Matching shapes by eigendecomposition of the Laplace-Beltrami operator

We present a method for detecting correspondences between non-rigid shapes, that utilizes surface descriptors based on the eigenfunctions of the Laplace-Beltrami operator. We use clusters of probable matched descriptors to resolve the sign ambiguity in matching the eigenfunctions. We then define a matching cost that measures both the descriptor similarity, and the similarity between corresponding geodesic distances measured on the two shapes. We seek for correspondence by minimizing the above cost. The resulting combinatorial problem is then reduced to the problem of matching a small number of feature points using quadratic integer programming.