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

Dongxun Jiang, Zhizhuo Yu, Jiyang Wu, Beichen Yang

Track: tiny paper (up to 4 pages)

Keywords: Manifold Space, Point Cloud Registration, Persistent Homology, Topological Structure

Abstract: 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.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Submission Number: 61