Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866916590990131200 |
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| author | Baumgärtner, Lukas Bergmann, Ronny Herzog, Roland Schmidt, Stephan Vidal-Núñez, José Weiß, Manuel |
| author_facet | Baumgärtner, Lukas Bergmann, Ronny Herzog, Roland Schmidt, Stephan Vidal-Núñez, José Weiß, Manuel |
| contents | We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving important features such as sharp edges. A discrete variant of the total variation of the unit normal vector field serves as a regularizing functional to achieve these goals. In order to solve the resulting problem, we use a version of the split Bregman (ADMM) iteration adapted to the problem. A new formulation of the total variation regularizer, as well as the use of an inexact Newton method for the shape optimization step, bring significant speed-up compared to earlier methods. Numerical examples are included, demonstrating the performance of our algorithm with some complex 3D geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_11748 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach Baumgärtner, Lukas Bergmann, Ronny Herzog, Roland Schmidt, Stephan Vidal-Núñez, José Weiß, Manuel Numerical Analysis Computational Geometry We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving important features such as sharp edges. A discrete variant of the total variation of the unit normal vector field serves as a regularizing functional to achieve these goals. In order to solve the resulting problem, we use a version of the split Bregman (ADMM) iteration adapted to the problem. A new formulation of the total variation regularizer, as well as the use of an inexact Newton method for the shape optimization step, bring significant speed-up compared to earlier methods. Numerical examples are included, demonstrating the performance of our algorithm with some complex 3D geometries. |
| title | Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach |
| topic | Numerical Analysis Computational Geometry |
| url | https://arxiv.org/abs/2012.11748 |