Anisotropic Fast-Marching on cartesian grids using Lattice Basis Reduction
This work provides a more efficient algorithm for solving eikonal equations with high anisotropy, benefiting applications in geodesic distance computation and wavefront propagation.
The paper introduces a modification of the Fast Marching Algorithm to solve the generalized eikonal equation for arbitrary continuous Riemannian metrics on 2D/3D domains, achieving logarithmic complexity in the maximum anisotropy ratio. Numerical experiments demonstrate efficiency for extreme anisotropies.
We introduce a modification of the Fast Marching Algorithm, which solves the generalized eikonal equation associated to an arbitrary continuous riemannian metric, on a two or three dimensional domain. The algorithm has a logarithmic complexity in the maximum anisotropy ratio of the riemannian metric, which allows to handle extreme anisotropies for a reduced numerical cost. We prove the consistence of the algorithm, and illustrate its efficiency by numerical experiments. The algorithm relies on the computation at each grid point of a special system of coordinates: a reduced basis of the cartesian grid, with respect to the symmetric positive definite matrix encoding the desired anisotropy at this point.