Numerical Algorithms

, Volume 48, Issue 1–3, pp 189–211 | Cite as

Generalized fast marching method: applications to image segmentation

  • Nicolas Forcadel
  • Carole Le GuyaderEmail author
  • Christian Gout
Original Paper


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 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  • Nicolas Forcadel
    • 1
    • 2
  • Carole Le Guyader
    • 3
    • 4
    Email author
  • Christian Gout
    • 5
    • 6
    • 7
  1. 1.Projet Commands, CMAP-INRIA FutursEcole PolytechniquePalaiseauFrance
  2. 2.ENSTA, UMAParis Cedex 15France
  3. 3.Centre de Mathématiques de l’INSAINSA de RennesRennes cedexFrance
  4. 4.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA
  5. 5.LAMAV-ISTV2, Université de ValenciennesValenciennes Cedex 9France
  6. 6.Laboratoire de Mathématiques de l’INSAINSA de RouenMont-Saint-Aignan CedexFrance
  7. 7.INRIA Bordeaux Sud Ouest Center Team-Project Magique3DPauFrance

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