When matching clustered point clouds, regularizing optimal transport with Laplacian terms from similarity graphs produces more meaningful alignments by respecting cluster structure instead of forcing precise point-to-point correspondence.
This paper proposes Laplacian Optimal Transport (LapOT), a method for matching point clouds that respects their cluster structure rather than forcing point-by-point alignment. By adding graph-based regularization to optimal transport, the approach finds region-to-region alignments that are more robust when points within clusters are interchangeable.