Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation

Yibao Li, Sungha Yoon, Jian Wang, Jintae Park, Sangkwon Kim, Chaeyoung Lee, Hyundong Kim, Junseok Kim

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We present a simple numerical solution algorithm for a gradient flow for the Modica-Mortola functional and numerically investigate its dynamics. The proposed numerical algorithm involves both the operator splitting and the explicit Euler methods. A time step formula is derived from the stability analysis, and the goodness of fit of transition width is tested. We perform various numerical experiments to investigate the property of the gradient flow equation, to verify the characteristics of our method in the image segmentation application, and to analyze the effect of parameters. In particular, we propose an initialization process based on target objects. Furthermore, we conduct comparison tests in order to check the performance of our proposed method.

Original languageEnglish
Article number2414209
JournalMathematical Problems in Engineering
Publication statusPublished - 2021

Bibliographical note

Funding Information:
Yibao Li was supported by the National Natural Science Foundation of China (nos. 11601416 and 11631012). Junseok Kim was supported by the National Research Foundation (NRF), Korea, under project no. BK21 FOUR.

Publisher Copyright:
© 2021 Yibao Li et al.

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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