The majority of existing point cloud registration (PCR) methods exhibit performance degradation under extremely low inlier ratios. To address this limitation, this paper presents a robust learning-free estimator called MAC1toK, which relaxes the feature matching with maximal cliques from the following three perspectives: 1) A novel one-to-K feature matching rectification that iteratively rectifies false matches from their multiple candidates, which improves the overall quality of correspondences, increasing the inlier ratio by 13.76% and 17.70% for FPFH and FCGF descriptors, respectively, on 3DMatch. 2) A novel hypothesis generation method utilizing putative seeds through voting to guide the construction of maximal clique pools, effectively preserving more potential correct hypotheses. 3) A progressive hypothesis evaluation method that continuously reduces the solution space with a “global-clusters-cluster-individual” manner rather than traditional one-shot techniques, greatly alleviating the issue of missing good hypotheses. Unlike MAC, MAC1toK exhibits a capacity to process data with an extremely low inlier ratio. For instance, it achieved 28.59% and 33.96% improvements in registration recall on 3DMatch and 3DLoMatch, respectively, with fewer than 1% inliers. Therefore, MAC1toK demonstrated the state-of-the-art performance.

Correspondence-based six-degree-of-freedom (6-DoF) pose estimation remains a mainstream solution for 3D point cloud registration. However, the heavy outliers pose great challenges to this problem. In this paper, we propose a random sample consensus (RANSAC) variant based on sampling locally and hypothesis globally (SLHG) for 6-DoF pose estimation and 3D point cloud registration. The key novelties are efficient sampling by guiding the sampling process locally and accurate pose estimation by generating hypotheses with global information. SLHG first generates a correspondence subset via compatibility clustering on the initial set. Second, locally guided graph sampling is performed. Third, 6-DoF hypotheses are generated by incorporating global information with a voting scheme. The best hypothesis serves as the estimation result by repeating the second and third steps. Extensive experiments on four popular datasets and comparisons with state-of-the-art methods confirm that: SLHG manages to 1) achieve accurate registrations with a few iterations, and 2) yield better accuracy performance than most competitors.