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Mumford and Shah Model and its Applications to Image Segmentation andImage Restoration

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Handbook of Mathematical Methods in Imaging

Abstract

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

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Author information

Authors and Affiliations

  1. University of Minnesota, Minnesota, USA

    Leah Bar

  2. University of California Los Angeles, Los Angeles, CA, USA

    Tony F. Chan

  3. Nanyang Technological University, Singapore, Singapore

    Ginmo Chung

  4. University of California Los Angeles, Los Angeles, CA, USA

    Miyoun Jung

  5. Tel Aviv University, Tel Aviv, Israel

    Nahum Kiryati

  6. University of California Los Angeles, Los Angeles, CA, USA

    Rami Mohieddine

  7. Tel Aviv University, Tel Aviv, Israel

    Nir Sochen

  8. University of California Los Angeles, Los Angeles, CA, USA

    Luminita A. Vese

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. Nahum Kiryati
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  6. Rami Mohieddine
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  7. Nir Sochen
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  8. Luminita A. Vese
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Editors and Affiliations

  1. Computational Science Center, University of Vienna, Nordbergstrasse 15, Vienna, Austria

    Otmar Scherzer

  2. RICAM, Austrian Academy of Sciences, Linz, Austria

    Otmar Scherzer

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Bar, L. et al. (2011). Mumford and Shah Model and its Applications to Image Segmentation andImage Restoration. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92920-0_25

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