Towards Global Sparse and Partial Point Set Registration with Pose-Robust Completion for Computer-Assisted Orthopedic Surgery

Abstract

In computer-assisted orthopedic surgery (CAOS), accurately registering sparse and partial intraoperative point sets with a complete preoperative model remains highly challenging due to limited overlap, extreme sparsity, and point localisation noise. In this paper, we propose a novel end-to-end completion–registration framework, to accurately register partial and sparse point sets in CAOS. First, we develop a three-branch network that separately encodes intraoperative pose and geometry, while extracting rotation-invariant geometric priors from the preoperative model in a canonical space. This structure-aware design provides strong and beneficial cues for completing missing regions using sparse and partial data. Second, to address the sensitivity of the completion to random input poses, the completion is specifically conducted in a canonical frame and a learned SE(3) transform maps the output back to the observed intraoperative space. Third, we introduce a probabilistic registration module based on a bidirectional hybrid mixture model that aligns the completed intraoperative and preoperative point sets in distribution space by jointly optimizing the source-to-target and target-to-source objectives, addressing density mismatch and geometric inconsistencies that may arise from completion. Finally, we present the individual loss formulations for both supervised and unsupervised learning paradigms respectively, enabling robust end-to-end optimization of the entire pipeline. We systematically validate our approach on (1,757) femur, (1,301) hip, and (397) tibia models, as well as real-world phantom experiments. Our method achieves state-of-the-art performance under low overlap (15–30%), sparse observations (64–128 points), and large initial misalignments (up to ([-180, 180]^circ) rotation and ([-100, 100]mm) translation), demonstrating strong robustness and generalization.