Partial transport for point-cloud registration

Abstract Point cloud registration is an important task in fields like robotics, computer graphics, and medical imaging, involving the determination of spatial relationships between point sets in 3D space. Real-world challenges, such as non-rigid movements and partial visibility, including occlusions and sensor noise, make non-rigid registration particularly difficult. Traditional methods are often computationally intensive, exhibit unstable performance, and lack strong theoretical guarantees. Recently, the optimal transport problem, including its unbalanced variations like the optimal partial transport problem, has emerged as a powerful tool for point-cloud registration. These methods treat point clouds as empirical measures and provide a mathematically rigorous framework to quantify the correspondence between transformed source and target points. In this paper, we address the non-rigid registration problem using optimal transport theory and introduce a set of non-rigid registration methods based on the optimal partial transportation problem. Additionally, by leveraging efficient solutions to the one-dimensional optimal partial transport problem and extending them via slicing, we achieve significant computational efficiency, resulting in fast and robust registration algorithms. We validate our methods by comparing baselines on various 3D and 2D non-rigid registration problems with noisy point clouds.