Fully Isotropic Fast Marching Methods on Cartesian Grids

  • Vikram Appia
  • Anthony Yezzi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6311)

Abstract

The existing Fast Marching methods which are used to solve the Eikonal equation use a locally continuous model to estimate the accumulated cost, but a discontinuous (discretized) model for the traveling cost around each grid point. Because the accumulated cost and the traveling (local) cost are treated differently, the estimate of the accumulated cost at any point will vary based on the direction of the arriving front. Instead we propose to estimate the traveling cost at each grid point based on a locally continuous model, where we will interpolate the traveling cost along the direction of the propagating front. We further choose an interpolation scheme that is not biased by the direction of the front. Thus making the fast marching process truly isotropic. We show the significance of removing the directional bias in the computation of the cost in certain applications of fast marching method. We also compare the accuracy and computation times of our proposed methods with the existing state of the art fast marching techniques to demonstrate the superiority of our method.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Vikram Appia
    • 1
  • Anthony Yezzi
    • 1
  1. 1.Georgia Institute of TechnologyUSA

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