Abstract
A mathematical theory for establishing correspondences between curves and for non-rigid shape comparison is developed in this paper. The proposed correspondences, called bimorphisms, are more general than those obtained from one-to-one functions. Their topology is investigated in detail. A new criterion for non-rigid shape comparison using bimorphisms is also proposed. The criterion avoids many of the mathematical problems of previous approaches by comparing shapes non-rigidly from the bimorphism. Geometric invariants are calculated for curves whose shapes can be exactly matched with a bimorphism. The invariants are related to the concave and convex segments of a curve and provide justification for parsing the curve into such segments.
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