Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration

Leah Bar (), Tony F. Chan (), Ginmo Chung, Miyoun Jung (), Luminita A. Vese, Nahum Kiryati () and Nir Sochen
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Leah Bar: Tel Aviv University, Department of Mathematics
Tony F. Chan: Office of the President, Hong Kong University of Science and Technology
Miyoun Jung: Hankuk University of Foreign Studies, Department of Mathematics
Luminita A. Vese: Hankuk University of Foreign Studies, Department of Mathematics
Nahum Kiryati: Tel Aviv University
Nir Sochen: Tel Aviv University

A chapter in Handbook of Mathematical Methods in Imaging, 2015, pp 1539-1597 from Springer

Abstract: 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.

Date: 2015
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DOI: 10.1007/978-1-4939-0790-8_25

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