Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport

2026-06-15 · Source: Computer Vision and Pattern Recognition · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, quick

Summary

Sinkhorn-CPD is a novel method for robust rigid point cloud registration, addressing limitations of the widely used Coherent Point Drift (CPD) algorithm. CPD struggles with heavy outliers and partial overlap because its target-side marginal constraint forces all observations, including noise, to receive unit probability mass. Sinkhorn-CPD overcomes this by replacing CPD's constraint with dual Kullback-Leibler penalties, allowing the algorithm to effectively discard outliers from both point clouds. This formulation creates a fully unbalanced entropic optimal transport problem, efficiently solved using generalized Sinkhorn iterations. Crucially, Sinkhorn-CPD maintains CPD's closed-form Procrustes and variance updates. Its variance parameter, sigma^2, functions as an automatic entropic regularization parameter, providing an annealing schedule from diffuse to sharp correspondences without requiring manual temperature tuning. Benchmark experiments across synthetic, cross-category, and scan-to-CAD datasets confirm Sinkhorn-CPD achieves high accuracy and strong robustness against outliers and partial overlap.

Key takeaway

For Computer Vision Engineers developing robust 3D perception systems, particularly those dealing with noisy or partially occluded point cloud data, you should consider integrating Sinkhorn-CPD. This method offers superior registration accuracy and strong robustness to outliers and partial overlap, eliminating the need for manual annealing schedule tuning. Its automatic variance-based regularization simplifies deployment and improves reliability compared to traditional CPD or other optimal transport approaches.

Key insights

Sinkhorn-CPD uses unbalanced entropic optimal transport with dual KL penalties for robust point cloud registration, automatically handling outliers and partial overlap.

Principles

• Unbalanced optimal transport handles missing data.
• Dual KL penalties enable outlier rejection.
• Variance parameter can automate annealing.

Method

Sinkhorn-CPD replaces CPD's target-side marginal constraint with dual Kullback-Leibler penalties, formulating an unbalanced entropic optimal transport problem. This is solved via generalized Sinkhorn iterations, preserving CPD's Procrustes and variance updates.

In practice

• Apply to cross-category point cloud alignment.
• Use for scan-to-CAD model registration.
• Improve robustness in outlier-heavy datasets.

Topics

• Point Cloud Registration
• Optimal Transport
• Sinkhorn Algorithm
• Outlier Rejection
• 3D Computer Vision
• Unbalanced Transport

Best for: Research Scientist, AI Scientist, Computer Vision Engineer, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Computer Vision and Pattern Recognition.