Characteristic-view modeling of curved-surface solids

Abstract

Given a 3-D object (solid), it is possible to divide the exterior viewing space of the solid into maximally connected subspaces of vantage points such that the perspective views of the solid from all vantage points within a subspace have identical labeled line-junction graphs. We refer to such subspaces as the characteristic-view domains (CVDs) of the solid, and to a representative perspective view from within a domain, as a characteristic view (CV). The concept suggests a scheme for modeling 3-D objects in which the infinite number of possible views of a given solid are represented by a finite set of characteristic views (together with their respective projection-defining parameters). The concept was introduced more than 15 years ago as a modeling scheme to facilitate real-time recognition of 3-D objects. However, the difficulty of determining the CVs hindered its application. This article describes a technique for computing the characteristic views of general solids bounded by quadric surfaces (including polyhedra as a special case), and suggests how the technique can be used for 3-D object recognition.