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A geometric flow approach for region-based image segmentation-theoretical analysis

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Abstract

In this paper, we analyze the well-posedness of an image segmentation model. The main idea of that segmentation model is to minimize one energy functional by evolving a given piecewise constant image towards the image to be segmented. The evolution is controlled by a serial of mappings, which can be represented by B-spline basis functions. The evolution terminates when the energy is below a given threshold. We prove that the correspondence between two images in the segmentation model is an injective and surjective mapping under appropriate conditions. We further prove that the solution of the segmentation model exists using the direct method in the calculus of variations. These results provide the theoretical support for that segmentation model.

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Author information

Authors and Affiliations

  1. School of Economics and Management, Beijing Jiaotong University, Beijing, 100044, China

    Zhu-cui Jing

  2. Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    Juntao Ye

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Guo-liang Xu

Authors
  1. Zhu-cui Jing
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  2. Juntao Ye
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  3. Guo-liang Xu
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Corresponding author

Correspondence to Zhu-cui Jing.

Additional information

Project support in part by NSFC grant 61379096 and Chinese-Guangdong’s S & T project (2014A050503004).

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Jing, Zc., Ye, J. & Xu, Gl. A geometric flow approach for region-based image segmentation-theoretical analysis. Acta Math. Appl. Sin. Engl. Ser. 34, 65–76 (2018). https://doi.org/10.1007/s10255-018-0723-4

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  • DOI: https://doi.org/10.1007/s10255-018-0723-4

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