Work

Solving Unbalanced Optimal Transport on Point Cloud by Tangent Radial Basis Function Method

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2412.14746

Authors: Pan, Jiangong, Wan, Wei, Bao, Chenlong, Shi, Zuoqiang

Institutions: Tsinghua University, North China Electric Power University, Beijing Institute of Mathematical Sciences and Applications

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1951465523, G2485535630

OpenAlex ID: W4405634153

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