The geometry of view space of opaque objects bounded by smooth surfaces

摘要

A view of a smooth, opaque object is a line drawing consisting of contour fragments which form closed loops, terminate, or form T-junctions. Given a compact object we have a global decomposition of the space of camera positions into cells from which topologically equivalent views are obtained. To apply certain image-based object recognition techniques based on characteristic views of an object one needs to know this cellular decomposition of view space. The boundaries of such cells of stable views are formed by the view bifurcation set from which transitional (degenerate) views are seen. We derive a finite list of geometrical models of the view bifurcation set—the view bifurcation set of any particular object is a combination of such model surfaces from this list. To match a characteristic view with an image one has to find the visible fragments of the apparent contour in the image, and we briefly describe an observation which might lead to an algorithm for finding such contour fragments.