Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport
2026-06-15 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors identify a problem in a popular method called Coherent Point Drift (CPD) for matching 3D points, which struggles when there are many outliers or partial matches. They propose a new method, Sinkhorn-CPD, that uses a technique from optimal transport theory to better ignore unmatched points on both sides. Their approach keeps the efficient updates of CPD but improves robustness without needing manual tuning. Tests show their method works well across different scenarios with noisy or incomplete data.
Coherent Point Driftpoint cloud registrationoptimal transportunbalanced optimal transportSinkhorn iterationsKullback-Leibler divergenceProcrustes analysisentropic regularizationannealing scheduleoutliers
Authors
Jin Zhang, Mingyang Zhao, Bing Liu, Xin Jiang
Abstract
Coherent Point Drift (CPD) is widely used for rigid point cloud registration because of its soft correspondences and closed-form parameter updates. However, CPD's target-side marginal constraint forces every observation, including outliers, to receive exactly unit probability mass. This assumption degrades registration accuracy under heavy outliers and partial overlap. Optimal transport (OT) methods can handle missing mass through unbalanced formulations, but require hand-tuned annealing schedules. In this paper, we propose Sinkhorn-CPD, which replaces CPD's target-side marginal constraint with dual Kullback-Leibler penalties, allowing the algorithm to discard outliers on both sides. The resulting formulation is a fully unbalanced entropic optimal transport problem, which can be efficiently solved by generalized Sinkhorn iterations. Moreover, Sinkhorn-CPD preserves the closed-form Procrustes and variance updates of CPD. In our method, the variance sigma^2 plays the role of the entropic regularization parameter, which induces an automatic annealing schedule from diffuse to sharp correspondences without manual temperature tuning. Experiments on synthetic, cross-category, and scan-to-CAD benchmarks show that Sinkhorn-CPD achieves state-of-the-art accuracy, with strong robustness to outliers and partial overlap.