Levy-Driven Correspondence Estimation for Registration

2026-09-26

AI Summary

This study addresses the high computational cost and limited accuracy of iterative refinement in low-overlap, non-rigid point cloud matching by proposing a Lévy-driven match refinement method. The approach optimizes soft correspondence matrices via stochastic jumps and Gamma clocks, introducing a novel fixed pre-loaded Gamma time allocation strategy to enhance early-stage update efficiency. Furthermore, it integrates geometric feedback from deep networks with explicit formulations of Brownian reference bridges to achieve precise corrections. A key contribution is that the method significantly boosts the performance of existing models without requiring retraining. Evaluated on the 4DMatch dataset, the proposed approach attains a non-rigid feature matching recall of 93.09%, substantially outperforming state-of-the-art methods.

Abstract

Finding reliable point correspondences is difficult when point clouds have low overlap or undergo non-rigid deformation. Iterative refinement can correct uncertain matches, but costly network evaluations limit the number of updates. We present LevyMatch, a L\'evy-driven method that uses random jumps to refine a soft matching matrix. At each step, a network uses the current matching state and geometric information to predict a target matching matrix. A Brownian reference bridge gives an explicit formula for the update toward this target. A Gamma random clock sets the time step for each update. The updated matches provide new geometric feedback for the next target prediction. We further propose a fixed front-loaded Gamma policy that assigns more expected clock time to early updates and less to later ones, without retraining or extra network evaluations. Reordering the same sampled Gamma increments shows that placing larger increments early gives higher accuracy than placing them late. On 4DMatch and 4DLoMatch, our method improves both non-rigid feature matching recall (NFMR) and inlier ratio (IR) over the compared methods. The front-loaded policy achieves 93.09% NFMR and 92.11% IR on 4DMatch, and 82.79% NFMR and 79.07% IR on 4DLoMatch.

Problem

• point cloud registration
• correspondence estimation
• non-rigid deformation
• low overlap
• iterative refinement

Innovation

• Lévy-driven correspondence estimation
• soft matching matrix refinement
• Brownian reference bridge
• front-loaded Gamma policy
• non-rigid point cloud registration