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

Natural statistics of depth edges modulate perceptual stability

Binocular fusion relies on matching points in the two eyes that correspond to the same physical feature in the world; however, not all world features are binocularly visible. Near depth edges, some regions of a scene are often visible to only one eye (so-called half occlusions). Accurate detection of these monocularly visible regions is likely to be important for stable visual perception. If monocular regions are not detected as such, the visual system may attempt to binocularly fuse non-corresponding points, which can result in unstable percepts. We investigated the hypothesis that the visual system capitalizes on statistical regularities associated with depth edges in natural scenes to aid binocular fusion and facilitate perceptual stability. By sampling from a large set of stereoscopic natural images with co-registered distance information, we found evidence that monocularly visible regions near depth edges primarily result from background occlusions. Accordingly, monocular regions tended to be more visually similar to the adjacent binocularly visible background region than to the adjacent binocularly visible foreground. Consistent with our hypothesis, perceptual experiments showed that perception tended to be more stable when the image properties of the depth edge were statistically more likely given the probability of occurrence in natural scenes (i.e., when monocular regions were more visually similar to the binocular background). The generality of these results was supported by a parametric study with simulated environments. Exploiting regularities in natural environments may allow the visual system to facilitate fusion and perceptual stability when both binocular and monocular regions are visible.

Illusory occlusion affects stereoscopic depth perception

When occlusion and binocular disparity cues conflict, what visual features determine how they combine? Sensory cues, such as T-junctions, have been suggested to be necessary for occlusion to influence stereoscopic depth perception. Here we show that illusory occlusion, with no retinal sensory cues, interacts with binocular disparity when perceiving depth. We generated illusory occlusion using stimuli filled in across the retinal blind spot. Observers viewed two bars forming a cross with the intersection positioned within the blind spot. One of the bars was presented binocularly with a disparity signal; the other was presented monocularly, extending through the blind spot, with no defined disparity. When the monocular bar was perceived as filled in through the blind spot, it was perceived as occluding the binocular bar, generating illusory occlusion. We found that this illusory occlusion influenced perceived stereoscopic depth: depth estimates were biased to be closer or farther, depending on whether a bar was perceived as in front of or behind the other bar, respectively. Therefore, the perceived relative depth position, based on filling-in cues, set boundaries for interpreting metric stereoscopic depth cues. This suggests that filling-in can produce opaque surface representations that can trump other depth cues such as disparity.

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.

The Stereoscopic Sliver: A Comparison of Duration Thresholds for Fully Stereoscopic and Unmatched Versions

Just as positional disparities of image features seen with both eyes provide depth information, the presence of an area visible to one eye but not the other within a binocularly viewed scene can indicate an occlusion at a depth discontinuity,. The close geometrical association between these two kinds of cues suggests they may both be exploited by stereopsis. To investigate this, we developed a novel binocular stimulus entirely lacking in classical disparity that contains an unmatched vertical sliver which elicits a warping of the surrounding surface to accommodate a depth discontinuity. We measured depth-discrimination performance at a range of stimulus durations, correcting for variations in stimulus visibility, to characterise the decline of the efficacy of the depth signal with limited integration time. Results show a close correspondence of performance for similar stimuli with unmatched features and classical binocular disparity across a sixtyfold range of viewing durations, supporting the notion of a close association between the two types of cues in human stereopsis. Control experiments excluded simple eye-of-origin cues and long-range false matches as explanatory factors.

Electrophysiological correlates of binocular stereo depth without binocular disparities

A small region of background presented to only one eye in an otherwise binocular display may, under certain conditions, be resolved in the visual system by interpreting the region as a small gap between two similar objects placed at different depths, with the gap hidden in one eye by parallax. This has been called monocular gap stereopsis. We investigated the electrophysiological correlate of this type of stereopsis by means of sum potential recordings in 12 observers, comparing VEP's for this stimulus ("Gillam Stereo", Author BG has strong reservations about this term) with those for similar stimuli containing disparity based depth and with no depth (flat). In addition we included several control stimuli. The results show a pronounced early negative potential at a latency of around 170 ms (N170) for all stimuli containing non- identical elements, be they a difference caused by binocular disparity or by completely unmatched monocular contours. A second negative potential with latency around 270 ms (N270), on the other hand, is present only with stimuli leading to fusion and the perception of depth. This second component is similar for disparity-based stereopsis and monocular gap, or "Gillam Stereo" although slightly more pronounced for the former. We conjecture that the first component is related to the detection of differences between the images of the two eyes that may then either be fused, leading to stereopsis and the corresponding second potential, or else to inhibition and rivalry without a later trace in the VEP. The finding that that "Gillam Stereo" leads to cortical responses at the same short latencies as disparity based stereopsis indicates that it may partly rely on quite early cortical mechanisms.

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.

Alternation frequency thresholds for stereopsis as a technique for exploring stereoscopic difficulties

When stereoscopic images are presented alternately to the two eyes, stereopsis occurs at F ≥ 1 Hz full-cycle frequencies for very simple stimuli, and F ≥ 3 Hz full-cycle frequencies for random-dot stereograms (eg Ludwig I, Pieper W, Lachnit H, 2007 “Temporal integration of monocular images separated in time: stereopsis, stereoacuity, and binocular luster” Perception & Psychophysics69 92–102). Using twenty different stereograms presented through liquid crystal shutters, we studied the transition to stereopsis with fifteen subjects. The onset of stereopsis was observed during a stepwise increase of the alternation frequency, and its disappearance was observed during a stepwise decrease in frequency. The lowest F values (around 2.5 Hz) were observed with stimuli involving two to four simple disjoint elements (circles, arcs, rectangles). Higher F values were needed for stimuli containing slanted elements or curved surfaces (about 1 Hz increment), overlapping elements at two different depths (about 2.5 Hz increment), or camouflaged overlapping surfaces (> 7 Hz increment). A textured cylindrical surface with a horizontal axis appeared easier to interpret (5.7 Hz) than a pair of slanted segments separated in depth but forming a cross in projection (8 Hz). Training effects were minimal, and F usually increased as disparities were reduced. The hierarchy of difficulties revealed in the study may shed light on various problems that the brain needs to solve during stereoscopic interpretation. During the construction of the three-dimensional percept, the loss of information due to natural decay of the stimuli traces must be compensated by refreshes of visual input. In the discussion an attempt is made to link our results with recent advances in the comprehension of visual scene memory.

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.

Amodal completion with background determines depth from monocular gap stereopsis

Grove, Gillam, and Ono [Grove, P. M., Gillam, B. J., & Ono, H. (2002). Content and context of monocular regions determine perceived depth in random dot, unpaired background and phantom stereograms. Vision Research, 42, 1859-1870] reported that perceived depth in monocular gap stereograms [Gillam, B. J., Blackburn, S., & Nakayama, K. (1999). Stereopsis based on monocular gaps: Metrical encoding of depth and slant without matching contours. Vision Research, 39, 493-502] was attenuated when the color/texture in the monocular gap did not match the background. It appears that continuation of the gap with the background constitutes an important component of the stimulus conditions that allow a monocular gap in an otherwise binocular surface to be responded to as a depth step. In this report we tested this view using the conventional monocular gap stimulus of two identical grey rectangles separated by a gap in one eye but abutting to form a solid grey rectangle in the other. We compared depth seen at the gap for this stimulus with stimuli that were identical except for two additional small black squares placed at the ends of the gap. If the squares were placed stereoscopically behind the rectangle/gap configuration (appearing on the background) they interfered with the perceived depth at the gap. However when they were placed in front of the configuration this attenuation disappeared. The gap and the background were able under these conditions to complete amodally.

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.

Quantitative perceived depth from sequential monocular decamouflage

We present a novel binocular stimulus without conventional disparity cues whose presence and depth are revealed by sequential monocular stimulation (delay > or = 80 ms). Vertical white lines were occluded as they passed behind an otherwise camouflaged black rectangular target. The location (and instant) of the occlusion event, decamouflaging the target's edges, differed in the two eyes. Probe settings to match the depth of the black rectangular target showed a monotonic increase with simulated depth. Control tests discounted the possibility of subjects integrating retinal disparities over an extended temporal window or using temporal disparity. Sequential monocular decamouflage was found to be as precise and accurate as conventional simultaneous stereopsis with equivalent depths and exposure durations.

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.

Greater depth seen with phantom stereopsis is coded at the early stages of visual processing

A visual search task was used to investigate the spatially parallel coding of depth from binocular disparity and from binocularly unmatched features. Experiment 1, using disparity noise, showed that detectability is higher for illusory phantom targets defined by unmatched features than for disparity-defined targets, although the two targets were equated as to theoretically minimum depth. Experiment 2, using binocularly unmatched noise whose width was equal to the disparity of the noise used in Experiment 1, showed that noise severely interferes with the detection of both the disparity and the phantom targets. These results are consistent with the idea that the greater depth seen with phantom stereopsis is coded at the early stages of visual processing.

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.