From object structure to object function

Stoyanka D. Zlateva; Lucia M. Vaina

doi:10.1117/12.45481

1 March 1991 From object structure to object function

Stoyanka D. Zlateva, Lucia M. Vaina

Proceedings Volume 1468, Applications of Artificial Intelligence IX; (1991) https://doi.org/10.1117/12.45481
Event: Orlando '91, 1991, Orlando, FL, United States

Abstract

In this paper we provide a mathematical support for the nature of the shape representation methods useful for the computation of possible functions of an objects as derived from its shape structure. We discuss the concepts of parts and subparts of objects in the framework of axis based shape representation methods and boundary based methods. We propose a new method for obtaining descriptions of parts which based on a theorem from differential geometry (Pogorelov 1974) that any regular surface can be approximated in a finite environment with a given accuracy by a parabolloid of one of the following types - elliptic, hyperbolic and a parabolloid degenerating into a plane or a parabolic cylinder. Based on these considerations we suggest a heuristic for the approximation of convex object parts by a polyhedra, cylinder, ellipsoid or generalized cone with straight axis depending on the presence of plane, parabolic, elliptic subsets in their boundary, and nonconvex object parts by generalized cones with curved axis. This approach allows to obtain a primitive based shape description after the decomposition of the object shape through the more general boundary-based methods. We present examples of decomposing and describing shapes of common objects in terms of their parts, subparts and associated features.

Citation Download Citation

Stoyanka D. Zlateva and Lucia M. Vaina "From object structure to object function", Proc. SPIE 1468, Applications of Artificial Intelligence IX, (1 March 1991); https://doi.org/10.1117/12.45481

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