Representing Objects Using Topology

In this paper we call for the revival of the study of topological representations in computer vision. Topology allows us to express the connectivity relationships which exist between different primitives in images and in scenes. Although topology was once of significant interest in vision, it has recently become over-shadowed by geometric considerations. We believe that it has a very important role to play in visual processing. First we introduce an object-oriented class hierarchy which records the topological descriptions which exist in images and scenes. Once we have shown how the image topology relates to that of the scene, we demonstrate how it can be extracted from raw images. Subsequent to this, we describe how the newly found topological descriptions can be employed to facilitate feature grouping, the recognition of polyhedra, and the evaluation of recognition hypothesis which result from a mature object recognition system.