Topology Robust Intrinsic Symmetries of Non-Rigid Shapes Based on Diffusion Distances
MINNESOTA UNIV MINNEAPOLIS INST FOR MATHEMATICS AND ITS APPLICATIONS
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Detection and modeling of self-similarity and symmetry is important in shape recognition, matching, synthesis, and reconstruction. While the detection of rigid shape symmetries is well established, the study of symmetries in non-rigid shapes is a much less researched problem. A particularly challenging setting is the detection of symmetries in non-rigid shapes affected by topological noise and asymmetric connectivity. In this paper, we treat shapes as metric spaces, with the metric induced by diffusion distances, and define non-rigid symmetries as self-isometries with respect to the diffusion metric. Experimental results show the advantage of the diffusion metric over the previously proposed geodesic metric for exploring intrinsic symmetries of bendable shapes with possible topological irregularities.
- Theoretical Mathematics