Quantitative stereoscopic depth without binocular correspondence

Induction of Kanizsa Contours Requires Awareness of the Inducing Context

It remains unknown to what extent the human visual system interprets information about complex scenes without conscious analysis. Here we used visual masking techniques to assess whether illusory contours (Kanizsa shapes) are perceived when the inducing context creating this illusion does not reach awareness. In the first experiment we tested perception directly by having participants discriminate the orientation of an illusory contour. In the second experiment, we exploited the fact that the presence of an illusory contour enhances performance on a spatial localization task. Moreover, in the latter experiment we also used a different masking method to rule out the effect of stimulus duration. Our results suggest that participants do not perceive illusory contours when they are unaware of the inducing context. This is consistent with theories of a multistage, recurrent process of perceptual integration. Our findings thus challenge some reports, including those from neurophysiological experiments in anaesthetized animals. Furthermore, we discuss the importance to test the presence of the phenomenal percept directly with appropriate methods.

How Configurations of Binocular Disparity Determine Whether Stereoscopic Slant or Stereoscopic Occlusion is Seen

A partially occluded contour and a slanted contour may generate identical binocular horizontal disparities. We investigated conditions promoting an occlusion resolution indicated by an illusory contour in depth along the aligned ends of horizontally disparate line sets. For a set of identical oblique lines with a constant width added to one eye's view, strength, depth, and stability of the illusory contour were poor, whereas for oblique lines of alternating orientations the illusory contours were strong, indicating a reliance on vertical size disparities rather than vertical positional disparities in generating perceived occlusion. For horizontal lines, occlusion was seen when the lines were of different lengths and absolute width disparity was invariant across the set. In all line configurations, when the additional length was on the wrong eye to be attributed to differential occlusion, lines appeared slanted consistent with their individual horizontal disparities. This rules out monocular illusory contours as the determining factor.

Perceived Depth in the ‘Sieve Effect’ and Exclusive Binocular Rivalry

An impression of a surface seen through holes is created when one fuses dichoptic pairs of discs, with one member of each pair black and the other member white. This is referred to as the ‘sieve effect’. The stimulus contains no positional disparities. Howard (1995, Perception24 67–74) noted qualitatively that the sieve effect occurs when the rivalrous regions are within the range of sizes, contrasts, and relative sizes where exclusive rivalry occurs, rather than binocular lustre, stimulus combination, or dominant rivalry. This suggests that perceived depth in the sieve effect should be at a maximum when exclusive rivalry is most prominent. We used a disparity depth probe to measure the magnitude of perceived depth in the sieve effect as a function of the sizes, contrasts, and relative sizes of the rivalrous regions. We also measured the rate of exclusive rivalry of the same stimuli under the same conditions. Perceived depth and the rate of exclusive rivalry were affected in the same way by each of the three variables. Furthermore, perceived depth and the rate of exclusive rivalry were affected in the same way by changes in vergence angle, although the configuration of the stimulus surface was held constant. These findings confirm the hypothesis that the sieve effect is correlated with the incidence of exclusive rivalry.

Disparity biasing in depth from monocular occlusions

Monocular occlusions have been shown to play an important role in stereopsis. Among other contributions to binocular depth perception, monocular occlusions can create percepts of illusory occluding surfaces. It has been argued that the precise location in depth of these illusory occluders is based on the constraints imposed by occlusion geometry. Tsirlin et al. (2010) proposed that when these constraints are weak, the depth of the illusory occluder can be biased by a neighboring disparity-defined feature. In the present work we test this hypothesis using a variety of stimuli. We show that when monocular occlusions provide only partial constraints on the magnitude of depth of the illusory occluders, the perceived depth of the occluders can be biased by disparity-defined features in the direction unrestricted by the occlusion geometry. Using this disparity bias phenomenon we also show that in illusory occluder stimuli where disparity information is present, but weak, most observers rely on disparity while some use occlusion information instead to specify the depth of the illusory occluder. Taken together our experiments demonstrate that in binocular depth perception disparity and monocular occlusion cues interact in complex ways to resolve perceptual ambiguity.

Binocular vision

This essay reviews major developments - empirical and theoretical - in the field of binocular vision during the last 25years. We limit our survey primarily to work on human stereopsis, binocular rivalry and binocular contrast summation, with discussion where relevant of single-unit neurophysiology and human brain imaging. We identify several key controversies that have stimulated important work on these problems. In the case of stereopsis those controversies include position vs. phase encoding of disparity, dependence of disparity limits on spatial scale, role of occlusion in binocular depth and surface perception, and motion in 3D. In the case of binocular rivalry, controversies include eye vs. stimulus rivalry, role of "top-down" influences on rivalry dynamics, and the interaction of binocular rivalry and stereopsis. Concerning binocular contrast summation, the essay focuses on two representative models that highlight the evolving complexity in this field of study.

The role of monocularly visible regions in depth and surface perception

The mainstream of binocular vision research has long been focused on understanding how binocular disparity is used for depth perception. In recent years, researchers have begun to explore how monocular regions in binocularly viewed scenes contribute to our perception of the three-dimensional world. Here we review the field as it currently stands, with a focus on understanding the extent to which the role of monocular regions in depth perception can be understood using extant theories of binocular vision.

Feature-based processing of audio-visual synchrony perception revealed by random pulse trains

Computationally, audio-visual temporal synchrony detection is analogous to visual motion detection in the sense that both solve the correspondence problem. We examined whether audio-visual synchrony detection is mediated by a mechanism similar to low-level motion sensors, by one similar to a higher-level feature matching process, or by both types of mechanisms as in the case of visual motion detection. We found that audio-visual synchrony-asynchrony discrimination for temporally dense random pulse trains was difficult, whereas motion detection is known to be easy for spatially dense random dot patterns (random dot kinematograms) due to the operation of low-level motion sensors. Subsequent experiments further indicated that the temporal limiting factor of audio-visual synchrony discrimination is the temporal density of salient features not the temporal frequency of the stimulus, nor the physical density of the stimulus. These results suggest that audio-visual synchrony perception is based solely on a salient feature matching mechanism similar to that proposed for high-level visual motion detection.

Monocular transparency and unpaired stereopsis

Howard and Duke [Howard, I. P. & Duke, P. A. (2003). Monocular transparency generates quantitative depth. Vision Research, 43, 2615-2621] recently proposed a new source of binocular information they claim is used to recover depth in stereoscopic displays. They argued that these displays lack conventional disparity and that the metrical depth experienced results from transparency rather than occlusion relations. Using a variety of modified versions of their stimuli, we show here that the conditions for transparency are not required to elicit the depth experienced in their stereograms. We demonstrate that quantitative and precise depth depended not on the presence of transparency but horizontal contours of the same contrast polarity. Depth was attenuated, particularly at larger target offsets, when horizontal contours had opposite contrast polarity for at least a portion of their length. We also show that a demonstration they used to control for the role of horizontal contours can be understood with previously identified mechanisms involved in the computations associated with stereoscopic occlusion. These results imply that the findings reported by Howard and Duke can be understood with mechanisms responsible for the computation of binocular disparity and stereoscopic occlusion.

Monocular transparency and unpaired stereopsis

Howard and Duke [Howard, I. P. & Duke, P. A. (2003). Monocular transparency generates quantitative depth. Vision Research, 43, 2615-2621] recently proposed a new source of binocular information they claim is used to recover depth in stereoscopic displays. They argued that these displays lack conventional disparity and that the metrical depth experienced results from transparency rather than occlusion relations. Using a variety of modified versions of their stimuli, we show here that the conditions for transparency are not required to elicit the depth experienced in their stereograms. We demonstrate that quantitative and precise depth depended not on the presence of transparency but horizontal contours of the same contrast polarity. Depth was attenuated, particularly at larger target offsets, when horizontal contours had opposite contrast polarity for at least a portion of their length. We also show that a demonstration they used to control for the role of horizontal contours can be understood with previously identified mechanisms involved in the computations associated with stereoscopic occlusion. These results imply that the findings reported by Howard and Duke can be understood with mechanisms responsible for the computation of binocular disparity and stereoscopic occlusion.

A long-distance stereoscopic detector for partially occluding surfaces

An external noise technique was used to investigate the stereoscopic process that generates an illusory phantom occluder from binocularly unmatched elements. Observers were required to identify the quadrant in which a binocularly defined target was presented. We had three targets: (a) two vertical binocular bars with the unmatched portions arranged to induce a stable phantom occluder (valid), (b) the same stimuli except the image for the left eye was switched with that for the right eye therefore not inducing a stable occluder (invalid), and (c) a single binocular bar with the same unmatched portion (single-bar). For each target, the luminance contrast of the signal required for 75% correct responses was measured at four levels of external interocular noise. Contrast thresholds were found to be lower for the valid target than for both the invalid and the single-bar targets. The results suggest that the visual system has a stereoscopic detector that responds to stimuli that meet a long-distance requirement for the perception of partially occluding surfaces.

Pictorial cues constrain depth in da Vinci stereopsis

"da Vinci stereopsis" is defined as depth seen in a monocular object occluded by a binocular one, and the visual system must solve its depth ambiguity [Nakayama, K., & Shimojo, S. (1990). da Vinci stereopsis: Depth and subjective occluding contours from unpaired image points. Vision Research, 30, 1811-1825]. Although fused images include various pictorial features, effects of pictorial depth cues have never been systematically investigated in da Vinci stereopsis. To examine this, we created stereograms consisting of a monocular bar flanked by binocular bars with a fixed large horizontal separation, in which the monocular bar induced a subjective occluding edge. Manipulating vertical size or contrast of the bars could affect the depth of the monocular bar. Conflicting these cues revealed that the effect of vertical size was stronger than that of contrast in all our subjects. Measurements of the depth indicated that the relative vertical size of the bars quantitatively determined the perceived depth, of which levels had large inter-subject differences. All these experiments indicate that the visual system can use the pictorial depth cues as a constraint to determine the depth of monocular elements.

Evidence for the correcting-mechanism explanation of the Kanizsa amodal shrinkage

An object phenomenally shrinks in its horizontal dimension when shown on a 2-D plane as if the central portion of the object were partially occluded by another vertical one in 3-D space (the Kanizsa amodal shrinkage). We examined the predictions of the correcting-mechanism hypothesis proposed by Ohtsuka and Ono (2002, Proceedings of SPIE 4864 167-174), which states that an inappropriate operation of the mechanism that corrects a phenomenal increase in monocularly visible areas accompanied by a stereoscopic occluder gives rise to the illusion. In this study we measured the perceived width (or height in experiment 3) of a square seen behind a rectangle, while controlling other factors which potentially influence the illusion, such as the division of space or depth stratification. The results of five experiments showed that (a) the perceived width was not influenced when the occluder had a relatively large binocular disparity, but was underestimated when the occluder did not have disparity, and (b) the shrinkage diminished when the foreground rectangle was transparent, was horizontally oriented, or contained no pictorial occlusion cues. These results support the hypothesis that the correcting mechanism, triggered by pictorial occlusion cues, contributes to the Kanizsa shrinkage.

Binocular depth perception from unpaired image points need not depend on scene organization

Dichoptic stimuli containing unmatched features can produce depth perception despite the absence of binocular disparity, a phenomenon known as da Vinci stereopsis. Unmatched points can arise from depth discontinuities and partial occlusion in the real world. It has been hypothesized that spatial organization of unmatched image features as dictated by the ecological optics of occlusion might determine perceived depth in da Vinci stereopsis. We tested this hypothesis by creating dichoptic stimuli containing unmatched points in which local cues and overall organization could be dissociated. For these stimuli, observers' perception of depth did not depend on the organization of the scene, but only on the local cues. This finding shows the perceived depth of unpaired points need not depend on reconstructing the spatial organization of depth discontinuities in real-world scenes.

Object Interpolation in Three Dimensions

Perception of objects in ordinary scenes requires interpolation processes connecting visible areas across spatial gaps. Most research has focused on 2-D displays, and models have been based on 2-D, orientation-sensitive units. The authors present a view of interpolation processes as intrinsically 3-D and producing representations of contours and surfaces spanning all 3 spatial dimensions. The authors propose a theory of 3-D relatability that indicates for a given edge which orientations and positions of other edges in 3 dimensions may be connected to it, and they summarize the empirical evidence for 3-D relatability. The theory unifies and illuminates a number of fundamental issues in object formation, including the identity hypothesis in visual completion, the relations of contour and surface processes, and the separation of local and global processing. The authors suggest that 3-D interpolation and 3-D relatability have major implications for computational and neural models of object perception.

Monocular discs in the occlusion zones of binocular surfaces do not have quantitative depth--a comparison with Panum's limiting case

Da Vinci stereopsis is defined as apparent depth seen in a monocular object laterally adjacent to a binocular surface in a position consistent with its occlusion by the other eye. It is widely regarded as a new form of quantitative stereopsis because the depth seen is quantitatively related to the lateral separation of the monocular element and the binocular surface (Nakayama and Shimojo 1990 Vision Research 30 1811-1825). This can be predicted on the basis that the more separated the monocular element is from the surface the greater its minimum depth behind the surface would have to be to account for its monocular occlusion. Supporting evidence, however, has used narrow bars as the monocular elements, raising the possibility that quantitative depth as a function of separation could be attributable to Panum's limiting case (double fusion) rather than to a new form of stereopsis. We compared the depth performance of monocular objects fusible with the edge of the surface in the contralateral eye (lines) and non-fusible objects (disks) and found that, although the fusible objects showed highly quantitative depth, the disks did not, appearing behind the surface to the same degree at all separations from it. These findings indicate that, although there is a crude sense of depth for discrete monocular objects placed in a valid position for uniocular occlusion, depth is not quantitative. They also indicate that Panum's limiting case is not, as has sometimes been claimed, itself a case of da Vinci stereopsis since fusibility is a critical factor for seeing quantitative depth in discrete monocular objects relative to a binocular surface.

Monocular gap stereopsis: manipulation of the outer edge disparity and the shape of the gap

A binocular stimulus that arises when two black frontal plane surfaces located at different depths have a gap between them for one eye but not for the other eye is interesting since the gap is monocular--it has no matching contours in the other eye--and yet binocular processes resolve a depth step effortlessly (Vision Research, 39, 493). In two experiments we investigate the processes and constraints underlying this depth resolution by varying the width of the solid image (the one without the gap) and the shape of the gap. The results show that the processes underlying monocular gap stereopsis can handle a situation in which the images of two surfaces in depth are effectively overlapping for one eye's view with the other eye seeing between them and that binocular depth is seen even when there is no disparity present. We also show that under ecologically appropriate conditions, depth curvature and warping can result when the monocular gap has a curved or warped edge. Both these experiments imply that the visual system responds to the ambiguity of the stimulus by adopting a minimum slant constraint.

How owls structure visual information

Recent studies on perceptual organization in humans claim that the ability to represent a visual scene as a set of coherent surfaces is of central importance for visual cognition. We examined whether this surface representation hypothesis generalizes to a non-mammalian species, the barn owl ( Tyto alba). Discrimination transfer combined with random-dot stimuli provided the appropriate means for a series of two behavioural experiments with the specific aims of (1) obtaining psychophysical measurements of figure-ground segmentation in the owl, and (2) determining the nature of the information involved. In experiment 1, two owls were trained to indicate the presence or absence of a central planar surface (figure) among a larger region of random dots (ground) based on differences in texture. Without additional training, the owls could make the same discrimination when figure and ground had reversed luminance, or were camouflaged by the use of uniformly textured random-dot stereograms. In the latter case, the figure stands out in depth from the ground when positional differences of the figure in two retinal images are combined (binocular disparity). In experiment 2, two new owls were trained to distinguish three-dimensional objects from holes using random-dot kinematograms. These birds could make the same discrimination when information on surface segmentation was unexpectedly switched from relative motion to half-occlusion. In the latter case, stereograms were used that provide the impression of stratified surfaces to humans by giving unpairable image features to the eyes. The ability to use image features such as texture, binocular disparity, relative motion, and half-occlusion interchangeably to determine figure-ground relationships suggests that in owls, as in humans, the structuring of the visual scene critically depends on how indirect image information (depth order, occlusion contours) is allocated between different surfaces.

Paired and unpaired features can be equally effective in human depth perception

The horizontal separation of the eyes results in the projection of slightly different images in each eye that are used to recover depth. One source of depth information is disparity, the relative position of paired features in the two eyes. Another source of depth information comes from features that are present in only one eye's view. These unpaired features arise from occlusion and by definition cannot generate a conventional disparity signal. Here we compare the depth signals generated by paired and unpaired features using stimuli that differ only in whether a given feature (a vertical gap) is paired or unpaired. Ecologically, both stimuli are consistent with two panels separated in depth at the gap, but only the paired gap provides a conventional disparity signal. We found strikingly that depth thresholds for the two gap conditions were the same and that there was perfect cross-adaptation of perceived depth from the unpaired to paired condition, strongly suggesting a common mechanism.

Amodal completion and the perception of depth without binocular correspondence

Half-occlusions and illusory contours have recently been used to show that depth can be perceived in the absence of binocular correspondence and that there is more to stereopsis than solving the correspondence problem. In the present study we show a new way for depth to be assigned in the absence of binocular correspondence, namely amodal completion. Although an occluder removed all possibility of direct binocular matching, subjects consistently assigned the correct depth (convexity or concavity) to partially occluded 'folded cards' stimuli. Our results highlight the importance of more global, surface-based processes in stereopsis.

Content and context of monocular regions determine perceived depth in random dot, unpaired background and phantom stereograms

Perceived depth was measured for three-types of stereograms with the colour/texture of half-occluded (monocular) regions either similar to or dissimilar to that of binocular regions or background. In a two-panel random dot stereogram the monocular region was filled with texture either similar or different to the far panel or left blank. In unpaired background stereograms the monocular region either matched the background or was different in colour or texture and in phantom stereograms the monocular region matched the partially occluded object or was a different colour or texture. In all three cases depth was considerably impaired when the monocular texture did not match either the background or the more distant surface. The content and context of monocular regions as well as their position are important in determining their role as occlusion cues and thus in three-dimensional layout. We compare coincidence and accidental view accounts of these effects.

The pursuit of Leonardo's constraint

Leonardo da Vinci (1452-1519) identified two stimulus situations that cannot be painted faithfully on a canvas: (a) when two objects are located in the same direction with respect to the painter's head, and (b) when parts of a surface are visible to one eye, but occluded from the other eye. He analysed these situations in terms of rays being emitted from the two eyes and, aside from the origin of the rays, the projective geometry he used was correct. His analyses showed that what can be seen from two vantage points cannot be represented on a canvas, because a 'correct' painting must be created from a single 'station point'. He was struck by the consequence of this fact that the depth seen on a canvas cannot match that of viewing the scene with two eyes. Subsequent visual scientists focused on Leonardo's observation about the lack of vivid depth in a picture. We argue that a complete understanding of what we see in the two stimulus situations requires consideration of visual direction in addition to visual depth. More specifically, we argue that the visual directions of the two objects, (a) above, and the visual direction of the monocular areas, (b) above, are dependent upon the constraint that two opaque objects cannot be represented in the same direction. Demonstrations that readers can perform, and that support this argument, are provided on the Perception website at http://www.perceptionweb.com/perc0102/ono.html.

Binocular integration of partially occluded surfaces

Normal binocular vision can provide a view of an object partially occluded so that no part of it is seen by both eyes but all of it is seen by one or other eye. We used two-dimensional filtered noise textures to explore the conditions under which the visual system can piece together the monocular fragments of such occluded surfaces. When the fragments seen by left and right eyes are drawn from a continuous texture with strong horizontal correlation, observers see coherent surfaces reliably located in depth. When textures are discontinuous or have weaker horizontal correlation, or the left and right eyes' views represent unnatural depth relationships, no coherent surface is perceived, and binocular rivalry ensues. The discovery of coherent surfaces under our conditions seems to reflect the operation of a high-level integration process, failures of which drive rivalry.

Curvature biases in stereoscopic vision: a nasotemporal asymmetry

The reliability of curvature judgments for linear elements was studied, with stereograms that contained a binocular arc with curvature in depth, and either a binocular frontoparallel arc or a monocular one, on a background representing a hemiellipsoid. The subjects made about 15% errors on binocular arcs with curvature in depth, and 60%-80% of these occurred when both the hemiellipsoid and the arc were convex, the arc being perceived as concave, by transparency through the hemiellipsoid. There were also about 15%-30% errors on frontoparallel arcs, but spread among all situations, with a small prevalence of concave judgments. Curvature in depth was assigned to the monocular stimuli in more than 60% of the cases. There was a curvature bias when the monocular arcs were on the nasal side, and were viewed against a concave background. Assuming parallel viewing, nasal ingoing arcs were usually perceived as concave, and nasal outgoing arcs usually perceived as convex, in agreement with geometrical likelihood. Nasal-side elements captured by one eye are, in general, those with the highest likelihood of having matching elements in the other eye. Then the observed nasal bias effect suggests that the matching process in stereopsis could be driven from the nasal sides of the projections in the two cerebral hemispheres.

Phantom surface captures stereopsis

A phantom surface is a stereoscopic illusory area that can be seen in depth although there is no conventional stereoscopic cues [Liu, L., Stevenson, S.B., & Schor, C.M. (1994). Quantitative stereoscopic depth without binocular correspondence. Nature, 367, 66-69; Gillam, B. & Nakayama, K. (1999). Quantitative depth for a phantom surface can be based on cyclopean occlusion cues alone. Vision Research, 39, 109-112]. The phenomenon has been explained as an example of half-occlusion processing in which the visual system uses information about cyclopean occlusion structure of the visual world. We created stereo capture stereograms in which phantom surfaces changed the perceived depth of conventionally defined binocular textures. Because conventional stereoscopic matching is strongly affected by half-occlusion processing, we suggest that half-occlusion processing is an integral part of the early stereoscopic processing and solving of the correspondence problem.

Neither occlusion constraint nor binocular disparity accounts for the perceived depth in the 'sieve effect'

Current notions of binocular depth perception include (1) neural computations that solve the correspondence problem and calculate retinal positional disparity, and (2) recovery of ecologically valid occlusion relationships. The former framework works well for stimuli with unambiguous interocular correspondence, but less so for stimuli without well-defined disparity cues. The latter framework has been proposed to account for the phenomenon of perceived depth in stimuli without interocular correspondence, but its mechanism remains unclear. In order to obtain more insight into the mechanism, we studied the depth percept elicited by a family of stereograms - 'sieve' stimuli, adapted from Howard (1995) [Perception, 24, 67-74] - with interocular differences but no well-defined positional disparity cue. The perceived depth was measured by comparison to references at various depths established by standard retinal disparity and was consistently found to lie behind the fixation plane. Moreover, the magnitude of the depth percept depended on both the horizontal and vertical spatial characteristics of the stimulus in ways that were at odds with constraints of occlusion geometry. In comparison to the depth percept elicited by stimuli with well-defined disparity cues, the precision of the percept from the sieve stimuli was 10-20 times worse, suggesting that a different underlying computation was involved. Thus, neither of the above frameworks accounts for the depth percept arising from these stimuli. We discuss implications of our results for physiologically based computations underlying binocular depth perception.

Response to motion in extrastriate area MSTl: disparity sensitivity

Many neurons in the lateral-ventral region of the medial superior temporal area (MSTl) have a clear center surround separation in their receptive fields. Either moving or stationary stimuli in the surround modulates the response to moving stimuli in the center, and this modulation could facilitate the perceptual segmentation of a moving object from its background. Another mechanism that could facilitate such segmentation would be sensitivity to binocular disparity in the center and surround regions of the receptive fields of these neurons. We therefore investigated the sensitivity of these MSTl neurons to disparity ranging from three degrees crossed disparity (near) to three degrees uncrossed disparity (far) applied to both the center and the surround regions. Many neurons showed clear disparity sensitivity to stimulus motion in the center of the receptive field. About (1)/(3) of 104 neurons had a clear peak in their response, whereas another (1)/(3) had broader tuning. Monocular stimulation abolished the tuning. The prevalence of cells broadly tuned to near and far disparity and the reversal of preferred directions at different disparities observed in MSTd were not found in MSTl. A stationary surround at zero disparity simply modulated up or down the response to moving stimuli at different disparities in the receptive field (RF) center but did not alter the disparity tuning curve. When the RF center motion was held at zero disparity and the disparity of the stationary surround was varied, some surround disparities produced greater modulation of MSTl neuron response than did others. Some neurons with different disparity preferences in center and surround responded best to the relative disparity differences between center and surround, whereas others were related to the absolute difference between center and surround. The combination of modulatory surrounds and the sensitivity to relative difference between center and surround disparity make these MSTl neurons particularly well suited for the segmentation of a moving object from the background.

Stereopsis based on monocular gaps: metrical encoding of depth and slant without matching contours

It is often the case in binocular vision that one eye can see between two objects lying at different distances but the other eye cannot. We have found that the visual system is able to correctly interpret images produced this way in which a single solid rectangle in one eye is fused with two half-sized rectangles in the other eye separated by a vertical gap comprising the background. Two rectangles in depth are seen. It is as if the solid rectangle is treated as two components which each match one of the physically separated rectangles in the contralateral eye. The sign of the depth depends on which eye's view has the gap and its magnitude increases with gap width. Measured depth is found to be equivalent to real stereoscopic depth with a relative disparity equal to the monocular gap. If overall disparity differences are eliminated, between the left and the right images, variations in perceived slant of the two rectangles are still seen with increasing gap size. That two surfaces can be seen in metric binocular depth despite complete camouflage of their separation in one eye's view, suggests that stereopsis be regarded as a broad process of surface recovery not necessarily requiring image disparity at the location of the depth step.

Quantitative depth for a phantom surface can be based on cyclopean occlusion cues alone

Liu, L., Stevenson, S.B., and Schor, C.M. (1994, Nature, 367, 66-669) reported quantitative stereoscopic depth in a phantom rectangle which appeared to lack conventional matching elements. Later, Gillam, B.J. (1995, Nature, 373, 202-203) and Liu, L., Stevenson, S.B., and Schor, C.M. (1995, Nature, 373, 203) and Liu, L., Stevenson, S.B., and Schor, C.M. (1997, Vision Research, 37(5), 633-644) indicated that the varying depth of the phantom rectangle could be based on stereoscopic matching. To remove the contaminating effects of conventional stereopsis from the Liu et al. (1994) original example, we presented a pair of parallel vertical lines to each eye where there is a central gap in the right line for the left eye's view and in the left line for the right eye's view. Observers saw a phantom rectangle bounded by subjective contours whose depth increased with the thickness of the lines. We attribute the quantitative variation of depth to a purely cyclopean (binocular) process sensitive to the pattern of contour presence and absence in the two eye's view.

Interocular suppression of a half-occluded region of stereoscopic images

We assessed the detectability d' of a monocular small gray dot target presented on a half-occluded region of stereoscopic three-dimensional background images by comparing it with that on a two-dimensional (2D) region. For our experiments we used a typical two-alternative temporal forced-choice procedure, in which the target was presented in one of two temporal intervals for approximately 67 ms, and observers selected the interval they believed to have contained the target by pressing the corresponding key. To vary target signal intensity, we changed the target contrast against the background. According to signal-detection theory, we converted the percent-correct data to detectability d' and found that the relationship between d' and the contrast of the target followed Legge's equation. We used Legge's equation to calculate the contrast threshold and found that the contrast threshold of the target on the half-occluded region was higher than that on the 2D region. This elevation of contrast threshold indicates that interocular suppression of the half-occluded region occurs more frequently than that of the 2D region. We also refer to the monocular performance of the human visual system.

Vergence eye movements elicited by stimuli without corresponding features

We have observed quantitative depth perception with a dichoptic stimulus which possessed no contrast-defined binocular corresponding features (phantom stereogram). The depth perception can be the result of appreciation of a partial-occlusion situation depicted by the stimulus, or the result of activities of low-level disparity detectors which are capable of combining dissimilar local features in the stimulus. Although both mechanisms predict similar depth perception, they predict different vergence eye-movement outputs, especially in the vertical dimension. To identify the underlying mechanisms of the phantom stereopsis, we recorded vergence tracking eye movements to four types of dichoptic stimuli: (a) conventional stereogram with horizontal disparity (HD); (b) horizontal phantom stereogram (HP); (c) conventional stereogram with vertical disparity (VD); and (d) vertical phantom stereogram (VP). We found that HD, HP, and VD stimuli could elicit robust vergence tracking eye movements but VP stimulus could not. While the success of HP stimulus in eliciting vergence tracking may be explained by proximal vergence, the failure of VP stimulus in eliciting vergence tracking clearly indicates that phantom stereogram could not elicit coherent responses among low-level disparity detectors. Partial occlusion, therefore, has to play an important role in the depth perception from the phantom stereogram.

Physiological computation of binocular disparity

We previously proposed a physiologically realistic model for stereo vision based on the quantitative binocular receptive field profiles mapped by Freeman and coworkers. Here we present several new results about the model that shed light on the physiological processes involved in disparity computation. First, we show that our model can be extended to a much more general class of receptive field profiles than the commonly used Gabor functions. Second, we demonstrate that there is, however, an advantage of using the Gabor filters: similar to our perception, the stereo algorithm with the Gabor filters has a small bias towards zero disparity. Third, we prove that the complex cells as described by Freeman et al. compute disparity by effectively summing up two related cross products between the band-pass filtered left and right retinal image patches. This operation is related to cross-correlation but it overcomes some major problems with the standard correlator. Fourth, we demonstrate that as few as two complex cells at each spatial location are sufficient for a reasonable estimation of binocular disparity. Fifth, we find that our model can be significantly improved by considering the fact that complex cell receptive field are, on average, larger than those of simple cells. This fact is incorporated into the model by averaging over several quadrature pairs of simple cells with nearby and overlapping receptive fields to construct a model complex cell. The disparity tuning curve of the resulting complex cell is much more reliable than the constructed from a single quadrature pair of simple cells used previously, and the computed disparity maps for random dot stereograms with the new algorithm are very similar to human perception, with sharp transitions at disparity boundaries. Finally, we show that under most circumstances our algorithm works equally well with either of the two well-known receptive field models in the literature.

Binocular matching of dissimilar features in phantom stereopsis

Previously we have demonstrated that quantitative depth perception can be elicited from a stereogram that lacks contrast defined binocular corresponding elements (phantom stereopsis). In this report, we use computer simulation to demonstrate that it is biologically plausible for some known binocular cortical cell types to combine non-conventional matching features. Therefore, binocular matching processes based on the responses of these cells could be a conventional one, namely, looking for similar response patterns in the two eyes. While at cell types we simulated gave identical disparity outputs to the conventional stereogram, they responded differently to the phantom stereogram. Processes other than low-level disparity detectors may have to be invoked in order to achieve a unique depth solution.

Depth perception in Alzheimer's disease

Abnormal depth perception contributes to visuospatial deficits in Alzheimer's disease. Disturbances in stereopsis, motion parallax, and the interpretation of static monocular depth cues may result from neuropathology in the visual cortex. We evaluated 15 patients with mild Alzheimer's disease and 15 controls matched for age, sex, and education on measures of local stereopsis (stereoscopic testing), global stereopsis (random dots), motion parallax (Howard-Dolman apparatus), and monocular depth perception by relative size, interposition, and perspective. Compared to controls, the patients were significantly impaired in over-all depth perception. This impairment was largely due to disturbances in local stereopsis and in the interpretation of depth from perspective, independent of other visuospatial functions. Patients with Alzheimer's disease have disturbed interpretation of monocular as well as binocular depth cues. This information could lead to optic interventions to improve their visual depth perception.

Stereopsis due to luminance differences in the two eyes

A local region in an image is seen as slanted when the two eyes are shown different luminance values in that region. The steepness of the slant depends upon the size of the region and the difference in the luminance values in the two eyes. Three examples where this phenomenon influences depth perception are given: (1) stereopsis without corresponding binocular luminance edges is shown to be a limiting case of the phenomenon; (2) edges less than 1 min arc apart can be seen in relative depth with respect to each other; and (3) regions that appear transparent or translucent can be seen in depth despite having all the luminance edges at zero disparity in simple stereo images.

Human stereovision without localized image features

Many theories of human stereovision are based on feature matching and the related correspondence problem. In this paper, we present psychophysical experiments indicating that localized image features such as Laplacian zerocrossings, intensity extrema, or centroids are not necessary for binocular depth perception. Smooth one-dimensional intensity profiles were combined into stereograms with mirror-symmetric half-images such that these localized image features were either absent or did not carry stereo information. In a discrimination task, subjects were asked to distinguish between stereograms differing only by an exchange of these half-images (ortho- vs. pseudoscopic stereograms). In a depth ordering task, subjects had to judge which of the two versions appeared in front. Subjects are able to solve both tasks even in the absence of the mentioned image features. The performance is compared to various possible stereo mechanisms. We conclude that localized image features and the correspondences between them are not necessary to perceive stereoscopic depth. One mechanism accounting for our data is correlation or mean square difference.

Binocular displacement of unpaired region

Binocular displacement of binocularly unpaired parts of the stimulus was examined by means of the Poggendorff figure. The Poggendorff figure can be used to investigate displacement since lateral displacement of the transversal may cause bias in judgments of its collinearity. In experiment 1, the transversal had a disparity, and thus binocularly unpaired parts, relative to the rectangle. The magnitude of the Poggendorff illusion should not have changed by addition of binocular disparity if displacement occurred. There was no or slight change when the transversal was seen behind the rectangle, but there was significant decrease when the transversal was seen in front of the rectangle, suggesting absence of displacement in this case. There were two possible explanations. One was that displacement depended on the positional relation between the unpaired stimuli and the binocularly presented rectangle, ie the occlusion constraint, which the case with the transversal in front did not satisfy. The alternative was that the decrease was due to the perceived front depth of the transversal, and not related to binocular displacement at all. In order to discriminate between these two possibilities, the transversal was reduced to only the unpaired parts, resulting in dichoptic stimulation in experiment 2. In this stimulus, the positional relation between the unpaired and the paired stimuli was the same as in the previous experiment, yet no front depth could be perceived. The results showed similar asymmetry as in experiment 1. Thus we conclude that binocular displacement depends on the positional relation between the unpaired and the paired stimuli, regardless of their perceived depth. This may imply that binocular displacement is not symmetric about the sign of disparity, hence that it is not just averaging but is a reconstruction of the spatial layout of objects in the outside world to keep the visual direction of the unsuppressed unpaired region veridical by using explicit cues to depth discontinuity.