Color image restoration using nonlocal Mumford-Shah regularizers

Miyoun Jung*, Xavier Bresson, Tony F. Chan, Luminita A. Vese

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations


We introduce several color image restoration algorithms based on the Mumford-Shah model and nonlocal image information. The standard Ambrosio-Tortorelli and Shah models are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, textures are not local in nature and require semi-local/non-local information to be denoised efficiently. Inspired from recent work (NL-means of Buades, Coll, Morel and NL-TV of Gilboa, Osher), we extend the standard models of Ambrosio-Tortorelli and Shah approximations to Mumford-Shah functionals to work with nonlocal information, for better restoration of fine structures and textures. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, and color image super-resolution. In the formulation of nonlocal variational models for the image deblurring with impulse noise, we propose an efficient preprocessing step for the computation of the weight function w. In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. Experimental results and comparisons between the proposed nonlocal methods and the local ones are shown.

Original languageEnglish (US)
Title of host publicationEnergy Minimization Methods in Computer Vision and Pattern Recognition - 7th International Conference, EMMCVPR 2009, Proceedings
Number of pages15
StatePublished - 2009
Externally publishedYes
Event7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2009 - Bonn, Germany
Duration: Aug 24 2009Aug 27 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5681 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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