Hull Concept for Silhouette-Based Image Understanding

Many algorithms for both identifying and reconstructing a 3-D object are based on the 2-D silhouettes of the object. In general, identifying a nonconvex object using a silhouettebased approach implies neglecting some features of its surface as identification clues. The same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object. This paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette-based image understanding. For this purpose, the geometric concept of visual hull of a 3-D object is introduced. The visual hull of a 3-D object S is the closest approximation of S that can be obtained with the volume intersection approach. An equivalent statement, relative to object identification, is that the visual bull of S is the maximal object silhouette-equivalent to S, i.e., which can be substituted for S without affecting any silhouette. Only the parts of the surface of S that also lie on the surface of the visual hull can be reconstructed or identified using silhouette-based algorithms. The visual hull of an object depends not only on the object itself but also on the region allowed to the viewpoint. Two main viewing regions can be considered, resulting in the external and internal visual hull. In the former case the viewing region is related to the convex hull of S, in the latter it is bounded by S itself. The internal visual hull also admits an interpretation not related to silhouettes: the features of the surface of S that is not coincident with the surface of the internal visual hull cannot be observed from any viewpoint lying outside the convex hull. After a general discussion of the visual hull and its properties, algorithms for computing the internal and external visual hulls of 2-D objects and 3-D planar face objects are presented and their complexity analyzed. In general, the visual hull of a 3-D planar face object turns out to be bounded by planar and curved patches. A precise statement of the concept of visual hull appears to be novel, as is the problem of its computation.