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 a2 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.
Publication:
COMPUTER-AIDED DESIGN
http://dx.doi.org/10.1016/j.cad.2026.104104
Author:
Zhang, Jin
Beihang Univ, LMIB, Beijing, Peoples R China
Beihang Univ, Sch Math Sci, Beijing, Peoples R China
Email：jinzhang2022@buaa.edu.cn
Liu, Bing
Beihang Univ, LMIB, Beijing, Peoples R China
Beihang Univ, Sch Math Sci, Beijing, Peoples R China
Email：liubingksy@buaa.edu.cn
Zhao, Mingyang
Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing, Peoples R China
Univ Chinese Acad Sci, Beijing, Peoples R China
Email：zhaomingyang@amss.ac.cn
Jiang, Xin(corresponding author)
Beihang Univ, Sch Artificial Intelligence, Beijing Key Lab Artificial Intelligence Innovat &, Beijing, Peoples R China
Email：jiangxin@buaa.edu.cn
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