Nonlocal Operators with Applications to Image Processing

We propose the use of nonlocal operators to define new types of flows and functionals for image processing and elsewhere. A main advantage over classical PDE-based algorithms is the ability to handle better textures and repetitive structures. This topic can be viewed as an extension of spectral grap...

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Bibliographic Details
Published inMultiscale modeling & simulation Vol. 7; no. 3; pp. 1005 - 1028
Main Authors Gilboa, Guy, Osher, Stanley
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Subjects
Algorithms
Control theory
Geometry
Graphs
Signal processing
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Summary:We propose the use of nonlocal operators to define new types of flows and functionals for image processing and elsewhere. A main advantage over classical PDE-based algorithms is the ability to handle better textures and repetitive structures. This topic can be viewed as an extension of spectral graph theory and the diffusion geometry framework to functional analysis and PDE-like evolutions. Some possible applications and numerical examples are given, as is a general framework for approximating Hamilton-Jacobi equations on arbitrary grids in high demensions, e.g., for control theory.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1540-3459
1540-3467
DOI:10.1137/070698592