这篇论文用拉普拉斯最优传输让点云匹配自动感知聚类结构，还附带一个同步聚类方法RSC，适合做形状匹配或聚类对齐的同行参考。
该论文提出了一种名为拉普拉斯最优传输（LapOT）的聚类感知匹配方法，核心是对最优传输问题添加基于相似图的二次拉普拉斯正则项，促使耦合矩阵尊重两个点集的聚类结构。作者还提出精细化同步聚类（RSC）方法，利用LapOT得到的聚类感知耦合生成跨点集的一致分区。实验证明，LapOT能产生比独立聚类更稳定、可解释的对齐结果。
Cluster-Aware Matching via Laplacian Optimal Transport
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.