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An Efficient and Effective Tool for Image Segmentation, Total Variations and Regularization

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6667))

Abstract

One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. MRF formulates many total variation and other optimization criteria used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is not due to the power of the model. Rather it is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm.

We describe here an implementation of a very efficient polynomial time algorithm, which is provably fastest possible, delivering the optimal solution to the MRF problem, Hochbaum (2001). It is demonstrated here that many continuous models, common in image segmentation, have a discrete analogs to various special cases of MRF. As such they are solved optimally and efficiently, rather than with the use of continuous techniques such as PDE methods that can only guarantee convergence to a local minimum.

The MRF algorithm is enhanced here demonstrating that the set of labels can be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Modifications in the set of labels (colors), for instance, are executed instantaneously. Several theoretical results on the properties of the algorithm are proved here and are demonstrated for examples in the context of medical and biological imaging.

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Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA

    Dorit S. Hochbaum

Authors
  1. Dorit S. Hochbaum
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technion — Israel Institute of Technology, 718 Taub Building Technion, 32000, Haifa, Israel

    Alfred M. Bruckstein

  2. Department of Biomedical Engineering, Biomedical Image Analysis and Interpretation, Eindhoven University of Technology, Den Dolech 2 – WH 2.101, 5600 MB, Eindhoven, The Netherlands

    Bart M. ter Haar Romeny

  3. Faculaty of Engineering, School of Electrical Engineering, Tel Aviv University, Ramat Aviv, 69978, Israel

    Alexander M. Bronstein

  4. Institute of Computationa Science, Faculty of Informatics SI-109, Università della Svizzera Italiana, Via Giuseppe Buffi 13, 6904, Lugano, Switzerland

    Michael M. Bronstein

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© 2012 Springer-Verlag Berlin Heidelberg

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Hochbaum, D.S. (2012). An Efficient and Effective Tool for Image Segmentation, Total Variations and Regularization. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_29

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  • DOI: https://doi.org/10.1007/978-3-642-24785-9_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24784-2

  • Online ISBN: 978-3-642-24785-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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