Perception &: Psychophysics 1991, 49 (3), 230-244 The interplay between and structure from motion

MARK NAWROT and RANDOLPH BLAKE Vanderbilt University, Nashville, Tennessee

In a series of psychophysical experiments, an adaptation paradigm was employed to study the influence of stereopsis on of rotation in an ambiguous kinetic depth (KD) display. Without prior adaptation or stereopsis, a rotating globe undergoes spontaneous reversals in per­ ceived direction of rotation, with successive durations of perceived rotation being random vari­ ables. Following 90 sec of viewing a stereoscopic globe undergoing unambiguous rotation, the KD globe appeared to rotate in a direction opposite that experienced during the stereoscopic adap­ tation period. This adaptation aftereffect was short-lived, and it occurred only when the adapta­ tion and test figures stimulated the same retinal areas, and only when the adaptation and test figures rotated about the same axis. The aftereffect was just as strong when the test and adapta­ tion figures had different shapes, as long as the adaptation figure contained multiple directions of motion imaged at different retinal disparities. Nonstereoscopic adaptation figures had no ef­ fect on the perceived direction of rotation of the ambiguous KD figure. These results imply that stereopsis and motion strongly interact in the specification of structure from motion, a result that complements earlier work on this problem.

This paper documents the interplay between stereop­ space; in the other instance, information is integrated over sis and motion information in the generation of three­ time. Besides their geometric similarities, stereopsis and dimensional (3-D) surface perception in human vision. motion also yield comparable levels of perfor­ It has long been known that retinal disparity can create mance on tasks involving the measurement ofdepth sen­ a robust sensation of depth and solidity (Wheatstone, sitivity (Rogers & Graham, 1982). Moreover, both stere­ 1838), and its effectiveness is most dramatically revealed opsis and motion parallax yield equivalent variations in in the case of texture stereograms devoid of monocular perceived depth that are dependent on the retinal orienta­ information about shape (Julesz, 1971). Equally impres­ tion of the depth gradient (Rogers & Graham, 1983). sive is the recovery of shape information when an ob­ Stereopsis and motion are also similar in that both are ject is viewed under conditions of motion (Wallach & degraded at equiluminance. Lu and Fender (1972) found O'Connell, 1953). Motion information can even reveal that stereopsis with random-dot stereograms was markedly the surface structure ofan object that is literally invisible impaired when the chromatic stereopair was equiluminant. when stationary. This well-known effect, sometimes called Similarly, Ramachandran and Gregory (1978) reported the (KDE), has received much atten­ that moving contours at equiluminance yield very feeble tion in recent years (Braunstein & Andersen, 1984; Lappin . The exact extent to which stereopsis & Fuqua, 1983; Sperling, Landy, Dosher, & Perkins, and motion perception are impaired at equiluminance re­ 1989; Todd, 1984, 1985). mains unsettled (Shapley, 1990). As numerous authors, including Helmholtz (1909/ Are these similarities between motion parallax and ste­ 1962), have pointed out, stereopsis and motion parallax reopsis coincidental or do they reveal important linkages are comparable geometrically. In the case of stereopsis, in the underlying processing architecture? Several lines of the utilizes two views ofa scene from slightly differ­ evidence suggest that the similarities are more than coin­ ent perspectives (i.e., the difference in location ofthe two cidental. For example, a significant correlation has been eyes) to derive a description of an object's depth and reported between an observer's level of competence on a shape. Similarly, from a single vantage point, slightly stereopsis task and thatperson's ability to judge depth when different views ofan object over time form the basis for given motion information. Specifically, Richards and the KDE. In one instance, information is integrated over Leiberman (1985) tested observers with varying degrees ofimpairment in stereopsis, as indexed by a deficiency to judge depthfrom disparity information. Next, Richards and Preliminaryresults from some of these experiments have been reported Leiberman measured the ability of these observers to iden­ in Nawrot and Blake, 1989. This work was supported by NIH Grant tify and judge the apparent 3-D size of a dynamic 2-D EY07760 and NIH Vision Core Grant P3D-EY08126. We thankMyron Braunstein for helpful discussion. Correspondence should be addressed display. The correlation between stereo performance and to Randolph Blake, Department of Psychology, Vanderbilt University, kinetic depth was 0.72. Richards and Leiberman also ob­ Nashville, TN 37240. served that people who performed particularly well on

Copyright 1991 Psychonomic Society, Inc. 230 STEREOPSIS AND STRUCTURE FROM MOTION 231

stereo displays containing crossed disparity information study, Wallach et al. used a mirror to exag­ also tended to exhibit better performance on the KD task, gerate the retinal disparities associated with viewing a whereas stereo performance with uncrossed disparities rotating wire figure. Following prolonged inspection of was less predictive of KD performance. Richards and this exaggerated stereoscopic depth, observers perceived Leiberman concluded that the outputs from kinetic depth a stationary version of the figure to be flattened, or com­ mechanisms and from convergent stereoscopic depth pressed in depth, even though it contained the same ex­ mechanisms are combined prior to an object's assignment aggerated disparities. This so-called satiation effect was to a given depth. While not quarreling with this conclu­ not observed, however, when the test figure was a mon­ sion, Bradshaw, Frisby, and Mayhew (1987) found that ocularly viewed KD version of the figure, implying that observers were adept at detecting structure from motion stereoscopic satiation did not generalize to motion. In a in displays imaged entirely at uncrossed disparities; this later paper, Wallach and Karsh (1963) proposed that the led them to question the tightness of the linkage between initial effect ofadaptation to exaggerated disparity results crossed disparities and KD. from the discrepancy between the depth signaled by KD Quite recently, Howard and Simpson (1989) reported and the depth signaled by the exaggerated disparities. that the gain of optokinetic nystagmus varies inversely According to this view, then, kinetic depth information with binocular disparity, which they attributed to neurons plays an essential role in the modification ofstereoscopic sensitive to both disparity and direction of motion. As . Richards (1985) pointed out, linkage between stereopsis In the present paper, we give the results of a series of and motion processing could serve to resolve ambigui­ psychophysical experiments in which we examined in ties inherent when disparity information or motion paral­ closer detail the interactions between stereopsis and mo­ lax information is available on its own. tion information in the specification of structure from mo­ Cross-adaptation studies also imply some form of in­ tion. We utilized a version of the cross-adaptation para­ teraction in the processing of stereoscopic information and digm, whereby adaptation to a stereoscopically defined, kinetic depth information. Smith (1976) found what he rotating object subsequently biases the perception of ro­ termed a "contingent depth aftereffect" with Lissajous tation ofan object defined solely by motion information. figures (a type of KD display easily generated on an os­ In particular, we have assessed the necessary and suffi­ cilloscope by applying the same signal to the horizontal cient stimulus conditions for adaptation by various 3-D and vertical amplifiers; see Braunstein, 1962). Viewed figures to affect the perception of subsequently presented normally, a Lissajous figure undergoes spontaneous rever­ 2-D figures. sals in the direction ofapparent rotation. However, place­ ment of a neutral density (ND) filter in front of one eye MEmOD produces a strong bias in the perceived direction of rota­ tion, presumably by generating a retinal disparity cue from Stimuli and Displays interocular delay (i.e., the Pulfrich effect). Smith found TIlestimuli for these experiments consisted of computer-generated that when the ND filter was removed following a 30-sec random-dot cinematograms depicting objects rotating in depth. Each observation period ofunambiguous motion, the Lissajous frame in a given cinematogram was a 2-D, parallel projection "snap­ shot" of the object at some degree of rotation around a stationary figure appeared to rotate in the direction opposite that ex­ axis in the mathematicallydefined3-D coordinate system. Presenting perienced with the filter in place. The stereo cue, in other the cinematogram frames quickly in succession on the face of the words, disambiguated the motion cue, and this disambig­ video monitor produced the KDE of a rotating object. Although uation in tum yielded a pronounced visual aftereffect. A the KD figure presented on a single monitor appears vividly to be rather similar cross-adaptation result was described by 3-D, it is devoid of retinal disparity information andis, hence, non­ Rogers and Graham (1984). They had observers stare at stereoscopic. Therefore, we will term the KD figure without dis­ a corrugated surface whose depth undulations were un­ parity "2-D" andthe KD figure with disparity information "3-D." It is important to keep in mind that the terms 2-D and 3-D refer ambiguously defined either by binocular disparity or by to the absence or presence of disparity information, not to the 3-D motion parallax created by perspective projection of mo­ quality of the resulting percept. tion translations. I Following this period of adaptation to With these random-dot cinematograrns, stereoscopic depth is depth, the observers viewed an ambiguous surface whose generated by presenting separate views ofthe 2-D figure to the left periodic depth corrugations could be seen in either oftwo and right eyes; slight differences between each eye's view simu­ phases. The observers reported that the perceived peaks late the conditions experienced with natural viewing. In a given instance, one eye views a slightly earlier or later frame in the and troughs appeared spatially in antiphase to the actual cinematogram sequence thandoes the other eye (Dosher, Sperling, undulations experienced during adaptation. This after­ & Wurst, 1986). The resulting stereoscopic information unambig­ effect was measurable even when the unambiguous adap­ uously specifies the direction of the figure's rotation; accordingly, tation surface was specified by motion parallax and the we will refer to this as the 3-D display, in contrast with the ambig­ ambiguous, postadaptation surface was specified by ste­ uous 2-D display. reopsis, and vice versa. The basic stimulus comprised 200 small (2' x 2') black dots depicting random placement on the surface of a 3-D sphere with Contrary to the above results, however, Wallach, 0 a diameter of 2.5 • The cinematograrns were created by rotating Moore, and Davidson (1963) found that KD was un­ the sphere 2 0 about its vertical axis between the generation of each affected by prior adaptation to stereoscopic depth. In their frame, thereby using 180 frames to depict the entire revolution of 232 NAWROT AND BLAKE

the sphere. The cinematograms were shown with a 30-msec frame 20 rate. To promote stable fixation during stereoscopic adaptation, a small cross (6' x 6') was shown in the center of the cinematograms. "0 15 A larger cross extended from the top and sides of the 180-pixel OJ (3°) diameter aperture (within which the cinematogram was pre­ ~ c sented) to the edges of the monitor. This larger cross helped keep o the fixation plane in register. An illustration of this stimulus con­ .~ figuration appears in Figure 1. c:J

Apparatus The cinematograms were generated and presented with a Macin­ 20 40 60 80 tosh computer on two matched- monochrome monitors (66.7-Hz n Successive periods of perceived rotation noninterlaced frame rate; P4 phosphor; 72 pixels/in.), While com­ fortably seated in a darkened room, the observer viewed these Figure 2. Successive durations of perceived rotation of an ambig­ matched monitors through a mirror stereoscope from an effective uous 2-D globe. Individual durations fluctuate randomly over time. viewing distance of 114 em. The observer used the keys on the A regression line fit to these data (not shown) had a negligible slope, computer terminal to signal responses, which were recorded by the indicating no tendency for durations to increase over the Io-min computer. tracking period.

Procedure Each trial consisted of a 9O-sec adaptation period immediately +" 1.00 followed by a 15-sec test period. Throughout the entire adapta­ c (IJ tion/test sequence, the observer tracked the direction of rotation o 0.75 ofthe figure by pressing one key to signal clockwise rotation (viewed -Qi 0.50 from the top) and another key to signal counterclockwise rotation. o The direction ofperceived rotation was tracked throughout the en­ o tire adaptation and test portions of a trial, and following each trial the observer rested for at least 2 min. Observers completed a of four trials with clockwise adapta­ ·0.25 tion and a set of four trials with counterclockwise adaptation; the -0.50 order of these two sets of trials was random. At least a 5-min break was interposed between the two sets oftrials, and an eight-trial ses­ -0.75 sion was usually completed within an hour. In earlier experiments (e.g., Rogers & Graham, 1984), observers simply indicated the appearance ofthe test display immediately fol­ lowing adaptation. However, we had observers track the test dis­ Lags play's direction of rotation for a period of time after adaptation. Figure 3. Autocorrelation coefficients over 25 lags. This analysis This tracking measure provides a more complete index of the ef­ was performed on the durations depicted in the previous figure. fectiveness of adaptation and information on the time course of recovery from adaptation.

Observers The observers consisted of2 naive, paid observers-one with nor­ RESULTS mal visual acuity (L.G.) and one with visual acuity corrected to normal (D.T.)-and the 2 authors (M.N. and R.B.), both with nor­ The Basic Phenomenon mal visual acuity. A few additional people within our laboratory When viewing the orthogonal projection of a rotating (all naive) also participated in the first experiment. KD figure, an observer experiences spontaneous rever­ sals! in the perceived direction of rotation (Fisichelli, 1947; Howard, 1961). We measured the temporal proper­ ties of these spontaneous perceptual reversals by having an observer track the reversals of a rotating 2-D globe (i.e., identical cinematograms presented to the two eyes) for 10 min. The results from this experiment are shown in Figure 2. There is no obvious periodicity in the suc­ cessive durations ofperceived rotation, nor is there a ten­ dency for durations to lengthen over time. To test specif­ left eye right eye ically for stochastic independence, an autocorrelation analysis was performed on the successive durations, for Figure I. Schematic of left- and rigbt-eye displays (not drawn to 25 lags. The resulting correlation coefficients, shown in scale). Cinematograms could be presented separately to the two eyes, Figure 3, were small and fluctuated irregularly around and except where noted, the rotating figure appeared centered on zero; this analysis hence reveals no hint of temporal de­ the display. A fixation mark and set of cross-hairs served as binocular fixation stimuli and defined the plane of zero disparity. The globe pendencies in the successive durations of perceived rota­ figure shown here represents one pair of stereoscopic frames from tion. Figure 4 shows the frequency distribution of these a cinematogram depicting a 3-D rotating globe. individual durations. STEREOPSIS AND STRUCTURE FROM MOTION 233

Recovery seems to be complete (i.e., either direction is equally probable) within 45 sec. In a second experiment, we interspersed a variable­ duration "blank" period between the 9O-sec adaptation phase and a 15-sec test phase. During this blank period, the observer kept the eyes closed until an auditory signal cued the observer to open the eyes and track the rotation of the 2-D globe. Figure 6B shows the total time during the 15-sec test period that the observer experienced the 2-D globe to be rotating in a direction opposite that seen during adaptation. Here it can beseen that the aftereffect

0-2 2-4 4-6 6-8 8-10 10-12 12-14 >14 decays monotonically during this blank period, although Phase duration (sees) the rate ofdecay is less than that measured when motion Figure 4. Frequency distribution of the individual durations of is experienced throughout the period following adapta­ perceived rotation depicted in Figure 2. tion (i.e., compare the slopes of the curves in Figures 6A and 6B). Retinal specificity of the aftereffect. Earlier experi­ In summary, individual durations of perceived rotation ments had yielded evidence for perceptual coupling be­ in a given direction resemble the durations ofperception tween the perceived direction of rotation of two spatially found with other kinds ofambiguous figures (Borsellino, separated 2-D rotating objects (Eby, Loomis, & Solomon, De Marco, Allazetta, Rinesi, & Bartolini, 1972; De Marco 1989). Such KD figures, in other words, appear to rotate et al., 1977) as well as the durations of in the same direction, and they reverse directions in phases (Fox & Herrmann, 1967). synchrony. This coupling suggests that the neural events underlying KD are rather global in nature. Is the effect Disambiguating the Perceived Direction of 3-D adaptation on 2-D motion also spatially exten­ of Rotation sive? To answer this question, we made measurements Retinal disparity information effectively disambiguates with the figure viewed during adaptation imaged on a dif­ the direction ofrotation ofa KD figure (see, e.g., Dosher ferent area ofthe retina from that on which the test figure et al., 1986). In particular, when a given cinematogram was imaged. frame is presented to the left eye slightly in advance of For this experiment, the center of the 3-D adaptation its presentation to the right eye, the object appears to ro­ globe was situated 10 to the left ofthe fixation mark, while tate clockwise (Burr & Ross, 1979). Reversing the tem­ the 2-D test figure was imaged 10 to the right offixation. poral order (i.e., right eye leading the left eye) causes the perceived direction of rotation to be counterclockwise. For most observers with normal stereo vision, this reti­ LG MN RB DT HW yy nal disparity information stabilizes the perceived direc­ 0- CD 15 tion of rotation. ~ c:: Q) .Q -iii 10 0 Adaptation of 2-D Motion by Stereopsis a. ~ a. 5 For our basic experiment, we had observers adapt to ~ 0 "0 a rotating 3-D (i.e., stereoscopic) globe and then track (ij 0 fluctuations in the perceived direction of rotation of an Q) 2 E 5 I1l ambiguous 2-D globe. After adaptation to the stable 3-D CD en C> figure, the rotation ofthe previously ambiguous 2-D figure eu 10 "- was predominantly perceived to be in the direction oppo­ CD > 15 site that experienced during the adaptation period (see -c Figure 5). Recovery from adaptation. Casual observation sug­ Figure 5. Effect of 90 sec of adaptation to a rotating 3-D gested that 90 sec of stereoscopic adaptation effectively (stereoscopic) globe on perceived direction of rotation of an ambig­ biased the 2-D figure's direction of rotation for somewhat uous 2-D globe viewed for a 15-sec test period immediately foUow­ less than a minute. To measure the actual time course of ing adaptation. Each histogram is the average of eight adaptation! test episodes, four with the adaptation globe rotating clockwise and recovery from 3-D adaptation, we had 2 observers track four with it rotating counterclockwise. Values plotted below the zero the perceived direction of rotation of the 2-D globe for line indicate rotation in the direction experienced during adapta­ 75 sec following a 90-sec period of stereoscopic adapta­ tion (same) and values above this line indicate rotation in the direc­ tion. Figure 6A divides this 75-sec postadaptation period tion opposite that experienced during adaptation (opposite). Verti­ into 15-sec bins and shows for each bin the proportion cal bars denote I SD. The test rlgDl'e sbowed a pronounced tendency to be seen rotating in the direction opposite that experienced dur­ of time the observer perceived the 2-D globe to be rotat­ ing adaptation, regardless of which adaptation direction was ex­ ing in a direction opposite that present during adaptation. perienced. 234 NAWROT AND BLAKE

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Figure 6. Recovery from 3-D adaptation. Each data point gives the average (n = 4) total duration that the 2-D test figure appeared to rotate in a direction opposite that experienced during an initial 9O-sec period of 3-D adaptation. In both panels, a value of 7.5 sec indicates no biasing effect. The vertical bars represent I SE. (A) Each data point summarizes the results for successive 15­ sec periods foUowing the end of adaptation. (8) Each data point summarizes the results for a IS-sec test period administered sometime after the termination of adaptation, with the abscissa specifying the duration elapsing between the end of adaptation and the beginning of the test.

The observers were instructed to maintain fixation on the tion. The latter finding implies that the results in Fig­ center cross at all times (fixation was not objectively moni­ ure 7A are not attributable to weak interhemispheric con­ tored). Two observers were tested under these conditions, nections. with four trials devoted to each of two adapting direc­ To becertain that peripheral stimulation per se was not tions of rotation. Adaptation lasted 90 sec and the 15-sec responsible for these results, a control condition was in­ test period followed immediately. As summarized in Fig­ cluded, in which the adaptation and test figures both ap­ ure 7A, both directions of rotation were experienced fol­ peared 10 to the left of fixation. Now, with both figures lowing 3-D adaptation. This failure of adaptation to bias imaged on the same retinal area, adaptation was very ef­ perceived rotation implies that the adaptation effect is reti­ fective in temporarily disambiguating the perceived direc­ nally specific, not global. The same pattern ofresults was tion of rotation, as is shown in Figure 7B. Thus peripheral found when the adaptation figure appeared 10 above the stimulation alone is not responsible for the results in fixation mark and the test figure appeared 10 below fixa- Figure 7A. STEREOPSIS AND STRUCTURE FROM MOTION 235

very little spatial spreading. Evidently the mechanisms 15 RS MN underlying adaptation differ from those responsible for '" 10 .~ perceptual linkage between multiple KD figures (Eby 0 0. 5 0. et al., 1989). In the same vein, Toppino and Long (1987) 0 found that the reversals in the perceived direction of a A u rotating Necker cube could be influenced by local, but Q) E'" 5 .e '"en not global, adaptation. c: 10 0 Adaptation to nat planes of motion seen in depth. .~ 15 Petersik, Shepard, and Malsch (1984) have proposed the "0'" existence of mechanisms responsive to the direction of rn rotation of objects in 3-D space. Such putative mecha­ § RS MN Q) 15 nisms could be invoked to explain the results reported in Cl ~ this paper. Rather than the "direction-selective rotation Q) .~'" 10 0 ~ 0. detectors" ofPetersik et al., however, one could also en­ 0. 5 0 vision a simpler explanation in which adaptation takes B place within unidirectional motion sensors (e.g., mecha­ Q) E 5 nisms of the sort posited by Watson & Ahumada, 1985) '"en 10 that are disparity-selective. These mechanisms would be selectively stimulated by the front and rear surfaces of 15 Figure 7. Average (n = 8; vertical bars denote 1 SD) total dura­ a rotating figure. To test the feasibility of this simpler ex­ tion of perceived rotation in the direction experienced during adap­ planation, we performed the following experiment. tation (same) and in the direction opposite that experienced during We created a stimulus that presumably would adapt adaptation (opposite); (A) 3-D adaptation rJgUre and 2-D test figure mechanisms specific for motion and stereo depth, but not were imaged on different retinal areas; adaptation had no effect. mechanisms responsive to rotation specifically. The dis­ (8) Adaptation and test figures were imaged on the same retinal areas, parafoveally from the rlXation mark; adaptation had a play consisted of two sheets of dots moving in opposite pronounced effect. directions, with one sheet placed in crossed disparity rela­ tive to the plane of fixation and the other sheet placed in uncrossed disparity. Each plane was composed of 100 Next we tried imaging the adaptation and test figures dots, and each dot made a horizontal excursion of2 pixels on more nearly adjacent retinal areas, to learn whether from frame to frame. A new frame was presented every the spread of adaptation might be found over smaller reti­ 30 msec. The magnitude of the disparities was 2', an nal distances. To implement this experiment, we halved amount that placed the two sheets of dots at the same dis­ the diameter of the adaptation and test globes, so that the tance from fixation as the front and rear surfaces of the 100 dots comprising the figure were contained within a 3-D globe used in our earlier experiments. The two planes 1.250 diameter circular region. When imaged on the same of dots appeared within a circular aperture, 2.5 0 in di­ retinal area, the small 3-D adaptation globe was very ef­ ameter (i.e., the same size as the cross section of the fective in biasing perception of the small 2-D test globe. sphere). The observers adapted to this modified 3-D When, however, the 3-D adaptation globe was situated stimulus for 90 sec and then tracked reversals in the direc­ up and to the left of fixation and the 2-D test figure was tion of rotation of the 2-D sphere. placed down and to the left, no biasing effect on perceived Adaptation to these multiple planes of moving dots rotation was found. This was true even though the two produced a robust aftereffect. When the front plane of small figures together occupied an area of the retina no dots moved leftward and the back plane rightward, the larger than that stimulated by a single, normally sized 2-D globe subsequently appeared to rotate counterclock­ globe. wise during the 15-sec test period. Reversing the direc­ Finally, we tried a condition in which the 3-D adapta­ tions of motion of the 3-D planes of dots reversed the bi­ tion and 2-D test figures appeared in the same location asing effect on the 2-D globe. We next tried adapting in visual space but were imaged on different retinal areas observers to a single sheet of moving dots imaged either during adaptation and during test. For this condition, the at 2' crossed disparity or at 2' uncrossed disparity (i.e., adaptation and test figures both appeared exactly in the a single component of the multiplane stereo figure). This center ofthe display (i.e., objectively straight ahead from condition of adaptation produced no effect on the rever­ the observer's vantage point). During adaptation, the ob­ sals in direction of the subsequently viewed 2-D figure. server fixated the left-hand edge of the 3-D figure, and These results are consistent with the hypothesis that during testing, the observer fixated the right-hand edge adaptation affects direction-selective motion sensors of the 2-D figure. (Thus the two rotating figures appeared whose activity is disparity-specific. Of course, one can in the same visual location, although they were imaged argue that two sheets of dots imaged at different dispari­ on different retinal areas.) This condition produced no bias ties approximate the front and rear surfaces of a large in the perceived direction of rotation of the test figure. sphere viewed through an aperture. Hence the neural pro­ These observations thus lead us to conclude that ste­ cess revealed by 3-D adaptationcould still be one designed reoscopic adaptation is tied to retinal coordinates, with to signal the direction of 3-D rotation. This argument also 236 NAWROT AND BLAKE implies that the conventional motion aftereffect resulting sion of this model has been detailed elsewhere (Nawrot from adaptation to a single sheet ofdots flowing in a sin­ & Blake, 1990, in press). gle direction arises from prolonged stimulation of this Specificity ofrotational axis. If3-D adaptation arises putative rotation-signaling mechanism when it "views" from simultaneous stimulation of direction-selective sen­ just the front surface of a large, opaque sphere exposed sors responsive to a given disparity, adaptation and test through a small aperture. , however, that a single figures would need to have common directions ofmotion sheet of adapting dots did not bias the direction of rota­ for biasing to occur; adaptation and testing with perpen­ tion ofa 2-D figure, which undermines the argument for dicular axes of rotation should be ineffective. Do or­ the existence ofa rotation-signaling mechanism. Rather, thogonally rotating figures indeed fail to interact? we favor the idea that 3-D adaptation arises from simul­ In one condition in this experiment, the 3-D globe ro­ taneous stimulation of direction-selective sensors respon­ tated about the horizontal axis while the 2-D globe ro­ sive to different disparities. tated about the vertical axis; in another condition, the Monocular versus Binocular Viewing. In the experi­ adaptation axis was vertical and the test axis was horizon­ ments described so far, the 2-D test figure was presented tal. Creation ofa stereo cinematogram ofthe sphere rotat­ to both eyes with zero disparity. Would the binocularly ing about the horizontal axis required a somewhat different viewed 3-D adaptation figure subsequently influence a animation procedure from the one used for stereoscopic monocularly viewed 2-D test figure? Ifthis is genuinely rotation about the vertical axis. For this cinematogram, a motion-specific disparity aftereffect, it should be pos­ two separate films were made of the sphere rotating about sible for a 3-D figure containing disparity to affect the the horizontal axis. After one such animation sequence appearance ofa 2-D figure viewed monocularly, ifmon­ had been generated, a second sequence was made of the ocular viewing is signaled as zero disparity. Can this same globe shifted 2 0 about the vertical axis. Using these prediction be realized? two film pairs, the stereoscopically defined direction of To find out, observers were adapted to the binocularly rotation about the horizontal axis depended on which eye viewed 3-D sphere for 90 sec. Following adaptation, a viewed which film. With one viewing condition, the front 2-D sphere was presented to only one eye, with the tested of the sphere appeared to move downward, but switch­ eye varied over trials. The nontested eye viewed only the ing the films viewed by each eye reversed the direction fixation mark and the fusion cross-hair lines. Observers of rotation such that the front of the sphere moved upward. were instructed, as always, to track the direction of rota­ For each of the two conditions described above, four tion of the 2-D test stimulus. As can be seen in Figure 8, adaptation/test trials were devoted to each oftwo directions 3-D adaptation yielded a strong bias in the perceived direc­ of rotation (i.e., upward/downward, leftward/rightward). tion of rotation of the monocularly viewed 2-D target. The duration ofadaptation was 90 sec, and the test period How do we explain this finding? Assume that monocular lasted I5-sec. For none of the 3 observers tested did the viewing stimulates those neural elements that are respon­ 3-D adaptation figure bias the perceived direction of ro­ sive to zero disparity under binocular viewing. Prolonged tation of the 2-D figure. The adaptation and test figures binocular viewing of a stimulus imaged at nonzero dis­ must share directions ofmotion for one to bias the other. parities produces a temporary shift in the balance of ac­ 3-D motion adaptation and a stationary 3-D test fig­ tivity associated with viewing a zero-disparity stimulus ure. The adaptation effect studied in our experiments in­ (including a monocularly viewed target); disparity af­ volves a bias in the perceived direction of rotation of a tereffects of this sort have been described by Blakemore 2-D figure whose constituent features (i.e., random dots) and Julesz (1971). Our present results simply add the con­ are actually moving during the test period. This aftereffect tingency of motion to this formulation. An elaborated ver- should be distinguished from the conventional motion aftereffect, in which a stationary 2-D figure appears to move in a direction opposite that viewed during adapta­ RB LG MN yy ~ tion to motion-in other words, illusory motion is seen .e where none actually exists. Now, suppose an observer c: o adapts to a 3-D sphere rotating in one direction and then ~ :> views a stationary 3-D sphere. Will the stationary sphere "'0 appear to rotate in the opposite direction? Such an out­ ~ come seems feasible, since it is possible to generate a Q) disparity-specific motion aftereffect (Anstis & Harris, ~ 10 Q) 1974). To find out whether a rotating 3-D sphere can in­ ~ 15 duce motion in a stationary 3-D sphere, the following two­ part experiment was performed. Figure 8. Average (n "" 8) duration of perceived rotation in the To begin, the observers adapted to a single sheet of 50 direction experienced during adaptation (same) and in the direc­ dots moving either leftward or rightward within a circu­ tion opposite that experienced during adaptation (opposite). The 0 adaptation stimulus was the 3-D rotating globe and the test stimu­ lar aperture 2.5 in diameter. After the adaptation period, lus the 2-D globe presented to just one eye; the untested eye viewed the observers verbally described the appearance ofa sta­ a blank screen with the flxation mark and cross-hairs. tionary 3-D globe (i.e., a single pair of cinematogram STEREOPSIS AND STRUCTURE FROM MOTION 237 frames from the stereoscopic animation sequence). Three ,• ~~ II" ~, adaptation conditions were tested: (1) the moving adap­ ", , ,., ", ~ tation dots were imaged with crossed disparity at the same depth plane as that of the front of the 3-D test sphere; (2) the adaptation dots were imaged with zero disparity A + at a plane cutting through the middle of the 3-D test sphere; and (3) the adaptation dots were imaged with un­ crossed disparity at a plane parallel to the rear surface of the 3-D test sphere. In all three conditions, observers reported a weak motion aftereffect: for a brief time im­ left eye right eye mediately following adaptation, the entire test sphere appeared to drift laterally, in a direction opposite that ex­ perienced during adaptation. However, there was abso­ lutely no sense of rotation of the stationary globe, only lateral displacement. B In a set of control measurements, we employed a sta­ tionary test figure that was strictly 2-D (i.e., a flat sheet of dots imaged with zero disparity). Following adapta­ tion to motion in one direction at zero disparity, a strong motion aftereffect was elicited: the static dots appeared Figure 9. Schematic of cube (panel A) and wire (panel B) rJgllres to move for many seconds in a direction opposite that ex­ used to examine tbe extent to which adaptation and test figures m~ be identical in shape. Readers capable of free fusion can experience perienced during adaptation. This, of course, constitutes the 3-D shapes of these figures but not, of course, their rotations a Simple motion aftereffect. during movement. So in comparison with these control measurements, the motion aftereffect was weakened considerably when the flat sheets of dots seen by the two eyes were stereoscopi­ the dimensions ofwhich were 80 min per side. This cube cally fused into a static 3-D sphere. This observation is appeared tilted 45 0 about its x- and z-axes, so that its new reminiscent of findings of Fox, Patterson, and Lehmkuhle vertical axis intersected two opposing corners; a single (1982), who found that the strength of the motion after­ frame of this stimulus appears in Figure 9A. Cinemato­ effect created using cyclopean stimuli varied with the grams of the cube were made by rotating the cube 2 0 about similarity between test and adaptation disparities. this vertical axis between each cinematogram frame (i.e., In the experiment just described, a single sheet of dots by an amount identical to that used for globe rotation). imaged at a given disparity failed to induce apparent ro­ The random wire figure was made by connecting 41 ran­ tation in a stationary 3-D figure. In this next experiment, domly selected points lying within the volume of the cube. we utilized a rotating stereoscopic sphere for adaptation, This produced a wire figure with 40 random but connected not just a single sheet of dots, reasoning that the 3-D 2' wide line segments, one example of which is shown sphere might be a more potent figure for inducing apparent in Figure 9B. This object was also rotated ZO between rotation in a stationary 3-D sphere. This expectation was cinematogram frames, to create the illusion of rotation not fulfilled, however; the stationary 3-D globe showed when the frames were presented in close succession. Us­ no hint of rotation or lateral motion following 90 sec of ing these new stimuli, we performed several experiments. adaptation to the rotating 3-D globe. Evidently the per­ For one experiment, the observers adapted to a stereo­ ceptual bias under study here is not simply a disparity­ scopic 3-D version of the cube. Following the 9O-sec adap­ contingent motion aftereffect. Rather, it appears to be a tation period, the observers tracked the rotation of a 2-D complex, motion-contingent disparity aftereffect, in that ambiguous sphere. Four trials were conducted in each of motion is a necessary but not sufficient condition for the the two biasing directions (clockwise and counterclock­ occurrence of the aftereffect. wise). As is shown in Figure lOA, the 3-D cube was ef­ Shape specificity. So far we have concentrated on fective in biasing the direction of rotation of the 2-D globe. direction of rotation and disparity selectivity as deter­ Next, we simply reversed the displays, so that the 3-D minants of this interesting aftereffect, and we have uti­ globe was the adaptation figure and the 2-D cube was the lized a globe-shaped figure to assess these effects. To what test figure. Again, the biasing effect was potent. Finally, extent is the interaction between stereopsis and KD shape­ we replaced the cube with the wire figure and repeated specific? Imagine, for instance, adapting to a 3-D globe these measurements. Again, there was strong interaction rotating, say, counterclockwise, and then inspecting a 2-D between the globe and the wire figure (see Figure lOB). cube whose direction of rotation is ambiguous. Can the These results show that figural differences have no in­ globe influence the cube? fluence on the interaction between stereopsis and KD. Of To answer this question, we generated two new figures: course, this definition of "figural difference" focuses on a cube and a random wire figure. The cube was made the global shapes of the adaptation and test objects. It is by randomly placing 200 dots on the surface of a cube possible that the globe, cube, and wire figure are com- 238 NAWROT AND BLAKE

spective) that revolved about the midline ofthe sheet. Our LG MN RB DT observers, like Petersik et al. 's, tended to see this plane 15 of dots as rotating in the direction specified by the per­ ~ 10 -Cij spective information, although reversals were sometimes 0 0- S 0- experienced with this stimulus too. Despite the tendency A 0 to rotate in one direction, however, 90 sec of adaptation 0- Q) to this 2-D figure failed to bias the perceived direction s. E'" 5 <: of rotation of the 2-D globe (Figure 11). 0 '"en 10 -~ Next we tried a version of what Dosher et al. (1986) 15 :::J have called a "proximity/luminance" cue. The adapting "0 g LG MN RB DT figure was a 2-D rotating globe whose "front-surface" .8 15 dots were larger (3' X 3') than the "rear-surface" dots Q) Cl (2' x 2'); because our displays were simply black and ~ -"5i'" 10 Q) 0 0- S white (i.e., 2-bit gray level) we were unable to make the ~ 0- 0 larger dots brighter. The additional depth information af­ B forded by dot size did indeed bias the perceived direction ~ 5 of rotation ofthe globe; it was seen predominantly to ro­ '"en 10 tate in the direction of the larger dots, which appeared 15 to form the front surface of the globe. As an adapting Figure 10. Average duration of perceived rotation in the oppo­ stimulus, however, this unambiguous 2-D globe was in­ site and in the same directions as that experienced during adapta­ effective, in that the subsequently viewed 2-D test globe tion. (A) The 3-Dadaptation figure was a cube and the 2-D test figure the rotating globe; the same pattern of results was obtained when (without proximity information) underwent spontaneous the adaptation figure was the globe and test figure the cube. (B) The reversals in direction of rotation (see Figure lIB). adaptation figure was the 3-D wire figure and the test figure the Finally, we devised a fourth unambiguous, non­ 2-D globe; again, the same results are obtained when globe and cube stereoscopic adaptation figure. This was an "opaque switch roles. sphere" generated by presentation of 100 dots all mov­ ing in a single direction; the dots appeared to be just those parable along some other stimulus dimension (e.g., their on the convex surface of the sphere facing the observer. 2-D Fourier spectra). Hence, as the sphere rotated, dots seemed to disappear as they passed behind what looked like the side of the Is Stereopsis Necessary? sphere. Note that there is a second geometrically plausi­ As Dosher et al. (1986) have demonstrated, retinal dis­ ble percept associated with this stimulus-a transparent parity effectively disambiguates a KD figure's direction globe with dots visible only on its back surface. In fact, of rotation. Indeed, this is undoubtedly why stereoscopi­ however, the perceived direction of rotation always coin­ cally defined 3-D figures are so effective as adaptation cided with the direction of motion of the dots, implying stimuli in our experiments. It is possible to produce un­ that the observers saw this object as an opaque globe." ambiguous rotation ofa 2-D figure, using nonstereoscopic Adaptation to this opaque sphere was ineffective in bi­ information (Braunstein, 1977; Dosher et al., 1986; Hersh­ asing the direction of rotation of the subsequently viewed berger, Stewart, & Laughlin, 1976). Can such unambig­ 2-D globe (Figure IIC). This result is not attributable to uous 2-D figures bias the direction of rotation of an am­ the reduced number of dots used to create the opaque biguous 2-D figure? In other words, is adaptation to globe, for we found that a stereo version of the opaque unambiguous rotation effective only when stereopsis is globe was very effective as an adaptation stimulus (Fig­ involved? To find out, we tested several different rotat­ ure lID). Depth from stereopsis thus seems to be a neces­ ing 2-D figures that might be perceived as rotating in a sary component in the adaptation phase. Moreover, to be single specific direction. effective, stereoscopic adaptation must involve multiple To start, we simply introduced perspective into the 2-D planes of depth (e.g., the two-sheet stimulus employed dot figure, a manipulation that was shown to improve ob­ earlier) or at least a disparity gradient (e. g., the stereo servers' judgments of direction of rotation in an experi­ opaque globe); recall that a single sheet ofdots at a given ment by Braunstein (1966). Although favoring the direc­ disparity is not an effective adaptation stimulus. Whether tion of rotation specified by perspective, our observers other depth cues such as shape-from-shading would be still reported numerous reversals upon 90 sec ofviewing sufficient to produce adaptation remains to be learned. the perspective-enriched 2-D globe, which is also what We reasoned that if stereopsis and motion have such Dosher et al. (1986) found. Hence, the 2-D perspective close connections, it should be possible for stereoscopic globe does not represent a particularly effective adapting adaptation to influence the perception of the opaque stimulus for our purposes. sphere. Recall that the opaque rotating sphere was nearly Following the lead of Petersik et al. (1984), we next always seen as convex. Since we could bias the direction tried a flat sheet of 200 dots (constructed with polar per- of rotation of the 2-D sphere, perhaps it would be possi- STEREOPSIS AND STRUCTURE FROM MOTION 239

ble to reverse temporarily the perceived direction of ro­ tation of the opaque globe. This was an interesting possi­ LG DT bility, for to alter the direction of rotation of the opaque 15 globe would also alter the direction of curvature of the S! 10 globe; the globe should appear concave, not convex. "w 0 Adaptation would thus transform a perfectly reasonable a. 5 a. 0 stimulus into a strange figure, namely a globe having an A 0 opaque rear surface but an invisible front surface. Can CI> E 5 3-D adaptation create this strange percept? '"Ul To answer this question, we used a rotating 3-D sphere 10 as the adaptation stimulus, and the opaque 2-D globe as 15 the test stimulus. Upon adaptation to counterclockwise 3-D rotation, an opaque globe defined by dots moving RB MN left to right appeared to be concave and rotating clock­ 15 wise. The reciprocal condition (clockwise 3-D rotation) S 10 yielded the converse result (a concave surface and counter­ "w 0 clockwise 2-D rotation of dots moving right to left). These IS: 5 0 results dramatize the potent linkage between stereopsis B 0 and motion. CI> E 5 0- Cll Q) Ul Bias of Other KD StimuU ~ 10 c: The test stimuli used so far consisted of dots, all of 0 ~ 15 which moved smoothly and continuously; their motion ::l paths, which were predetermined, coincided with the ro­ "tl tation of a 3-D object. In the experiments described in (ij RB MN £ 15 this section, the motion stimuli were not nearly so con­ Q) strained. In recent years, in certain laboratories (Treue g S! 10 Qj "w & Andersen, 1990; Williams & Phillips, 1986, 1987), 0 > a. 5 -c a. novel KD stimuli have been developed that have stochas­ 0 tic motions: motion displays in which not all of the con­ c 0 CI> stituent dots have a predetermined path and velocity. E 5 Despite the stochastic nature ofsuch displays, observers Ul '" 10 typically perceive structure and rotational motion when viewing them. It is tempting to conclude that thesestochas­ 15 tic motion displays engage the same neural mechanisms as those stimulated by more conventional KD displays. RB MN Accordingly, we felt it would be informative to determine 15 whether or not 3-D adaptation could bias perception of .~ 10 Ul these locally random motion figures. a.0 a. 5 The first stimulus, devised by Williams and Phillips 0 (1986), consisted of 200 moving dots whose direction of D motion was limited to a subset of all possible directions. CI> E 5 These 200 dots appeared within a circular aperture 2.5 0 '"rn 10 in diameter. Between cinematogram frames the dots were displaced 4' according to the following two rules: From 15 frame to frame, each dot's direction of displacement was independent of its previous displacement, and each dot's Figure 11. Effect of adapting for 90 sec to different nonstereo­ direction of displacement fell somewhere within a 1200 scopic, rotating figures. (A) The adapting figure was a Oat sheet of range centered on vertical (see Figure 12). This stimu­ dots whose direction of rotation was specified by perspective. This adapting figure, though its direction of rotation was relatively sta­ lus, despite its local randomness, is globally perceived ble, had no effect on the subsequent direction of rotation of the am­ as a rotating cylinder viewed through an aperture; as it biguous2-D globe. (8) The adapting figure wasa 2-D globe in which rotates, the cylinder also seems to move slowly upward. the front surface dots were larger than the rear surface dots. Ada~ The direction of rotation of this cylinder is ambiguous tation was ineffective. (C) The adapting figure was a 106-dotopaque (i.e., it reverses between clockwise and counterclockwise globe. Adaptation was ineffective. (D) The adaptation figure was a stereoscopic version of the opaque globe. Adaptation was highly over time). Can 3-D adaptation temporarily stabilize the effective. direction of rotation of the cylinder? 240 NAWROT AND BLAKE

during which they viewed the rotating 3-D sphere; both clockwise and counterclockwise adaptation were tested. This random-velocity stimulus was indeed affected by the stereoscopic adaptation figure: during the IS-sec test phase, it always appeared to rotate in the direction oppo­ site that experienced during adaptation. In summary, two forms of stochastic motion are sus­ ceptible to stereoscopic adaptation. In this sense, these random-motion stimuli behave similarly to more conven­ tional KD figures (e.g., our 2-D globe), in which rigid rotation is explicitly specified.

DISCUSSION

It is well established that a rotating 2-D figure can ap­ Range of possible dot movements pear to undergo spontaneous reversals in the perceived direction of rotation; our 2-D cinematogram displays are Figure 12. This figure summarizes possible directions of motion just another example of this ubiquitous motion phenome­ present in the random-dot cinematogram. From frame to frame, a dot could move in any direction ±60° to either side of vertical. non. Multistable visual phenomena, including reversible A given dot's direction of movement varied randomly from frame rotating figures, have fascinated psychologists over the to frame within this constraint. This stimulus looks like a transpar­ years. To explain reversible figures, workers have in­ ent cylinder rotating either clockwiseor counterclockwise, with the voked the concept of neural , which has been vari­ direction of rotation varying over time. ously attributed to changes in synaptic resistance (McDou­ gall, 1906), to electrotonic spread of cortical potentials (Kohler & Wallach, 1944), and to an autoinhibitory pro­ To answer this question, we employed the standard cess (Howard, 1961). The present findings demonstrate adaptation/test sequence. The observers viewed the 3-D that this putative "fatigue" process, whatever its neural adaptation sphere for 90 sec, after which they indicated basis, can be activated by prolonged viewing of an un­ the direction of rotation of the rotating stochastic cylinder ambiguous figure, which in our experiments was a 3-D during a IS-sec test period. On four trials, 3-D adaptation object whose direction of rotation was specified by ste­ was clockwise, and on four other trials, it was counter­ reoscopic information. Virsu (1975) found that stereop­ clockwise. The ambiguous 2-D random motion was in­ sis can also temporarily disambiguate perspective rever­ deed affected by 3-D adaptation; Throughout the IS-sec sals in a static figure, the Schroder staircase. test phase, the cylinder always appeared to rotate in the Our results, which are summarized in the Appendix, direction opposite that experienced during adaptation. further strengthen the case for a strong linkage between The second novel stimulus that we used was developed stereopsis and motion perception, a linkage already sug­ by Williams and Phillips (1987; see also Treue & Ander­ gested by earlier psychophysical work (e.g., Howard & sen, 1990); we shall refer to it as random-velocity I-D Simpson, 1989; Rogers & Graham, 1984; Smith, 1976; motion. This stimulus again comprised 200 dots randomly Wallach et al., 1963). In particular, we have found that placed within a 2.5 0 aperture. Between every cinemato­ stereopsis exerts a potent influence on the perception gram frame, each dot was displaced horizontally, either of structure from motion. This influence is global, in leftward or rightward. The size of the displacement was the sense that a single stereoscopic sheet of moving dots variable; it ranged anywhere from l ' to 6' between any has no subsequent effect on KD; the 3-D stimulus ex­ two frames. The size and direction (left vs. right) of each perienced during adaptation must consist of a complex­ dot's displacement were independent of its displacement disparity field of moving dots. Moreover, the influence on previous frames. This stimulus resembled a spheroid of stereopsis on motion generalizes across figural shapes with dots distributed throughout its volume. When dis­ (e.g., a globe adapts a cube). At the same time, the placements were horizontal, the sphere seemed to rotate influence is specific to the retinal area stimulated by about the vertical axis, with the direction of rotation vary­ the adaptation stimulus, implying that the underlying neu­ ing over time. It should be stressed that this stimulus was ral processes operate on motion fields defined in retinal not simply a version of dynamic visual noise of the sort coordinates. studied by Tyler (1977) or by Morgan and Ward (1980); Chang (1990) has recently investigated the interaction their noise stimulus required stereopsis (i.e., introduction between motion defined by luminance information and of an interocular delay), whereas the random-velocitymo­ depth defined from random-element stereograms. In a tion stimulus gave compelling depth and rotation even sense, her work complements ours. She studied how mo­ when viewing was monocular. tion signals portrayed by luminance information could bias Observers reported on the direction of rotation of this the perception of direction of motion of cyclopean con­ random-velocity stimulus after a 9O-secadaptation phase tours defined by disparity. In general, she found that a STEREOPSIS AND STRUCTURE FROM MOTION 241

cyclopean pattern portrayed in a random-element stereo­ question of parallel pathways other than to provide prima gram appeared to move smoothly only when the consti­ facie evidence that motion and stereopsis share a com­ tuent luminance dots also moved in a direction consistent mon neural basis, or at least arise from processes that with the cyclopean movement. Our results, as well as strongly interact. It has not escaped our that neu­ those of Dosher et al. (1986), show the converse; lu­ rons comprising the magnocellular pathway are particu­ minance dots defining a 2-D figure appear to move larly responsive to motion and, at higher stages, are selec­ smoothly and unambiguously if stereopsis defines the lo­ tive for retinal disparity (DeYoe & Van Essen, 1988). At cation in depth of those dots. still higher stages in this pathway are visual centers (the Petersik et al. (1984) have also studied reversals in per­ middle superior temporal cortical area) whose neurons ceived direction of rotation of ambiguous figures. Using are responsive to rotation and to expansion (Saito et al., monocular perspective cues to disambiguate motion, they 1986; Tanaka et al., 1986). In general, neurons in this found that adaptation to unambiguous rotation temporar­ occipitotemporal processing stream possess the kinds of ily caused an ambiguous-motion stimulus to rotate in the receptive field properties one would expect to find in neu­ direction opposite that experienced during adaptation. ral mechanisms underlying kinetic depth perception. This, of course, represents a nonstereoscopic version of Inspired by these suggestive physiological data, we the effect that we studied. Similarly, Rogers and Graham (Nawrot & Blake, 1990) have developed a neural model (1984) were able to bias the perception ofambiguous mo­ of KD and its interaction with stereopsis. S The model tion by prior adaptation to unambiguous structure from posits binocularly activated units selective for both dis­ motion. We were unsuccessful, however, in biasing 2-D parity and direction of motion. Each unit is directly acti­ motion using a nonstereoscopic adaptation stimulus (i.e., vated by a given direction of motion imaged at a particu­ the opaque globe, the proximity/size globe, the perspec­ lar retinal disparity. The activity of these binocular units tive plane). One could argue that the earlier experiments is also determined by connections from other binocular ofRogers and Graham (1984) and Petersik et al. (1984) units preferring the same direction of motion; for units involve a "depth" aftereffect, whereas our work involves whose preferred disparities are similar, this influence is a "motion" aftereffect. This argument is based on an in­ facilitatory, and for units whose preferred disparities are appropriate characterization ofour findings, though. The quite different, this influence is inhibitory. At a given dis­ phenomenon explored in our work is, in fact, a depth af­ parity plane, units preferring opposite directions of mo­ tereffect, one that is contingent on motion. During adap­ tion are mutually inhibitory. In response to a 2-D KD tation, the observer views motion in a given direction at stimulus ofthe sort used in our experiments (i.e., a rotat­ a given disparity plane; following adaptation, figure ele­ ing globe), activity in the network quickly segregates into ments moving in that direction appear to occupy a differ­ disparity planes other than the zero-disparity plane de­ ent depth plane. It is the plane of depth that is "rnisper­ fined by the physical stimulus. This segregated pattern ceived, " not the direction of motion. Moreover, the plane of activity fluctuates with a time course mimicking the of depth of stationary dots is not misperceived (although reversals in perceived direction of rotation of a 2-D KD the dots may appear to move); the depth aftereffect pro­ stimulus. The addition of disparity information to the duced by motion in a given direction at a given disparity stimulus activates disparity planes appropriate for the plane is contingent on the presence ofmotion in the same stimulus, and, moreover, this pattern of activity is sta­ direction during the postadaptation test phase. Thus while ble. Immediately following removal of stimulus dispar­ agreeing with Petersik et al. (1984) and with Rogers and ity information, the network activity pattern switches to Graham (1984) that adaptation to perceived motion in one signaling rotation in the opposite direction and re­ depth affects an ambiguous KD figure, we are left won­ mains in this activity pattern for an unusually long period. dering about the sufficient conditions for defining depth This behavior, in other words, mimics the psychophysi­ in the adaptation stimulus. cal observations described in this paper. With respect to the physiological basis of the stereop­ sis/motion interaction studied here, it has become fa­ REFERENCES shionable to think ofdifferent aspects of the visual scene as being processing in separate pathways. The latest ver­ ANSTIS, S. M., '" BARJUS, I. P. (1974). Movement aftereffects contin­ gent on binocular disparity. Perception, 3, 153-168. sion ofthis idea has been championed by Livingstone and BLAKEMORE, C., '" Jutasz, B. (1971). 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WILLIAMS, D., &; PHILLIPS, G. (1986). Structure from motion in a sequential presentation of frames on the two monitors. This temporal stochastic display. Journal ofthe Optical Society ofAmerica A, 3, 12. disparity, in the absence of luminance compensation, produced a WILUAMS, D., &; PHILUPS, G. (1987). Rigid 3-D percept from stochastic stereoscopic cue in the absence of spatial disparity (Burr & Ross, 1979). 1-0 motion. Journal of the Optical Society ofAmerica A, 4, 35. With luminance compensation, the 2-D globe contained no disparity in­ formation and therefore appeared to be bistable. 3. During reversals, the figure does not seem to cease rotating and then NOTES resume rotation in the opposite direction. Instead, the object appears to twist within itself in a nonrigid fashion, such that the direction of 1. Unambiguous depth from motion in the Rogers and Graham (1984) the rearmost surface becomes the direction of the frontmost surface and motion displays can be produced either by moving the head or by mov­ vice versa. This peculiarpercept has no obvious "real world" analogue; ing the display concomitantly with translation of the motion elements. it is most likely an illusory effect caused by the transparency of the en­ In the rotating KD displays used in the present experiments (created vironmentally uncommon and ambiguous stimulus properties of the KDE. by parallel projection of motion elements), velocity of motion elements 4. The authors, who have had considerable experience viewing this specifies relative distances within the object but not distance from the opaque 2-D globe, occasionally see it as concave rather thanconvex. observer to the object. For this reason, depth is reversible in the The role of familiarity in generating this percept is quite interesting and KD display. deserves examination. 2. We lowered the luminance of the left-eye display by 0.4 log units 5. The model was constructed to deal explicitly with the perception to eliminate a residual stereoscopic cue. Specifically, this slight luminance of depth in dynamic displays devoid of retinal disparity information. mismatch counteracted the brief interocular time disparity caused by It does not deal with the perception ofshape/structure from such displays.

APPENDIX Summary of Experimental Results

Question Adaptation Stimulus Test Stimulus Result Temporal properties 2-D globe Successive durations are stochastically independent Stereo Adaptation 3-D globe 2-D globe Adaptation temporarily disambiguates perceived direction of rotation Recovery from stereo 3-D globe 2-D globe Recovery from adapta­ adaptation tion occurs within 30 sec Retinal specificity 3-D globe 2-D globe Adaptation is specific to retinal location of adap­ tation figure Adaptation to sheets in 3-D flat sheets 2-D globe Two 3-D sheets needed stereo depth to bias perceived direc­ tion of rotation Monocular versus 3-D globe 2-D globe Bias found with both binocular viewing of test binocular and monocular figure viewing of test figure Axis of rotation 3-D globe, horizontal 2-D globe, vertical axis Adaptation ineffective Stationary 3-D test axis figure 3-D globe Stationary 3-D globe No rotational aftereffect Shape specificity 3-D cube, 3-D globe 2-D globe, 2-D cube, Adaptation and test 2-D wire figure figures need not be the same shape for adapta­ tion to be effective Perspective adaptation 2-D globe 2-D globe with perspective Adaptation does not disambiguate perceived direction of rotation Perspective sheet 2-D rotating plane with 2-D globe Adaptation does not perspective disambiguate perceived direction of rotation Changing size depth cue 2-D globe with prox­ 2-D globe Adaptation does not imity cue disambiguate perceived direction of rotation Opaque globe 2-D opaque globe, 3-D 2-D globe Adaptation does not opaque globe disambiguate perceived direction of rotation 244 NAWROT AND BLAKE

Question Adaptation Stimulus Test Stimulus Result

Does stereo affect 2-D 3-D globe 2-D random motion Adaptation temporarily random motion disambiguates perceived direction of rotation Does stereo affect I-D 3-D globe I-D random motion Adaptation temporarily random motion disambiguates perceived direction of rotation

(Manuscript received June 8, 1990; revision accepted for publication October 9, 1990.)