Non-Rigid Shape Comparison of Plane Curves in Images
- Cite this article as:
- Tagare, H.D., O'Shea, D. & Groisser, D. Journal of Mathematical Imaging and Vision (2002) 16: 57. doi:10.1023/A:1013938519103
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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.