Directed Spatial Consistency-Based Partial-to-Partial Point Cloud Registration with Deep Graph Matching

3D point cloud registration is an essential problem in computer vision, robotics, surgical navigation and augmented reality. Accurate registration of partially overlapped intraoperative point clouds (e.g., femoral reconstruction) remains critical yet challenging in orthopedic navigation due to incomplete overlap and dynamic noise. In this study, we propose a partial-to-partial point cloud registration framework based on directional spatial consistency. First, we extract overlapped areas from partially overlapping point clouds and leverage the point registration graph matching module to calculate the hard point matching matrix. Second, we sample nodes from the source point cloud and generate translation-invariant edge vectors (direction/scale-preserving) via their k-nearest neighbors, guided by predicted point correspondences. This bypasses translation ambiguities by encoding spatial consistency through edges, reducing pose estimation to 3DoF alignment (rotation). The loss explicitly couples point-level matches with edge-level geometric constraints for dual optimization. Building upon this framework, we extract reliable overlapping edge representations and prune their similarity matrix by thresholding low-confidence scores, effectively suppressing spurious matches. The proposed edge-aware matching mechanism further exploits the translation invariance of local structures to refine point correspondences with enhanced accuracy. Finally, we introduce a bidirectional registration mechanism to reinforce optimization stability, achieving state-of-the-art performance across benchmarks. Extensive experiments on ModelNet40, ShapeNet, and MedShapeNet validate our method under diverse scenarios: partial-to-partial, unseen categories, partial-to-full, and cross-dataset generalization, surpassing existing methods in registration accuracy. The codes are available at https://github.com/pidan0824/DSCGM.