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Solving unbalanced optimal transport on point cloud by tangent radial basis function method.

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Titel: Solving unbalanced optimal transport on point cloud by tangent radial basis function method.
Autoren: Pan, Jiangong1 (AUTHOR) mathpjg@sina.com, Wan, Wei2 (AUTHOR) weiwan@ncepu.edu.cn, Bao, Chenlong3,4 (AUTHOR) clbao@tsinghua.edu.cn, Shi, Zuoqiang1,3,4 (AUTHOR) zqshi@tsinghua.edu.cn
Quelle: Computers & Mathematics with Applications. Oct2025, Vol. 195, p161-176. 16p.
Schlagwörter: *POINT cloud, *RADIAL basis functions, *POISSON'S equation, *COMPUTER simulation, *GEOMETRY, *TOPOLOGY, *OPTIMIZATION algorithms
Abstract: In this paper, we solve unbalanced optimal transport (UOT) problem on surfaces represented by point clouds. Based on alternating direction method of multipliers algorithm, the original UOT problem can be solved by an iteration consists of three steps. The key ingredient is to solve a Poisson equation on point cloud which is solved by tangent radial basis function (TRBF) method. The proposed TRBF method requires only the point cloud and normal vectors to discretize the Poisson equation which simplify the computation significantly. Numerical experiments conducted on point clouds with varying geometry and topology demonstrate the effectiveness of the proposed method. • This work presents an efficient approach to solve the UOT problem on point cloud surfaces using the ADMM, breaking the problem into three iterative steps for robust computation. • The key computational step involves solving a Poisson equation on point clouds, achieved through a novel tangent RBF method that avoids traditional mesh dependency, enabling accurate and flexible discretization. • The proposed TRBF method only requires point cloud data and normal vectors, significantly reducing preprocessing complexity while maintaining high computational efficiency for UOT problems. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:In this paper, we solve unbalanced optimal transport (UOT) problem on surfaces represented by point clouds. Based on alternating direction method of multipliers algorithm, the original UOT problem can be solved by an iteration consists of three steps. The key ingredient is to solve a Poisson equation on point cloud which is solved by tangent radial basis function (TRBF) method. The proposed TRBF method requires only the point cloud and normal vectors to discretize the Poisson equation which simplify the computation significantly. Numerical experiments conducted on point clouds with varying geometry and topology demonstrate the effectiveness of the proposed method. • This work presents an efficient approach to solve the UOT problem on point cloud surfaces using the ADMM, breaking the problem into three iterative steps for robust computation. • The key computational step involves solving a Poisson equation on point clouds, achieved through a novel tangent RBF method that avoids traditional mesh dependency, enabling accurate and flexible discretization. • The proposed TRBF method only requires point cloud data and normal vectors, significantly reducing preprocessing complexity while maintaining high computational efficiency for UOT problems. [ABSTRACT FROM AUTHOR]
ISSN:08981221
DOI:10.1016/j.camwa.2025.07.015