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Generalized fast marching method: applications to image segmentation

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Abstract

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.

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Authors and Affiliations

  1. Projet Commands, CMAP-INRIA Futurs, Ecole Polytechnique, 91128, Palaiseau, France

    Nicolas Forcadel

  2. ENSTA, UMA, 32 Bd Victor, 75739, Paris Cedex 15, France

    Nicolas Forcadel

  3. Centre de Mathématiques de l’INSA, INSA de Rennes, 20 Avenue des Buttes de Coësmes, CS 14315, 35043, Rennes cedex, France

    Carole Le Guyader

  4. Department of Mathematics, University of California, Los Angeles, 405, Hilgard Avenue, Los Angeles, CA, 90095-1555, USA

    Carole Le Guyader

  5. LAMAV-ISTV2, Université de Valenciennes, Le Mont Houy, 59313, Valenciennes Cedex 9, France

    Christian Gout

  6. Laboratoire de Mathématiques de l’INSA, INSA de Rouen, Place Emile Blondel, BP 08, 76 131, Mont-Saint-Aignan Cedex, France

    Christian Gout

  7. INRIA Bordeaux Sud Ouest Center Team-Project Magique3D, Pau, France

    Christian Gout

Authors
  1. Nicolas Forcadel
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  2. Carole Le Guyader
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  3. Christian Gout
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Correspondence to Carole Le Guyader.

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Forcadel, N., Le Guyader, C. & Gout, C. Generalized fast marching method: applications to image segmentation. Numer Algor 48, 189–211 (2008). https://doi.org/10.1007/s11075-008-9183-x

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  • DOI: https://doi.org/10.1007/s11075-008-9183-x

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