Total roto-translational variation

Chambolle Antonin, Thomas Pock

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We consider curvature depending variational models for image regularization, such as Euler’s elastica. These models are known to provide strong priors for the continuity of edges and hence have important applications in shape- and image processing. We consider a lifted convex representation of these models in the roto-translation space: in this space, curvature depending variational energies are represented by means of a convex functional defined on divergence free vector fields. The line energies are then easily extended to any scalar function. It yields a natural generalization of the total variation to curvature-dependent energies. As our main result, we show that the proposed convex representation is tight for characteristic functions of smooth shapes. We also discuss cases where this representation fails. For numerical solution, we propose a staggered grid discretization based on an averaged Raviart …
Original languageEnglish
Pages (from-to)611-666
JournalNumerische Mathematik
Publication statusPublished - 2019

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Curvature
Energy
Divergence-free Vector Fields
Elastica
Variational Model
Staggered Grid
Total Variation
Characteristic Function
Image Processing
Regularization
Image processing
Discretization
Numerical Solution
Scalar
Dependent
Line
Model
Generalization

Cite this

Total roto-translational variation. / Antonin, Chambolle; Pock, Thomas.

In: Numerische Mathematik, 2019, p. 611-666.

Research output: Contribution to journalArticleResearchpeer-review

Antonin, Chambolle ; Pock, Thomas. / Total roto-translational variation. In: Numerische Mathematik. 2019 ; pp. 611-666.
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