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

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Handbook of Mathematical Methods in Imaging

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.

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Authors and Affiliations

  1. Department of Mathematics, Tel Aviv University, Minneapolis, MN, USA

    Leah Bar

  2. Office of the President, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

    Tony F. Chan

  3. Los Angeles, CA, United States

    Ginmo Chung

  4. Department of Mathematics, Hankuk University of Foreign Studies, Los Angeles, CA, USA

    Miyoun Jung & Luminita A. Vese

  5. Tel Aviv University, Tel Aviv, Israel

    Nahum Kiryati & Nir Sochen

Authors
  1. Leah Bar
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  2. Tony F. Chan
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  3. Ginmo Chung
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  4. Miyoun Jung
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  5. Luminita A. Vese
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  6. Nahum Kiryati
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  7. Nir Sochen
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Correspondence to Leah Bar .

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  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Bar, L. et al. (2015). Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_25

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