Current point cloud registration algorithms struggle to effectively handle both deformations and occlusions simultaneously. Our manifold analysis reveals this limitation arises from the inaccurate modeling of the shape's underlying manifold and the lack of an effective optimization strategy for fragmented manifold structures. In this paper, we present AniSym-Net, a novel non-rigid registration framework designed to address near-isometric deformation registration in the presence of occlusions. To encode object's coarse topological properties and local geometric information, AniSym-Net introduces a novel anisotropic hybrid shape-motion deformation field. The effectiveness of the anisotropic hybrid shape-motion fields relies on both the holonomic constraints from the symplectic structure modeling in AniSym-Net and the motion-conditional cross-attention during fusion, which calibrates geometric features using velocity-boundary constrained point motion patterns. The harmonization of correspondences derived from anisotropic hybrid fields and those from motion-shape fields significantly mitigates registration errors and occlusions. This is achieved through the optimization of loop closures of cotangent bundles within the symplectic manifold framework. We conduct comprehensive evaluation across five popular benchmarks, namely CAPE, DT4D, SAPIEN, FAUST, and DeepDeform, to demonstrate our AniSym-Net's superior performance compared to the state-of-the-art methods. Code will be publicly available.
Wang et al. (2025) studied this question.