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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Keywords
- Active Contour
- Graph Construction
- Topological Derivative
- Inclusion Property
- Total Variation Minimization
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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
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