Point cloud registration in environments lacking rich textures or containing repetitive structures remains highly susceptible to misalignments. The core challenge lies in balancing the demand for extracting highly distinctive local features with the computational cost of global context modeling. In this paper, we propose a robust registration framework that efficiently combines rotation-equivariant geometric representations with state space models of linear complexity to mitigate feature ambiguity and mismatch. First, a multivariate geometric encoding mechanism is embedded within convolutional layers, enhancing local feature distinctiveness under strict rotation equivariance by explicitly leveraging surface properties. Second, to efficiently establish long-range spatial dependencies, we replace standard dense attention with a hybrid geometry-state aggregation module. This module integrates local geometric self-attention with the Mamba architecture, strengthening focus on overlapping regions without the quadratic computational burden. Finally, we optimize the generated correspondences through a physically consistent hypothesis generator to compute reliable rigid transformation results. On standard benchmarks, our framework demonstrates exceptional robustness to ambiguous matches, achieving a 96.3% registration recall on the 3DMatch dataset and outstanding accuracy on the KITTI dataset.
Li et al. (Mon,) studied this question.