Globally optimal regions and boundaries as minimum ratio weight cycle

Ian H. Jermyn*, Hiroshi Ishikawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

133 Citations (Scopus)


We describe a new form of energy functional for the modelling and identification of regions in images. The energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modelling information both from the boundary (intensity gradients, etc.) and from the interior of the region (texture, homogeneity, etc.). We describe two polynomial-time digraph algorithms for finding the global minima of this energy. One of the algorithms is completely general, minimizing the functional for any choice of modelling information. It runs in a few seconds on a 256×256 image. The other algorithm applies to a subclass of functionals, but has the advantage of being extremely parallelizable. Neither algorithm requires initialization.

Original languageEnglish
Pages (from-to)1075-1088
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number10
Publication statusPublished - 2001 Oct
Externally publishedYes


  • Active contour
  • Energy minimization
  • Global optimum
  • Ratio
  • Region identification
  • Segmentation
  • Snake

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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