LapOT and RSC enable cluster-aware point cloud matching with robust alignments
New Laplacian Optimal Transport method aligns point clouds region-by-region, not point-by-point.
A new paper on arXiv (2607.16178) from Gabriel Samberg, YoonHaeng Hur, Yuehaw Khoo, and Nir Sharon tackles a common challenge in point cloud matching: when data points naturally form clusters but are interchangeable within regions, traditional point-to-point correspondence fails. Their solution, Laplacian Optimal Transport (LapOT), modifies the optimal transport objective by adding quadratic Laplacian regularization derived from similarity graphs of each point cloud. This encourages the transport plan to align entire clusters rather than individual points, yielding robust region-to-region alignments.
The authors also introduce Refined Simultaneous Clustering (RSC), which uses the cluster-aware coupling from LapOT to produce consistent partitions across both point sets. Unlike independent clustering, RSC leverages cross-set structure for more stable and interpretable results. Theoretical analysis and experiments on synthetic and real datasets demonstrate that LapOT+RSC outperforms standard optimal transport and independent clustering baselines, achieving meaningful alignments even with heavy noise or density variations.
- LapOT uses Laplacian regularization on similarity graphs to encourage cluster-aware transport couplings.
- Refined Simultaneous Clustering (RSC) produces consistent partitions across point sets using LapOT's coupling.
- Achieves robust region-to-region alignment without requiring point-level correspondence, ideal for noisy real-world data.
Why It Matters
Offers practical method for robust shape matching and data alignment, improving downstream tasks like registration and clustering.