Perception & Psychophysics1992, 52 (4), 415-424

Properties of the recombination ofone-dimensional motion signals into

a pattern motion signalFRANK L. KOOl, KAREN K. DE VALOIS, DAVID H. GROSOF, and RUSSELL L. DE VALOIS

University of California, Berkeley, California

We have examined the human ability to determine the direction of movement of a variety ofplaid patterns. The plaids were composed of two orthogonal sine-wave gratings. When the plaidcomponents are of unequal spatial frequency or sometimes of unequal cont-rast, observers judgethe direction ofmovement incorrectly. In terms of the two-stage model of Adelson and Movshon(1982), these errors may result from either a misjudgment in the perceived speeds of each of thecomponents or a failure in the combination of one-dimensional-component movements into a co-herent direction of motion of the two-dimensional plaid pattern, or both. A comparison of theperceived direction of motion of plaids with the relativeperceived-speeds of the plaid componentgratings suggests that both failuresoccur, but in different circ-umstances The relative perceivedspeed of the plaid components was measured with a spatial and a temporal forced-choice tech-nique, the former leading to larger differences. Our results support the notion that the visualsystem decomposes a moving plaid into oriented components and subsequently recombines thecomponent motions.

A considerable amount of psychophysical, physiologi-cal, and anatomical evidence has accumulated to indicatethat the initial stages of the visual system perform a localtwo-dimensional (2-D) spatial frequency filtering of visualstimuli (see R. L. De Valois & K. K. De Valois, 1988,for a review). The physiological evidence, for instance,indicates that cells in striate cortex have receptive fieldslocalized to a particular patch of visual space, and thatthey respond to a pattern within that local region only in-sofar as it has power in the particular orientation and spa-tial frequency range to which that cell is tuned. K. K.De Valois, R. L. De Valois, and Yund (1979) and laterMovshon, Adelson, Gizzi, and Newsome (1986) showedthat cells in striate cortex do not respond to the overallpatterndirection, but rather that they respond to the spa-tial frequency components within the cells’ spatiotemporalpassbands. For example, in the case of patterns definedas the sum of two gratings, which they termedplaids, re-sponses were predictable from the orientation of the twoFourier components, but not from the perceived direc-tion of the pattern as a whole.Such local 2-D spatial filtering of images is advanta-

geous for many aspects of vision, but it also poses

The research reported in this paperwas supported by Grant EY00014from the National Eye Institute and Grant BNS 8819867 from theNa-tional ScienceFoundation. F. L. Kooi andD. H. Grosof were associatedwith thePhysiological Optics and Neurobiology Groups, respectively,at theUniversity of California, Berkeley. D. H. Grosof is presently attheCenter for Neural Science, New York University. Correspondenceshould be addressed to F. L. Kooi, who is now at TNO Institute forPerception, Kampweg 5, 3769 DESoesterberg, The Netherlands (e-mail:kooi@izf.tno.nl).

problems—in particular, the problem of how the visualsystem detects the real direction of motion of complexpatterns. Consider the case of the plaid composed of twosine gratings as shown in Figure 1. As the plaid is driftedto the right behind the aperture, the results of K. K.De Valois et al. (1979) and Movshon et al. (1986) indi-cate that V1 cells will instead respond to the diagonal com-ponent motions. The true direction ofmotion of the overallpattern is therefore not explicitly coded at this stage ofvisual processing.It has been proposed (Adelson & Movshon, 1982) that

the filtering stage is followed by a second stage in whichinformation from the filters is recombined to yield the truedirection of motion. Following Fennema and Thompson(1979), Adelson and Movshon show that the velocity ofany 2-D stimulus, such as the plaid, is fully determinedand is given by the intersectionof the two constraint linesbelonging to the components (see Figure 1). The ques-tion remains whether or not the visual system actuallymakes use of such a process.A possible physiological basis for the second stage has

been reported by Movshonet al. (1986) and Rodman andAlbright (1989) in area MT. Although many of the MTcells were similar to Vi cells in their responses to mov-ing plaids, 30% were different in that they responded tothe true direction ofmovement rather than to the individ-ual components. Movshon et al. (1986) suggest that thesepattern-movement-selective MT cells combine the ori-ented component motions to compute the overall direc-tion of movement. Alternatively, MT cells may receiveinput from nonoriented Vi cells or from the pulvinar(Rodman, Gross, & Albright, 1989), in which case acomponent-to-pattern transformation may be unnecessary.

415 Copyright 1992 Psychonomic Society, Inc.

416 KOOl, DE VALOIS, GROSOF, AND DE VALOIS

Figure 1. Schematic of the patterns used, the aperture problem, and the intersection-of-constraintsmodel for component recombination (adapted fromAdelson &Movshon, 1982, Fig-ure 1). The top figure represents a plaid, the superposition of two gratings, separately repre-sented below. The solid vectors represent the perceived velocities as each pattern is moved tothe right. The dashed lines are constraint lines, representing the familyof motions that are in-distinguishable since only motion perpendicular to the grating orientation results in a changein position. For the plaid (top), the pointof intersection is the single velocity that is consistentwith both sets of constraints.

Psychophysical support for the existence of a secondstage has come fromvarious sources. The “sliding” per-cept of a moving plaid, in which the two components ap-pear to move independently (Adelson& Movshon, 1982;Kooi, De Valois, Switkes, & Grosof, in press; Welch &Bowne, 1990), is likely to reflect the output from the firststage under conditions that do not allow the recombina-tion to occur. Component and pattern motion exhibit dif-ferential adaptation (Movshon et al., 1986) and masking(Ferrera &Wilson, 1987). Welch (1989) showed that thespeed discrimination threshold for a coherently movingplaid is limited by the orientation component stage, sug-gesting that the two stages are serial rather than parallel.Several studies have shown that the perceived direction

of a moving plaid may deviate from the actual directionof motion. The perceived direction is dominated by thecomponent of higher contrast (Stone, Watson, & Mulli-gan, 1990) and lower spatial frequency (Smith & Edgar,1991). Derrington and Suero (1991) examined perceivedplaid direction as a function ofmotion adaptation. The ex-istence of such perceiveddirection errors placesconstraintson models of l-D component to 2-D pattern motion per-ception. Each study suggests that the error in perceivedplaid direction is linked to the perceived speeds of the com-

ponents. The latter two studies quantitatively tested the hy-pothesis by measuring the perceived component speeds andby applying the intersection of constraints model (Adelson& Movshon, 1982) to them. In this way, the errors in per-ceived plaid direction could be accounted for.We have further tested the recombination of 1 -D mo-

tion signals into a pattern motion signal by examining theperceived direction of moving plaids, with componentsdiffering in both contrast and spatial frequency, at threeeccentricities. The motion system has been shown to bedisproportionately sensitive to lower spatial frequencies(Ramachandran &Cavanagh, 1987; Smith &Edgar, 1990),especially in the peripheral visual field (Ramachandran,1987). This leads one to expect the same also to be thecase for the perceived direction of moving plaids. Wedirectly compare some of these perceived plaid directionerrors with the perceived speeds of the individual com-ponents, as a test of the intersection of constraints model.The perceived speeds were measured with two differenttechniques (spatial and temporal forced choice), yieldingdifferent results and clarii~’ingsome of the confusion inthe literature about perceived speed. A unique measure of“perceived speed” therefore does not seem toexist. Stoneand Thompson (1992) recently reached the same conclu-

PROPERTIES OF MOTION SIGNAL RECOMBINATION 417

sion. In another paper (Kooi & K. K. De Valois, 1992),we tested the sameconditions for equiluminant and coloredpatterns such that the results for luminanceand color couldbe directly compared. These results have been presentedin short form elsewhere (Kooi, K. K. De Valois, Grosof,& R. L. De Valois, 1988; Kooi, R. L. De Valois, &Wy-man, 1988).

GENERAL METHODS

ApparatusStimuli were generated by a Data General Nova 4X computer

with a Lexidata graphics unit, as described more fully elsewhere(Switkes, Bradley, & K. K. De Valois, 1988), and displayed ona Mitsubishi RGB monitor. The plaid patterns were made up oftwo 1-cycle/degree (cpd) sine-wave gratings oriented at 45°and135°relative to horizontal, forming a sine—sine plaid. The stimuliwere 2.5° in size. For the foveal presentations, a small fixationdot was placed in the center of the viewing circle in the middleof a small translucent diffuser patch made of tracing paper(radius= 0.67°)that transmitted most of the light but little of the under-lying pattern structure. The stimulus region was surrounded by adiffuser ring with a square drawn upon it to serve as a referencefor vertical and horizontal. The space-averaged luminance of thedisplay was 27.4 cd/rn2, with diffuse background lighting in theroom. The mean chromaticity was yellow (CIE x = 0.504, andy = 0.434).

Spatiotemporal and Contrast LimitationsThe 60-Hz interlaced monitor hada spatial resolution of 26 pixels/

deg at the 172-cm viewing distance. Continuous motion was ap-proximated by small jumps. For low-contrast luminance plaids, thesmall resultant positional jumps were invisible and the motion ap-peared smooth. In addition to the intensity resolution of 8 bits ofthe graphics unit, which allowed the simultaneous presentation of256 intensity levels, the average contrast could be adjusted by meansof an added attenuator that operated under computer control. Thus,a full range of contrasts, including those near threshold, could beaccurately displayed.

SubjectsSix experienced subjects, three of whom (S.L., M.B., and S.S.)

were naive about thepurpose ofthe particular experiments, partic-ipated in theexperiment. Three subjectshad normal vision; the other3 subjects (F.K., D.G., and S.S.) hadcorrected-to-normal vision.

Sensitivity MeasurementsTo scale the various plaid components in terms of visibility or

multiples of threshold contrast, we measured each subject’s con-trast sensitivity for each ofthe sine-wave grating components usedin the plaids. The procedure was the same as that described bySwitkes et al. (1988). Using a temporal two-alternative, forced-choice (2AFC) staircasemethod converging on 75% correct, thresh-olds were measured with a temporally Gaussian-ramped presenta-tion of gratings drifting at 3 Hz. The rise and fall times were100 msec, and the plateau was 500 msec. Feedback was provided.These measurements allowed us to scale the results of subsequentexperiments in terms of multiples of threshold contrasts.’

EXPERIMENT 1Effect of Contrast, Spatial Frequency, and RetinalLocation on the Perceived Direction of Plaids

MethodA drifting plaid pattern was presented, and the subject was asked

to report the apparent direction of motion. Stimuli were randomized

with respect to both the direction of motion and the type of plaidpresented. The predominant, baseline direction of motion was ran-domly chosen to be up, down, to the left, or to the right in orderto avoid directional adaptation or an expectation of a certain direc-tion of motion.On any particular trial, the actual direction of motion of the plaid

differed from one of these baseline directions by a small angle.Within a given session, six different small angles of direction ofmotion were presented in randomorder (methodof constant stim-uli). Each of these could be added to any of the four basic direc-tions. Thus, there could be any of six small deviations from hori-zontal movement to the right, for instance, or six small deviationsfrom vertical upward movement. The speed of the plaid was keptconstant. On each trial, thesubject reported whether the plaid movedtoward thefirst or third quadrant (1-3 quad) or, alternatively, towardthe second or fourth quadrant (2-4 quad). The subjects did notreceive feedback.To reduce an observer’s ability to recognize the patterns, weem-

ployed two mirror images of the same plaid in each block. Fromtrial to trial, this stimulus variable of plaid version was randomlyvaried in addition to the small angle and the basic direction. In to-tal, each trial session contained six directions, two plaid versions(the mirror images), and five trials per condition, yielding a totalof 60 trials per set.2To reduce contamination of the motion of the pattern by an on-

set transient the plaid was presented in a stationary position for333 msec before the pattern beganto move. In preliminaryexperi-ments, we foundno significant effect of movement duration on ourmeasures ofmovement directionoverarangeof 333 to 1,300 msec.The plaids were drifted for 667 msec at 4.24°/sec.Thesubject’s responses for the twomirror-image conditions and

the four main directions (up, down, left, right) were averaged. Pat-terns of results for two mirror versionsshould be opposites of eachother. Any directional bias not dependent on the difference betweenthe sine-wave components, such as a subject’s tendency to preferone pair of quadrants over another, was thereby averaged out.Responses for the direction angles were tabulated in a psycho-

metric function (Figure 2). Perceived-direction responses are plottedversus the actual direction(angle) ofplaid motion. Thedashedlineindicates veridical responses. For the example given, the plaid ap-peared to move slightly off-axis in the direction of the higher con-trast component, while it was actually moving on-axis. To make

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ACTUAL DIRECTION OF MOTION (DEG)

Figure 2. A representativepsychometric function demonstratingthe determination of the direction bias. The percentage of trials inwhich the plaid is seen moving in the direction of the higher con-trast grating component is plotted vertically versus theactual direc-tion of plaid motion. The dashed line indicatesveridical responses.The direction bias is defined as the actual direction of motion forwhich the plaid is perceived to be moving exactly horizontally orvertically (on-axis). The exact location is determined by probit anal-ysis. In the example given, the direction bias iscomputed to he +3.6°.Typical standard errors are on the order of 0.4°.

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418 KOOl, DE VALOIS, GROSOF, AND DE VALOIS

it appear on-axis, the physical pattern direction had to be shifted+ 3.6°.This point was taken as the measure ofthe amount of per-ceptual “direction bias.” The direction bias is defined as the an-gle necessary to make the apparent direction of the plaid on-axis.At still larger deviations fromon-axis, the plaid appeared to movein the direction of the lower contrast component. The location ofthecrossover and the standard errorwere estimated by probit anal-ysis (Finney, 1971) on at least five trial sets (a minimum of 300measurements per data point) for the contrast and retinal locationexperiments and on at least three trial sets for the spatial frequencyexperiment. Typical standard errors, a measure ofthe confidencein the crossover estimate, were on the order of 0.4°.

ResultsContrast. The apparent direction ofmotion was mea-

sured for plaidswith components identical in spatial fre-quency but different in contrast. The contrast ratio (C,1C2)ofthe two components was fixed (0.8), whereas the mean[(C, + C2)/2] ofthe contrasts was varied. Both componentsalways were above threshold. In Figure 3, bias in per-ceived direction isplotted as a function ofmean contrast.It can be seen that as themean contrast increased, the sizeof the direction bias decreased. Thus, at the fixed con-trast ratio (0.8), a lowermean contrast resulted in a largerperceived direction error. The direction bias became verysmall at a mean contrast of about 5 % (with the exceptionthat Subject M.B. showed a small residual effect), whichis approximately 12 times threshold at these spatial andtemporal frequencies. The perceived-direction error istherefore present only over a relatively small contrastrange, demonstrating the robustness of the motion sys-tem with respect to contrast, in agreement withStone et al.(1990). Similar contrast saturations occur in other typesofmotion experiments (motion aftereffect, motion hyper-acuity, speed judgment accuracy, perceived speed, anddirection discrimination: Campbell & Maffei, 1981; Der-rington & Goddard, 1989; Keck, Palella, & Pantle, 1976;McKee, Silverman, & Nakayama, 1986; Nakayama &Silverman, 1985).

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Figure 3. Direction bias for a luminance plaid with componentsof equal spatial frequencies (1 cpd) and unequal contrasts (C,/C2= 0.8). Direction bias (in degrees) is plottedversus the average con-trast of the two plaid components [(C, +C2)/2]. The direction biasis ourmeasureof the error in perceived direction of plaid motion.Positive direction bias indicates that the higher contrastcomponentdominated the perceived directionofmotion. Data are plotted for3 subjects. Except for Subject M.B., significant direction bias oc-curs only below an average contrast of 5%.

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Figure 4. Direction bias for luminance plaids with unequal spa-tial frequencies. The components are 1 and 1.5 cpd. For the fourgraphs, themean plaid contrasts [C = (C, +C2)/2J are 2.25%, 4.5%,9.0%, and 18%. For each graph, direction bias is plotted versus thecontrast ratio of the higher spatial frequency to the lower spatialfrequency component (C,.,/C,.0). The three symbols indicate the 3subjects. Positive direction bias indicates that the higher spatial fre-quency componentdominated theperceiveddirection ofmotion. Forequal multiples of threshold (contrast ratio near 0.95), all subjectsshow low-spatial-frequencydominance at each average contrast level.Only at the lowest average contrast (2.25%) does the high spatialfrequency ever significantly dominate.

Spatial frequency. The original experiment wasrepeated with plaid components of 1.0 and 1.5 cpd. Themeancontrast was fixed at one of four levels, and the con-trast ratio of the components was varied. (In the previousexperiment, the contrast ratio was fixed and the mean con-trast was varied.) At zero direction bias, both componentspeeds were 3°/sec.The contrast sensitivities for thesetwo gratings differ very little (Figure 7 shows data for2 subjects). Averaged over all subjects, equal visibility(i.e., equal multiples of threshold) occurred near a con-trast ratio of 0.95.Thedata from this experiment are plotted in Figure 4.

The four graphs show the same experiment carried outat four different mean contrast levels. Direction bias isplotted versus the ratio of the high spatial frequency tothe low-frequency component contrast. A positive direc-tion bias indicates high-spatial-frequency dominance; anegative direction bias indicates low-spatial-frequencydominance. It canbe seen that at equal multiples of thresh-

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PROPERTIES OF MOTION SIGNAL RECOMBINATION 419

old, the lower spatial frequency component clearly dom-inates the direction of motion of the plaid at all mean con-trasts. Increasing the contrast ratio reduces the amountof the low-spatial-frequency dominance, but only at thelowest mean contrast (2.25%) does the high spatial fre-quency ever dominate. The shallowness of the slopes forthe higher mean contrasts is consistent with the low-contrast saturation demonstrated in the previous experi-ment, which showed that above 5% average contrast theinfluence of a contrast difference is minimal. The low-spatial-frequency dominance, on theother hand, is mostlyindependent of average contrast.

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Figure 5. Direction biasas a function of eccentricity for unequalspatial frequency plaids (1- and l.5-cpd components). For con-venience, the condition in which the plaid is presented between 0.67°and 2.5°eccentricity is indicated by “0 deg eccentricity.” The aver-age contrast is 4.5%, and the contrast ratio 1.0. Data are plottedfor 4 subjects. The amount of direction bias increases significantlywith eccentricity for the unequal spatial frequency plaids.

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Figure 6. Direction bias as a function of eccentricity for unequalcontrast plaids (C,/C~= 0.8). The mean contrasts are 2% and 4%.Data are plotted separately for 2 subjects. Except for the 2% condi-tion at 10°,only a minimal change in direction biasoccurs as a func-tion of eccentricity.

ECCENTRICITY (DEG)

Figure 7. Contrast sensitivity of the plaid components. Log con-trast sensitivity is plotted for 1- and 1.5-cpd horizontal gratings asa function of eccentricity for 2 subjects.

Retinal location. Sample conditions from the previousexperiments were repeated at two locations in the periph-eral visual field. The stimulus was presented at 5°and 10°in the temporal visual field ofthe righteye. The small cen-tral fixation spot used for the previous experiments (herenoted as the 0°,or fovea!, condition) was left out. Usingunequal spatial frequency plaids with4.5% mean contrastand a contrast ratio of 1.0, we found that the low-frequencycomponent dominated perceived direction much morestrongly at 5°and 10°(Figure 5) than it did foveally.The direction bias due to a contrast difference, on the

other hand, is not dependent on eccentricity (Figure 6).We tested unequal contrast plaids (contrast ratio = 0.8)for the 2% and 4% mean contrast conditions. Only at the2% mean contrast at 10°did the directionbias rise signif-icantly, probably due to the reduction in contrast sensitiv-ity (see Figure 7).3

EXPERIMENT 2Relative Perceived Speed of the Plaid Components

MethodTwo psychophysical methods were used: spatial and temporal

2AFC. The spatial or temporal position (left-right or first-second)was randomized from trial to trial. The spatial 2AFC technique hasthe two grating components presented simultaneously at the sameorientation and drift direction, in neighboring apertures. The dura-tion was 500 msec, with lOO-msec on and off ramps. Each aperturewas square, 4.1° on each side, the two being separated by a 0.77°strip. The subject was instructed to fixate between the two patchesand was asked which of the two components appeared to move faster.The speeds varied around a mean of 3°/sec.Threshold was deter-mined by a 2AFC staircase paradigm in which the relative speed ofthe two components was varied. At least eight staircases per condi-tion were run. Typical standard errors were on the order of 1.5%.The temporal 2AFC procedure involved presenting gratings in two

successive 500-msec intervals, separated by a blank period of500 msec, in thesame aperture configuration used for the direction-bias experiments. The subject was again asked which of the two grat-ings appeared to move faster. A method of constant stimuli analo-

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420 KOOI, DE VALOIS, GROSOF, AND DE VALOIS

gous to the direction-bias task was used. Insteadof six different plaiddirections, six different speed ratioswere presented (the average speedwaskept constant at 3°/sec).The data analysis was the same as forthe plaid-direction task.

ResultsContrast. For the unequal-contrast conditions, the higher

contrast grating always appeared tobe moving faster thanthe lower when matched for actual speed. In Figure 8, theperceived-speed ratio is plotted as a function ofmeancon-trast. The largest mismatches were observed at the lowermean contrasts. The temporal technique (filled symbols)yielded noticeably smaller speed mismatches than did thespatial technique (open symbols). A simple change in tech-nique thus can lead to a rather different estimate of per-ceived speed.Spatial frequency and retinal location. The relative

perceived speed of the 1- and 1 .5-cpd gratings was mea-sured for some of our subjects (Figure 9). With the spa-tial 2AFC technique (filled symbols), only small differ-ences were found in the fovea. In the periphery, the lowerspatial frequency grating gained noticeably in perceivedspeed, relative to the higher spatial frequency. With thetemporal 2AFC technique (opensymbols), perceived speedwas measured only in the fovea. Dataare shown for 4 sub-jects. For each, the higher spatial frequency appeared tomove faster than the lower spatial frequency.We do not have a firm explanation for why spatial and

temporal 2AFC differ for both the contrast and spatial-frequency experiments, but we can offer some suggestions.Informally, it seemed easier to extract the true physicalspeedwith the temporal 2AFC paradigm. Attention is nec-essarily divided with spatial 2AFC but not with temporal2AFC. Perhaps two mechanisms to determine speed ex-ist: one attentional and the other not. With spatial 2AFC,the task had a different character; the most natural way

Figure 8. Speed-matching results for componentsdiffering in con-trast (C,/C2 = 0.8). The speed ratio that makes the two gratingsappear tomove equally fast is plotted as a function of the averagecontrast.A positive perceived-speed ratio indicates that the highercontrast grating appeared to move faster atequal speed. Open sym-bols = spatial speed matching (spatial 2AFC for 3 subjects). Closedsymbols = temporal speed matching (temporal2AFC for 2 subjects).Largeperceived speedmismatches only occur at lowmean contrast.

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Figure 9. Speed-matching results for componentsdiffering in spa-tial frequency (1 and 1.5 cpd). The speed ratio that makes the twogratings appear to move equally fast is plotted as a function of ec-centricity. Apositive perceived-speed ratio indicates that the higherspatial frequency grating appeared tomove faster at equal speed.Closed symbols = spatial speed matching (3 subjects). Open sym-bols = temporal speedmatching (4 subjects, only at 00 eccentricity).

to match the two patterns was more according to the“momentum” than according to the speed ofthe gratings.The term “perceived motion strength” thus might be amore suitable choice than “perceived speed,” even thoughthe subjects were instructed to judge speed. In any case,the discrepancy in results suggests that the spatial and tem-poral techniques measure different properties.The perceivedvelocity of a stimulus is dependent on the

motion of the surrounding area (Duncker, 1938). Thisphe-nomenon of motion induction might account for some ofthe difference between the temporal and spatial paradigms.During a temporal presentation sequence, induction clearlycannot play a role since the grating stimulus is the onlymoving element of the display. However, with the spatialspeed-matching technique, as well as with moving plaids,motion induction could play a role, because two movingelements are present in each case (side by side or or-thogonally overlapping). The motion induction would haveto be strongly dependent on contrast.Previous experiments measuring perceived speed have

yielded different and often conflicting outcomes. Thesestudies may be reinterpreted in terms of the spatial versustemporal forced-choicedistinction. On the one hand, high-spatial-frequency slowdown has been reported (Smith &Edgar, 1990); on the other hand, low-spatial-frequencyslowdown has been found (Campbell & Maffei, 1981;Diener, Wist, Dichgans, &Brandt, 1976; Ferrera&Wil-son, 1991; McKee et a!., 1986). The former study (Smith& Edgar, 1990) used a spatial 2AFC paradigm; the latterstudies temporally separated the stimuli invarious ways.Campbell and Maffei (1981), using stimuli separated inboth space and time, found low-contrast slowdown verysimilar to our spatial 2AFC results. The contrast effectsaturated near 5%. Thompson (1982) also recorded low-contrast slowdown with a spatial method of adjustmenttask. His results do not show as strong a low-contrast satu-ration, however. To conclude, perceived speed shows astrong but consistent dependence on the psychophysicalmeasure used.

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PROPERTIES OF MOTION SIGNAL RECOMBINATION 421

RELATION BETWEEN DIRECTION BIASAN!) PERCEIVED COMPONENT SPEED

TheoryThe actual direction ofmotion of a ±450 plaid is linked

to the relative speed of the two components:tan(45 — 0) = S1/S2. (1)

where S1 and S2 are the speeds of the components ando is the angular difference in degrees from the plaid direc-tion whenthe speedsare equal. Similarly, a hypotheticalrelation between the perceived direction of the plaid (asmeasured by the direction bias) and the perceived speedof the components (indicated by lowercase s~and s2) canbe proposed:

tan(45 — direction bias) = s5/s2. (2)

The direction bias is the 0 necessary to make the perceivedplaid direction on-axis; the perceived speed ratio is therelative speed necessary tomake the perceived speeds ofthe components equal. Our direction bias data can there-fore also be viewed in terms of effective “motionstrengths” of the components. Conversely, the measuredperceived speeds of the components can be transformedto yield apredicteddirection bias. For the followinganal-ysis, the relative perceived speeds measured in Experi-ment 2 have been transformed according to Equation 2to yield predicted directionbiases. The validity of the hy-pothesis canbe tested by the degree of agreement betweenpredicted and measured bias.

ContrastIn Figure 10, the measured biases from Figure 3 are

replotted separately for each subject, together with the pre-clicted biases basedupon Equation 2 and our speed-matchingresults. The predicted biases are quite close to the spatial2AFC speed-matching data for Subjects S.L. and F.K.and somewhat less so for Subject M.B., for whom smallerdirection biases were predicted than were observed. Over-all, the perceived-plaid-direction error correlates fairlywell with the perceived-speed error as measuredwith thespatial 2AFC technique, suggesting that pattern directionmay indeed be computed by Equation 2 (or a similar equa-tion), with perceived component speed substituted forphysical component speed. Biases may therefore arisefrom a faulty analysis of the speeds of the 1-D compo-nents rather than froma faulty recombination of the com-ponent signals.

Spatial Frequency and Retinal LocationIn Figure 11, the measured biases from Figure 5 are

replotted separately for 2 subjects, together with the pre-dicted biases based upon Equation 2 and our spatial 2AFCspeed-matching results from Figure 9. Predicted and mea-sured direction biases do not match exactly, though bothcurves show increasing low-spatial-frequency dominance

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4 8 12 16MEAN CONTRAST (%)

L1igure 10. Comparison of perceived-speedand perceived-directionresults for unequal contrast plaids. The direction bias data fromFigure 3 are replotted separately for eachsubject, together with thepredictions based upon the speed-matching results. The measuredrelative speed of the two components is converted into a predicteddirection biasby Equation 2. Closed circles = perceivedplaid direc-tion as measured with the direction-bias technique. Open symbols= expected or predicted direction biases based on the experimen-tally measured relative perceived speeds of the two plaid compo-nents. Open circles = spatial 2AFC. Open triangles = temporal2AFC. With spatial2AFC, the agreement is quite close for SubjectsS.L. and F.K., and for SubjectM.B. itis a little less so. Speedmatch-ing measured with temporal 2AFC always significantly under-estimated the expected direction biases.

with eccentricity. The perceived-speedmeasurements con-sistently underestimate the measured-direction bias. Withfovea! fixation, a direction bias exists even though the per-ceived speedof the two plaid components is nearly equal.The discrepancy is worsewhen plaid direction is comparedwith the temporal 2AFC data (Figure 9) and with mostother speed-matching studies (Campbell & Maffei, 1981;Diener et a!., 1976; Ferrera & Wilson, 1991; McKeeet al., 1986), which show high-spatial-frequency speedup.On the other hand, Smith and Edgar (1991), who mea-sured perceived plaid direction and perceived speed as afunction of overall speed, reached the conclusion that theerrors are well correlated. The lower spatial frequency wasdominant in both cases, the deviations being largest at hightemporal frequencies. For our conditions, however, thecoarser component has an inherent advantage in determin-ing plaid direction overdetermining perceived speed, sug-gesting that there may be more to determining plaid direc-tion than the perceived speed of the components alone.

•—• OBSERVED

6 0—0 PREDICTED (SSU)

V—V PREDICTED (TSM)4-

FK

FI— ,.~(‘ -

~ ?~~a:°0

6

MB9~o~

422 KOOI, DE VALOIS, GROSOF, AND DE VALOIS

FK

_0—

ssI I0 5 10ECCENTRICITY (DEG)

Figure 11. Comparison of perceived-speed and perceived-directionresults for unequal spatial frequency plaids. The direction-bias datafromFigure 5 are replotted separately for 2 subjects, together withthe predictions basedon the speed-matching results. The measuredrelative speed of the two components is converted into a predicteddirection bias by Equation 2. Closed circles = perceived plaid direc-tion as measured with the direction-bias technique. Open circles =expected direction biases based on the experimentally measured rel-ative perceived speedsof the two plaid components. Both measuredandpredicted direction biasesshowmore low-spatial-frequency dom-inance in the periphery. However, the two do not match quantita-tively. The perceiveddirection of unequal spatial frequency plaidstherefore cannot be completelyaccounted for by the perceived speedsof the components.

DISCUSSION

Thepercept of a sliding versus a coherent sine-wave plaidhas been the subject of several psychophysical and theo-retical studies. The main concerns have been to understandwhat detennines whether the plaid appears coherent (Adel-son & Movshon, 1982; Kooi et al., in press; Krauskopf& Farell, 1990; Welch & Bowne, 1990), and what direc-tion and speed is assigned tocoherent plaids (Derrington& Suero, 1991; Ferrera&Wilson, 1990; Heeger, 1987;Kooi & K. K. De Valois, 1992; Smith & Edgar, 1991;Stone et al., 1990). The other goal is to elucidate themechanism by which the components could be firstdecomposed and then recombined. Weconfirmed two fac-tors that cause the perceived direction ofmotion to devi-ate from the real physical direction. A plaid’s trajectoryis biased toward the directionof the component of highercontrast or lower spatial frequency. The size of the latteradvantage is dependent on the eccentricity.

Relation Between Perceived Direction and SpeedThe reasonable agreement between measured- and

predicted-direction biases due to a contrast difference (mea-sured with spatial 2AFC) indicates that the perceiveddirec-tion of motion of a plaid can be accounted for by the per-

ceived, rather than real, speeds of its components. Theagreement indicates a common source for the two errors.The intersection-of-constraints model canbe made to in-corporate these results by letting it operate on perceived,rather than real, speed. This agreement supports the ex-istence of a component-to-pattern transformation precededby a Fourier-like decomposition and provides support forthe intersection-of-constraints model as the recombina-tion mechanism. Ourresults are also consistent with a vec-tor summation model, because in our experiments theplaid components were always oriented perpendicularly.However, the inadequacy of vector summation is easy todemonstrate with plaids of other relative orientations(Movshon et al., 1986) and is not a realistic option forthe component-to-pattern transformation.A possible second source of plaid direction mispercep-

tion, low-spatial-frequency dominance, appears tobe in-dependent of the direction bias due to contrast. In addi-tion, for our limited conditions, this error can onlypartially be accounted for in terms of perceived compo-nent speed, suggesting that part of the “error” may bemade in the component-to-pattern transformation itself:the lower spatial frequency appears to be weighted moreheavily than one would expect on the basis of its speed.Given the results of Smithand Edgar (1991), who did findreasonable correlations between apparent plaid directionand perceived speed at other temporal frequencies, it isunclear whether this interpretationcan be extrapolated toother spatial or temporal frequency combinations.We suggest that the low-spatial-frequency dominance

may be akin to the motion capture described by Rama-chandran and Cavanagh (1987), in that the higher spatialfrequency component appears to move along with thelower spatial frequency component. Our stimulus is dif-ferent though in that the plaid is moving rigidly; the ex-amples in the literature ofmotion capture all involve con-flicting motion stimuli. One simple explanation for themotion capture we observe is inhibition or masking fromlow- onto high-spatial-frequency mechanisms at a stagepreceding the component signal recombination stage. Themotion signal from the low-spatial-frequency channelwould thereby be weighted more heavily than that fromthe high-spatial-frequency channel, not only in perceiv-ing plaids but also in experiments with compound 1-Dgratings (Grosof, 1989).The increase in low-spatial-frequency dominance with

eccentricity, both in perceived plaid direction and rela-tive perceived speed, is consistent with the increase ofmotion capture in the periphery reported by Ramachan-dran (1987). We suggest that the visual system assignsa strongerweight to low-spatial-frequency motion signalswhen the short-range motion system is adequately stimu-lated (e.g., in the present experiments), as well as whenit is not (e.g., in Ramachandran & Cavanagh, 1987).An alternative explanation for the analysis of plaid

direction is that the visual system detects the movementof the intersections (“blobs”) rather than integrating thecomponent motions. The direction biases could be dueto the asymmetric profiles (shapes) of the nodes in the

6

0

—6

—12

•—S OBSERVED0—0 PREDICTED (SsM)

~(0LU0

(1)

0I-(0LU

a 0

—6

—12

PROPERTIES OF MOTION SIGNAL RECOMBINATION 423

plaids (Perrone, 1990). Given the other evidence for theexistence of a component stage and the reasonableexpla-nation of the direction-bias data by the misperception ofcomponent speed, the interpretation offered above is morelikely. The agreement between judged direction of motionand perceived speed shown in Figure 10 would have tobe pure coincidence or would have to be the result of amechanism relating component speed and pattern direc-tion other than the simple one described in Equation 2. Thestrong correlation between perceived plaid direction andperceived component speed obtained with equiluminantplaids (Kooi & K. K. De Valois, 1992) also strongly favorsan initial decompositionand subsequent recombination ofa plaid. However, the possibility that perceived plaid direc-tion is determined from a combination of component andnode motions is left open. Different experimental condi-tions might highlight one or the other.

SlidingAdelson and Movshon (1982) showed that the amount

of sliding in a plaid is dependent upon the contrast andspatial frequency difference between the two componentgratings. The plaids with components of unequal contrastbut equal spatial frequencies always appeared coherent.In order to maximize the coherence of the other plaids,the spatial frequency difference was chosen to be small,a factor of 1.5. Nevertheless, the unequal spatial fre-quency plaidsdid exhibit a small amount of sliding (Kooiet al., in press), making it more difficult to judge thedirection ofmotion. Smith and Edgar (1991), using 1- and3-cpd components, also acknowledge the occurrence ofthe sliding percept. Ferrera and Wilson (1990) found thatthe apparent direction of a partially sliding plaid couldbe nonveridical. (Their plaids probably exhibited somesliding due to the large differences in component orien-tation and temporal frequency.) This suggests the possi-bility that sliding may be a necessary condition for theperceived-direction error, due to a spatial frequency dif-ference, to manifest itself. However, all observers notedthat the amount of sliding did not change with eccentricviewing; if anything, the plaids became more coherentas eccentricity increased. This result argues against thesuggestion that direction bias depends strongly on motionincoherence, since the size of the direction bias increasedwith eccentricity .3

Possible Relation to PhysiologyMovshon et al. (1986) have suggested that MT is the

area involved in combining the component motions (1-D)into the pattern motion (2-D) because some cells respondto pattern direction, not component direction. Further-more, area MT receives its main input from the magnopathway (DeYoe & van Essen, 1988), which is generallyconsidered to be specialized for the detection and process-ing ofmotion (Livingstone & Hubel, 1987; Zeki, 1978).If indeedMT is critical in the perception of direction, then

the processes responsible for the apparent slowdown ofsome grating patterns and the spatial frequency interactionmust occur at or before MT.The rapid falloff of the perceived-direction and

perceived-speed errors as a function of contrast showssimilarities to physiological contrast saturation observedin the M pathway (Sclar, Maunsell, & Lennie, 1990;Shapley, Kaplan, & Soodak, 1981), as explained in de-tail in Stone et a!. (1990). Nakayama and Silverman(1985) proposed that the psychophysical contrast satura-tion found in various motion tasks, such as motion after-effects and motion hyperacuity, may be linked to thisphysiological saturation of cells in the magno stream. Themotion errors found with both of our techniques, plaid-direction bias and speed matching, disappear near 5% con-trast. IfNakayama and Silverman’s hypothesis is correct,the motion system is subject to error when cells in themagno stream are not saturated. Thecomponent-to-patterntransformation thus may only operate completely correctlyon input that is invariant with contrast.Regarding the site of low-spatial-frequency dominance,

Grosof (1989) examined interfrequency interactions be-tween two components of the same orientation but withopposingmotion energy in area V 1. Not finding the kindneeded to explain motion capture, he concluded that itmust occur at a later stage in the visual pathway.4 It wouldtherefore be interesting to examine V2-and MT cells forthe presence of low- on high-spatial-frequency inhibition.

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NOTES

1. Threshold was measured at 3 Hz, As the direction of movementof a plaid is changed, one component increases and the otherdecreasesin speed. Consequently, the measured contrast sensitivities would beslightly off, the inaccuracy depending on the direction ofmotion of theplaid and on the slopeof the contrast sensitivity function near our stim-ulus conditions. We chose conditions such that the rangeof plaid direc-tions was small and the errors in contrast sensitivity were negligible.2. For some experiments, a slightly different technique was used.

Rather than presenting one of the two mirror versions of the plaid andasking toward which quadrant it appeared to move, both versions werepresented in succession and the subject was asked toward which quad-rant the second plaid moved relative to the first plaid. The order of theplaid presentations was randomized. The main advantage of this tech-nique is that the subject is required to compare only the perceived direc-tions of two plaids rather than the direction of the plaid relative to anexternal frame. We did not find significant differences in the resultsfrom these two techniques.3. The observed changes in plaid-direction bias at 10°eccentricity,

but not at 5°,could be due to changes in contrast sensitivity with ec-centricity (Figure 7). At 10°,the contrast sensitivity of both frequen-cies drops and the relative sensitivity changes in favorof the lower spa-tial frequency component. The latter effect should increase thelow-spatial-frequency dominance. At 5°,the relative contrast sensitiv-ity remains the same, yet a significant increase in low spatial frequencyis observed.4. Interfrequency inhibition has been reported by, among others, K. K.

De Valois and Tootell (1983). However, the inhibition they reporteddid not show the spatial frequency asymmetry necessary to explainmo-tion capture.

(Manuscript received September 19, 1991;revision accepted for publication April 2, 1992.)