A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-Rigid Shape Matching
MINNESOTA UNIV MINNEAPOLIS INST FOR MATHEMATICS AND ITS APPLICATIONS
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In this paper, the problem of non-rigid shape recognition is viewed from the perspective of metric geometry, and the applicability of diffusion distances within the Gromov-Hausdorff framework is explored. While the commonly used geodesic distance exploits the shortest path between points on the surface, the diffusion distance averages all paths connecting between the points. The diffusion distance provides an intrinsic distance measure which is robust, in particular to topological changes. Such changes may be a result of natural non-rigid deformations, as well as acquisition noise, in the form of holes or missing data, and representation noise due to inaccurate mesh construction. The presentation of the proposed framework is complemented with humorous examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points, its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non-rigid shapes.
- Numerical Mathematics
- Theoretical Mathematics