Fully Isotropic Fast Marching Methods on Cartesian Grids
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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.
- 2.Bronstein, A.M., Bronstein, M.M., Devir, Y.S., Kimmel, R., Weber, O.: Parallel algorithms for approximation of distance maps on parametric surfaces (2007)Google Scholar
- 5.Cohen, L.D., Kimmel, R.: Global minimum for active contour models: A minimal path approach. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, p. 666 (1996)Google Scholar
- 8.Kim, S., Folie, D.: The group marching method: An o(n) level set eikonal solverGoogle Scholar