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A spatially continuous max-flow and min-cut framework for binary labeling problems

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Abstract

We propose and investigate novel max-flow models in the spatially continuous setting, with or without i priori defined supervised constraints, under a comparative study of graph based max-flow/min-cut. We show that the continuous max-flow models correspond to their respective continuous min-cut models as primal and dual problems. In this respect, basic conceptions and terminologies from discrete max-flow/min-cut are revisited under a new variational perspective. We prove that the associated nonconvex partitioning problems, unsupervised or supervised, can be solved globally and exactly via the proposed convex continuous max-flow and min-cut models. Moreover, we derive novel fast max-flow based algorithms whose convergence can be guaranteed by standard optimization theories. Experiments on image segmentation, both unsupervised and supervised, show that our continuous max-flow based algorithms outperform previous approaches in terms of efficiency and accuracy.

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Acknowledgments

This research has been supported by Natural Sciences and Engineering Research Council of Canada (NSERC) Accelerator Grant R3584A04, the Norwegian Research Council eVita project 166075 and eVita project 214889.

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Authors and Affiliations

  1. Computer Science Department, Middlesex College, University of Western Ontarion, London, ON, N6A 5B7, Canada

    Jing Yuan & Yuri Boykov

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

    Egil Bae

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

    Xue-Cheng Tai

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  1. Jing Yuan
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  2. Egil Bae
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  3. Xue-Cheng Tai
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  4. Yuri Boykov
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Correspondence to Xue-Cheng Tai.

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Yuan, J., Bae, E., Tai, XC. et al. A spatially continuous max-flow and min-cut framework for binary labeling problems. Numer. Math. 126, 559–587 (2014). https://doi.org/10.1007/s00211-013-0569-x

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