The author presents a theoretical investigation of the use of the aspect graph (AG) for topological recognition of polyhedral objects from multiple views. The idea of the AG is to cluster the infinite possible views of an object into a finite set of representative views or aspects. In principle, an aspect could be any collection of features of a 2D image, invariant or relatively invariant under some limited displacement of the viewpoint.

The purpose of this paper is to explore two ideas related to the AG theoretically. First, the full information stored in the AG, that is aspects and transitions, suggests a multiple views approach, possibly in relation to an active inspection algorithm. Second, topologically matching images of an unknown object and stored aspects appears a most straightforward consequence of the topological nature of the AG. The paper first discusses the topological matching process, and gives a suitable topological definition of aspect. Next, the author addresses the question of the “similarity” of two polyhedra with the same AG. The similarity implied by the perspective AG and the parallel AG are compared with isomorphism for general and convex polyhedra. Five propositions concerning the topological recognition and similarity of polyhedra are proven.

The author feels that the smaller size, as well as the practical problems in observing visual events, make the reduced (perspective) AG and the (perspective) aspect set interesting tools for topological recognition.

The paper is clearly written and there are many references on theoretical topological recognition.