Surface separation decreases stereoscopic slant but a monocular aperture increases it

Binocular Depth Judgments on Smoothly Curved Surfaces

Binocular disparity is an important cue to depth, allowing us to make very fine discriminations of the relative depth of objects. In complex scenes, this sensitivity depends on the particular shape and layout of the objects viewed. For example, judgments of the relative depths of points on a smoothly curved surface are less accurate than those for points in empty space. It has been argued that this occurs because depth relationships are represented accurately only within a local spatial area. A consequence of this is that, when judging the relative depths of points separated by depth maxima and minima, information must be integrated across separate local representations. This integration, by adding more stages of processing, might be expected to reduce the accuracy of depth judgements. We tested this idea directly by measuring how accurately human participants could report the relative depths of two dots, presented with different binocular disparities. In the first, Two Dot condition the two dots were presented in front of a square grid. In the second, Three Dot condition, an additional dot was presented midway between the target dots, at a range of depths, both nearer and further than the target dots. In the final, Surface condition, the target dots were placed on a smooth surface defined by binocular disparity cues. In some trials, this contained a depth maximum or minimum between the target dots. In the Three Dot condition, performance was impaired when the central dot was presented with a large disparity, in line with predictions. In the Surface condition, performance was worst when the midpoint of the surface was at a similar distance to the targets, and relatively unaffected when there was a large depth maximum or minimum present. These results are not consistent with the idea that depth order is represented only within a local spatial area.

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.

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.

Approximation, torsion, and amodally-completed surfaces

Consider a stereoscopic display simulating two rectangular patches, the lower frontoparallel and the upper slanted around the vertical axis. When the two patches are amodally completed and appear as the unoccluded parts of a smooth surface partially hidden by a foreground frontoparallel surface, either real or illusory, their relative slant is underestimated with respect to a baseline condition in which they are perceived as separate rectangles. Slant assimilation was studied in three experiments using with- vs. without-occluder displays and two methods, slant matching and speeded classification of twist direction. In Experiments 1 and 2 we found slant assimilation in with-occluder displays and slant contrast in without-occluder displays. In Experiment 3 we isolated a component of slant assimilation attributable to the mere presence of the occluder. Twist classification performance was impaired even when edge geometry hindered amodal completion, but the performance loss was larger when surface patches were amodally completed. To minimize the required amount of torsion, input fragments are misperceived, indicating that in limiting conditions amodal completion is mediated by approximation rather than interpolation. Slant assimilation decreases as twist angle increases, up to a limit above which the visual system does not support the formation of a smooth amodal surface with torsion.

Hinge versus twist: the effects of 'reference surfaces' and discontinuities on stereoscopic slant perception

Stereoscopic slant perception around a vertical axis (horizontal slant) is often found to be strongly attenuated relative to geometric prediction. Stereo slant is much greater, however, when an adjacent surface, stereoscopically in the frontal plane, is added. This slant enhancement is often attributed to the presence of a 'reference surface' or to a spatial change in the disparity gradient (introducing second and higher derivatives of disparity). Gillam, Chambers, and Russo (1988 Journal of Experimental Psychology: Human Perception and Performance 14 163-175) questioned the role of these factors in that placement of the frontal-plane surface in a direction collinear with the slant axis (twist configuration) sharply reduced latency for perceiving slant whereas placing the same surface in a direction orthogonal to the slant axis (hinge configuration) had little effect. We here confirm these findings for slant magnitude, showing a striking advantage for twist over hinge configurations. We also examined contrast slant measured on the frontal-plane surface in the hinge and twist configurations. Under conditions where test and inducer surfaces have centres at the same depth for twist and hinge, we found that twist configurations produced strong negative slant contrast, while hinge configurations produced significant positive contrast or slant assimilation. We conclude that stereo slant and contrast effects for neighbouring surfaces can only be understood from the patterns and gradients of step disparities present. It is not adequate to consider the second surface merely as a reference slant for the first or as having its effect via a spatial change in the disparity gradient.

Dissociations between slant-contrast and reversed slant-contrast

A vertical test probe is misperceived as slanted in the opposite direction to an inducer when disparity specifies the inducer slant while monocular cues specify a frontoparallel surface (slant-contrast). In reversed cue conditions with vertical axis slant the test probe is misperceived as slanted in the same direction as the inducer (reversed slant-contrast). We found reliable slant-contrast and reversed slant-contrast with inducers having horizontal-axis slant. The reversed slant-contrast was not influenced when the inducer and probe were separated in the frontal plane or in disparity depth whereas slant contrast was degraded, especially in the latter condition. Slant contrast was most pronounced when the inducer was slanted like a ceiling compared to like a ground. No such difference was found for the reversed slant-contrast. When the cue conflict was minimized slant-contrast was reduced, but only with inducers having ground-like slant. Implications for an existing model explaining the slant effects are discussed.

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.

3-d interpolation in object perception: evidence from an objective performance paradigm

Object perception requires interpolation processes that connect visible regions despite spatial gaps. Some research has suggested that interpolation may be a 3-D process, but objective performance data and evidence about the conditions leading to interpolation are needed. The authors developed an objective performance paradigm for testing 3-D interpolation and tested a new theory of 3-D contour interpolation, termed 3-D relatability. The theory indicates for a given edge which orientations and positions of other edges in space may be connected to it by interpolation. Results of 5 experiments showed that processing of orientation relations in 3-D relatable displays was superior to processing in 3-D nonrelatable displays and that these effects depended on object formation. 3-D interpolation and 3-D relatabilty are discussed in terms of their implications for computational and neural models of object perception, which have typically been based on 2-D-orientation-sensitive units.

Perspective based on stereopsis and occlusion

Perspective is usually considered a monocular pictorial cue, distinct from other cues such as occlusion and stereopsis. We cut across these distinctions by asking whether purely binocular (cyclopean) contours, created by stereoscopically shifting a region of homogeneous texture nearer or further than its surround, can act as a linear-perspective cue and whether the contours' ability to do this is influenced by their surface belongingness. We found that the left/right orientation of cyclopean trapezoids nearer than a surround strongly influenced perceived slant, showing that perspective constraints are applied to stereoscopically derived contours. Further regions, however; appeared as surfaces seen through a trapezoidal aperture. Because the aperture "owned" the trapezoidal contours, their orientation had little effect on perceived slant. We conclude that the application of perspective constraints depends critically on how contours are classified by stereo-specified occlusion relationships among surfaces and that perspective, stereopsis, and occlusion are not distinct processing systems.

Perceptual learning without feedback and the stability of stereoscopic slant estimation

Subjects were examined for practice effects in a stereoscopic slant-estimation task involving surfaces that comprised a large portion of the visual field. In most subjects slant estimation was significantly affected by practice, but only when an isolated surface (an absolute disparity gradient) was present in the visual field. When a second, unslanted, surface was visible (providing a second disparity gradient and thereby also a relative disparity gradient) none of the subjects exhibited practice effects. Apparently, stereoscopic slant estimation is more robust or stable over time in the presence of a second surface than in its absence. In order to relate the practice effects, which occurred without feedback, to perceptual learning, results are interpreted within a cue-interaction framework. In this paradigm the contribution of a cue depends on its reliability. It is suggested that normally absolute disparity gradients contribute relatively little to perceived slant and that subjects learn to increase this contribution by utilizing proprioceptive information. It is argued that--given the limited computational power of the brain--a relatively small contribution of absolute disparity gradients in perceived slant enhances the stability of stereoscopic slant perception.

Effects of disparity-perspective cue conflict on depth contrast

The role of disparity-perspective cue conflict in depth contrast was examined. A central square and a surrounding frame were observed in a stereoscope. Five conditions were compared: (1) only disparity was introduced into either the centre or surround stimulus, (2) only perspective was introduced into the centre or surround, (3) concordant perspective and disparity were introduced into the centre or surround, (4) disparity was introduced into one stimulus and perspective into the other, and (5) only the centre stimulus was presented with horizontal shear disparity and perspective manipulated independently. The results show that individual differences in depth contrast were related to individual differences in the weighting of disparity and perspective in the single-stimulus conditions. We conclude that conflict between disparity and perspective contributes to depth contrast. However, significant depth contrast occurred when there was no disparity-perspective cue conflict, indicating that this cue conflict is not the sole mechanism producing depth contrast.