Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images

Martin Burger; Lin He; Carola-Bibiane Schönlieb

doi:10.1137/080728548

Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images

Martin Burger, Lin He, Carola-Bibiane Schönlieb

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

129 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1129-1167
Number of pages	39
Journal	SIAM Journal on Imaging Sciences
Volume	2
Issue number	4
DOIs	https://doi.org/10.1137/080728548
State	Published - Jan 2009
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1137/080728548

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title = "Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images",

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.",

author = "Martin Burger and Lin He and Carola-Bibiane Sch{\"o}nlieb",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2009",

month = jan,

doi = "10.1137/080728548",

language = "English (US)",

volume = "2",

pages = "1129--1167",

journal = "SIAM Journal on Imaging Sciences",

issn = "1936-4954",

publisher = "Society for Industrial and Applied Mathematics Publications",

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AU - He, Lin

AU - Schönlieb, Carola-Bibiane

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N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/597702

UR - http://epubs.siam.org/doi/10.1137/080728548

UR - http://www.scopus.com/inward/record.url?scp=84904732030&partnerID=8YFLogxK

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DO - 10.1137/080728548

M3 - Article

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EP - 1167

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

IS - 4

ER -

Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images

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