ETC-PCR: Coarse-to-Fine Edge-Triangle Compatibility for Robust and Accurate Point Cloud Registration

Accurately estimating the 6D pose of objects or scenes is a fundamental challenge in point cloud registration (PCR), especially when dealing with partially overlapping scenarios. Typically, features are first extracted—either through hand-crafted descriptors or deep learning-based methods—to establish a putative correspondence set. However, despite advances in deep learning for feature extraction and matching, the presence of a low inlier ratio often complicates the estimation process. To address these challenges, this paper proposes a novel inlier estimation approach in PCR that leverages edge-triangle combined compatibility for progressively filtering out outliers. First, geometric compatibility is exploited by randomly selecting two points to form an edge. If the compatibility test is passed, both endpoints receive a vote, and the top-ranked correspondences are retained for the next stage, enabling rapid removal of a large portion of outliers. Next, a stricter constraint is introduced based on triangles, requiring all three edges to satisfy compatibility conditions, which further refines the candidate set. The refined correspondences are then processed through a lightweight RANSAC module for hypothesis generation and selection. Finally, a geometry-based pose refinement module is presented, which utilizes the original geometric information and formulates registration as a nonlinear least squares problem. To enhance robustness against outliers, Welsch function is selected as a robust kernel, efficiently solving the optimization using the Majorization-Minimization algorithm. Extensive experiments on benchmark datasets, including 3DMatch, 3DLoMatch, and KITTI, validate the effectiveness of the proposed approach. The results demonstrate state-of-the-art performance, particularly in scenarios with extremely low inlier ratios.