A Well-Posedness Framework for Inpainting Based on Coherence Transport

Thomas März

doi:10.1007/s10208-014-9199-7

A Well-Posedness Framework for Inpainting Based on Coherence Transport

Thomas März

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

8 Scopus citations

Abstract

Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278, 2007) introduced a very efficient method, called image inpainting based on coherence transport, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.

Original language	English (US)
Pages (from-to)	973-1033
Number of pages	61
Journal	Foundations of Computational Mathematics
Volume	15
Issue number	4
DOIs	https://doi.org/10.1007/s10208-014-9199-7
State	Published - Apr 23 2014
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-07
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The author would like to thank Folkmar Bornemann and Colin Macdonald for their advice and the inspiring discussions. This work was supported in part by the Graduiertenkolleg Angewandte Algorithmische Mathematik (GKAAM) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Technische Universität München (TUM), and by Award KUK-C1-013-04 granted by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Computational Theory and Mathematics
Computational Mathematics
Theoretical Computer Science
Applied Mathematics
General Mathematics

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10.1007/s10208-014-9199-7

Cite this

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title = "A Well-Posedness Framework for Inpainting Based on Coherence Transport",

abstract = "Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and M{\"a}rz (J Math Imaging Vision, 28:259–278, 2007) introduced a very efficient method, called image inpainting based on coherence transport, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.",

author = "Thomas M{\"a}rz",

note = "KAUST Repository Item: Exported on 2022-06-07 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: The author would like to thank Folkmar Bornemann and Colin Macdonald for their advice and the inspiring discussions. This work was supported in part by the Graduiertenkolleg Angewandte Algorithmische Mathematik (GKAAM) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Technische Universit{\"a}t M{\"u}nchen (TUM), and by Award KUK-C1-013-04 granted by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1007/s10208-014-9199-7",

language = "English (US)",

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N2 - Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278, 2007) introduced a very efficient method, called image inpainting based on coherence transport, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.

AB - Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278, 2007) introduced a very efficient method, called image inpainting based on coherence transport, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.

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A Well-Posedness Framework for Inpainting Based on Coherence Transport

Abstract

Bibliographical note

ASJC Scopus subject areas

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