Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images

Handle URI:
http://hdl.handle.net/10754/597702
Title:
Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images
Authors:
Burger, Martin; He, Lin; Schönlieb, Carola-Bibiane
Abstract:
The Cahn–Hilliard equation is a nonlinear fourth order diffusion equation originating in material science for modeling phase separation and phase coarsening in binary alloys. The inpainting of binary images using the Cahn–Hilliard equation is a new approach in image processing. In this paper we discuss the stationary state of the proposed model and introduce a generalization for grayvalue images of bounded variation. This is realized by using subgradients of the total variation functional within the flow, which leads to structure inpainting with smooth curvature of level sets.
Citation:
Burger M, He L, Schönlieb C-B (2009) Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images. SIAM Journal on Imaging Sciences 2: 1129–1167. Available: http://dx.doi.org/10.1137/080728548.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Imaging Sciences
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jan-2009
DOI:
10.1137/080728548
Type:
Article
ISSN:
1936-4954
Sponsors:
This work was partially supported by the WWTF (Wiener Wissenschafts-, Forschungs- und Technologiefonds) project CI06 003, by the FFG project Erarbeitung neuer Algorithmen zum Image Inpainting project 813610, and the Ph.D. program Wissenschaftskolleg taking place at the University of Vienna. Further, this publication is based on work supported by award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorBurger, Martinen
dc.contributor.authorHe, Linen
dc.contributor.authorSchönlieb, Carola-Bibianeen
dc.date.accessioned2016-02-25T12:44:42Zen
dc.date.available2016-02-25T12:44:42Zen
dc.date.issued2009-01en
dc.identifier.citationBurger M, He L, Schönlieb C-B (2009) Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images. SIAM Journal on Imaging Sciences 2: 1129–1167. Available: http://dx.doi.org/10.1137/080728548.en
dc.identifier.issn1936-4954en
dc.identifier.doi10.1137/080728548en
dc.identifier.urihttp://hdl.handle.net/10754/597702en
dc.description.abstractThe Cahn–Hilliard equation is a nonlinear fourth order diffusion equation originating in material science for modeling phase separation and phase coarsening in binary alloys. The inpainting of binary images using the Cahn–Hilliard equation is a new approach in image processing. In this paper we discuss the stationary state of the proposed model and introduce a generalization for grayvalue images of bounded variation. This is realized by using subgradients of the total variation functional within the flow, which leads to structure inpainting with smooth curvature of level sets.en
dc.description.sponsorshipThis work was partially supported by the WWTF (Wiener Wissenschafts-, Forschungs- und Technologiefonds) project CI06 003, by the FFG project Erarbeitung neuer Algorithmen zum Image Inpainting project 813610, and the Ph.D. program Wissenschaftskolleg taking place at the University of Vienna. Further, this publication is based on work supported by award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.titleCahn–Hilliard Inpainting and a Generalization for Grayvalue Imagesen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Imaging Sciencesen
dc.contributor.institutionInstitut fur Numerische und Angewandte Mathematik, Fachbereich Mathematik und Informatik, Westfalische Wilhelms Universitat (WWU) Munster, Einsteinstrasse 62, D-48149 Munster, Germanyen
kaust.grant.numberKUK-I1-007-43en
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