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

doi:10.1007/978-1-4939-0790-8_25

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 proceeding › Chapter › peer-review

11 Scopus citations

Abstract

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 language	English (US)
Title of host publication	Handbook of Mathematical Methods in Imaging
Subtitle of host publication	Volume 1, Second Edition
Publisher	Springer New York
Pages	1539-1597
Number of pages	59
ISBN (Electronic)	9781493907908
ISBN (Print)	9781493907892
DOIs	https://doi.org/10.1007/978-1-4939-0790-8_25
State	Published - Jan 1 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media New York 2011, 2015.

ASJC Scopus subject areas

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

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10.1007/978-1-4939-0790-8_25

Cite this

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AU - Vese, Luminita A.

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AB - 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.

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

Abstract

Bibliographical note

ASJC Scopus subject areas

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