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

Authors:
Egil Bae;Xue-Cheng Tai
Affiliations:
Department of Mathematics, University of Bergen, Norway;Department of Mathematics, University of Bergen, Norway and Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

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.