A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model View Full Text


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Article Info

DATE

2002-12

AUTHORS

Luminita A. Vese, Tony F. Chan

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. More... »

PAGES

271-293

References to SciGraph publications

  • 2002-04-12. A Level Set Model for Image Classification in SCALE-SPACE THEORIES IN COMPUTER VISION
  • 2000-06. Implementation of an adaptive finite-element approximation of the Mumford-Shah functional in NUMERISCHE MATHEMATIK
  • 1989-11. Existence theorem for a minimum problem with free discontinuity set in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1989. New Functionals in Calculus of Variations in NONSMOOTH OPTIMIZATION AND RELATED TOPICS
  • 2002-04-12. An Active Contour Model without Edges in SCALE-SPACE THEORIES IN COMPUTER VISION
  • 1993-03. Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2000-12. A Level Set Model for Image Classification in INTERNATIONAL JOURNAL OF COMPUTER VISION
  • 1998-12. On minimizing partitions with infinitely many components in ANNALI DELL' UNIVERSITÀ DI FERRARA
  • 2002-04-12. Riemannian Drums, Anisotropic Curve Evolution and Segmentation in SCALE-SPACE THEORIES IN COMPUTER VISION
  • 1996. Optimal Approximation by Piecewise Constant Functions in VARIATIONAL METHODS FOR DISCONTINUOUS STRUCTURES
  • 1993-01. On the finiteness of optimal partitions in ANNALI DELL' UNIVERSITÀ DI FERRARA
  • 2000. Coupled Geodesic Active Regions for Image Segmentation: A Level Set Approach in COMPUTER VISION — ECCV 2000
  • 1998-03. A New Approach to Front Propagation Problems: Theory and Applications in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1992-07. A variational method in image segmentation: Existence and approximation results in ACTA MATHEMATICA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1020874308076

    DOI

    http://dx.doi.org/10.1023/a:1020874308076

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1035462968


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