The visual contour in depth JAN

828 One of the most basic constraints in optically guided behavior (or vision for short) is due to the fact that typical objects in the ken of a human observer are optically opaque solids. This is true for the typical office or living environment (walls of our houses, furniture, other people , etc.), as well as for outside environments (buildings, cars, trees, hills, etc.). For one thing, this means that we see only the frontal side of most objects, and we are unaware of optical specification of about half of their surfaces. Obviously, the frontier between the visible and invisible parts is of vital interest. This is the " occlusion boundary " or " visual contour. " In this paper, we need to distinguish sharply between the visual contour as an entity in the two-dimensional (2-D) visual field and the frontier between visible and invisible parts on the surface of the object in three-dimensional (3-D) space. We denote the former entity as the contour, and the latter as the rim. Thus, the contour is the central projection of the rim, where the center of projection is the vantage point of the observer. Both the contour and the rim depend on the object, as well as on the relative position of the observer with respect In many cases, it might be of interest to distinguish also between the silhouette and the contour proper, where the silhouette is the boundary of the visual projection of the object. In this paper, there is no need to do so; we deal only with the contour proper. Despite the vital importance of the rim, most people possess only a rudimentary and most often erroneous understanding of its structure. For instance, it is common enough to hear the opinion that the rim is a planar curve and runs in a frontoparallel (to the observer) plane. This is indeed the case for any sphere that confronts the observer. The spheres also exhaust the class of objects for which the opinion holds true. More generally, the rim is a planar curve (though not necessarily frontoparallel) for all quadrics (e.g., triaxial ellipsoids) but for no other smooth solid objects (Blaschke, 1967). Thus, the common opinion holds true in certain degenerate cases that indeed often apply within the confines of the laboratory, but in few other places. Yet even Marr (1982), writing expressly on the geometry of vision, makes this …