A Multiphase Image Segmentation Method Based on Fuzzy Region Competition

Fang Li, Michael K. Ng*, Tie Yong Zeng, Chunli Shen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

104 Citations (Scopus)
40 Downloads (Pure)


The goal of this paper is to develop a multiphase image segmentation method based on fuzzy region competition. A new variational functional with constraints is proposed by introducing fuzzy membership functions which represent several different regions in an image. The existence of a minimizer of this functional is established. We propose three methods for handling the constraints of membership functions in the minimization. We also add auxiliary variables to approximate the membership functions in the functional such that Chambolle's fast dual projection method can be used. An alternate minimization method can be employed to find the solution, in which the region parameters and the membership functions have closed form solutions. Numerical examples using grayscale and color images are given to demonstrate the effectiveness of the proposed methods.

Original languageEnglish
Pages (from-to)277-299
Number of pages23
JournalSIAM Journal on Imaging Sciences
Issue number3
Publication statusPublished - 13 Jul 2010

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Alternative minimization
  • Fuzzy membership function
  • Image segmentation
  • Multiphase
  • Region competition


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