This paper reports progress toward the development of a representation of significant surface changes in dense depth maps. We call the representation the Surface Primal Sketch by analogy with representation of intensity changes, image structure, and changes in curvature of planar curves. We describe an implemented program that detects, localizes, and symbolically describes: steps, where the surface height function is discontinuous; roofs, where the surface is continuous but the surface normal is discontinuous; smooth joins, where the surface normal is continuous but a principle curvature is discontinuous and changes sign; and shoulders, which consists of two roofs and correspond to a step viewed obliquely. We illustrate the performance of the program on range maps of objects of varying complexity.

The problems under consideration center around the interpretation of binocular stereo disparity. In particular, the goal is to establish a set of mappings from stereo disparity to corresponding three-dimensional scene geometry. An analysis has been developed that shows how disparity information can be interpreted in terms of three-dimensional scene properties, such as surface depth, discontinuities, and orientation. These theoretical developments have been embodied in a set of computer algorithms for the recovery of scene geometry from input stereo disparity. The results of applying these algorithms to several disparity maps are presented. Comparisons are made to the interpretation of stereo disparity by biological systems.

This paper reviews a number of aspects of visual motion analysis in biological systems from a computational perspective. We illustrate the kinds of insights that have been gained through computational studies and how these observations can be integrated with experimental studies from psychology and the neurosciences to understand the particular computations used by biological systems to analyze motion. The particular areas of motion analysis that we discuss include early motion detection and measurement, the optical flow computation, motion correspondence, the detection of motion discontinuities, and the recovery of three-dimensional structure from motion.

This paper continues our work on visual representation s of three-dimensional surfaces [Brady and Yuille 1984b]. The theoretical component of our work is a study of classes of surface curves as a source of constraint n the surface on which they lie, and as a basis for describing it. We analyze bounding contours, surface intersections, lines of curvature, and asymptotes. Our experimental work investigates whether the information suggested by our theoretical study can be computed reliably and efficiently. We demonstrate algorithms that compute lines of curvature of a (Gaussian smoothed) surface; determine planar patches and umbilic regions; extract axes of surfaces of revolution and tube surfaces. We report preliminary results on adapting the curvature primal sketch algorithms of Asada and Brady [1984] to detect and describe surface intersections.

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