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Main Authors: Pan, Jiangong, Wan, Wei, Bao, Chenlong, Shi, Zuoqiang
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2412.14746
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author Pan, Jiangong
Wan, Wei
Bao, Chenlong
Shi, Zuoqiang
author_facet Pan, Jiangong
Wan, Wei
Bao, Chenlong
Shi, Zuoqiang
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_14746
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Solving Unbalanced Optimal Transport on Point Cloud by Tangent Radial Basis Function Method
Pan, Jiangong
Wan, Wei
Bao, Chenlong
Shi, Zuoqiang
Mathematical Physics
Optimization and Control
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.
title Solving Unbalanced Optimal Transport on Point Cloud by Tangent Radial Basis Function Method
topic Mathematical Physics
Optimization and Control
url https://arxiv.org/abs/2412.14746