TopoPointPWC: Manifold Topology-Aware Point Cloud Registration via Persistent Homology

Medical point cloud registration has been extensively studied, but current methods still pay insufficient attention to the topological structure of the intrinsic manifold space. A topology-aware non‑rigid point cloud registration framework TopoPointPWC is proposed in manifold space to enhance alignment of anatomically complex structures. We construct Vietoris‑Rips filtrations on local k-nearest neighbor graphs to extract persistent homology features, embeds them as differentiable persistence images, and integrates a topology‑gated mechanism with curriculum‑weighted loss into a hierarchical registration network, thereby prioritizing alignment at critical anatomical landmarks. Experiments demonstrate that this topology-aware strategy enforces anatomical plausibility by preserving hierarchical vascular branching without geometric shortcuts, while simultaneously ensuring dynamic consistency through physically coherent deformation fields, offering a robust framework for clinically reliable registration.