Topological recognition of polyhedral objects from multiple views

Abstract

The aspect graph (AG) has been proposed as a viewer-centered tool for object recognition. Although the aspects could be used for recognition from one image, the full information stored in the AG (aspects and visual events) suggests a multiple views, possibly active, approach. The topological nature of the AG also suggests a topological match of images of the unknown object and stored aspects. In this paper we present a theoretical investigation on the use of the AG for topological recognition from multiple views of polyhedral objects. First, we discuss the topological matching process, and give a suitable topological definition of aspect. Moreover, since topological identification is approximate, we tackle the problem of understanding the ability of the AG to topologically discriminate different objects. More precisely, we address the question: how “similar” are two polyhedra with the same AG? The isomorphism of polyhedra is chosen as the reference similarity condition. The cases of general and convex polyhedra are discussed under perspective and parallel projections. In practice, it could be difficult to identify the visual events from the images of the unknown object. Thus, we also compare isomorphism and the similarity induced by: (i) a topologically reduced aspect graph; (ii) the set of topologically different aspects, neglecting visual events.