Numerical Implementation of the Ambrosio-Tortorelli Functional Using Discrete Calculus and Application to Image Restoration and Inpainting View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017

AUTHORS

Marion Foare , Jacques-Olivier Lachaud , Hugues Talbot

ABSTRACT

The Mumford-Shah (MS) functional is one of the most influential variational model in image segmentation, restoration, and cartooning. Difficult to solve, the Ambrosio-Tortorelli (AT) functional is of particular interest, because minimizers of AT can be shown to converge to a minimizer of MS. This paper takes an interest in a new method for numerically solving the AT model [11]. This method formulates the AT functional in a discrete calculus setting, and by this way is able to capture the set of discontinuities as a one-dimensional set. It is also shown that this model is competitive with total variation restoration methods. We present here the discrete AT models in details, and compare its merit with recent convex relaxations of AT and MS functionals. We also examine the potential of this model for inpainting, and describe its implementation in the DGtal library, an open-source project. More... »

PAGES

91-103

Book

TITLE

Reproducible Research in Pattern Recognition

ISBN

978-3-319-56413-5
978-3-319-56414-2

From Grant

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-56414-2_7

DOI

http://dx.doi.org/10.1007/978-3-319-56414-2_7

DIMENSIONS

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