HIG-PCN: Higher Order Structure Guided Point Cloud Completion

Point cloud completion aims to recover complete object geometry from partial observations, supporting 3D shape understanding and robotic interaction when occlusion and limited viewpoints prevent complete scans. Existing methods commonly combine local geometric features with global shape context to infer missing surfaces. However, when an entire component is unobserved, nearby points may provide insufficient evidence, while a global representation may not explicitly preserve the relationships among the visible regions that constrain its geometry. For example, the remaining frame and bars of a partially observed chair back can jointly constrain the placement and arrangement of missing supports. Recovering such structures therefore requires considering how multiple regions relate to one another, rather than treating each missing region independently. This motivates explicit modeling of higher-order relationships that capture shared geometric context among sets of points. We propose HIG-PCN, a point cloud completion framework that represents these relationships using hypergraphs, where each hyperedge associates multiple related points. Its central idea is to combine local geometric groups with learned nonlocal groups and carry their shared context from shape encoding through point generation and refinement. In this way, evidence distributed across visible regions remains available when reconstructing unobserved geometry, without requiring semantic part annotations. Experiments assess completion accuracy and surface coverage on standard benchmarks, while controlled analyses show that both local and nonlocal group correspondences influence the reconstructed geometry.