Laparoscopic liver point cloud registration via hyperbolic-topology interaction

In laparoscopic liver resection, precise registration between preoperative 3D models and intraoperative laparoscopic point clouds remains challenging due to liver deformation, respiratory motion, and limited visibility. This study aims to develop a robust registration method achieving stable alignment under low-overlap and non-rigid conditions.

We propose a novel framework centered on a Hyperbolic-Topology Interaction Module. The module maps rotation-invariant features extracted by the backbone into hyperbolic space, leveraging its negative curvature to amplify subtle geometric differences, while simultaneously constructing a topological graph that propagates spatial relationships to enhance feature consistency. Finally, based on the refined features, a coarse-to-fine matching strategy combined with a hypothesis generation mechanism establishes robust correspondence estimation.

Evaluation of our method with comparative methods on both simulated and real datasets shows that our method achieves state-of-the-art results. On the public DePOLL dataset, our method achieved the lowest surface target registration error (TRE) of 6.2 mm and the lowest internal TRE of 7.0 mm. Additional non-rigid experiments further validate the strong generalization capability of the proposed features under varying deformation conditions.

The proposed method effectively combines local geometric discrimination with global topological reasoning, achieving notable gains in accuracy, robustness, and efficiency. It delivers reliable rigid initialization for augmented reality (AR)-guided resection navigation and establishes a solid foundation for subsequent non-rigid estimation, demonstrating strong potential for clinical use.