the first.After the presentation of the second stimulus, bothfixationpoint and moviewere extinguished.At thispoint,the subjecthad to decidewhich stimulushad dotsmovingat the greater average speed. Participantswere urged toignore all. aspects of the stimulus except the averagespeed of the random dots, and they were discouragedfromformulatingtheirjudgmentsbased on the movementof individualdots. The subjects pressed “1“ or “2” onthe keyboard, depending on whether the first or secondstimulushad dots with greater perceived speed.

For each trial, a “standard” expansion stimulusappeared as one of the two movies compared. The othermovie in a trial was chosen from a set of “test” rotationpatternswith dot speedsequalto 70,80,90,100,110,120and 130% of those present in the standard movie. Theorder of the standardand test movieswas randomized,as

NOVEL SPEED ILLUSION 3283

FIGURE 1. Stimuli used in Experiment 1. (A) shows an example ofcounter-clockwiserotationwhile (B) is an exampleof expansion.Eacharrow is a motionvector that represents the directionand magnitudeofindividualdots makingup these patterns. Note that the lengthof thesevectors increases moving outward from the center of the stimuli. Asexplained in the text, transforming one pattern into the other simplyinvolvesrotatingeach local motionvector by 90 deg in the appropriate

direction.

was the particular test pattern shown. The frequency atwhich subjects reported the rotation faster than theexpansionpattern was plotted as a function of the actualrotation to expansion speed ratio. From these plots,perceptual equivalence points were recovered by fittingthe data to a logit function and obtaining the 50%judgmentpoint. For a subsetof the experiments,the logitcurveswere refittedusing the log of the speed ratio as thedependent variable, which would be the appropriatefunction if the data obeyed Weber’s law. Because this

change in axis had no effect on the perceptualequivalencepoints recovered, we report the data with alinear scale.

Because of the 2-AFC design of the experiment,exact95% confidenceintervalsfor the data points could not beestablished. It is not possible to produce a binomialconfidenceintervalthatwill satisfy the strict definitionofa confidence interval, namely one that will have thespecified probability P of containing the unknown butfixed parameter p This problem arises because theobserved probabilitiesfor each data point can only takeon discrete values. Although probability estimates forbinomial data do not follow a normal distribution, theyapproachthis form for largeIV,and by usinga “continuitycorrection”, confidence intervals were estimated by thestandard methods (Snedecor & Cochran, 1989).

The brokencurvesbracketingthe solid regressionlinesin Figs 3, 5, 7 and 8 represent the 95V0confidencebandsfor the data.They were obtainedby fittinga logit functionto the upper and lower bounds of the 95T0confidenceintervals. The dotted drop-lines extending downwardfrom these curvesbracket the equivalencepoint obtainedfrom the data. This technique will be used to get anestimate of the uncertainty associated with measuringeach equivalence point. An effect will be considered“significant“ if this interval does not include the “noeffect” condition.

Subjectswere encouragedto take breaks from the taskif they felt themselves becoming fatigued. Generally, a

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FIGURE2. Individualsubjects’ data from Experiment 1. The x-axis represents the actual speed ratios of a set of test rotationpatterns to a fixedstandardexpansionpattern.They-axis representsthe fractionof trials in whicha test rotationpattern isjudgedmovingfaster than the standard expansionpattern. If the two types of motionpattern being comparedappear to move equallyfast when their actual speeds are the same, the point of inflectionof the logit functionwouldbe at a speed ratio of unity. Theabscissal locationof this point for real data shifts to the left or right,dependingon the subjectivejudgmentof relative speed.Theordinal locationof the inflectionpoint is constrainedby the general form of the Iogit functionto be always at 0.5. The slope ofthe curve is inverselycorrelatedwith a particularsubject’sability to consistentlyjudge differencesin speed.Eachplot showsthepsychophysicalperformance curve for a different observer. In each case, the point of perceptual equivalencyis shifted to theright, indicatingthat each subject tendedto judge dots in expansionpatterns as movingmore quickty.Errorbars represent95’%

confidenceintervals.

3284 B. J. GEESAMANand N. QIAN

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bands. as described in tbe text.

few training trials were allowed prior to data collection.At no time was any feedback given to the subject aboutperformance. For Experiments 2-6, two to three naiveobserversand the two authorsserved as subjects.For thefirst experiment, three additional naive subjects partici-pated. None of the subjectsreportedexperiencingvectionwhile lookingat the displaysand generallyfound the tasksimple, although boring.

E x p e1

R a t i o n aT basic stimulus patterns wereused to demonstrate the basic finding of this investiga-tion.The stimuliused are shownin Fig. 1.The speedfor aparticular dot in the standard stimulus was establishedaccording to the formula: speed = k x (distance from theorigin in pixels). In all cases, k was fixed at 0.02/frame,which meant that the speedof a dot at the very edge of thestimulus window was 2 pixels/frame or 4.6 deg/sec. Inthe unlikely event that a dot happened to appear inexactly the center of the display, its velocity would bezero. This velocityfieldwas chosenbecause it effectivelysimulatesan approachingflat surface. However, becausethe velocity field and size of the stimulusdid not changeover time, the simulateddistance of this object remainedunchanged,i.e. the stimulusdid not evolve.As discussedabove in General Methods, by rotating each velocityvector defining the expansion by 90 deg to the left, acounter-clockwiserotating pattern was achieved. Theserotation patterns had an angular speed of 68.7 deg/sec.Rotation stimuli of various average speeds, both slowerand faster, also were created to completethe set of “test”patterns, as discussedabove. It shouldbe pointedout thatwhen we refer to a distribution of velocity vectors asbeing “identical” we mean statisticallyidentical and notliterally so. Because every dot for each pattern israndomly assigned a location, we do not literally rotate

FIGURE 4. Stimuli compared in Experiment 2. These patterns areidentical to those used in the previousparadigm,except that the radialspeed gradient has been removedand speeds of all dots in a particular

stimulus are identical.

the exact sameset of vectors in transformingone stimuluspattern into another. However, because the number ofthese randomeventsis large in constructingthesestimuli,we were not concerned that stochastic fluctuations inaverage speed could have any effect on the results.

R eFigure 2 shows the experimental results. Thefraction of times the rotation stimulus was judged“faster” is plotted against the ratio of rotation speed toexpansion speed. By following the horizontal line at the50% judgment point over to the performance curve andthen down to the abscissa, the point of perceptualequivalencecan be recovered. For the “no effect” case,this is of course a speed ratio of 1. Each frame representsdata collected from a single subject. In each graph, theperceptual equivalencepoint (shown in the lower right-hand corner of each frame) was greater than 1.0,indicating that all eight subjects perceived the dots inthe expansion pattern moving faster than those in therotation pattern. The bars drawn for each data pointrepresent 95% confidence intervals. Figure 3 shows thedata from the eight subjects used in Fig. 2 pooled into asingle curve. From this last plot, it is seen that theequivalencepoint for the set of subjectsas a whole was aspeed ratio of 1.21. In other words, the dot speed for therotation pattern needed to be increased 21% before theperceived speed was the same as for the expansionpattern. For reasons addressed in the Discussion, themagnitudeof the illusionwas potentiallyunderestimatedby our experimentaldesign.

The experimentwas repeated using a rotation patternas the standard stimulus and expansion patterns as thecomparison stimuli. The direction and magnitude of theillusionwere unchanged(data not shown).

E x2

R a t iWe decided to explore system-aticallywhich aspectsof the stimuliwere responsibleforthe speed illusion documented in the first experiment.There were at least two components to the globalorganizationof the velocityvectors definingthe previouspatterns, i.e. the original stimulihad both a direction andspeed gradient. In the previousmovies, the speed of eachdotwas a linear functionof its distancefrom the centerofthe display.In this secondexperiment,we eliminatedthis

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NOVEL SPEEDILLUSION 3

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FIGURE5. Data collected using stimuli lacking a speed gradient.Therightwardshift of the equivalencepoint is comparableto tbat obtainedwith patterns containing a s pg r aD f e o t fobservers is plotted. These data were pooled for the purpose ofobtaining the solid regression line. Broken flankingcurves represent

95% confidencebands, as described in the text.

aspect of the stimuli, giving all dots the same speed,regardlessof location.Two representativevelocity fieldsfrom thesepatternsare shownin Fig.4. The speedof eachdotwas the same as a dot located71 pixelsaway from thecenter of the display in the standard pattern fromExperiment 1. In this way, the a vs po t din the two experiments was approximately the same,although this was a relatively unimportant detail sincethese different types of patterns were not directlycompared. We call these new stimuli “direction fields”to distinguish them from the “velocity fields” exploredpreviously.

R e sFigure 5 stows the data organized into thesame plot format as the previousexperiment.For brevity,although discrete data points from all four subjects areplotted, the curve from this figure was obtained bypooling data across all subjects. The speed ratioequivalence points for individual subjects werebg = 1.14, nq = 1.18, eg = 1.28, yz = 1.18. As seen fromthe plot of the pooled data, the overall equivalencepointwas a speed ratio of 1.19 and this effect was significant.Although the illusion was slightly less for the directionfieldcompared to the velocity field in Experiment1 (1.19compared with 1.21, with overlapping confidence inter-vals), in each case the curves deviated significantlyfromveridical expectations. We concluded that the speedgradient contributed relatively little to the illusion.

E x p e3

R a t i o n aIn the previous experiment, thespeed range of the individual dots was restricted. Next,the analogousexperimentwas performed with respect tothe range of motion directions present. The “axial”

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FIGURE6. Stimuli used in Experiment3. The patterns shown in (A)and (B) represent examplesof axial rotation and expansion,with onlytwo directions of motion definingthese global motion patterns. For aparticularstimulus,the speedof all the dotswas identical.The soliddot

in the center of each pattern represents the fixationpoint.

patterns used are illustrated in Fig. 6. Within a stimulus,all dot speedsare equaland only two directionsof motionare represented in each pattern. As in the otherexperiments, the expansion stimulus was used as thestandard in the 2-AFC task. To transform the expansionpattern into a rotation pattern with identical velocitydistributions, the expansion stimulus was effectivelybisected orthogonal to its long axis. The left half of thestimuluswas then placed on top of the right half, creatingthe axial rotation.

Because of the way these patterns were constructed,the expansion stimulus was 100 pixels wide and 100pixelshighwhile the rotationpatternwas 200 pixelswideand 50 pixels high. Because the shape of the two patterntypeswas not identical and their motion borders differedin length,an unwantedvariablewas introducedthat couldpotentially affect the perception.To control for this, wecreated axial expansionand rotationpatternslike those inFig. 6(B). In these stimuli, the expansion patterns were

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3286 B. J. GEESAMANand N. QIAN

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FIGURE 7. Comparison of axial expansion and rotation. Thedifference in perceived speed between expansion and rotation

disappears when axial patterns are compared.

oriented horizontally and the rotation patterns weresquare. By pooling the data from these two stimulussets, the confounding effect of stimulus dimension waseliminated (this assumes there is no interactionbetweenthe two possibleeffects).

R e sUnlike the first two experiments,no consistenteffect of motion pattern on perceived average speed wasevident. When stimuli like those of Fig. 6(A) werecompared, the individual subjective equivalence pointswere bg = 1.09, dk = 1.01, nq = 1.12, eg = 0.84, yz =1.12.The equivalencepoint obtained from pooling thesedata was 1.03, a much smaller effect than that reportedabove for the isotropic patterns. Furthermore, the range

of equivalence points bracketed by the 9590confidencebands includes the “no effect” case. When stimuli likethose of Fig. 6(B) were compared, the individualsubjective equivalence points were bg = 0.98, dk =0.89, nq = 1.04,eg = 0.84, yz = 0.89. The pooled equiva-lencepoint in this conditionwas 0.94 and again the effectwas not significant.Figure 7 plots the result of poolingthese two sets of data. The individual subjectiveequivalence points in this final case were bg = 1.04,dk = 0.95, nq = 1.08, eg = 0.84, yz = 1.00. The equiva-lence point obtained by averaging over all five subjectswas 0.99, indicating that the speed illusion previouslyobtained for isotropic patterns was not present for axialpatterns. We conclude that the presence of a wide rangeof directionsin the originalpatternsused in Experiment1is required for the speed illusion. Note that thisexperimentalso suggeststhat the centrifugalorganization(away from the fixationpoint) of the motion vectors,ps is not responsible for the phenomenon. Despitepossessing more centrifugally oriented local motionsignals in the axial expansion displays compared torotation, the perceived dot speed was the same. Weexamine this issue further in the next experiment.

E x4

R a t iTwo competing hypothesescouldexplain the data obtainedfrom the first two experiments.One possibility is that the illusion depends only on theglobal organization of the stimuli’s component motionvectors. Alternatively, since in the previous paradigmsthe subject foveated the center of the stimuli, the illusioncould also depend on the location of the motion patternon the retina.

To distinguish between these two alternatives, wealtered the experimental paradigm and presented the

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NOVEL SPEEDILLUSION 3287

A B

FIGURE9. Stimuli used in Experiment5. These patterns were createdidenticallyto those shownin Fig. 1except that a doublewedge-shaped

mask was applied.

stimuli side by side, with an interveninggap of 48 pixels(1.83 deg). The fixation point was in the center of thisgap. By placing the stimuli in the periphery, on averagethe two types of patterns had the same number ofcentrifugally oriented component motion vectors. Be-cause this task was much more difficult, because of theeccentricallyplaced stimuli, the movieswere shownfor afull 3 sec. Subjects pressed “l” or “2” depending onwhether the movie to the left or right of fixation,respectively, appeared to have faster moving dots.

R e s

Figure 8 shows the results for this experiment, usingdata pooled over four subjects.The individualsubjectiveequivalencepoints were bg = 1.20, nq = 1.30, eg = 1.39,yz = 1.23. The overall effect was somewhat larger thanthat observedin the firsttwo studies,with the equivalencepoint from the pooled data established at 1.27, signifi-cantly above the “no effect” condition. This resultsuggeststhat it is the global motionpattern of the stimulithat is responsiblefor the illusion,since the effect did not

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E x p5

R a t iBased on the results of comparingaxial patterns in Experiment 3, we predicted that thegreater the rangeof localmotiondirectionswhich definedthe motionpatterns, the strongerthe speed illusionwouldbe. TO test this hypothesis, we constructed double“wedge” patterns as shown in Fig. 9. We used the samerules established for the stimuli in Experiment 1 for themovement of the random dots, but used two wedge-shapedmasks insteadof a circularone. This was repeatedfor wedges of angles30,60,90,120,150 and 180 deg. Awedge pair of 180 deg is equivalent to two semi-circlesand therefore was identical to the circular patterns ofExperiment1. For this data point,we used the previouslycollecteddata rather than repeat the identicalstudy.Onlywedges of the same size were compared with oneanother.

R eFigure 1O(A)shows the pooled data from fivesubjects. The six curves represent data collected usingeach of the six wedge sizes. Rather than show the entirecurve, a small portionof thex-axis has been expanded toshow the shift in the equivalence point more clearly.Figure 1O(B)shows these data organized into a differentformat. In thisplot, subjectiveequivalenceratio is plottedas a function of stimulus wedge size. A clear trend isevident in both these graphs: the larger the area of thestimulusexposed,the more a subject’sjudgment of speedmagnitude favored the expansion pattern. Two-wayANOVA showed a significant effect of wedge size onthe equivalencepoint (P c 0.05).

For small wedge sizes, a reversal of the illusion wasseen for some subjects — the rotation patterns werejudged more frequently as possessing greater averagespeeds.We attributethis as arisingfrom the phenomenonof “temporal capture” (Treue e a 1993). Dots in

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3288 B. J. GEESAMANand N. QIAN

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FIGURE11.Effect of dot densityon the locationof the subjectiveequivalencepoint.Eachcurve in (A) was obtainedby poolingdata across the four subjects tested. T f c uc o rt t d id l i(B) plots the subjectiveequivalencepoints for each subject as a functionof dot number.The solid line connectingpointsof the pooleddata set showsa

generally upward slope. Beyondthe four-dotcase, this increase largely plateaus.

narrow wedge rotation patterns will have, on average,shorter life-times than those in expansion patternsbecause it is more likely that the dots will rotate off thetwo long sides of the wedge. This effect is reduced aswedge width increases, and the effect of motion patternon perceived speed quickly dominates. Although thetrend in the data reflects two competing effects, theresults are consistentwith an increasing effect of globalmotion pattern with an increase in the range of motionvectors that define these patterns.

E x p e6

R a t i o n aIn order to test further the hypoth-esis that the magnitude of the illusionwas related to thestrength of the global motion signal, we systematicallyran a seriesof experimentswith differentdot densities.2,4,8, 16,32,64, 128and 256 dotswere used with patternsthatwere otherwiseidenticalto thoseof Experiment1.Atlow dot densities, problems associated with stochasticfluctuationsin averagespeedpotentiallybecame an issue.To avoid this problem, the random number seed for theprogram generating the stimuluspatterns was saved andreusedbefore each moviewas created.As a consequence,the initial spatial location of the random dots wasidentical for the patterns being compared.

Based on results from Experiment5 which suggestedapositive relationship between the range of local motiondirectionspresentin the patternsand the magnitudeof theillusion, we predicted the difference in perceived speedwould increase with the number of dots in the display.Because the dots were repositionedevery 12 frames, thenumber of motion directions represented in the stimuluspatterns over the duration of the movie was greater thanthe numberof dots present at any one time on the screen.For example, in the two-dot condition approximately

2 x ( frames)/(12 frames), or 10 different motiondirectionswere sampledover the courseof a 1 sec movie.

R eFigure 11 shows that the results wereconsistent with expectations. The magnitude of theillusion is considerably less for the two- and four-dotconditions than for the remaining cases. Figure 11(A)shows a series of eight curves, one for each dot density,for data pooled over four subjects.Figure 11(B)shows aclear positive correlation between dot density and therightwardshift in the perceptualequivalencepoint.Two-way ANOVA was performed, and a significanteffect ofdot density on the subjective equivalence point wasestablished(P< 0.05). The results are consistentwith therest of the data collected in this study: the illusion isdirectly correlatedwith the strengthof the global motionpattern present in the stimulus.

DISCUSSION

This study has documented a novel illusion involvingthe perceived speed of random dots in rotation andexpansion motion patterns. When a given set of motionvectors is organized into an expanding global motionpattern, the average perceived speed of these features isgreater than with a rotation pattern of the same vectorcomposition. This finding supports the possibility thatexpansionand rotation motion are processed in separateperceptual channels.

The findingof Experiment4, that the illusionwas notdependenton a specificretinalstimuluslocation,supportsthe hypothesisthat the phenomenoncannot be explainedin terms of a local motion system and providesevidencefor independent processing of expansion and rotationmotion. This illusion may make sense from an evolu-tionary point of view: approaching objects are morerelevantbehaviorallythan rotatingones and, by contain-

NOVEL SPEEDILLUSION 3289

ing featureswhich appear to move faster, are more likelyto grab the observer’s attention.

M a g no t s pi l la e x pd e

The 2-AFC paradigm used in this study potentiallycould have led to an underestimation of the illusion’smagnitude. Because subjects more frequently chose theexpanding pattern, they may have consciously orsubconsciously tried to balance their responses byfavoring rotation when the perception was ambiguous.Although they were instructed against such biases, itmany have been difficultto avoid this tendency.Anotherexperimentaldesign, such as a staircaseparadigm,wouldhave avoided this potential problem. However, side byside comparisonof expansionand rotationpatterns,at theperceptual equivalence points recovered from our data,appear to move at the same speed, indicating that the2-AFCdesign, althoughnot ideal,gave reasonableresults.

Another potential source of underestimationis relatedto the way the stimulus patterns were constructed. Asdiscussed in the Methodssection, individualdots movedwith a constantvelocity throughouttheir life-times.Thiswas done to avoidproblemssuch as path curvaturewhichwould prevent a balancedcomparisonof the two types ofmotion. If the motion of each dot was updated everyframe (rather than just at the beginningof its trajectory),it would be impossible to rule out local motiondifferences,e.g. curvedvs straightdot paths, contributingto the illusion.Unfortunately,because individualdots inthe expanding patterns did not increase in speed as theymoved outward, on average expanding dots movedslightly slower than rotating dots at the same distancefrom the pattern’scenter. When we compared expandingpatterns with and without acceleration, the patternswithacceleration appeared slightly faster (data not shown).Fortunately, it is relatively easy to adjust for thisdiscrepancyp o sWe calculated that the dots in theexpanding patterns were all moving 13.070too slowlyand, therefore,the equivalencepoints in experiments1,4,5 and 6 should be shifted further rightward by thisamount.Taking this into account,the actualmagnitudeofthe speed illusion reported in Experiment 1 is approxi-mately 30%. This is not an issue for the patterns used inExperiments2 and 3, where a speed gradient is absent.

Fortunately, both of these problems will produce anunderestimationin the magnitude of the illusion and donot qualitativelyjeopardize any of the findings.However,in order to experimentally recover a more accurateestimationof the illusion’smagnitude,Experiment1 wasslightly modified and repeated, using the two authors assubjects. The trajectories of the dots in the expansionpatterns were updated every frame, allowing individualdots to speed up as they moved outward. The rotationpatterns were constructed as they were before, with adot’s trajectory updated only on the first frame of its 12-frame life-time. As discussed in the Methods section,updating the trajectories of rotating dots every framewould introducelocal dot path curvatureand reduceeachdot’s net displacement, inappropriately reducing the

perceiveddot speed.Althoughcomparing“acceleration”e xw “ n or h td i so i na q ud ithe local motion of the dots, statistically the averagespeed of the dots in the patterns in now better matched.The expected increased shift in the subjective equiva-lence pointswould further confound the underestimationproblemassociatedwith the 2-AFC paradigm.To nullifythis bias and anticipating the -3070 shift calculatedabove, we sampled evenly around a speed ratio of 1.3ratherthan 1.0.As expected,expansionwasjudged fasterthan rotation approximately 50’% of the time. Thesubjectiveequivalencepoint for BG was 1.27 (comparedto 1.16without expansionacceleration)and for NQ 1.35(compared to 1.24 without expansion acceleration), inline with the 13% adjustment of the original datapredicted on mathematicalgrounds.

We should emphasize that it is not clear whether theexpansion pattern with or without acceleration is moreappropriatefor comparisonwith the rotation stimuli. Asdiscussed above, both types of comparison have draw-backs. Fortunately, in both cases the illusion is in thesame direction, and it is simple to adjust the subjectiveequivalencepoints by the addition of a constant.

Finally, it shouldbe mentionedthat becauseexpandingdots born near the edges of the stimulus window candisappear off the edge of the display before living outtheir full life-times,expandingdots have slightly shorterlife-timesthan rotatingdots. It is well knownthat for dotsof identical speed, the shorter the dot life-time, thegreater the average perceived speed (Treue et a 1993).If t p hw a cf t ir ei t p w w e t it l iof the dots in the stimulus patterns shouldincrease the magnitude of the illusion. This is becausewith longer dot life-times, there is more opportunityfordots in expansionpatternsto prematurelymoveout of thestimuluswindow. In a pilot experiment,we found that, ifanything, the oppositeeffect was observed.

O s i la p ea n

Although more attention has been paid to directionthan to speed perception, the literature is scattered withreports of various speed illusions. Watamaniuk et a(1993) noticed that increasing the dot density intranslational motion fields increased the perceived dotspeed. Along similar lines, Thompson (1982) reportedthat sine wave gratings appear to move faster when theycontain higher contrast and found that the orientationofthe grating affected perceived speed. Another study withdrifting sinusoidal gratings found that these stimuliappear to move more slowly in the periphery thanfoveally (Johnston& Wright, 1986).Finally,Treue e a(1993) reported that decreasing the dot life-times ofstimulus features defining motion patterns increasesperceived feature speed. This effect was evident evenwhen non-movingflickeringdots were added to movingrandom dot displays, a phenomenon which they call“temporal capture”.

3 2B J G Ea N Q

The only speed illusion we could find that involvedrotating stimuli was in a report by Vicario and Bressan(1990)which examined the perceptionof rotatingwheelson vehicles undergoing forward translation.They foundthat subjects consistently overestimate the angularvelocity of the wheel relative to the forward velocity ofthe vehicle. This illusion creates the impression of thewheels partially “slipping” relative to the surfaces withwhich they are in contact. This is interesting because,given the results of this study, it might be expected thatsubjects underestimate the speed of rotating objects ingeneral.

There are numerousreportsof perceptualdistortionsinthe human motion processingsystem.Thresholdsfor thedetectionof coherentmotion in displayswith low signal-to-noise ratios are generally higher along the verticalmeridian, particularly for motion moving either upwardor downward (van de Grind e a 1993).Another study(Raymond, 1994) reported that although foveal motionsensitivity was isotropic, a small but significant (about0.1 log units) difference in sensitivity in favor ofcentripetalmotionwas observedat eccentricitiesbetween5.0 and 12.5deg out from the fovea. This was true for theentire horizontal meridian and the inferior half of thevertical meridian. Motion sensitivities for the superiorportion of the vertical meridian were isotropic (i.e.identical for all motion directions.) Consistentwith theprevious study, motion thresholdswere generally higheralong the vertical axis.

The phenomenon reported in the current study cannotbe explained by any combination of the above factors,because the effect was invariant with regard t r es t ip l a cT i i m pb ei s adependence of perceived speed on the global organiza-tion of a stimulus” motion vectors.

P o sr e lt c o ra M

Cells in the dorsal part of the MSTd of the macaquemonkey have been found that respond to motion stimulicontaining elements of expansion, contraction androtation (Graziano e a 1994; Sakata e a 1985;1986; Saito e a l1986; Tanaka e a 1986, 1989;Tanaka & Saito, 1989).

MSTd is thought to be part of the motion-processingstream that courses dorsally in cortex from V1 to MT toarea MST (Boussaoud e a 1990). Both V1 and MTcontain units tuned to linear motion (Albright, 1984;Hubel & Wiesel, 1962; Livingstone & Hubel, 1988;Maunsell & van Essen, 1983a, b) and the selectivity ofMSTd cells to more complex motion patterns is thoughtto be built up from these more simple inputs. It is likelythat motion direction and speed discrimination areprocessed together in the same cortical pathway. Recentstudies (Pasternak & Merigan, 1994) have showed thatlesions to the fundus of the superior temporal SUICUS(STS), known to affect both MT and MST areas, haveraised both speed and motion direction detection thresh-olds for noisy stimuli.

The distribution of units in MSTd tuned to different

motion patterns is biased in favor of expansion. Manymore cells are tuned to stimulicontainingexpansionthaneither clockwiseor counter-clockwiserotation,by a ratioof about3:1 (Duffy & Wurtz, 1991;Grazianoe a 1994;Saito e a 1986;Tanaka & Saito, 1989).

The results of the current study were we!i correlatedwith the response characteristics of MSTd neurons.Reducingthe number of local motion directionsdefiningexpansion and rotation in Experiment 3 (down to twodirections in the case of axial expansion/rotation)eliminatedthe illusion,consistentwith the poor responsesreported when these patterns were used to drive MSTdunits (Tanaka & Saito, 1989). Removing the speedgradients from the patterns, thus reducing them to“direction fields”, had little effect on either the speedillusionor responsesin MSTd neurons (Tanaka & Saito,1989). The centrifugal bias of MT direction selectivityreported by Albright (1989) cannot explain the illusion,as demonstrated in Experiment 4, where moving thepatterns away from the fovea did not diminish thesubjectivespeed difference between motion patterns.

Although it seems plausible that an anisotropy inMSTd response selectivity could affect the perceivedspeed of complex motion patterns, a real explanation ofthe illusion requires a computationalmodel that relatesMSTd cell activities to the perception of global patternspeeds. Unfortunately,such a model does not yet exist,althoughevidence from lesion experiments(Durstelerea 1987)suggestssome relationbetween neuronnumberand perceivedspeed. Many modelsfor local translationalvelocity computation have been proposed in the past(Horn & Schunck, 1981; Hildreth, 1984; Heeger, 1987;Gryzwacz & Yuille, 1990).These models cannot predictadequately our speed illusion because, as we havedemonstrated, the illusion is a global phenomenondependingon the overall arrangementsof many differentdirections of motion and it disappears when the globalpatterns we used are viewed through narrow, wedge-shaped apertures. However, if we assume that thecomputation of global pattern speed involves similarsteps as in some physiologically inspired local transla-tional velocity models (Heeger, 1992, 1993), our speedillusion could be explained. A key element in thesemotionmodelsis a normalizationstep at which the outputof a specific translationalmotion mechanism is dividedby the sum of outputs of all the translational motionmechanisms.We could generalize this procedure to thecase of global pattern speed computation by assumingthat the output of the expansion(or rotation)mechanismis normalized by the outputs of all global motionmechanisms present in MSTd. It is also reasonable toassume that the signal strength of a given global motionmechanism before normalization is proportional to thenumber of MSTd cells tuned to that global motion type.Because there are more MSTd cells tuned to expansionthan rotation, the output of the expansion mechanismafter normalization would remain stronger than therotation mechanism. This could be the physiological

NOVELSPEED ILLUSION 3291

basisof the speed illusionreported in this paper, althougha more formal model is obviouslyneeded.

In a pilot study using two naive subjects and the twoauthors, we repeated Experiment 1 with expansion andcontraction dot patterns. The expansion patterns wereprepared as described above in Experiment 1. Thecontraction patterns were created by showing thecorrespondingexpansion pattern in reverse, allowing anexact matching of dot speeds, life-times and spatialdistribution. In this case, dot speeds in the expansionpattern appeared faster than contraction, although theeffect is small (5–10%). This is consistent with oursuggestion that an MSTd anisotropy in responseselectivity is responsible for the illusion, as expansioncells outnumber contraction cells in MSTd by a ratio ofabout 2:1 (Duffy & Wurtz, 1991; Graziano et a 1994;Saito et a l1986;Tanaka & Saito, 1989).

Alternatively, curved motion may appear slower thanstraightmotion of the same speed. Since the rotation,butnot the expansion, patterns contained globally curvingmotion, this could be the basis of the illusion we havereported. Although locally the motion of each dot isstraight, the nervous system perceives the motion ascurved in the rotation patterns because of spatialintegration.More work needs to be done to pinpoint theexact stimulus attributes contributing to the speedillusion.

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Vicario, G. B. & Bressan, P. (1990). Wheels: A new illusion in the Arrdersenfor his invaluable support and his comments on an earlierperception of rolling objects. P e r c1 5 7version of this manuscript. We would also like to thank the naive

Watamaniuk, S. N. J., Grzywacz, N. M. & Yuille, A. L. (1993). subjects who agreed to serve as observers, particularly Ellen Geesa-Dependenceof speed and directionperceptionon cinematogramdotdensity. V i sR e s e3 8 4 9

man,DavidKaneand YudongZhufor participatingin the completeset

Werkhoven,P. & Koenderink,J. J. (1991).Visual processingof rotaryof studies. Ning Qian is supported by a research grant from the

motion.P e r c ea P s y c h o4 7 3McDonnell-Pew Program in Cognitive Neuroscience and by NIHgrant MH54125.This work was also funded by NIH grant EY07492and the Human Frontiers Scientific Program awarded to Professor

A c k n o w l e dwould like to thank Professor Richard A. Richard A. Andersen.

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