Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909866827710464 |
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| author | Baumgärtner, Lukas Bergmann, Ronny Herzog, Roland Schmidt, Stephan Weiß, Manuel |
| author_facet | Baumgärtner, Lukas Bergmann, Ronny Herzog, Roland Schmidt, Stephan Weiß, Manuel |
| contents | We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on the unit sphere. Our formulation extends previous discrete TGV models for piecewise constant scalar data that utilize a Raviart-Thomas function space. To extend this formulation to the manifold setting, a tailor-made tangential Raviart-Thomas type finite element space is constructed in this work. The new regularizer is compared to existing methods in mesh denoising experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_13530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising Baumgärtner, Lukas Bergmann, Ronny Herzog, Roland Schmidt, Stephan Weiß, Manuel Computer Vision and Pattern Recognition Differential Geometry Optimization and Control We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on the unit sphere. Our formulation extends previous discrete TGV models for piecewise constant scalar data that utilize a Raviart-Thomas function space. To extend this formulation to the manifold setting, a tailor-made tangential Raviart-Thomas type finite element space is constructed in this work. The new regularizer is compared to existing methods in mesh denoising experiments. |
| title | Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising |
| topic | Computer Vision and Pattern Recognition Differential Geometry Optimization and Control |
| url | https://arxiv.org/abs/2507.13530 |