Graph Cut Optimization for the Piecewise Constant Level Set Method Applied to Multiphase Image Segmentation

  • Egil Bae
  • Xue-Cheng Tai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5567)


The piecewise constant level set method (PCLSM) has recently emerged as a variant of the level set method for variational interphase problems. Traditionally, the Euler-Lagrange equations are solved by some iterative numerical method for PDEs. Normally the speed is slow. In this work, we focus on the piecewise constant level set method (PCLSM) applied to the multiphase Mumford-Shah model for image segmentation. Instead of solving the Euler-Lagrange equations of the resulting minimization problem, we propose an efficient combinatorial optimization technique, based on graph cuts. Because of a simplification of the length term in the energy induced by the PCLSM, the minimization problem is not NP hard. Numerical experiments on image segmentation demonstrate that the new approach is very superior in terms of efficiency, while maintaining the same quality.


Image Segmentation Gradient Descent Length Term Iterative Numerical Method Fast Approximate Energy Minimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Egil Bae
    • 1
  • Xue-Cheng Tai
    • 2
  1. 1.Department of MathematicsUniversity of BergenNorway
  2. 2.Department of Mathematics, University of Bergen, Norway and Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore

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