Total generalized variation of the normal vector field and applications to mesh denoising
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in ℝ3. The normal vector is considered as a manifold-valued function, taking values on the unit sphere. Our formulation extends previous discrete TGV mo...
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| Hauptverfasser: | , , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
March 2026
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| In: |
SIAM journal on imaging sciences
Year: 2026, Jahrgang: 19, Heft: 1, Pages: 584-611 |
| ISSN: | 1936-4954 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/25M1779437
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| Verfasserangaben: | Lukas Baumgärtner, Ronny Bergmann, Roland Herzog, Stephan Schmidt, and Manuel Weiß |
| Zusammenfassung: | We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in ℝ3. 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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| Beschreibung: | Online veröffentlicht: 17. März 2026 Gesehen am 29.04.2026 |
| Beschreibung: | Online Resource |
| ISSN: | 1936-4954 |