Solving Unbalanced Optimal Transport on Point Cloud by Tangent Radial Basis Function Method
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915252843577344 |
|---|---|
| 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 |