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Section: New Results

Topologically-Robust 3D Shape Matching

Participant : Edmond Boyer.

3D Shape matching is an important problem in computer vision. One of the major difficulties in finding dense correspondences between 3D shapes is related to the topological discrepancies that often arise due to complex kinematic motions. In this work done in collaboration with Jan Cech, Radu Horaud and Avinash Sharma a shape matching method is proposed that is robust to such changes in topology. The algorithm starts from a sparse set of seed matches and outputs dense matching. We use a shape descriptor based on properties of the heat-kernel and which provides an intrinsic scale-space representation. This descriptor incorporates (i) heat-flow from already matched points and (ii) self diffusion. At small scales the descriptor behaves locally and hence it is robust to global changes in topology. Therefore, it can be used to build a vertex-to-vertex matching score conditioned by an initial correspondence set. This score is then used to iteratively add new correspondences based on a novel seed-growing method that iteratively propagates the seed correspondences to nearby vertices. The matching is farther densified via an EM-like method that explores the congruency between the two shape embeddings. The method is compared with two recently proposed algorithms and we show that we can deal with substantial topological differences between the two shapes[15] .