A multiphase level set framework for image segmentation using the Mumford and Shah model

Luminita A. Vese*, Tony Chan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2057 Scopus citations

Abstract

We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space '99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141-151) and T. Chan and L. Vese (2001. IEEE-IP, 10(2):266-277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap; it needs only log n level set functions for n phases in the piecewise constant case; it can represent boundaries with complex topologies, including triple junctions; in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.

Original languageEnglish (US)
Pages (from-to)271-293
Number of pages23
JournalInternational Journal of Computer Vision
Volume50
Issue number3
DOIs
StatePublished - Dec 1 2002

Keywords

  • Active contours
  • Curvature
  • Denoising
  • Edge detection
  • Energy minimization
  • Image segmentation
  • Level sets
  • Multi-phase motion
  • PDE's

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

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