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arXiv · 2507.13530

Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising

Lukas Baumgärtner·Ronny Bergmann·Roland Herzog·Stephan Schmidt·Manuel Weiß
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Abstract

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.

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Lukas Baumgärtner, Ronny Bergmann, Roland Herzog, Stephan Schmidt, Manuel Weiß. 2025-07-17. Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising. https://arxiv.org/abs/2507.13530

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