Gradients of relative disparity underlie the perceived slant of stereoscopic surfaces.

Perceived stereoscopic slant around a vertical axis is strongly underestimated for isolated surfaces, suggesting that neither uniocular image compression nor linear gradients of absolute disparity are very effective cues. However, slant increases to a level close to geometric prediction if gradients of relative disparity are introduced, for example by placing flanking frontal-parallel surfaces at the horizontal boundaries of the slanted surface. Here we examine the mechanisms underlying this slant enhancement by manipulating properties of the slanted surface or the flanking surfaces. Perceived slant was measured using a probe bias method. In Experiment 1, an outlined surface and a randomly textured surface showed similar slant underestimation when presented in isolation, but the enhancement in slant produced by flankers was significantly greater for the textured surface. In Experiment 2, we degraded the relative disparity gradient by (a) reducing overall texture density, (b) reducing flanker width, or (c) adding disparity noise to the flankers. Density had no effect while adding noise to the flankers, or reducing their width significantly decreased perceived slant of the central surface. These results support the view that the enhancement of slant produced by adding flanking surfaces is attributable to the presence of a relative disparity gradient and that the flanker effect can spread to regions of the surface not directly above or below the gradient.

Phantom surfaces in da Vinci stereopsis.

In binocular viewing of natural three-dimensional scenes, occlusion relationships between objects at different depths create regions of the background that are visible to only one eye. These monocular regions can support depth perception. There are two viewing conditions in which a monocular region can be on the nasal side of a binocular surface--(a) when a background surface is viewed through an aperture and (b) when a region is camouflaged against the background in one eye's view. We created stimuli with a monocular region using complex textures in which camouflage was not possible, and for which there was no physical aperture. For these stimuli, observers perceived a strong phantom contour in near depth at the edge of the monocular region, with the monocular texture perceived behind at the depth of the binocular surface. Depth-matching with a probe showed that the depth of the phantom occluding surface was as precise as for stimuli with regular binocular disparity. Monocular regions of texture on the opposite (temporal) side of the binocular surface were perceived behind, as predicted by occlusion geometry, and there was no phantom surface. We discuss the implications for models of da Vinci stereopsis and stereoscopic edge processing, and consider the involvement of a form of Panum's limiting case. We conclude that the visual system uses a combination of occlusion geometry and complex matching to precisely locate edges in depth that lack a luminance contour.

Local and non-local effects on surface-mediated stereoscopic depth.

The magnitude and precision of stereoscopic depth between two probes is often determined by the disparity each has to a common background. If stereoscopic slant of the background is underestimated, a bias is introduced in the PSE of the probes (G. Mitchison & G. Westheimer, 1984). Using random dot stimuli, we show here how more remote surfaces can influence probe PSE via their influence on perceived background surface slant. The bias was reduced when frontal flanking surfaces were placed above and below the background surface, increasing its perceived slant. In a similar experiment, the flankers were slanted and the central background surface was frontal. For flankers alone, probe bias did not diminish up to a 4.4° separation of flankers and probes. When the central surface was present, the effect of the flankers on probe bias was mediated by this surface and diminished with flanker separation, presumably because of the diminishing contrast slant of the background surface. Stereoscopic depth between probes is thus influenced by a common background surface, by neighboring surfaces acting (contiguously or non-contiguously) on the background surface, and by distant surfaces acting directly on the probes.

Stereoscopic discrimination of the layout of ground surfaces.

Safe and effective locomotion depends critically on judgements of the surface properties of the ground to be traversed. Little is known about the role of binocular vision in surface perception at distances relevant to visually guided locomotion in humans. Programmable arrays of illuminated targets were used to present sparsely textured surfaces with real depth at distances of 4.5 and 9.0 m. Psychophysical measurements of discrimination thresholds demonstrated a clear superiority for stereoscopic over monocular judgments of relative and absolute surface slant. Judgements of surface roughness in particular demonstrated a substantial binocular advantage. Binocular vision is thus shown to directly contribute to judgements of the layout of terrain up to at least 4.5 m, and its smoothness to at least 9.0 m. Hence binocular vision could support moment-to-moment wayfinding and path planning, especially when monocular cues are weak.

Failure of facial configural cues to alter metric stereoscopic depth.

J. Burge, M. A. Peterson, and S. E. Palmer (2005) reported that an ordinal cue to depth can influence the perception of metric depth in stereoscopic displays. They argued that when a familiar figure--a face--is placed stereoscopically closer than a background there is greater perceived depth relative to the ground than when the face shape is placed stereoscopically further and becomes the ground. This result suggests the possibility that a non-metric depth cue--the familiarity of a figure--can influence the perception of metric depth in stereoscopic displays. However, the method leaves open the possibility that these results were due to a response bias, rather than from a genuine change in perceived depth. To assess this possibility, we used the same basic stimulus but directly measured the perceived depth difference between the face and non-face surfaces when arranged as figure and ground or ground and figure respectively using a separate double depth probe to measure perceived depth. We found no difference between the perceived depth of familiar and unfamiliar figures as a function of whether they were stereoscopically figure or ground. We conclude that the J. Burge et al. (2005) result depends on their particular task and is likely to reflect a response bias. It is premature to conclude that facial configural cues distort perception of metric depth although we argue that there are circumstances in which ordinal cues do influence metric depth.

Binocular depth discrimination and estimation beyond interaction space.

The benefits of binocular vision have been debated throughout the history of vision science yet few studies have considered its contribution beyond a viewing distance of a few meters. In the first set of experiments, we compared monocular and binocular performance on depth interval estimation and discrimination tasks at 4.5, 9.0 or 18.0 m. Under monocular conditions, perceived depth was significantly compressed. Binocular depth estimates were much nearer to veridical although also compressed. Regression-based precision measures were much more precise for binocular compared to monocular conditions (ratios between 2.1 and 48). We confirm that stereopsis supports reliable depth discriminations beyond typical laboratory distances. Furthermore, binocular vision can significantly improve both the accuracy and precision of depth estimation to at least 18 m. In another experiment, we used a novel paradigm that allowed the presentation of real binocular disparity stimuli in the presence of rich environmental cues to distance but not interstimulus depth. We found that the presence of environmental cues to distance greatly enhanced stereoscopic depth constancy at distances of 4.5 and 9.0 m. We conclude that stereopsis is an effective cue for depth discrimination and estimation for distances beyond those traditionally assumed. In normal environments, distance information from other sources such as perspective can be effective in scaling depth from disparity.

Stereomotion perception for a monocularly camouflaged stimulus.

Under usual circumstances, motion in depth is associated with conventional stereomotion cues: a change in disparity and differences between object velocities in each monocular image. However, occasionally these cues are unavailable due to the fact that in one eye the object may be occluded by, or camouflaged against appropriately positioned binocular objects. We report two experiments concerned with stereomotion perception under conditions of monocular camouflage. In Experiment 1, the visible half-image of a monocularly camouflaged object translated laterally. In this binocular context, percepts of lateral motion and motion in depth were equally consistent with the stimulus. Subjects perceived an oblique trajectory of 3D motion, compared to the more direct 3D trajectory experienced for binocularly matched stimuli. In Experiment 2, the perceived velocity of stereomotion was assessed. Again, for the stimulus used in Experiment 1, perceived stereomotion speed was lower than that for matched stimuli. However, when additional background objects were present, tightening the ecological constraints, perceived stereomotion velocity was often equivalent to that for matched stimuli. These results demonstrate for the first time that the motion of a monocularly camouflaged object can result in the perception of stereomotion, and that the perceived trajectory and speed are influenced by the ecological constraints of binocular geometry.

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.

The swinging doors of perception: stereomotion without binocular matching.

Until recently, it was considered necessary for features in the two eyes to be matched before the evaluation of differences in their locations (binocular disparities) could reveal depth information. Motion in depth can also be perceived binocularly from related changes in the locations of matched binocular features. However, unmatched features can arise when a binocular object occludes more distant features in one eye but not the other. The presence and extent of such features can provide quantitative depth information, although perceived depth relative to geometrical predictions may vary from one such arrangement to another. The ability of humans to perceive motion in depth from unmatched stimuli has not previously been explored. Here, we use B. Gillam, S. Blackburn, and K. Nakayama's (1999) "monocular gap" stimuli to investigate perception of motion in depth simulated by a change in the extent of a monocularly occluded feature in a binocular display. Settings of a motion in depth probe revealed that the magnitude of perceived motion in depth is generally as large as that for a stimulus containing matchable binocular features. We show that our stimuli provide disambiguating information not present in similar static stimuli. We conclude that in the computation of motion in depth, a binocular match is not required. A new cue-dynamic half-occlusion-can be used to reach an accurate percept.

The effect of surface placement and surface overlap on stereo slant contrast and enhancement.

Stereoscopic slant contrast is an apparent slant induced in a stereoscopically frontal plane surface (the test) opposite in direction to the specified stereoscopic slant of a neighbouring surface (the inducer). Test surfaces offset from the inducer in a direction collinear with the axis of slant (twist) show more contrast than those offset in a direction orthogonal to the axis of slant (hinge). We attribute this anisotropy to the presence and extent of a gradient of relative disparity in twist configurations and the absence of such a gradient in hinge configurations. This hypothesis was tested by measuring the perceived slant of the test and inducer surfaces for horizontal and vertical axes of inducer slant and collinear and orthogonal surface offsets. For vertical axis slant, the hypothesis was supported; contrast variations with position of the test surface could be explained by variations in relative slant. For horizontal axis slant, variations in contrast could be accounted for by normalisation of the slanted surface, with relative slant remaining constant. Two further experiments showed that the extent of the gradient of relative disparity rather than the area of texture overlap of the two surfaces best predicted the contrast results and that perceived relative slant did not vary with the absolute slants of the two surfaces. The arrangement of stereo surfaces is critical in predicting their relative slant.

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.

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.

Monocular and binocular edges enhance the perception of stereoscopic slant.

Gradients of absolute binocular disparity across a slanted surface are often considered the basis for stereoscopic slant perception. However, perceived stereo slant around a vertical axis is usually slow and significantly under-estimated for isolated surfaces. Perceived slant is enhanced when surrounding surfaces provide a relative disparity gradient or depth step at the edges of the slanted surface, and also in the presence of monocular occlusion regions (sidebands). Here we investigate how different kinds of depth information at surface edges enhance stereo slant about a vertical axis. In Experiment 1, perceived slant decreased with increasing surface width, suggesting that the relative disparity between the left and right edges was used to judge slant. Adding monocular sidebands increased perceived slant for all surface widths. In Experiment 2, observers matched the slant of surfaces that were isolated or had a context of either monocular or binocular sidebands in the frontal plane. Both types of sidebands significantly increased perceived slant, but the effect was greater with binocular sidebands. These results were replicated in a second paradigm in which observers matched the depth of two probe dots positioned in front of slanted surfaces (Experiment 3). A large bias occurred for the surface without sidebands, yet this bias was reduced when monocular sidebands were present, and was nearly eliminated with binocular sidebands. Our results provide evidence for the importance of edges in stereo slant perception, and show that depth from monocular occlusion geometry and binocular disparity may interact to resolve complex 3D scenes.

Orientation contrast and entropy contrast in the genesis of subjective contours along thin lines.

Subjective contours are widely considered to be an aspect of the perception of occlusion, but considerations of occlusion do not always drive predictions of their strength. Occluding surfaces have no necessary relationship to the contours they occlude, yet it is commonly predicted that subjective contours will be strongest for inducer alignments that are orthogonal to inducer orientations. In several papers we have proposed that a lack of relationship between inducers and their alignment promotes seeing subjective contours. We explore this further here using horizontal or near-horizontal thin-line inducers arranged vertically with linearly aligned terminations along central gaps. Subjective contour strength was measured using the method of paired comparison in two experiments. The weakest subjective contours were found when the gap was orthogonal to the inducers and parallel to the outer edges of the line set. Subjective contours were strengthened by orientation contrast, defined either as a nonorthogonal relationship between the gap and the inducers or as nonparallelism between the gap and the outer alignments of the inducers. The effect was replicated at both high and low line densities. We also confirmed a strong effect of high inducer entropy (variations in inducer orientation and separation) with thin-line inducers. The results support the view that the lack of a relationship of alignments to what is aligned is a major determinant of subjective contour strength.

Color constrains depth in da Vinci stereopsis for camouflage but not occlusion.

Monocular regions that occur with binocular viewing of natural scenes can produce a strong perception of depth--"da Vinci stereopsis." They occur either when part of the background is occluded in one eye, or when a nearer object is camouflaged against a background surface in one eye's view. There has been some controversy over whether da Vinci depth is constrained by geometric or ecological factors. Here we show that the color of the monocular region constrains the depth perceived from camouflage, but not occlusion, as predicted by ecological considerations. Quantitative depth was found in both cases, but for camouflage only when the color of the monocular region matched the binocular background. Unlike previous reports, depth failed even when nonmatching colors satisfied conditions for perceptual transparency. We show that placing a colored line at the boundary between the binocular and monocular regions is sufficient to eliminate depth from camouflage. When both the background and the monocular region contained vertical contours that could be fused, some observers appeared to use fusion, and others da Vinci constraints, supporting the existence of a separate da Vinci mechanism. The results show that da Vinci stereopsis incorporates color constraints and is more complex than previously assumed.

Stereopsis loses dominance over relative size as target separation increases.

Binocular disparity produces less stereoscopic depth if the targets are separated by several degrees. It is thus possible that separation decreases the influence of stereopsis as a relative depth cue. Here, four experiments tested the strength of disparity in determining the direction of relative depth in the face of strongly conflicting relative size for a range of target separations. Under conditions of natural fixation-permitting sequential stereopsis-disparity dominated completely at small separations (0.42 degrees) but gradually gave way to relative size domination at large separations. However, when brief presentations prevented changes in fixation, disparity completely dominated at a separation of 0.5 degrees while relative size mostly dominated by 0.75 degrees - 1 degrees of separation. By varying target separation at different retinal eccentricities, we showed that separation per se was the critical factor in the dominance switch. Stereoacuity as a function of target separation for the same observers did not predict the switch from disparity to relative size. Stereoscopic dominance was found for the same small separations that are immune to stereoscopic reversals (Gillam, 1993 Perception 22 1025-1036). Our results suggest that relative disparity has a compulsory influence on perceived depth at small separations, suggesting a different mechanism from the one operating at larger separations.

Contour entropy: a new determinant of perceiving ground or a hole.

Figure-ground perception is typically described as seeing one surface occluding another. Figure properties, not ground properties, are considered the significant factors. In scenes, however, a near surface will often occlude multiple contours and surfaces, often at different depths, producing alignments that are improbable except under conditions of occlusion. We thus hypothesized that unrelated (high entropy) lines would tend to appear as ground in a figure-ground paradigm more often than similarly aligned ordered (low entropy) lines. We further hypothesized that for lines spanning a closed area, high line entropy should increase the hole-like appearance of that area. These predictions were confirmed in three experiments. The probability that patterned rectangles were seen as ground when alternated with blank rectangles increased with pattern entropy. A single rectangular shape appeared more hole-like when the entropy of the enclosed contours increased. Furthermore, these same contours, with the outline shape removed, gave rise to bounding illusory contours whose strength increased with contour entropy. We conclude that figure-ground and hole perception can be determined by properties of ground in the absence of any figural shape, or surround, factors.

The role of remote closure in the perception of occlusion at junctions and illusory contours.

Abstract. Perceived occlusion at T-junctions or illusory contours at implicit T-junctions are often modelled by using edge information without surface context. We explored the effect of closure on perceived occlusion at T-junctions. Two vertical lines separated by a gap each had six abutting horizontal lines on opposite sides forming T-junctions. These lines were either closed or not closed into pairs at the stem ends of the Ts. In experiment 1, closed T-junction stems gave a much stronger sense of occlusion at the vertical lines than unclosed ones, even though closure information was remote from the putative occlusion and local T-junction information remained constant. When the outer two T-junctions were converted to L-junctions, perceived occlusion considerably diminished. The effect of closure on illusory-contour strength for stimuli like those of experiment 1 but with the vertical lines omitted was explored in experiment 2. The two sets of horizontal lines, separated by a gap, were either closed or not closed into pairs at their outer ends. Illusory-contour strength along the vertical alignments was much greater for closed pairs. Line terminations on both sides of the gap enhanced illusory-contour strength, but whether they were collinear or not had little effect.