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.

An ecological approach to binocular vision.

An ecological approach to binocular vision was already demonstrated in Wheatstone's initial stereograms and was explicitly called for by J. J. Gibson, but detailed analysis and experimentation supporting this approach has been more recent. This paper discusses several aspects of this more recent research on environmentally occurring spatial layouts that can influence binocular vision. These include gradients of depth and regions that can be seen by only one eye. The resolution of local stereoscopic ambiguity by more global factors is also discussed.

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 perception of real depths at large distances.

There has been no direct examination of stereoscopic depth perception at very large observation distances and depths. We measured perceptions of depth magnitude at distances where it is frequently reported without evidence that stereopsis is non-functional. We adapted methods pioneered at distances up to 9 m by R. S. Allison, B. J. Gillam, and E. Vecellio (2009) for use in a 381-m-long railway tunnel. Pairs of Light Emitting Diode (LED) targets were presented either in complete darkness or with the environment lit as far as the nearest LED (the observation distance). We found that binocular, but not monocular, estimates of the depth between pairs of LEDs increased with their physical depths up to the maximum depth separation tested (248 m). Binocular estimates of depth were much larger with a lit foreground than in darkness and increased as the observation distance increased from 20 to 40 m, indicating that binocular disparity can be scaled for much larger distances than previously realized. Since these observation distances were well beyond the range of vertical disparity and oculomotor cues, this scaling must rely on perspective cues. We also ran control experiments at smaller distances, which showed that estimates of depth and distance correlate poorly and that our metric estimation method gives similar results to a comparison method under the same conditions.

The role of binocular vision in walking.

Despite the extensive investigation of binocular and stereoscopic vision, relatively little is known about its importance in natural visually guided behavior. In this paper, we explored the role of binocular vision when walking over and around obstacles. We monitored eye position during the task as an indicator of the difference between monocular and binocular performances. We found that binocular vision clearly facilitates walking performance. Walkers were slowed by about 10% in monocular vision and raised their foot higher when stepping over obstacles. Although the location and sequence of the fixations did not change in monocular vision, the timing of the fixations relative to the actions was different. Subjects spent proportionately more time fixating the obstacles and fixated longer while guiding foot placement near an obstacle. The data are consistent with greater uncertainty in monocular vision, leading to a greater reliance on feedback in the control of the movements.

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.

Biases in judgments of separation and orientation of elements belonging to different clusters.

If two demarcated dots are embedded in separate clusters of similar dots in off centre positions, their perceived separation is biased towards the separation between the centres of the clusters (Morgan, Hole, & Glennerster, 1990). We replicated these results and went on to determine whether a similar bias is present for orientation judgments, using a staircase method and a range of cluster orientations and separations. A complex pattern of biases was found including biases for targets at centroids. Orientation attraction towards tangents to the clusters seemed to be involved. We conclude that orientation is subject to different contextual constraints from separation, and that bias towards the edges of clusters needs to be included in models of position coding.

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.

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.

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.

Visual perception of touchdown point during simulated landing.

Experiments examined the accuracy of visual touchdown point perception during oblique descents (1.5 degrees -15 degrees ) toward a ground plane consisting of (a) randomly positioned dots, (b) a runway outline, or (c) a grid. Participants judged whether the perceived touchdown point was above or below a probe that appeared at a random position following each display. Although judgments were unacceptably imprecise and biased for moving dot and runway displays, accurate and unbiased judgments were found for grid displays. It is concluded that optic flow per se does not appear to be sufficient for a pilot to land an airplane and that the systematic errors associated with optic flow under sparse conditions may be responsible for the common occurrence of landing incidents in so-called "black hole" situations.

Depth of monocular elements in a binocular scene: the conditions for da Vinci stereopsis.

Quantitative depth based on binocular resolution of visibility constraints is demonstrated in a novel stereogram representing an object, visible to 1 eye only, and seen through an aperture or camouflaged against a background. The monocular region in the display is attached to the binocular region, so that the stereogram represents an object which is only partially visible to the eye that sees it. The results show that this feature is necessary for quantitative depth, which is not found for a fully visible monocular object in the same location, and that depth in these displays, although very precise, is not based on fusional Stereopsis. The findings provide clear support for the existence of a process of da Vinci Stereopsis, but one more sophisticated than the one proposed by K. Nakayama and S. Shimojo (1990).

Slant or occlusion: global factors resolve stereoscopic ambiguity in sets of horizontal lines.

Perceived slant was measured for horizontal lines aligned on one side and of varying lengths whose length disparity was either a constant linear amount for all lines (consistent with uniocular occlusion) or proportional to line length (consistent with global slant). Although the disparity of any line was ambiguous with respect to these two possibilities, slant of individual lines did not occur in the former case, but a subjective contour in depth was reported along the alignment. For proportional disparity of the set, global slant was seen. Adding a constant length to each line on the invalid eye for occlusion resulted in multiple slants. Smooth uniocular variations in alignment shape elicited subjective contours slanting or curving in depth. Global context can disambiguate the depth status of individual disparate lines.

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.