Mumford and shah model and its applications to image segmentation and image restoration

Leah Bar*, Tony F. Chan, Ginmo Chung, Miyoun Jung, Nahum Kiryati, Nir Sochen, Luminita A. Vese

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

10 Scopus citations


This chapter presents an overview of the Mumford and Shah model for image segmentation. It discusses its various formulations, some of its properties, the mathematical framework, and several approximations. It also presents numerical algorithms and segmentation results using the Ambrosio-Tortorelli phase-field approximations on one hand and level set formulations on the other hand. Several applications of the Mumford-Shah problem to image restoration are also presented.

Original languageEnglish (US)
Title of host publicationHandbook of Mathematical Methods in Imaging
Subtitle of host publicationVolume 1, Second Edition
PublisherSpringer New York
Number of pages59
ISBN (Electronic)9781493907908
ISBN (Print)9781493907892
StatePublished - Jan 1 2015
Externally publishedYes

ASJC Scopus subject areas

  • General Biochemistry, Genetics and Molecular Biology
  • General Computer Science
  • General Engineering
  • General Mathematics
  • General Medicine


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