Perception & Psychophysics 1996,58 (2),271-282
How is motion disparity integrated with binocular disparity in depth perception? MAKOTO ICHIKAWA Osaka City University, Osaka, Japan and SHINYA SAIDA National Institute ofBioscience and Human Technology, Tsukuba, Japan
Two experiments presented motion disparity conflicting with binocular disparity to examine how these cues determined apparent depth order (convex, concave) and depth magnitude. In each experiment, 8 subjects estimated the depth order and depth magnitude. The first experiment showed the following. (1) The visual system used one of these cues exclusively in selecting a depth order for each display. (2) The visual system integrated the depth magnitude information from these cues by a weighted additive fashion if it selected the binocular disparity in depth order perception and if the depth magnitude specified by motion disparity was small relative to that specified by binocular disparity. (3) The visual system ignored the depth magnitude information of binocular disparity if it selected the motion disparity in depth order perception. The second experiment showed that these three points were consistent whether the subject's head movement or object movement generated motion disparity. Some recent studies on depth perception demonstrated the interaction between binocular disparity and motionon-the-retina cues (motion disparity and kinetic depth). For example, the adaptation to binocular disparity affected the depth perception from the kinetic depth (Nawrot & Blake, 1991). The presence of binocular disparity lowered the threshold of depth perception from motion disparity (Comilleau-Peres & Droulez, 1993). Moreover, the presence of kinetic depth cue made the perceived depth from binocular disparity stable regardless ofthe interference by texture element density (Tittle & Braunstein, 1993). These interactions suggest that the processing of these depth cues have a common stage and that this stage concerns the integration of depth information from these cues. The process to integrate these cues in the depth order perception and depth magnitude perception, however, remains to be investigated. Rogers and Collett (1989) presented motion disparity in conflict with binocular disparity in terms of the depth order (convex, concave) and the depth magnitude. They reported that binocular disparity always determined apparent depth order and that binocular disparity was asThis research is part of a doctoral dissertation submitted by the first author to the Osaka City University in 1994. It was supported by an Application of Measuring Human Sense to Product Design grant. During revisions, the first author was supported by JSPS Fellowships for Japanese Junior Scientists. The authors would like to thank Hisao Miyano, Hiroshi Ono, Gary Rollman, and Igor Wisniewski for helpful discussions, and Mike Braunstein, Michael Landy, and two anonymous reviewers for their useful comments on the previous version of this manuscript. Correspondence should be addressed to M. Ichikawa, Department of Psychology, York University, 4700 Keele Street, North York, ON, Canada M3J I P3 (e-mail:
[email protected]).
signed to a larger weight than was motion disparity in a weighted additive integration of depth magnitude information. Considering the effectiveness ofthese cues, however, we can expect that motion disparity determines apparent depth order under some other situations when these cues conflict with each other in depth order. That is, motion disparity is effective in determining perceived depth order when presented by itself(Rogers & Graham, 1979) and even when conflicting with other cues that are geometrically unambiguous in specifying depth order, such as occlusion (Ono, Rogers, Ohmi, & Ono, 1988). On the other hand, binocular disparity does not always determine apparent depth order when conflicting with occlusion (Braunstein, Andersen, Rouse, & Tittle, 1986), monocular contours (Stevens & Brookes, 1988; Stevens, Lees, & Brookes, 1991), and spatial frequency difference (Brown & Weisstein, 1988). Moreover, when binocular disparity conflicts with other cues in depth order, the visual system modifies the depth order perceived from binocular stereopsis (Ichikawa & Egusa, 1993; Shimojo & Nakajima, 1981). The interests of this study were to complement the study of Rogers and Collett (1989) by using larger motion disparity and smaller binocular disparity than they used and to comprehend in more detail how the visual system integrated binocular disparity and motion disparity. For these purposes, we investigated in which situation binocular disparity was a determinant of the depth order perception and in which situation it was not and, in the latter situation, how the visual system used the depth magnitude information from these two cues. The study of threshold showed that the sensitivity of depth perception from binocular disparity was higher than that from
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Copyright 1996 Psychonomic Society, Inc.
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ICHIKAWA AND SAIDA
motion disparity when these cues specified sinusoidal corrugation (Rogers & Graham, 1982). From this report, we inferred that, in suprathreshold level, binocular disparity should dominate over motion disparity when both cues were similar to each other, but it might not dominate when motion disparity was extremely larger than binocular disparity. Therefore, we examined how the magnitude of binocular and motion disparities affected the integration of these cues when they conflicted with each other in depth order and magnitude. EXPERIMENT 1
Random dot stimuli specified the surfaces vertically corrugating in a sinusoidal function (Figure la) by motion disparity and/or binocular disparity with different depth magnitudes and depth orders. We investigated the apparent depth order and magnitude for these stimuli. Motion disparity was generated by yoking the subject's head movement with each dot movement. We predicted that, if the apparent depth magnitude was unequal to that specified by motion disparity, the whole surface would appear to rock synchronously with the head movement (Figure 1b). In Experiment 1, we also investigated whether the relation between the apparent depth order and the apparent rocking direction (turning against the subject, turning with the subject) fitted this prediction.
Method Subjects Eight subjects (5 females and 3 males) participated: 2 authors, I member of the institute, and 5 paid undergraduate students of Tsukuba University. All subjects had stereoscopic acuity of at least 20" of arc on the Randot stereo test at a distance of about 50 ern. Before the experiment, in order to be familiar with the equipment, they had at least 2 h of practice with the stimuli presenting motion disparity and the stimuli presenting binocular disparity. Apparatus and Stimulus Two monitor displays (Mitsubishi JUM-1491 A), one mirror and one half-silvered mirror, were used to present the stimulus. The mirror and the half-silvered mirror were slanted vertically 45° and were fixed 95 and 70 ern, respectively, from the center of the rails, on which the chinrest was movable horizontally within the range of 6.5 em. One monitor display was fixed at 15 em above the mirror, and another display was placed 40 em below the half-silvered mirror; the viewing distance to each display was 110 em, In order to present different displays to each eye, two pairs of orthogonal Polaroid filters covered the displays and the eyes. A frame memory (Astro Design VP-1122) and a personal computer (NEC PC 9801-XL2) operated the random dot stimuli. The frame memory registered the 52 frames of random dot stimuli. The size ofa random dot stimulus was 8° X 8° in the visual arc. The dots, each measuring 9.2' high X 19.6' wide in the visual arc, were distributed over 52 rows so that they occupied 40% of the stimulus area. By varying the horizontal coordination of the random dots, motion disparity and/or binocular disparity specified the surfaces vertically corrugating in a sinusoidal function with 0.25 cycles per degree (cpd) spatial frequency (with three troughs and two peaks, or vice versa). In order to present binocular disparity, 26 frames for the right eye were paired with the remaining 26 frames for the left eye. Each pair presented the same magnitude of binocular disparity.Zero binocular disparity specified a flat surface, and three binoc-
ular disparity magnitudes, 0.5', I', or 2' in the visual arc, specified the sinusoidal corrugations; the physical depth magnitudes simulated by these four magnitudes of binocular disparity were about 0, 3,6, and 12 mm, respectively. These disparity magnitudes included the lower range in Rogers and Collett's (1989) study (0', 2',4', and 8'). In order to present motion disparity, the horizontal coordinates of the 26 pairs of stimuli presenting binocular disparity were shifted with consistent steps following the sinusoidal function, and the displays showed I of the 26 pairs appropriate for the chinrest position measured by a potentiometer. Four motion disparity magnitudes in the equivalent disparity (see Rogers & Graham, 1982, for the unit of equivalent disparity), 0', 3', 10', and 20' in the visual arc, were used; the physical depth magnitudes simulated by these four magnitudes of motion disparity were about 0, 18, 60, and 120 mm, respectively. These disparity magnitudes included the higher range used in Rogers and Collett's study (0', 2', 4', 8', and 12'). The stimuli presenting binocular disparity simultaneously with motion disparity were called composite stimuli (CS). Seven binoc-
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Figure 1. The depth surface specified by motion disparity. (a) Motion disparity specifies a still and rigid surface corrugating in a sinusoidal function in a random dot display.The part with an empty double circle is concave, and that with a filled double circle is convex. (b) The ambiguity ofthe motion on display.When an eye moves from Eye 1 to Eye 2, the empty and filled circles specify the depth, dl, corresponding to the empty double circle and the filled double circle in (a), respectively. This motion on display should be compatible with any depth relation composed of the elements on the line of sight through the empty and iIlled circles--for example, the surfaces whose depth magnitude is smaller than dl turning against the subject (d2), whose depth maguitude is larger than dl turning with the subject (113), whose depth order is opposite to dl turning with the subject (d4), and flows nonrigidIy on the display as shown by bold arrows (d5), and so on.
MOTION DISPARITY AND BINOCULAR DISPARITY
ular disparity conditions (0' and three magnitudes in each depth order) and seven motion disparity conditions (0' and three magnitudes in each depth order) were combined to make 49 kinds ofCS. Opposite-order composite stimuli (OCS) indicated the CS in which two cues specified opposite depth order. Same-order composite stimuli (SCS) indicated the CS in which two cues specified same depth order. The stimuli presenting only one of two cues were called binocular disparity stimuli (BOS) or motion disparity stimuli (MOS). Procedure
Each stimulus was viewed eight times; for each subject, there were 512 trials that were divided into eight blocks, binocular disparity magnitudes (4) X repetition (2). The subjects viewed CS and BOS presenting the same magnitude of binocular disparity in the same blocks and CS and BOS presenting 0' binocular disparity in the same block with MDS. In one block, the depth order specified by binocular disparity (in the block presenting 0' binocular disparity, MOS, CS, or BOS) and motion disparity conditions were presented four times in a random order. In the former four blocks, four magnitudes of binocular disparity (0', OS, 1" and 2') were viewed in a random order. In the remaining four blocks, the order of the binocular disparity magnitude conditions was the same as the former. During the CS trials, the subjects viewed the displays binocularly with head movement. For MOS and BDS, they viewed one of the displays monocularly with head movement and the two displays binocularly without head movement, respectively. There was no limit in viewing time and no fixation point. Viewing the stimulus in a dim room, the subjects judged the depth order and estimated the depth magnitude by adjusting the interval between the two bars (2-cm height, 1.5-mm diameter); when a flat surface was perceived, the subjects responded verbally.They also stated whether or not apparent depth inverted during each trial and whether or not the surface rocked with the head movement; if it rocked, they reported the direction of the rocking.
Results and Discussion Perception of Depth Order During MDS and CS trials with nonzero motion disparity, the subjects sometimes reported that the perceived depth order inverted within a trial. The inversion occurred instantly, all over the surface, and occurred once or repeatedly. BDS and MDS trials. In viewing nonzero BDS and MDS, the subjects perceived the depth order specified by each disparity in 99.7% and 96.9% of the average of all subjects, respectively. These indicate that both binocular disparity and motion disparity used in Experiment I determined apparent depth order when presented by themselves. In 51.6% (SD = 44.54) of 0' BDS trials and in 70.3% (SD = 35.94) of 0' MDS trials, a flat surface was perceived; in the remaining trials, an irregular and nonsinusoidal tiny corrugation was perceived. CS trials. In viewing SCS, the subjects perceived the depth order specified by binocular disparity and motion disparity in 99.5% (SD = 0.72) of the trials. They perceived the depth order specified by binocular disparity in 98.6% (SD = 1.47) of the trials ofCS combining 0' motion disparity and nonzero binocular disparity, and the depth order specified by motion disparity in 89.6% (SD = 7.45) of the trials of CS combining 0' binocular disparity and nonzero motion disparity. For CS trials in which both cues presented 0' disparity, the flat surface
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was perceived in 56.3% (SD = 47.25) of the trials, and the tiny irregular corrugation was perceived in the remaining trials. In OCS trials, the depth order specified by binocular disparity was perceived in 80.2% (SD = 32.72) of the trials. Figure 2 shows the individual percentages of the OCS trials in which the depth order specified by binocular disparity was perceived (including the case in which the depth order specified by binocular disparity was perceived ultimately after apparent depth order inversions). The 3 subjects who most frequently perceived the depth order specified by motion disparity were 2 authors and 1 other subject (M.I., S.S., and O.K.). The individual bias in Figure 2 could not be attributed to the variance in stereo acuity since each subject perceived the depth order specified by binocular disparity at least in 97.9% (Subject O.K.) of the nonzero BDS trials and since there was no significant difference in this frequency among subjects. Effects of disparity magnitude. We examined the relationship between the magnitude of disparities and the frequency in which motion disparity determined depth order perception in OCS trials (sum of white and dotted parts in Figure 3). A three-way repeated measures analysis of variance (ANOVA) was performed, with depth order (three or two troughs; see left and right columns in Figure 3), binocular disparity magnitude (0.5', 1', or 2'), and motion disparity magnitude (3', 10', or 20') as factors. There were significant main effects for binocular disparity magnitude [F(2,14) = 4.64, p < .05] and for depth order [F(l,7) = 7.72, p < .05] and a significant interaction between these two factors [F(2,14) = 4.80, p < .05]. These indicate that the visual system selected the depth order specified by motion disparity more frequently in viewing OCS presenting smaller binocular disparity.
Perception of Depth Magnitude For MDS, BDS, and SCS, paired t tests were performed for the differences in the perceived depth magnitude depending on the depth order specified by motion and/or binocular disparity (df = 7). For OCS, both when motion
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disparity determined the apparent depth order and when binocular disparity determined the apparent depth order, same-paired t tests were performed separately (dfs were from 7 to 1). No significant difference was found for any ofthe conditions. Therefore, the depth orders were combined in Figure 4. BDS and MDS trials. Figure 4 shows that the perceived depth magnitude for 10' or 20' ofMDS tended to be larger than for all the conditions ofBDS. This should be attributed to the inequality in the physical magnitude between the motion disparity and the binocular disparity used in this experiment. Figure 4 also shows that there
was an underestimation of depth magnitude for 20' of MDS, although there was an overestimation for all of BDS and 3' ofMDS. Linearity in CS trials. For es trials, we examined whether the apparent depth magnitude varied linearly with the depth magnitude specified by each cue. The stepwise multiple regression analysis tested whether the apparent depth magnitude for ses and oes increased or decreased with the apparent depth magnitudes in viewing BDS and in viewing MDS presenting the same magnitude of disparity as ses or oes did. In order to avoid the bias due to individual variance in the absolute value of apparent depth magnitude, the depth magnitude for each stimulus that a subject perceived was normalized in terms of her/his average of apparent magnitude from all of MDS and BDS trials as 1; the numbers used as 1 in the normalization were 34.41, 39.05, 31.96, 16.01,21.21, 46.84, 54.40, and 19.82 mm for Subjects S.M., O.K., H.I., S.S., M.I., D.B., K.T., and T.N., respectively. For ses, analysis included the data of es presenting nonzero binocular or motion disparity with 0' of motion or binocular disparity. For oes, if the subject had data for a condition of oes, analysis included also her/his data of es presenting the same magnitude of binocular or motion disparity with 0' of motion or binocular disparity. The results in Table 1 show that the regression analysis entered (l) the apparent depth magnitude for MDS regardless of whether motion disparity determined apparent depth order or not and (2) the apparent depth magnitude for BDS except for the oes trials in which motion disparity determined the apparent depth order. These imply that the perceived depth magnitude in all es trials increased with the magnitude specified by motion disparity and with that by binocular disparity only if this cue determined the perceived depth order; the fashion of integrating depth magnitude information from binocular disparity varied according to the selected cue in depth order perception. Figure 4 shows that the apparent depth magnitude for es tended to increase with the apparent depth magnitude for BDS only when the motion disparity was small. In order to confirm this tendency, the simple regression analysis was performed by using the same normalized data as the above-mentioned multiple regression analysis. It was shown that the perceived depth magnitude increased only for es with 0' and 3' of motion disparity with the depth magnitude specified by binocular disparity (Table 2). The slopes of regression lines for binocular (motion) disparity increased inversely with the magnitude of motion (binocular) disparity. The regressions with negative slope in oes were not significant; there was no consistent subtraction in apparent depth magnitude when the depth order specified by one cue was opposed by another cue. Perception of Rocking The subjects hardly perceived the rocking of the surface in viewing MDS with 0' motion disparity; however, they perceived it in 89.2%, 97.8%, and 99.2% of the
MOTION DISPARITY AND BINOCULAR DISPARITY
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trials of MDS with nonzero motion disparity, SCS, and OCS, respectively. In these trials, the percentages of the trials in which the subject perceived the depth order specified by motion parallax and reported the surface turning against the subject were 99.7%, 99.7%, and 96.7% for MDS, SCS, and OCS, respectively. For OCS, the percentage of the trials in which the subject perceived the depth order by binocular disparity and reported the surface turning with the subject was 97.7%. All subjects reported that the direction of the rocking inverted when the depth order inversion occurred.
EXPERIMENT 2 The results of Experiment 1 show that, when binocular disparity conflicted with motion disparity in both depth order and depth magnitude, the apparent depth order depended not only on binocular disparity but also on motion disparity and that the apparent depth magnitude always depended on motion disparity and depended
on binocular disparity only in restricted cases. These apparently contradict the results of Rogers and Collett (1989). The procedure to generate motion disparity in our Experiment 1 was different from that in Rogers and Collett's (1989) study; in ours, the motion disparity was generated in terms of yoking the subject's head movement to the movement of each dot, whereas, in theirs, it was generated by yoking the movement of the whole monitor display to the movement of each dot. Rogers and Graham (1979) reported that motion disparity was more effective for depth order perception when it was generated by subject's head movement rather than when it was generated by object movement. Cornilleau-Peres and Droulez (1994) found the advantage of subject's head movement in the discrimination between curved surface and flat surface in depth perception from motion disparity. Moreover, Ono and Steinbach (1990) and Rogers and Graham (1979) reported that the presence of head movement increased the apparent depth magnitude from motion dis-
Table 1 Results of Stepwise Multiple Regression Analysis for the Perceived Depth Magnitude in CS Observation in Experiment 1 Entered Factor
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ses I.MDS 0.441 0.380 .799 F(2,117) = 102.982* 2. BDS 0.379 oes (Binocular Disparity Determined Apparent Depth Order) I. MDS 0.423 0.400 .738 F(2,112) = 66.815* 2. BDS 0.404 oes (Motion Disparity Determined Apparent Depth Order) I. MDS 0.380 0.614 .716 F(l,60) = 63.261* Note-MDS = perceived depth magnitude in MDS observation. BDS = perceived depth magnitude in BDS observation. The number (lor 2) to the left of the factor indicates the step in which the factor was entered. *p < .001.
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Table 2 Results of Simple Regression Analysis, r, and Slope for Apparent Depth Magnitude for CS in Each Motion Disparity and Binocular Disparity in Experiment 1
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parity. Therefore, it must be investigated whether there is a difference in the effectiveness of depth information from motion disparity depending on the procedures to generate it and whether this difference caused the contradictions between our results and Rogers and Collett's (1989). In Experiment 2, it was examined whether the fashion to integrate binocular disparity and motion disparity varied with the procedures to generate motion disparity (object moving, head moving). Method Subjects Eight subjects (2 females and 6 males) participated: 4 who had participated in Experiment I (Subjects M.I., O.K., S.M., and D.B.), I member ofthe institute, and 3 paid students ofTsukuba University. They were selected using the same criteria as in Experiment I.
Apparatus and Stimulus The apparatus was the same as in Experiment I. Two viewing conditions, head moving and object moving, were prepared. In the former condition (which was the same as that in Experiment I), the motion disparity was generated by yoking the dot motion to the subject's head movement. In the latter condition, the subject, whose head was fixated at the center of movable range of chinrest, viewed the stimulus horizontally traversing backward and forward; motion disparity was generated by yoking the motion of each dot to the traversing movement of the stimulus. A sine wave with 0.6-Hz frequency generalized by a function synthesizer (NF WFS-1930) controlled the traverse of the stimulus. Both the movable range of head movement and the traverse range of the stimulus in each viewing condition were 6.5 ern. The stimulus specified surfaces corrugating in a vertically sinusoidal function with 0.25-cpd spatial frequency. Procedure There were five binocular disparity conditions (0', and 0.5' and 2' in each depth order) and three motion disparity conditions (0', and 10' equivalent disparity in each depth order). Five binocular disparity conditions, three motion disparity conditions, and two viewing conditions were combined into 30 kinds of es, six kinds of MDS, and five kinds of BDS. Each stimulus was viewed eight
times; each subject had 328 trials that were divided in six blocks, binocular disparity magnitude (3) X repetition (2). The subject viewed CS and BDS with the same binocular disparity magnitude in the same blocks, and CS and BDS with 0' binocular disparity in the same blocks with MDS; in a block, the depth order specified by binocular disparity (in the block with 0' binocular disparity, MDS, CS, or BDS) and three motion disparity conditions were viewed four times in random order. In each block, half of the subjects viewed the stimuli in the head-moving condition before the object-moving condition, and half viewed the stimuli in the objectmoving condition before the head-moving condition. In the first three blocks, the order of three magnitudes of the binocular disparity (0.5', 2', and 0' with MDS) were random. In the last three blocks, it was the same as in the first three blocks. The subjects' tasks were the same as those in Experiment I.
Results and Discussion Perception of Depth Order As in Experiment 1, the subjects sometimes reported that the perceived depth order inverted during MDS and CS trials. DDS and MDS trials. Each cue by itself almost always determined the perceived depth order; on the average, the sinusoidal corrugation with the depth order specified by disparity was perceived in 99.6% (SD = 1.03) of the nonzero BDS trials, 94.5% (SD = 7.28) of the 10' MDS trials in the head-moving condition, and 96.9% (SD = 4.41) of the 10' MDS trials in the objectmoving condition. The flat surface was perceived in 50.0% (SD = 35.36) of the 0' BDS trials, 75.0% (SD = 37.80) ofthe 0' MDS trials in the head-moving condition, and 76.6% (SD = 35.63) of the 0' MDS trials in the object-moving condition. The tiny irregular corrugation was perceived in the remaining trials. CS trials. For the SCS with nonzero disparities in both head-moving and object-moving conditions, the depth order specified by disparities was perceived in 100.0% of the trials. For the CS presenting 0' motion disparity and nonzero binocular disparity, the depth order
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specified by binocular disparity was perceived in 96.1% = 11.05) of the trials in the head-moving condition and 96.9% (SD = 6.68) of the trials in the object-moving condition. For CS presenting 0' binocular disparity and 10' motion disparity, the subjects perceived the depth order specified by motion disparity in 85.2% (SD = 12.47) of the trials in the head-moving condition and 98.4% (SD = 2.89) of the trials in the object-moving condition. For CS presenting 0' of binocular and motion disparities, the flat surface was perceived in 67.2% (SD = 42.22) of the trials in the head-moving condition and 73.4% (SD = 39.21) of the trials in the object-moving condition. The tiny irregular corrugation was perceived in the remaining trials. For OCS, the subjects perceived the depth order specified by binocular disparity in 84.4% (SD = 11.05) of the trials in the head-moving condition and 80.0% (SD = 10.47) of the trials in the object-moving condition. Figure 5 shows the individual percentages in which the depth order specified by binocular disparity was perceived for OCS. Subjects S.M. and O.K. perceived the depth order specified by motion disparity more frequently in the object-moving condition of Experiment 2 than they did in Experiment 1 (Figure 5), whereas Subjects M.1. and D.S. did not show such a change. Effects of disparity magnitude. A three-way repeated measures ANOYA was performed, with viewing condition, depth order, and binocular disparity magnitude (0.5' and 2') as factors for the frequency in which the depth order specified by motion disparity was perceived for each condition ofOCS (the sum of white and dotted parts in Figure 6). A significant main effect was found only for binocular disparity magnitude [F(l,7) = 25.636, p < .001). This indicates that, in both viewing conditions, the visual system selected the depth order specified by motion disparity more frequently in viewing OCS presenting smaller binocular disparity. (SD
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Perception of Depth Magnitude Paired t tests for the difference depending on the depth order specified by motion and/or binocular disparity found no significant difference for any of the stimulus conditions. Therefore, the depth orders were combined in Figure 7. BDS and MDS. Figure 7 shows that the subjects underestimated the depth magnitude for the 10' MDS in the object-moving condition, although they overestimated for all BDS. Using the values in Figure 7, a repeated measures ANOYA, with viewing condition and motion disparity magnitude as factors for the perceived depth magnitude for MDS, was conducted. There were significant main effects of viewing condition [F(l,7) = 5.57,p < .05] and motion disparity magnitude [F(l,7) = 121.93,p < .001] and a significant interactionbetweenthese factors [F(I,7) = 7.77,p < .05]. A Newman-Keuls test for the interaction found that the perceived depth magnitude was significantly smaller for the 10' condition in the object-moving condition than for the 10' condition in the head-moving condition (p < .05) and was significantly smaller for the 0' condition in both viewing conditions than for the 10' condition in both viewing conditions (p < .05). Linearity in CS trials. The stepwise multiple regression analysis was conducted to examine whether the apparent depth magnitude in the SCS and OCS trials changed according to the viewing condition and according to the apparent depth magnitude for BDS and MDS with the same magnitude of disparity. The depth magniHead Moving Condition
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Figure 6. The percentages of depth order perception in OCS trials. Each part represents the percentages ofthe depth order perception, as in Figure 3. The left (right) columns in each condition show the results of the case in which binocular disparity and motion disparity specified the corrugation with three (two) troughs and two (three) peaks, respectively.
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10
Magnitude of Disparity (min) Figure 7. Averages of perceived depth magnitude. The numbers below the horizontal axis show the magnitudes of binocular disparity (upper) and motion disparity (lower). Standard errors were shown for 2' ofBDS, SCS, and CS with 0' of motion disparity. Vertical thick bars indicate the perceived depth magnitude for MDS. Each symbol indicates the stimulus presenting the binocular disparity with the same magnitude as in Figure 4.
tude for each stimulus that a subject perceived was normalized in terms of her/his average of perceived magnitude from all of MDS and BDS as I; the numbers used as 1 in the normalization were 37.42, 22.08, 27.53, 35.50, 20.94, 39.13, 22.72, and 11.29 mm for Subjects D.B., H.R., S.O., S.M., WN., O.K., M.l., and O.E., respectively. For SCS, analysis included the data ofCS presenting nonzero disparity with 0' ofmotion or binocular disparity. For OCS, ifthe subject had data for a condition ofOCS, analysis also included her/his data of CS presenting the same magnitude ofbinocular or motion disparity with 0' of motion or binocular disparity. Table 3 shows the results; the regression analysis entered the apparent depth magnitude specified by motion disparity in all cases and that by binocular disparity only ifthis cue determined the apparent depth order. These were similar to results in Experiment 1. Viewing condition was not entered in any case. The simple regression analysis was conducted by using the same normalized data as the multiple regression analysis. It showed that the perceived depth magnitude increased with the depth magnitude specified by
Perception of Rocking For MDS with 10' motion disparity, SCS, and OCS, respectively, the subjects perceived rocking in 93.8%, 100.0%, and 100.0% of the trials in the head-moving condition and 86.7%, 93.8%, and 99.6% of the trials in the object-moving condition. In these trials, the subjects perceived the depth order specified by motion parallax and reported the stimulus turning against the subject for MDS, SCS, and OCS, respectively, in 100.0%, 99.6%, and 93.8% of the trials in the head-moving condition and 98.2%,98.8%, and 100.0% of the trials in the objectmoving condition. For OCS, the subjects perceived the depth order by binocular disparity and reported the stimulus turning with the subject in 99.5% of the trials in both the head-moving condition and the object-moving condition. All subjects reported that the direction of the rocking inverted with the depth order inversion. GENERAL DISCUSSION The results of our two experiments confirmed Rogers and Collett's (1989) finding that perceived depth magnitude was a compromise between the magnitudes specified by both cues. Moreover, we made the following new findings about the factors deciding the effectiveness of depth order and magnitude information from motion and binocular disparities.
Integration of Depth Order The visual system used one of the cues exclusively in selecting a depth order for each display regardless of which procedure, object moving or head moving, generated motion disparity. In this exclusive selection of depth order information, there were two factors to determine
Table 3 Results of Stepwise Multiple Regression Analysis for the Perceived Depth Magnitude in CS Observation in Experiment 2 Entered Factor
Weight for Factor
Intersection
R
F
ses 1. MDS 0.324 0.537 .726 2. BDS 0.461 oes (Binocular Disparity Determined Apparent Depth Order) 1. MDS 0.351 0.492 .753 2. BDS 0.501 oes (Motion Disparity Determined Apparent Depth Order) 1. MDS 0.692 0.374 .749
F(2,n) = 42.932*
F(2,n) = 50.328*
F(1,45) = 57.672*
Note-MDS = perceived depth magnitude in MDS observation. BDS = perceived depth magnitude in BDS observation. The number (I or 2) to the left side of the factor indicates the step in which the factor was entered. *p < .001.
MOTION DISPARITY AND BINOCULAR DISPARITY
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Table 4 Results of Simple Regression Analysis, r, and Slope for Apparent Depth Magnitude for CS in Each Motion Disparity and Binocular Disparity in Experiment 2 OCS Binocular Disparity Determined Apparent Depth Order
SCS Disparity
Condition
r
Slope
N
r
Slope
Motion Disparity Determined Apparent Depth Order
N
r
Slope
N
Simple Regression Due to Binocular Disparity Motion 10' 0'
Head moving .067 .923t
0.042 0.930
24 24
.122
0.081
24
.235
-0.257
14
.610t .935t
0.369 1.014
24 24
.676t
0.444
24
.163
0.142
17
Object moving 10' 0'
Simple Regression Due to Motion Disparity Binocular 2'
Head moving
OS 0'
.468 .850t .918t
0.153 0.383 0.692
16 16 16
.509* .686t
0.179 0.425
16 16
.805t
0.396
0 14
.005 .661t .928t
0.003 0.414 0.696
16 16 16
.087 .686t
0.050 0.440
16 16
1.000 .632t
0.540 0.346
2 16
Object moving 2'
OS 0' *p < .05.
tp < .01.
which ofthe cues the visual system selected: the subject's bias and the magnitude of binocular disparity. Factor 1: Bias of Subjects Stevens and Brookes (1988) also reported that the subject's bias decided the dominant cue in the integration of binocular disparity with monocular configuration. Moreover, it has been reported in studies concerned with visual adaptation that there are salient individual differences in the utilization of binocular disparity (Ichikawa & Egusa, 1993; Shimojo & Nakajima, 1981). In these studies, however, the cause of such individual difference in the use of each cue was not explained. In our two experiments, the authors were the subjects who most frequently perceived depth order specified by motion disparity in the OCS trials. The most important difference between the authors and the other subjects was the experience in viewing the display presenting motion disparity. While all subjects had practice sessions in which they viewed the corrugation specified by binocular or motion disparity before the two experiments, the authors had viewed similar stimuli not only in the practice sessions but also in preliminary experiments for present two experiments and for others dealing with depth perception from motion parallax. Subject O.K. was another subject who took part in preliminary experiments other than the training sessions. He also showed a relatively high percentage of perceiving the depth order by motion disparity. Moreover, Subjects S.M. and O.K. perceived the depth order specified by motion disparity with a higher percentage in Experiment 2 (Figure 2) than in Experiment 1 (Figure 5). It is plausible that the more a subject has experience in viewing the display presenting motion disparity, the more this cue is effective in depth order per-
ception. A similar shift to the one shown by Subjects S.M. and O.K. was reported in Stevens and Brookes (1988): the subjects' bias shifted from monocular configuration to binocular disparity during the experiment. The results oftheir study and ours suggest that the subjects' biases are not constant but are changeable due to their experience. Rogers and Collett (1989) did not report any individual bias. It is inferred that their subjects had little difference in their experience in viewing the display presenting motion disparity. Factor 2: Magnitude of Binocular Disparity In the OCS trials, the frequency with which the visual system selected the depth order specified by motion disparity increased as the magnitude ofthe presented binocular disparity decreased. It was not affected, however, by the motion disparity magnitude. The study concerning the threshold reported that, when each cue was viewed by itself, the sensitivity was higher for binocular disparity than for motion disparity in specifying sinusoidal corrugation (Rogers & Graham, 1982) or the difference of Gaussian profile (Rogers & Graham, 1985). Our results suggest that, in suprathreshold levels ofthese cues, (1) binocular disparity is more dominant as an informative source of depth order, (2) which cues are more dominant as determinants of depth order perception depends upon the magnitude of binocular disparity, and (3) as discussed in the preceding section, this dominant relation between the cues might be changed by the subjects' experience. Rogers and Collett (1989) presented the motion disparity by yoking the movement of the monitor to that of each dot. So, the object-moving condition in our Experiment 2 did not reproduce their procedure. From the above-
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mentioned discussion, however, the contradiction between our results and theirs should be attributed not to the difference of the procedure to generate motion disparity but to the difference of the subject's bias and to the difference of binocular disparity magnitude in each study.
Integration of Depth Magnitude The regression analysis showed that, in some CS conditions, the apparent depth magnitude increased with the depth magnitude specified by both cues. This is compatible with the results of the studies concerning the integration of different depth cues that specified unequal depth magnitude to one another: they showed that apparent depth had a magnitude intermediate between that specified by each cue (binocular disparity and monocular configuration, Stevens & Brookes, 1988, and Stevens et al., 1991; binocular disparity and kinetic depth, Johnston, Cumming, & Landy, 1994; binocular disparity and spatial frequency difference, Brown & Weisstein, 1988; motion disparity and occlusion, Ono et al., 1988; luminance and kinetic depth, Dosher, Sperling, & Wurst, 1986; kinetic depth and texture, Landy, Maloney, & Young, 1991, and Young, Landy, & Maloney, 1993; shading and texture, Curran & Johnston, 1994). These confirm the notion that integration of depth magnitude information from these cues is performed in a weighted additive fashion as proposed by Rogers and Collett (1989), Landy (1993), and Maloney and Landy (1989). The weighted addition might be a general fashion in which the visual system integrates the depth magnitude information from different cues. Moreover, the present two experiments showed that, in the addition to depth magnitude information from motion and binocular disparities, there were at least two factors to restrict the effect of binocular disparity: the depth order perception and the relationship of the apparent depth magnitude from each cue. Factor 1: Depth Order Perception Regression analysis showed that the effectiveness of binocular disparity as an informative source for depth magnitude depends on the depth order perception. When this cue determined the apparent depth order in the CS trial, the apparent depth magnitude was not predicted by only one, binocular disparity or motion disparity; it increased with the depth magnitude specified by both cues (Tables 1 and 3). When motion disparity determined the apparent depth order in the OCS trial, however, there was neither significant increment nor decrement in apparent depth magnitude due to binocular disparity, and the subjects perceived smaller depth than that due only to motion disparity (Figures 4 and 7, Tables 1 and 3). These results indicate that, when binocular disparity was ignored in depth order perception, the visual system also ignored the depth magnitude information from this cue and that the perceived magnitude depending only on motion disparity was reduced because of the interference due to neglecting binocular disparity.
Factor 2: Relationship ofthe Apparent Magnitude From Each Cue In Experiment 1, the simple regression analysis (Table 2) showed that the apparent depth magnitude for CS increased with the magnitude specified by binocular disparity only for CS with 0' and 3' of motion disparity. This and Figure 4 suggest that binocular disparity was effective for depth magnitude perception only if the depth magnitude specified by this cue was larger than or almost the same as that specified by any motion disparity condition. Experiment 2 confirmed this notion: the increment of the apparent depth magnitude due to binocular disparity was found in all SCS except for the condition with 10' of motion disparity in the head-moving condition in which the depth magnitude specified by motion disparity was larger than those by all binocular disparity conditions (Table 4, Figure 7). Moreover, Tables 2 and 4 show that the slopes of regression line increased inversely with the magnitude of the other disparity. Maloney and Landy (1989) proposed a model in which the weight assigned to each cue in the additive integration was assumed to be constant regardless ofthe depth magnitude specified by each cue. If our data fit their model, the slope due to each cue should be constant regardless ofthe depth magnitude specified by another cue. Curran and Johnston (1994), in their study concerning the integration of shading and texture, found results similar to ours: the apparent curvature due to texture increased inversely with the curvature specified by shading. We propose that, in the weighted addition of the depth magnitude information from motion disparity, binocular disparity, and texture, the weight assigned to a certain cue depends on the relationship of the depth magnitude specified by each cue involved in the scene. Perceived Depth and Rocking In the present study, for MDS and CS with nonzero motion disparity, if the subjects perceived the depth order specified by motion disparity, they almost always perceived the surface turning against them. This should be the case of d2 in Figure 1; the visual system interpreted some rate of motion disparity as motion. If they perceived the depth order opposite to that specified by motion disparity, they perceived the surface turning with them. This should be the case of d4 in Figure 1. These imply that the depth order perception determined the apparent direction of rocking. This notion is compatible with the studies of Gogel (1979) and Peterson and Shyi (1988) in which depth perception determined the apparent concomitant motion with head motion ofthe surface. The present results suggest that the perception of rocking motion is closely associated with the exclusive selection of depth order information from binocular and motion disparities and that the visual system interprets the surplus motion on the retina, not matched to perceived depth order, as the motion caused by the object's rocking.
MOTION DISPARITY AND BINOCULAR DISPARITY
Underestimation of Depth Magnitude of Motion Disparity In our experiments, the subjects overestimated the depth magnitude for all nonzero BDS. These misperceptions suggest that our subjects overestimated the viewing distance (see Ono & Comerford, 1977, for the effects of misperception of viewing distance on depth perception from disparity). In overestimating viewing distance, depth due to motion disparity should also be overestimated. But, in the present case, the subjects underestimated the depth for some conditions of MDS. One possible explanation is that, for larger motion disparity magnitude, the visual system did interpret some rate of motion on the retina as motion, not as depth, despite overestimating viewing distance. This explanation is supported by the above-mentioned fact that, in MDS and SCS trials, the subjects tended to perceive the stimulus as rocking so that it turned against them, as shown in d2 in Figure 1. Moreover, this explanation concerns the fact that, in Experiment 2, underestimation for MDS was found only in the object-moving condition. Ono and Steinbach (1990) and Rogers and Graham (1979) report similar underestimation of the apparent depth magnitude in the objectmoving situation. Ono and Steinbach proposed that there was a tradeoff between apparent magnitude of depth and motion and that apparent depth magnitude was larger when the head moved than when the object moved because of the degradation of sensitivity to motion when the head moves. Their proposal is compatible with our explanation about the misperception in viewing MDS and CS: underestimation for larger magnitude of motion disparity should be more salient in the object-moving situation than in the head-moving situation. Cancellation of Depth Information In the OCS trial, the visual system did not cancel the depth information from binocular disparity and motion disparity. That is, if the visual system used the depth information from binocular disparity, it interpreted the motion on the retina as the depth order opposite to that inherently specified by motion disparity and rocking so that the stimulus turns with the subject, as predicted in d4 in Figure 1. This means that the cancellation should be impossible in this case since the visual system interpreted the motion disparity as being the same depth order with binocular disparity. Consequently, the apparent depth magnitude increased with the magnitude specified by both cues. Otherwise, if motion disparity was selected in depth order perception, the visual system used only the information of depth magnitude from motion disparity, as shown in Tables 2 and 4. In this case, the cancel!ation should also be impossible since the visual system Ignored binocular disparity. Although we found no cancellation of depth magnitude information from motion disparity and binocular disparity, other studies have reported that in certain situations the cancellation of depth magnitude information
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might be possible. Graham and Rogers (1982a, 1982b) and Rogers and Graham (1984) reported that the aftereffects due to viewing the corrugation specified by binocular (motion) disparity can be canceled by the motion (binocular) disparity specifying the corrugation with the opposite depth order to the aftereffects. The difference in cancellation between our results and theirs should be attributed to the difference in the stages with which each study was concerned. Our study investigated the stage that integrates the depth information from both cues presented simultaneously and in which the effectiveness of depth magnitude information from binocular disparity depends on the cue selected in depth order perception. On the other hand, their studies investigated the stage that registers the depth information from each cue presented successively, causing depth aftereffect, and in which the depth magnitude information from binocular disparity is effective regardless of depth order perception. Also, if each disparity cue is integrated with other cues-for example, with spatial frequency difference (binocular disparity, Brown & Weisstein, 1988) or with occlusion (motion disparity, Ono et aI., 1988)-the depth information from one cue can cancel the information from the other cue specifying opposite depth order. This implies that the depth magnitude information from each cue is effective regardless of depth order perception. This contrasts with what we found in the integration of motion disparity with simultaneous binocular disparity. The difference among these cue interactions in cancellation suggests that the process integrating depth information from different cues varies with the particular cues that are involved in the interaction. REFERENCES BRAUNSTEIN, M. L., ANDERSEN, G. J., ROUSE, M. W., & TITTLE, J. S. (1986). Recovering viewer-centered depth from disparity, occlusion, and velocity gradients. Perception & Psychophysics, 40, 216-224. BROWN, J. M., & WEISSTEIN, N. (1988). A spatial frequency effect on perceived depth. Perception & Psychophysics, 44, 157-166. CORNILLEAU-PERES, V., & DROULEZ, J. (1993). Stereo-motion cooperation and the use of motion disparity in the visual perception of3-D structure. Perception & Psychophysics, 54, 223-239. CORNILLEAU-PERES, v., & DROULEZ, J. (1994). The visual perception of three-dimensional shape from self-motion and object-motion. Vision Research, 34, 2331-2336. CURRAN. w., & JOHNSTON, A. (1994). Integration of shading and texture cues: Testing the linear model. Vision Research, 34, 1863-1874. DOSHER, B., SPERLING, G., & WURST, S. A. (1986). Tradeoffs between stereopsis and proximity luminance covariance as determinants of perceived 3D structure. Vision Research, 26, 973-990. GOGEL, W. C. (1979). The common occurrence of errors of perceived distance. Perception & Psychophysics, 25, 2-11. GRAHAM, M., & ROGERS, B. J. (l982a). Interactions between monocular and binocular depth aftereffects. Investigative Ophthalmology & Visual Science, 22(Suppl.), 272. GRAHAM, M., & ROGERS, B. J. (l982b). Simultaneous and successive contrast effects in the perception of depth from motion-parallax and stereoscopic information. Perception, 11,247-262. ICHIKAWA, M., & EGUSA, H. (1993). How is depth perception affected by long term wearing ofleft-right reversing spectacles? Perception, 22, 971-984. JOHNSTON, E. B., CUMMING, B. G., & LANDY, M. S. (1994). Integration of stereopsis and motion shape cues. Vision Research, 34, 2259-2275.
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(Manuscript received November 30, 1993; revision accepted for publication June 20, 1995.)
