An approximation scheme for the minimum time function
SIAM Journal on Control and Optimization
Optimal Algorithm for Shape from Shading and Path Planning
Journal of Mathematical Imaging and Vision
An $\cal O(N)$ Level Set Method for Eikonal Equations
SIAM Journal on Scientific Computing
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
Computational Study of Fast Methods for the Eikonal Equation
SIAM Journal on Scientific Computing
A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations
Journal of Scientific Computing
Fast Semi-Lagrangian Schemes for the Eikonal Equation and Applications
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
An Efficient Data Structure and Accurate Scheme to Solve Front Propagation Problems
Journal of Scientific Computing
Fast marching method for generic shape from shading
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
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In this paper we present a generalization of the Fast Marching method introduced by J.A. Sethian in 1996 to solve numerically the eikonal equation. The new method, named Buffered Fast Marching (BFM), is based on a semi-Lagrangian discretization and is suitable for Hamilton-Jacobi equations modeling monotonically advancing fronts, including Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations which arise in the framework of optimal control problems and differential games. We also show the convergence of the algorithm to the viscosity solution. Finally we present several numerical tests comparing the BFM method with other existing methods.