SIGMAR-3D: scale-invariant guaranteed monotone accurate registration for 3D scenes

Abstract SIGMAR-3D is a training-free framework for robust pairwise 3D point-cloud registration. It combines a handcrafted local descriptor, SIGMA, with a scene-adaptive coarse-to-fine registration stage, R-3D. SIGMA builds a repeatable local reference frame at each keypoint and aggregates spatial-angular geometric cues within a spherical support, producing a compact rotation-normalized descriptor without any learning. R-3D forms tentative correspondences by descriptor matching, estimates a coarse pose using robust hypothesis verification, and refines the alignment on a voxel pyramid with generalized ICP and robust losses. Key support radii, matching gates, and refinement thresholds are tied to local spacing statistics and overlap-related heuristic signals, enabling a single configuration to transfer across indoor RGB-D and outdoor LiDAR data. Monotone decrease of the trimmed-RMSE refinement objective is enforced through an acceptance rule that accepts an update only when that objective decreases. On standard benchmarks, SIGMAR-3D achieves 84.3% FMR and 79.0% registration recall on 3DMatch, and 72.7% FMR on ETH. These results position SIGMAR-3D as a practical and competitive training-free alternative when retraining, domain-specific supervision, or model maintenance is undesirable.