Original Paper

Numerical Algorithms

, Volume 48, Issue 1, pp 189-211

First online:

Generalized fast marching method: applications to image segmentation

  • Nicolas ForcadelAffiliated withProjet Commands, CMAP-INRIA Futurs, Ecole PolytechniqueENSTA, UMA
  • , Carole Le GuyaderAffiliated withCentre de Mathématiques de l’INSA, INSA de RennesDepartment of Mathematics, University of California, Los Angeles Email author 
  • , Christian GoutAffiliated withLAMAV-ISTV2, Université de ValenciennesLaboratoire de Mathématiques de l’INSA, INSA de RouenINRIA Bordeaux Sud Ouest Center Team-Project Magique3D

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In this paper, we propose a segmentation method based on the generalized fast marching method (GFMM) developed by Carlini et al. (submitted). The classical fast marching method (FMM) is a very efficient method for front evolution problems with normal velocity (see also Epstein and Gage, The curve shortening flow. In: Chorin, A., Majda, A. (eds.) Wave Motion: Theory, Modelling and Computation, 1997) of constant sign. The GFMM is an extension of the FMM and removes this sign constraint by authorizing time-dependent velocity with no restriction on the sign. In our modelling, the velocity is borrowed from the Chan–Vese model for segmentation (Chan and Vese, IEEE Trans Image Process 10(2):266–277, 2001). The algorithm is presented and analyzed and some numerical experiments are given, showing in particular that the constraints in the initialization stage can be weakened and that the GFMM offers a powerful and computationally efficient algorithm.


Fast marching method Level set methods Chan–Vese model for segmentation

Mathematics Subject Classifications (2000)

65M06 68U10 49Lxx