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Image Segmentation Using the Cahn–Hilliard Equation

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Abstract

In this paper, we propose a novel model for image segmentation by using the Cahn–Hilliard equation. An interesting feature of this model lies in its ability of interpolating missing contours along wide gaps in order to form meaningful object boundaries, which is often achieved by curvature dependent models in the literature. To solve the associated equation, we employ a recently developed technique, that is, the tailored-finite-point method, which helps preserve sharp jumps and thus helps locate segmentation contours more exactly. Numerical experiments are presented to demonstrate the effectiveness of the proposed model and its features. In addition, analytical results on the existence and uniqueness of the associated equation are also provided.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Wenli Yang & Zhongyi Huang

  2. Department of Mathematics, University of Alabama, Tuscaloosa, AL, 35487, USA

    Wei Zhu

Authors
  1. Wenli Yang
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  2. Zhongyi Huang
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  3. Wei Zhu
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Correspondence to Zhongyi Huang.

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This work was partially supported by National Key Research and Development Program of China 2017YFC0601801 and NSFC Project No. 11871298.

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Yang, W., Huang, Z. & Zhu, W. Image Segmentation Using the Cahn–Hilliard Equation. J Sci Comput 79, 1057–1077 (2019). https://doi.org/10.1007/s10915-018-00899-7

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  • DOI: https://doi.org/10.1007/s10915-018-00899-7

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