EQUR: Equivariant Uncertainty Quantification and Refinement for Point Cloud Registration

Point cloud registration is a crucial task for robotics and mixed reality applications, serving as a foundational component for problems such as 3D reconstruction and localization. Arbitrary poses and real-world artifacts, including noise and occlusions, increase registration uncertainty and limit the performance of current point cloud registration algorithms. This paper proposes a novel, sampling-free uncertainty quantification and refinement method for point cloud registration, termed EQUR. To consistently predict uncertainty with high robustness, we extract equivariant point features, from which we regress an uncertainty score, enabling robust quantification of registration uncertainty. Subsequently, we leverage the estimated registration uncertainty as an auxiliary input to enhance the prediction of transformation refinement terms. We employ an introspective learning strategy to train EQUR based on the errors of a baseline registration model. Through quantitative and qualitative analyses on synthetic ShapeNet and real-world ScanObjectNN datasets, we showcase the effectiveness of EQUR, demonstrating both high accuracies in uncertainty quantification and uncertainty-aided refinement of point cloud registration.