Introduction to algorithms
Network flows: theory, algorithms, and applications
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Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Fast Approximate Energy Minimization via Graph Cuts
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A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
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ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?
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An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
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Image Analysis and Mathematical Morphology
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Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
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Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability)
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Total variation minimization and a class of binary MRF models
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A fast and exact algorithm for total variation minimization
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Perfect sampling: a review and applications to signal processing
IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Efficient Global Minimization for the Multiphase Chan-Vese Model of Image Segmentation
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
An active surface model for volumetric image segmentation
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
Computer Vision and Image Understanding
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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 L1-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.