Numerical Algorithms

, Volume 48, Issue 1, pp 189–211

Generalized fast marching method: applications to image segmentation


  • Nicolas Forcadel
    • Projet Commands, CMAP-INRIA FutursEcole Polytechnique
    • ENSTA, UMA
    • Centre de Mathématiques de l’INSAINSA de Rennes
    • Department of MathematicsUniversity of California, Los Angeles
  • Christian Gout
    • LAMAV-ISTV2, Université de Valenciennes
    • Laboratoire de Mathématiques de l’INSAINSA de Rouen
    • INRIA Bordeaux Sud Ouest Center Team-Project Magique3D
Original Paper

DOI: 10.1007/s11075-008-9183-x

Cite this article as:
Forcadel, N., Le Guyader, C. & Gout, C. Numer Algor (2008) 48: 189. doi:10.1007/s11075-008-9183-x


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 methodLevel set methodsChan–Vese model for segmentation

Mathematics Subject Classifications (2000)

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© Springer Science+Business Media, LLC. 2008