Computing the visual hull of solids of revolution

Abstract

The visual hull VH( S, V) of an object S relative to a viewing region V is a geometric entity useful for silhouette–based image understanding. For instance, two objects can be distinguished from their silhouettes only if their visual hulls are different; an object can be exactly reconstructed from its silhouettes only if equal to its visual hull. The visual hull idea also allows to define a measure of the reconstruction accuracy of an object from its silhouettes. There are two main cases of visual hull: the internal visual hull, if V is only bounded by S, and the external visual hull, if V is bounded by the convex hull of S. This paper addresses the problem of computing both visual hulls of solids of revolution. Two cases are considered: smooth polynomial and piecewise linear generators. The algorithm has been implemented for the latter case. The surface of the visual hulls, when it is not coincident with the surface of S, turns out to consist of segments of cones, annular rings and hyperboloids of one sheet.