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A Note on the Discrete Binary Mumford-Shah Model

  • Conference paper
Book cover Computer Vision/Computer Graphics Collaboration Techniques (MIRAGE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4418))

Abstract

This paper is concerned itself with the analysis of the two-phase Mumford-Shah model also known as the active contour without edges model introduced by Chan and Vese. It consists of approximating an observed image by a piecewise constant image which can take only two values. First we show that this model with the L 1-norm as data fidelity yields a contrast invariant filter which is a well known property of morphological filters. Then we consider a discrete version of the original problem. We show that an inclusion property holds for the minimizers. The latter is used to design an efficient graph-cut based algorithm which computes an exact minimizer. Some preliminary results are presented.

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Authors and Affiliations

  1. Department of Mathematics, University of California (UCLA), Los Angeles, CA Box 90095, USA

    Jérôme Darbon

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  1. Jérôme Darbon
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André Gagalowicz Wilfried Philips

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Darbon, J. (2007). A Note on the Discrete Binary Mumford-Shah Model. In: Gagalowicz, A., Philips, W. (eds) Computer Vision/Computer Graphics Collaboration Techniques. MIRAGE 2007. Lecture Notes in Computer Science, vol 4418. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71457-6_26

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  • DOI: https://doi.org/10.1007/978-3-540-71457-6_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71456-9

  • Online ISBN: 978-3-540-71457-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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