### Abstract

Original language | English |
---|---|

Pages (from-to) | 611-666 |

Journal | Numerische Mathematik |

Publication status | Published - 2019 |

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### Cite this

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

Research output: Contribution to journal › Article › Research › peer-review

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TY - JOUR

T1 - Total roto-translational variation

AU - Antonin, Chambolle

AU - Pock, Thomas

PY - 2019

Y1 - 2019

N2 - 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 …

AB - 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 …

M3 - Article

SP - 611

EP - 666

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

ER -