Generalized fast marching method: applications to image segmentation

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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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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Keywords

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

Mathematics Subject Classifications (2000)

  • 65M06
  • 68U10
  • 49Lxx