Allen Brookes

Integrating stereopsis with monocular interpretations of planar surfaces

Experiments are reported that involved spatial judgments of planar surfaces that had contradictory stereo and monocular information. Tasks included comparing the relative depths of two points on the depicted surface and judging the surfaces apparent spatial orientation. It was found that for planar surfaces the 3D perception was dominated by the monocular interpretation, despite the strongly contradictory stereo information. We propose that stereo information is effectively integrated only where the surface exhibits curvature features or edge discontinuities, i.e. where the second spatial derivatives of disparity are nonzero. Planar surfaces induce constant gradients of disparity and are thus effectively featureless to stereopsis. Further observations are reported regarding nonplanar surfaces, where contradictory monocular information can still be effectively rivalrous with that suggested stereoscopically.

The Analogy between Stereo Depth and Brightness

Apparent depth in stereograms exhibits various simultaneous-contrast and induction effects analogous to those reported in the luminance domain. This behavior suggests that stereo depth, like brightness, is reconstructed, ie recovered from higher-order spatial derivatives or differences of the original signal. The extent to which depth is analogous to brightness is examined. There are similarities in terms of contrast effects but dissimilarities in terms of the lateral inhibition effects traditionally attributed to underlying spatial-differentiation operators.

Probing depth in monocular images

It is generally expected that depth (distance) is the internal representational primitive that corresponds to much of the perception of 3D. We tested this assumption in monocular surface stimuli that are devoid of distance information (due to orthographic projection and the chosen surface shape, with perspective projection used as a control) and yet are vividly three-dimensional. Slant judgments were found to be in close correspondence with the actual geometric slant of the stimuli; the spatial orientation of the surfaces was perceived accurately. The apparent depth in these stimuli was then tested by superimposing a stereo depth probe over the monocular surface. In both the perspective and orthographic projection the gradient of perceived depth, measured by matching the apparent depth of the stereo probe with that of the monocular surface at a series of locations, was substantial. The experiments demonstrate that in orthographic projection the visual system can compute from local surface orientation a depth quantity that is commensurate with the relative depth derived from stereo disparity. The depth data suggests that, at least in the near field, the zero value for relative depth lies at the same absolute depth as the stereo horopter (locus of zero stereo disparity). Relative to this zero value, the depth-from-slant computation seems to provide an estimate of distance information that is independent of the absolute distance to the surface.

Detecting structure by symbolic constructions on tokens

Geometric organization is readily detected in discrete textures such as dot patterns. A common proposal is that orientation-tuned receptive field mechanisms provide the local orientation information from which the global organizations emerge. Alternatively, the local orientation might be attributed to grouping constructions between adjacent tokens, each representing the position of a dot and its attributes such as color, size, and contrast. Geometric organization would then emerge by grouping operations on selected tokens that are similar, adjacent, and aligned. It is the ability to group on the basis of similarity that most strongly differentiates this from the energy-summating receptive field approach. Using dot patterns with rivalrous organization, we demonstrate grouping phenomena that are difficult to attribute to a broad class of energy summation detectors operating in the spatial frequency domain, which we therefore attribute to perceptual groupings on tokens. We discuss the computational differences between feature detection and structure detection, and suggest that orientation-tuned receptive field mechanisms, while appropriate for the former task, have little application to the latter.

The Concave Cusp as a Determiner of Figure—Ground

The tendency to interpret as figure, relative to background, those regions that are lighter, smaller, and, especially, more convex is well known. Wherever convex opaque objects abut or partially occlude one another in an image, the points of contact between the silhouettes form concave cusps, each indicating the local assignment of figure versus ground across the contour segments. It is proposed that this local geometric feature is a preattentive determiner of figure—ground perception and that it contributes to the previously observed tendency for convexity preference. Evidence is presented that figure—ground assignment can be determined solely on the basis of the concave cusp feature, and that the salience of the cusp derives from local geometry and not from adjacent contour convexity.

Combining Binocular and Monocular Curvature Features

A study is reported of the perception of visual surfaces in wire-frame stimuli generated by combinations of monocular surface contours and binocular disparity that provide differing information about 3-D relief. Observers vary considerably in the relative contribution made by the binocular and monocular cues to the perception of overall 3-D form. Without training, many observers may entirely fail to perceive surface curvature from the binocular disparity patterns, interpreting the form of the surface only according to the monocular information. For other observers, both cues contribute to the end percept, with the monocular interpretation dominating where the disparity information indicates planarity and with disparity dominating where disparity information suggests curvature and the monocular interpretation suggests planarity. Where stereo and monocular interpretations indicate inconsistent surface curvature features at a common location, more complex resolution strategies are suggested.

Binocular depth from surfaces versus volumes.

Subjects were asked to compare the relative depths of two binocular targets embedded in different random dot stereogram backgrounds. The disparities of the background points were either randomized, corresponding to a scattering of points within a volume, or arranged according to a sawtooth (triangle-wave) disparity profile (i.e., a set of slanted planar surfaces separated by sharp depth discontinuities). When the targets were embedded in the random volume, their depths were perceived in accordance with their relative disparities. But when the target points were embedded in the sawtooth surfaces their depths were systematically misperceived in a manner predicted by the incorrect depth interpretation of the background points. Rather than seeing a sawtooth pattern, the background points resembled a staircase in depth, and the targets, which appeared embedded in different steps, were misjudged in depth accordingly. The effect suggests a distinction between the depth processing of isolated binocular features and those associated with continuous surfaces.

Symbolic grouping versus simple cell models

The apparent line-like structure in dot patterns derives substantially from the orientation defined by pairings of adjacent dots. Two alternative models have been proposed for making these pairings, one in which the individual dots are treated as discrete grouping tokens, and the second in which the pairing orientation derives from spatial summation by simple cell receptive fields. Contradictory evidence has been found both directly in support of, and directly against, both models. Much of the debate about these two models has hinged on the degree of linearity of summation expected in the simple cell model. Recent neurophysiological evidence changes the balance of the debate, invalidating certain earlier arguments based on linearity and providing a novel way of showing that simple cells do indeed play a major, but not necessarily exclusive, role in dot groupings.