We introduce a modification of the fast-marching algorithm, which solves the anisotropic
eikonal equation associated to an arbitrary continuous Riemannian metric \calM on a two-or …

Fast Marching and Fast Sweeping are the two most commonly used methods for solving the
eikonal equation. Each of these methods performs best on a different set of problems. Fast …

We study the discretization of the escape time problem: find the length of the shortest path
joining an arbitrary point zz of a domain Ω Ω, to the boundary ∂ Ω∂ Ω. Path length is …

We introduce a generalized Fast-Marching algorithm, able to compute paths globally
minimizing a measure of length, defined with respect to a variety of metrics in dimension two …

We address the numerical computation of distance maps with respect to Riemannian metrics
of strong anisotropy. For that purpose we solve generalized eikonal equations, discretized …

We define a δ-causal discretization of static convex Hamilton-Jacobi Partial Differential
Equations (HJ PDEs) such that the solution value at a grid node is dependent only on …

In this article, we consider shortest path problems in a directed graph where the transitions
between nodes are subject to uncertainty. We use a minimax formulation, where the …

Many applications require efficient methods for solving continuous shortest path problems.
Such paths can be viewed as characteristics of static Hamilton--Jacobi equations. Several …

We present an algorithm that, given a representation of a road network in lane-level detail,
computes a route that minimizes the expected cost to reach a given destination. In doing so …

We consider discretizations of anisotropic diffusion and of the anisotropic eikonal equation,
on two-dimensional cartesian grids, which preserve their structural properties: the maximum …