Articulated Shape Matching by Robust Alignment of Embedded Representations

In this paper we propose a general framework to solve the articulated shape matching problem, formulated as finding point-to-point correspondences between two shapes represented by 2-D or 3-D point clouds. The original point- sets are embedded in a spectral representation and the actual matching is carried out in the embedded space. We analyze the advantages of this choice as well as the reasons for which the task remains a difficult one. In particular, we show that although embedded-space matching still has intrinsic combinatorial difficulties, it can be solved by searching for an optimal orthogonal transformation that aligns the two shape embeddings. Relying on the model based clustering formalism, we propose a probabilistic formulation which casts the matching into an EM algorithm. Outliers are properly handled by the algorithm and a simple strategy is adopted to initialize it. Experiments are performed with three embedding methods (Isomap, LLE, and Laplacian embedding) and with 3-D voxelsets representing a human-motion sequence.