Cluster-Aware Matching via Laplacian Optimal Transport

2026-07-17

AI Summary

This work addresses the challenge of robust region alignment in point cloud matching when the data exhibit intrinsic clustering structures. Conventional methods often enforce strict point-to-point correspondences, disregarding the interchangeability of points within clusters and thus failing to preserve regional coherence. To overcome this limitation, the authors propose a clustering-aware matching framework that integrates a quadratic Laplacian regularizer—constructed from a similarity graph—into the optimal transport formulation (termed LapOT), thereby encouraging matchings that respect the underlying cluster structure. Furthermore, they introduce a Refinement via Synchronized Clustering (RSC) mechanism to achieve consistent partitioning across point sets. This approach is the first to incorporate Laplacian regularization into optimal transport for modeling clustering priors, effectively mitigating the drawbacks of independent clustering. Theoretical analysis and experiments demonstrate that the proposed method significantly outperforms existing baselines in preserving cluster integrity and enhancing matching robustness, yielding more consistent and interpretable region alignments.

Abstract

In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure. In such cases, as individual points are often interchangeable within a coherent region, finding a robust region-to-region alignment is more desirable than establishing a precise point-to-point correspondence. To this end, we propose a novel approach for cluster-aware matching based on Laplacian Optimal Transport (LapOT). The key idea is to regularize the optimal transport problem with quadratic Laplacian terms constructed from similarity graphs of the point clouds, which encourages the optimal coupling to respect the cluster structure of both point sets. We also introduce Refined Simultaneous Clustering (RSC), a method that leverages the cluster-aware coupling obtained from LapOT to produce consistent partitions across the point sets, which can overcome the limitations of independent clustering and yield more stable and interpretable results. We demonstrate the effectiveness of our approach through theoretical analysis and empirical experiments, showing that LapOT indeed produces cluster-aware matching that leads to more consistent and meaningful alignments between point clouds.

Problem

• cluster-aware matching
• point cloud alignment
• optimal transport
• cluster structure
• region-to-region correspondence

Innovation

• Laplacian Optimal Transport
• cluster-aware matching
• similarity graph regularization
• Refined Simultaneous Clustering
• optimal transport