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Many algorithms for the computation of correspondences between deformableshapes rely on some variant of nearest neighbor matching in a descriptor space.Such are, for example, various point-wise correspondence recovery algorithmsused as a post-processing stage in the functional correspondence framework.Such frequently used techniques implicitly make restrictive assumptions (e.g.,near-isometry) on the considered shapes and in practice suffer from lack ofaccuracy and result in poor surjectivity. We propose an alternative recoverytechnique capable of guaranteeing a bijective correspondence and producingsignificantly higher accuracy and smoothness. Unlike other methods our approachdoes not depend on the assumption that the analyzed shapes are isometric. Wederive the proposed method from the statistical framework of kernel densityestimation and demonstrate its performance on several challenging deformable 3Dshape matching datasets.

Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Space