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Simultaneous Convex Optimization of Regions and Region Parameters in Image Segmentation Models

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Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

This work develops a convex optimization framework for image segmentation models, where both the unknown regions and parameters describing each region are part of the optimization process. Convex relaxations and optimization algorithms are proposed, which produce results that are independent from the initializations and closely approximate global minima. We focus especially on problems where the data fitting term depends on the mean or median image intensity within each region. We also develop a convex relaxation for the piecewise constant Mumford-Shah model, where additionally the number of regions is unknown. The approach is based on optimizing a convex energy potential over functions defined over a space of one higher dimension than the image domain.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA, USA

    Egil Bae

  2. Computer Science Department, University of Western Ontario, London, ON, Canada

    Jing Yuan

  3. Department of Mathematics, University of Bergen, Bergen, Norway

    Xue-Cheng Tai

Authors
  1. Egil Bae
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  2. Jing Yuan
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  3. Xue-Cheng Tai
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Correspondence to Egil Bae .

Editor information

Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Bae, E., Yuan, J., Tai, XC. (2013). Simultaneous Convex Optimization of Regions and Region Parameters in Image Segmentation Models. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_19

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