Orientation-based representations of 3-D shape

Orientation-based representations are well-suited to vision tasks including viewpoint independent object recognition and 3D attitude determination. The key property that orientation-based representations share is that they rotate in the same way as the object rotates. Combinations of orientation-based representations of a model and of a sensed object determine inequalities that become equalities if and only if the object and model match both in identity and in attitude. This results in optimization problems that can be solved by standard numerical methods. The paper unifies and extends previous work based on the Extended Gaussian Image (EGI) representation. It provides the theoretical basis for new approaches to object recognition and attitude determination using dense surface data. It extends results on convex polyhedra to the domain of smooth, strictly convex surfaces. The class of shapes covered also is extended to include starshaped sets. The theoretical results lead to feasible algorithms that are both accurate and robust. A proof-of-concept system has been implemented and experiments conducted both on synthesized data and on data obtained from real objects