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Split Bregman Method for Minimization of Fast Multiphase Image Segmentation Model for Inhomogeneous Images

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Abstract

In this paper, we present a fast multiphase image segmentation model in a variational level set formulation. The proposed model is mainly used for images with inhomogeneity. The newly defined energy functional combines the local intensity information, the global intensity information, and the edge information to deal with the inhomogeneity. We use a weight function varying with locations to control the force of the local and global information dynamically. The special structure of the new energy functional ensures that the split Bregman method can be used for fast minimization. We apply the split Bregman method to minimize the new energy functional and summarize important results in several theorems. Theoretical evidences for these results are given. Several numerical results are also presented.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 61301208), China Postdoctoral Science Foundation (No. 2013M531018), Natural Science Foundation Project of Guangdong (No. S2013040016230) and Shenzhen Fundamental Research Plan (Nos. JC201005260116A and JCYJ20120613144110654).

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Authors and Affiliations

  1. Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China

    Yunyun Yang & Yi Zhao

  2. Department of Mathematics, Harbin Institute of Technology, Harbin, China

    Boying Wu

Authors
  1. Yunyun Yang
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  2. Yi Zhao
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  3. Boying Wu
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Correspondence to Yunyun Yang.

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Yang, Y., Zhao, Y. & Wu, B. Split Bregman Method for Minimization of Fast Multiphase Image Segmentation Model for Inhomogeneous Images. J Optim Theory Appl 166, 285–305 (2015). https://doi.org/10.1007/s10957-014-0597-4

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  • DOI: https://doi.org/10.1007/s10957-014-0597-4

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