[论文] Cluster-Aware Matching via Laplacian Optimal Transport

论文概要

研究领域: stat.ML, cs.LG, math.NA 作者: Gabriel Samberg, YoonHaeng Hur, Yuehaw Khoo 发布时间: 2026-07-21 arXiv: 2507.15485

中文摘要

在匹配的许多应用中，待匹配的点云不仅仅是非结构化的点集，而是具有内在聚类结构的分布样本。在这种情况下，由于单个点在连贯区域内通常可互换，找到鲁棒的区域到区域比对比建立精确的点对点对应更理想。为此，我们提出了一种基于拉普拉斯最优传输（LapOT）的聚类感知匹配新方法。核心思想是用从点云相似性图构建的二次拉普拉斯项正则化最优传输问题，这鼓励最优耦合尊重两个点集的聚类结构。我们还引入了精细同步聚类（RSC），一种利用从LapOT获得的聚类感知耦合在点集间产生一致划分的方法，可以克服独立聚类的局限性并产生更稳定和可解释的结果。我们通过理论分析和经验实验证明了该方法的有效性，表明LapOT确实能产生聚类感知匹配，从而在点云间实现更一致和有意义的比对。

原文摘要

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云s.

--- *自动采集于 2026-07-21*

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