Image Segmentation Using the Cahn–Hilliard Equation

  • Wenli Yang
  • Zhongyi HuangEmail author
  • Wei Zhu


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.


Image segmentation Cahn–Hilliard equation Tailored finite point method 

Mathematics Subject Classification

Primary: 65M32 68U10 Secondary: 65K10 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.Department of MathematicsUniversity of AlabamaTuscaloosaUSA

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