NDLI: Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems

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Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems

Content Provider	Scilit
Author	Bergmann, Ronny Herrmann, Marc Herzog, Roland Schmidt, Stephan Vidal-Núñez, José
Copyright Year	2020
Description	Journal: Inverse Problems An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element computations. The analysis of the functional is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. It is found to agree with the discrete total mean curvature known in discrete differential geometry. A split Bregman iteration is proposed for the solution of discretized shape optimization problems, in which the total variation of the normal appears as a regularizer. Unlike most other priors, such as surface area, the new functional allows for piecewise flat shapes. As two applications, a mesh denoising and a geometric inverse problem of inclusion detection type involving a partial differential equation are considered. Numerical experiments confirm that polyhedral shapes can be identified quite accurately.
Related Links	https://iopscience.iop.org/article/10.1088/1361-6420/ab6d5c/pdf
ISSN	02665611
e-ISSN	13616420
DOI	10.1088/1361-6420/ab6d5c
Journal	Inverse Problems
Issue Number	5
Volume Number	36
Language	English
Publisher	IOP Publishing
Publisher Date	2020-01-20
Access Restriction	Open
Subject Keyword	Journal: Inverse Problems Applied Mathematics Interdisciplinary Mathematics Total Variation of the Normal
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Signal Processing Mathematical Physics Computer Science Applications

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