Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Space
This addresses the issue of poor accuracy and surjectivity in shape matching for deformable 3D shapes, offering a robust alternative without relying on restrictive isometric assumptions.
The paper tackles the problem of non-rigid shape correspondence by proposing a method that guarantees bijective correspondences with higher accuracy and smoothness, achieving significant improvements over existing techniques on challenging 3D shape datasets.
Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used 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 of accuracy and result in poor surjectivity. We propose an alternative recovery technique capable of guaranteeing a bijective correspondence and producing significantly higher accuracy and smoothness. Unlike other methods our approach does not depend on the assumption that the analyzed shapes are isometric. We derive the proposed method from the statistical framework of kernel density estimation and demonstrate its performance on several challenging deformable 3D shape matching datasets.