A Stereo Advantage Generalizing 1 Running Head: a Stereo Advantage Generalizing a Stereo Advantage in Generalizing over Changes in Viewpoint on Object Recognition Tasks

Four experiments examined whether generalization to unfamiliar views was better under stereo viewing as opposed to nonstereo viewing across different tasks and stimuli. The first three experiments used a sequential matching task in which observers matched the identity of shaded tube-like objects. Across Experiments 1-3, we manipulated the presentation method of the nonstereo stimuli (eye-patch versus showing the same screen image) and the magnitude of the viewpoint change (30° versus 38°). In Experiment 4, observers identified “easy” and “hard” rotating wireframe objects at the individual level under stereo and nonstereo viewing conditions. We found a stereo advantage for generalizing to unfamiliar views in all experiments. However, in these experiments, performance remained view-dependent even under stereo viewing. These results strongly argue against strictly 2D image-based models of object recognition, at least for the stimuli and recognition tasks used, and they suggest that observers used representations that contained view-specific local depth information. A Stereo Advantage Generalizing 3 INTRODUCTION We easily recognize many familiar and unfamiliar objects that vary in shape, color, texture, movements, and so on. Although any or all of these properties can be used for recognition, it is largely assumed that recognition is predominantly based on matching shapes recovered from the visual input to shapes encoded in short-term and long-term visual memory. This assumption has several motivations. First, shape can be derived from different sources of visual information, such as motion or stereo (Bülthoff, 1991; Marr, 1982). Second, because of multiple inputs to the shape representation, shape is robust to changes or degradation to the visual input. Finally, in most circumstances, shape can be used to reliably identify objects (e.g., Hayward, 1998). Despite the importance of shape for object recognition, how 3D shape is represented for recognition remains elusive (Bülthoff, Edelman, & Tarr, 1995). In this regard, one outstanding issue is the extent to which the object representation encodes object-centered 3D depth and structure (e.g., Marr & Nishihara, 1978) as opposed to viewer-centered 2D views (e.g., Poggio & Edelman, 1990). Another possibility is that the object representation encodes some intermediate shape representation, such as view-invariant qualitative parts (e.g., Biederman, 1987) or view-specific local depth of visible surface patches, such as Marr’s (1982) 2.5D sketch (see also Edelman & Bülthoff, 1992; Williams & Tarr, 1999). Building on previous work (Edelman & Bülthoff, 1992; Farah, Rochlin, & Klein, 1994; Humphrey & Kahn, 1992), in the present study we examined the role of stereo information in object recognition, as this is a strong source of information A Stereo Advantage Generalizing 4 about 3D depth and structure, alone or in combination with other depth cues (e.g., Bülthoff, 1991; Bülthoff & Mallot, 1988; Landy, Maloney, Johnston, & Young, 1995). Specifically, we examined whether the addition of stereo information facilitates the recognition of objects when these are presented at an unfamiliar viewpoint relative to when they are presented at a familiar viewpoint. We did not test novel objects with distinctive part structure, which is often found in real world objects (Biederman, 1987). Rather, we varied the recognition task and stimuli in other important ways over four experiments in an effort to explore at least some of the conditions under which the visual system may encode depth and 3D structure information. Our secondary aim was to compare our results with previous studies that used similar novel objects with no distinctive part structure. Edelman and Bülthoff (1992) initially found that subjects were more accurate at recognizing novel objects under stereo than under nonstereo viewing. Their stimuli were computer generated wire forms, constructed by joining thin straight tubes together end to end. This stereo advantage was found across a range of viewpoint changes up to 120° from trained viewpoints. However, a similar advantage was also found for the trained viewpoints (i.e., 0° change in viewpoint), suggesting that stereo information did not improve view generalization but improved overall recognition performance. These findings could have been due to two aspects of their design. First, during training, objects were always shown in stereo whereas during testing, the learned targets were shown in both stereo and nonstereo presentations in randomly intermixed trials. As a result, the overall stereo advantage may have been due to the viewing condition mismatch between the training and testing trials (see also Sinha & A Stereo Advantage Generalizing 5 Poggio, 1994). Second, with the objects used, subjects already generalized well under nonstereo viewing (e.g., miss rates of around 20% in their Experiment 4). A stereo advantage in view generalization may only be evident when subjects find it difficult to generalize to unfamiliar views under nonstereo viewing. What is clear in Edelman and Bülthoff’s data, and as they pointed out in their conclusion, is that 3D depth specified by stereo information is encoded in a view-sensitive fashion. Our present data lend further support to this claim. Other investigators have found indirect evidence for a stereo advantage in view generalization across a range of novel objects. First, Farah et al. (1994) compared subjects’ ability to generalize to unfamiliar views of thin, smooth, potato-chip like surfaces and their wire form outlines, presented as either real objects seen from a close distance or as videotape recordings. These investigators found that subjects performed better at generalizing to unfamiliar views when presented with physical objects, presumably because they have access to stereo information about 3D shape. That said, Farah et al. did not provide any statistical justification for this conclusion, and their experiments do not readily admit a stereo versus nonstereo comparison (which was not the primary aim of their study); e.g., different initial orientations and different rotations were used across the stereo versus nonstereo experiments. Humphrey and Kahn (1992) also found evidence suggestive of a stereo advantage in view generalization using novel objects that had distinctive parts and part-structures (these stimuli were also presented as real, physical objects). They found that subjects were more accurate under stereo than nonstereo viewing when the view changed, but that these subjects performed equally well under stereo and A Stereo Advantage Generalizing 6 nonstereo viewing when the view did not change. However, the authors raised the possibility that the stereo advantage in their experiment may have resulted from a speed versus accuracy trade-off, combined with a ceiling effect when the initial and test stimuli were shown from the same view. As they suggested, the slower stereo response times observed in their study may well have resulted from the shutter apparatus they used: refocusing from the shutter to the stimuli may have taken longer under stereo viewing. That said, a speed versus accuracy trade-off cannot be definitely ruled out. Very recently, Burke (2005) reported that stereo information reduced both response times and error rates for large viewpoint differences (between 40° and 80°) in a same-different matching task, as used in Experiments 1-3 (though Burke does not infer that 3D information is encoded in the object representations). His stimuli consisted of stereo photographs of four bent paper-clips. A prism stereoscope was used to present these stimuli. However, it is not clear that the photographed and thin paper-clips were clearly seen as 3D objects under nonstereo viewing. It is, therefore, of interest to see if there is a stereo advantage with stimuli in which monocular cues to depth are clearly available (e.g., shading and motion), as is the case under most everyday viewing. It is also of interest to see if there is a stereo advantage in an identification task that requires long-term object representations. So far, the existing evidence suggests a stereo advantage in view generalization, but it is not definitive, at least for some important kinds of stimuli and tasks. It is important to address this issue because the pattern of view generalization in the presence or absence of stereo cues may reveal the degree to which 3D depth A Stereo Advantage Generalizing 7 information is encoded in the object representation. Purely image-based theories of object recognition have a strong history (e.g., Poggio & Edelman, 1990; Rock & DeVita, 1987). Such accounts have not been definitively ruled out, although the results from the behavioral studies reviewed so far suggest that some depth information is encoded in the object representations used in object recognition tasks (Burke, 2005; Edelman & Bülthoff, 1992; Farah et al., 1994; Humphrey & Kahn, 1992). In addition, a computational study by Liu, Knill, and Kersten (1995) complements these behavioral studies, showing that human subjects performed better than an ideal-observer model that used strictly 2D information. In their study, Liu et al. (1995) compared ideal-observer performance to human performance on a form-comparison task to infer the information that humans rely on to carry out the task (using forms similar to those used in Edelman & Bülthoff, 1992). They defined ideal-observers that used strictly 2D view information (e.g., x and ycoordinates of features), strictly 3D information (e.g., x, y, and z-coordinates of features), or intermediate depth information to perform the comparison task. Their results and analyses ruled out what they call a “2D/2D” template-matching scheme as a model for the performance of their human subjects with symmetric stimuli, even if it is assumed that new templates learned during testing were stored as the experiment proceeded. On the assumption that subjects do not form new stored templates during testing, Liu et al. also ruled out the “2D/2D” scheme as a model of subject performance with nonsymmetrical stimuli. However, with these stimuli, subjects performed considerably worse than a corresponding “2D/2D” learning ideal observer—raising the possibility that humans still operated with the basic “2D/2D” A Stereo Advantage Generalizing 8 scheme but learned new 2D templates as the experiment proceeded (e.g., Jolicoeur, 1985; Tarr & Pinker, 1989). The net result is that, at least for their nonsymmetrical stimuli, a strictly 2D image-based scheme remains an open possibility as a model of subject performance. Thus, from a computational perspective, it is also not conclusive whether human observers do or do not use 3D depth information. To summarize, the evidence to date suggests that subjects rely on some 3D depth information rather than strictly 2D views for recognizing various kinds of 3D objects (Burke, 2005; Edelman & Bülthoff, 1992; Farah et al., 1994; Humphrey & Kahn, 1992; Liu et al., 1995). The main goal in the present study is to determine more conclusively the extent to which 3D depth information is encoded in the visual memory of shapes. To that end, following previous studies, we tested for a stereo advantage in view generalization. In contrast to previous studies, we used a range of different stimuli and different tasks. We also provided a range of monocular cues to 3D depth, including shading, occlusions, and motion (Bülthoff, 1991). In Experiments 1-3 we used a same-different sequential matching task that tapped short-term memory. For these experiments, we used shaded, closed tube-like objects. In Experiment 4 we used an identification task that tapped long-term memory representations. The stimuli in this last experiment were wire-frame objects that rotated in depth. Both of these tasks have been used in many previous studies, and they reflect everyday aspects of visual object recognition. If subjects show a stereo advantage for view generalization across these experiments, but performance is still view dependent even under stereo viewing, this would provide direct evidence for object representations that were view dependent but contained view-specific depth A Stereo Advantage Generalizing 9 information (Edelman & Bülthoff, 1992)—at least for the range of stimuli and tasks used in the current experiments. EXPERIMENT 1 Example stimuli are shown in Figure 1. The stimuli were randomly deformed tori, with tube diameter held close to constant. With these stimuli it was not possible to do the same-different task by “counting humps” or by looking for local distinguishing features. That is, the stimuli were designed to push subjects towards a global encoding of form. The motivation for these stimuli was to make it more difficult to generalize over changes in viewpoint—and so, in light of the evidence surveyed above, more likely to yield a stereo advantage in view generalization—since subjects could not consistently do the task by comparing abstract descriptions (e.g., numbers of humps) or local 2D image features. However, even in nonstereo viewing, there was substantial depth and 3D structure information available: interposition, shading, and attenuation of illumination with (simulated) distance. In this experiment, subjects wore an eye-patch over one eye to form the nonstereo viewing condition. ----------------------Figure 1 about here ----------------------Method Subjects. Nineteen subjects completed the experiment, but one did not meet a pre-set criterion of 1/3 correct responses in both conditions. Most of the subjects were A Stereo Advantage Generalizing 10 Brown University undergraduates, and all subjects gave informed consent and were paid for their participation. Apparatus. The displays were generated on a Silicon Graphics Onyx2 and displayed on a 19” monitor with a resolution of 1,280 x 1,024 pixels. The vertical resolution was halved so that the left and right frames could be interleaved. The screen edges were masked off using black poster board. An adjustable riser with its top close to subjects just below eye-level masked any remaining reflections from the screen light. In this configuration, the riser itself perceptually disappeared. Subjects’ arms and the computer mouse were hidden from view beneath a table-like construction that supported the riser. The subject’s head was stabilized using a chin rest and a padded headrest (though some slight side-to-side head movement was possible). Stimuli. The stimuli consisted of deformed tori defined by an interpolated circle of seven rings of points. For each stimulus, the simulated large diameter of the original torus was 11.7 cm and the simulated small diameter was 1.8 cm (simulated magnitudes refer to the measures determined, ideally, by vergence angle and angular extent). The rings of points were then deformed up-down and in-out within ranges of 6.5 cm, with the constraint that the deformations in these two directions differed by at least 2.25 cm from the deformations of the immediately adjacent rings. Imagine rays drawn from the center of the undeformed torus to the centers of the seven rings of points. The ray to the first circle of points was initially aligned with the x-axis, which was the axis that the stimuli rotated around. The angle of this ray, relative to this axis, was randomly varied by approximately 51.4° (so that the first ring of points, defining A Stereo Advantage Generalizing 11 the undeformed torus, would not always be aligned with the axis that the stimuli rotated around). Before interpolating the final surface, seven additional intervening rings were inserted and positioned to keep the tube diameter approximately constant. The distance to the screen was 90 cm; and the simulated distance to the center of the undeformed tori was 115 cm. The average horizontal visual angle of the stimuli was about 12° whereas the average vertical visual angle was about 7°. Although the simulated distance of the deformed tori placed them just behind the computer screen, the impression—given the care taken to perceptually isolate the stimuli—was of shapes floating in space, with no impression of a screen surface (Watt, Akeley, Ernst, & Banks, 2005, present evidence that, under stereo viewing and with care taken to perceptually isolate the stimuli, screen cues played no role in a slant perception task; see also Bennett, 2005). Stereo viewing was simulated using Stereographics liquid crystal goggles. Asymmetric viewing frustums (viewing pyramids defined by eye position and screen dimensions) were defined for each eye, with the dimensions adjusted depending on inter-pupilary distance (which was measured for each subject by sighting over a clear plastic ruler placed on the bridge of each subject’s nose). For the nonstereo condition an eye patch was placed over the “nonsighting” eye, as indicated (roughly) by handedness. The eye patch was placed under the stereo goggles and eye width was set to zero. The program to generate the stimuli and collect responses was written in C and Silicon Graphics’ GL graphics programming language. On each trial, the deformed tori could be rotated about the x-axis by equal amounts “front up” or “front down” as shown in Figure 2. This rotation ensured that A Stereo Advantage Generalizing 12 the amount of self-occlusion was, on average, the same across trials. The stimuli were blue and they were shown against a gray background. As already noted, selfocclusion, shading, and attenuation of illumination with (simulated) distance provided monocular cues to depth and 3D structure. ----------------------Figure 2 about here ----------------------Design and Procedure. Viewing (stereo, nonstereo) was a within-subject factor, blocked by session. Half the subjects ran in the stereo condition first, and half the subjects ran in the nonstereo session first. The task was a same-different sequential matching task. Each trial began with the presentation of the first stimulus for 4000 ms, followed by a blank gray field for 1750 ms. The second stimulus was presented and left in view until subjects responded. After that, a pattern mask was presented, which consisted of a grid of squares of varying lightness (with sides of 4.45°). Subjects were instructed to respond as quickly as possible while still remaining accurate. Feedback about accuracy was given throughout the experiment (not just during practice trials). Subjects were also given a screen presented message, “too slow” when their response times exceeded 4000 ms. Responses were made by pressing the right mouse button if the two stimuli presented were the same torus, and the left button if they were different tori. The center mouse button was used to begin each trial. For each session, there were 144 trials over-all, broken into three blocks of 48 trials. Half the trials were “same” trials, in which the first and second stimuli were the A Stereo Advantage Generalizing 13 same deformed torus, and the remaining trials were “different” trials, in which the two stimuli presented were two different tori. On two-thirds of the “same” trials (48/72 trials), the second stimulus presented was rotated about the x-axis relative to the orientation of the first stimulus (“different orientation” condition). On the remaining third of “same” trials (24/72 trials), the second stimulus was shown at the same orientation as the first (“same orientation” condition). Subjects were informed of these percentages. The percentages of “different orientation” and “same orientation” trials were the same for the different trials. Half the trials began with the first stimulus rotated “front up” and half began with the first stimulus rotated “front down” (see Figure 2). In Experiment 1, rotations were always 19° up or down, so that subjects were required to generalize over total rotations of 38° on “different orientation” trials. Subjects were informed that the stimuli were only rotated about the x-axis. The experimental trials were preceded by 36 practice trials. In addition, right before the practice trials, subjects were shown the various trial conditions. On these example trials, two stimuli were presented side by side (after being shown in succession). The subjects were shown how these two stimuli could or could not be rotated to coincide with the same torus. For example, for a “same, different orientation” trial, one stimulus was rotated to correspond to the other. For a “different, different orientation” trial it was shown that it was not possible to rotate either stimulus to coincide with the other. A Stereo Advantage Generalizing 14 Each of the two sessions (one stereo and one nonstereo) took approximately 3540 minutes. There were at least two days between sessions and no more than two weeks. Results The results of Experiment 1 are shown in Figures 3 and 4. A Viewing (stereo, nonstereo) x Orientation Analysis of Variance (ANOVA), with percent correct as the dependent variable, yielded main effects of Viewing, F(1, 17) = 36.69, p < .001, and Orientation, F(1, 17) = 134.70, p < .001. Importantly, the Viewing x Orientation interaction was significant, F(1,17) = 16.31, p = .001, reflecting the fact that subjects generalized better under stereo viewing (see Figure 3). ----------------------Figure 3 about here --------------------------------------------Figure 4 about here ----------------------For the “same, same orientation” trials subjects were close to ceiling for both stereo conditions (stereo: Msame view =97.0%, SEsame view = 1.1%; nonstereo: Msame view = 96.7%, SEsame view = 1.5%). By comparison, observers were more accurate under stereo than nonstereo viewing for “same, different orientation” trials (stereo: Mdifferent view = 70.6%, SEdifferent view = 3.4%; nonstereo: Mdifferent view = 57.3%, SEdifferent view = 3.4%). A post-hoc test showed that this difference on these trials were significantly A Stereo Advantage Generalizing 15 different, t(17) = 5.15, p < .001. Furthermore, though subjects clearly found the task demanding, performance under nonstereo viewing (“same, different orientation” trials) was greater than chance, t(17) = 2.16, p < .025. The pattern for response times (RTs) was very different from the accuracy data (see Figure 4). There was a large effect of Orientation, F(1,17) = 51.00, p < .001, but there was no effect of Viewing, F(1,17) < 1. Further, there was no Viewing x Orientation interaction, F(1,17) < 1. Indeed, Figure 4 shows that RTs were virtually identical for the two viewing conditions. The key observation is that there is no evidence that a speed versus accuracy trade-off accounted for the stereo advantage in generalizing to new viewpoints (cf. Humphrey & Khan, 1992). Discussion Consistent with several previous studies, performance was view dependent under both stereo and nonstereo viewing (e.g., Edelman & Bülthoff, 1992; Farah et al., 1994; Humphrey & Khan, 1992; Sinha & Poggio, 1994). Importantly, there was a clear stereo advantage in view generalization. That is, observers responded equally accurately under both stereo and nonstereo viewing when the stimuli were presented at the same orientation, but their accuracy was much poorer in the nonstereo than the stereo condition when the stimuli were presented at different orientations (with only a 38° difference in viewpoint). This stereo advantage is evidence against a purely 2D image-based model of subject performance. However, the marked view dependency of performance—even under stereo viewing—suggests that subjects did not build up and use full 3D models, although information about 3D structure was available in A Stereo Advantage Generalizing 16 both viewing conditions (e.g., shading). That said, however, there were also selfocclusions, and it is possible that this inhibited subjects from building such models. Subjects were not tested for stereo anomaly in either Experiment 1 or in Experiments 2-4. However, we do not believe that any stereo defects would affect the main results. To begin, subjects who are stereoanomalous with brief stimulus presentations are often normal or show reduced stereoanomaly with long stimulus presentations as well as with repeated exposure (Newhouse & Uttal, 1982; Patterson & Fox, 1984). In the current study, we used relatively long stimulus presentation times and subjects were repeatedly exposed to similar, stereoscopically presented stimuli. More importantly, any stereo defects work against our hypothesis, as stereoanomalous subjects would not be expected to show a stereo advantage. That said, it would be interesting to test stereoanomalous subjects to examine whether 3D information from monocular cues (e.g., shading, texture, motion, etc.) may facilitate view generalization. There are other possible explanations for the advantage under stereo viewing in Experiment 1 that stem from using an eye patch to form the nonstereo condition. First, the stereo advantage may be due to the fact that separate estimates are available for the same 2D features under stereo viewing (associated with the two images, one for each eye). However, this seems unlikely given the small differences in the left and right eye images under stereo viewing. Another potential problem with using an eyepatch to produce the nonstereo condition is that subjects may find viewing with one eye unnatural and unfamiliar, and perhaps this somehow inhibited performance in the nonstereo condition. To address these concerns the nonstereo condition in Experiment A Stereo Advantage Generalizing 17 2 was formed by presenting the same screen image to each eye (which meant that the projected retinal images were essentially identical, given the viewing distance of 90 cm). EXPERIMENT 2 Experiment 2 was the same as Experiment 1, except that the nonstereo condition was formed by presenting the same image to each eye. Method Subjects. Twenty-seven subjects completed the experiment, but one did not meet a pre-set criterion of scoring greater than 1/3 correct in both conditions. Most of the subjects were undergraduates at Brown University, and all subjects gave informed consent and were paid for their participation. Stimuli, Design, and Procedure. The stimuli, design, and procedure were the same as in Experiment 1, except that for the nonstereo condition each eye was presented with the same screen image. Results The results are shown in Figures 5 and 6. A Viewing (stereo, nonstereo) x Orientation ANOVA, with percent correct as the dependent variable, yielded main effects of Viewing, F(1, 25) = 8.20, p < .01, and Orientation, F(1, 25) = 204.54, p < .001. Further, the Viewing x Orientation interaction was significant, F(1,25) = 4.40, p A Stereo Advantage Generalizing 18 < .05, reflecting the fact that subjects generalized better under stereo viewing (see Figure 5). Because the stereo advantage in view generalization seemed to be reduced in Experiment 2 compared to Experiment 1 (see Figures 3 and 5), an Experiment (nonstereo method) x Viewing (stereo, nonstereo) x Orientation ANOVA was conducted with percent correct as the dependent variable (with Experiment as a between-subject factor, and Viewing and Orientation as within-subject factors). However, the three-way interaction was not significant, F(1, 42) =1.54, p = .222. ----------------------Figure 5 about here --------------------------------------------Figure 6 about here ----------------------As in Experiment 1, for the “same, same orientation” trials subjects were equally at ceiling in the stereo and nonstereo conditions (stereo: Msame view = 97.4%, SEsame view = 0.8%; nonstereo: Msame view = 97.0%, SEsame view = 1.7%). In contrast, for the “same, different orientation” trials subjects were more accurate under stereo viewing (stereo: Mdifferent view = 64.3%, SEdifferent view = 2.7%; nonstereo: Mdifferent view = 56.8%, SEdifferent view = 3.3%) This difference was again significant, t(25) = 2.72, p = .006. Lastly, performance under nonstereo viewing (“same, different orientation” trials) was greater than chance, t(25) = 2.06, p = .025. A Stereo Advantage Generalizing 19 For RTs (see Figure 6), there were effects of Viewing, F(1,25) = 4.73, p = .039, and Orientation, F(1,25) = 48.89, p < .001. However, unlike the accuracy data, there was no Viewing x Orientation interaction, F(1,25) = 1.67, p = .208. It is not clear why there was a significant effect of the viewing condition on RTs (unlike in Experiment 1—or Experiment 3 below). The important observation is that subjects were faster under stereo viewing, so the stereo advantage in generalizing to new views observed in accuracy was not due to a speed versus accuracy trade-off, coupled with a ceiling effect when the orientation was the same. Discussion In Experiment 2, we replicated the results of Experiment 1 using a different method to form the nonstereo viewing condition. First, we found that recognition performance was markedly view dependent in both viewing conditions. Second, we found a stereo advantage in view generalization when the same image was shown to each eye under nonstereo viewing. Thus, the stereo advantage reported cannot simply be due to the fact that subjects had access to redundant information about 2D features under stereo viewing, or to the fact that they had to view the stimuli unnaturally while wearing an eye patch under nonstereo viewing. Taken together, the results of Experiments 1 and 2 provide evidence that depth information is encoded in a viewdependent manner (e.g., Edelman & Bülthoff, 1992; Farah et al., 1994; Humphrey & Khan, 1992). These results therefore provide evidence against strictly 2D image-based models or strictly 3D structural models (see also Liu et al., 1995). A Stereo Advantage Generalizing 20 EXPERIMENT 3 Part of the aim in designing the stimuli and choosing the rotation magnitudes for Experiments 1 and 2 was to arrive at a generalization task that was challenging. In fact, performance in the “same, different orientation” trials in the first two experiments was slightly but significantly above chance. It is of interest to see whether the stereo advantage in view generalization holds in a task that is, or is expected to be, easier. Therefore, we tried to replicate the stereo advantage with smaller depth rotations. This would presumably make view generalization easier. Thus, Experiment 3 was the same as Experiment 2, except that “front-up” and “front down” rotations of 15° were used so that subjects were required to generalize over rotations of 30° rather than 38° on “different orientation” trials. Method Subjects. Twenty-six subjects participated in the experiment. Most of the subjects were undergraduates at Brown University, and all subjects gave informed consent and were paid for their participation. Stimuli, Design, and Procedure. The stimuli, design, and procedure were the same as in Experiment 2 (so, for the nonstereo condition, each eye was presented with the same screen image), except for the difference in depth rotations.