article

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

Authors:

Luminita A. Vese,

Tony F. ChanAuthors Info & Claims

International Journal of Computer Vision, Volume 50, Issue 3

Pages 271 - 293

https://doi.org/10.1023/A:1020874308076

Published: 01 December 2002 Publication History

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.

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Index Terms

A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
        Image segmentation
        Video segmentation
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations

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Published In

cover image International Journal of Computer Vision

International Journal of Computer Vision Volume 50, Issue 3

December 2002

124 pages

ISSN:0920-5691

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Copyright © Copyright © 2002 Kluwer Academic Publishers.

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Kluwer Academic Publishers

United States

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Published: 01 December 2002

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