{"ID":2893680,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.13530","arxiv_id":"2507.13530","title":"Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising","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.","short_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 piecewi...","url_abs":"https://arxiv.org/abs/2507.13530","url_pdf":"https://arxiv.org/pdf/2507.13530v2","authors":"[\"Lukas Baumgärtner\",\"Ronny Bergmann\",\"Roland Herzog\",\"Stephan Schmidt\",\"Manuel Weiß\"]","published":"2025-07-17T20:44:49Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"math.DG\",\"math.OC\"]","methods":"[]","has_code":false}