Jean-Marie Mirebeau

Anisotropic Fast-Marching on cartesian grids using Lattice Basis Reduction

We introduce a modification of the fast-marching algorithm, which solves the anisotropic eikonal equation associated to an arbitrary continuous Riemannian metric

Greedy bisection generates optimally adapted triangulations

{\cal M}

Sparse Non-negative Stencils for Anisotropic Diffusion

on a two- or three-dimensional domain. The algorithm has a complexity

Efficient fast marching with Finsler metrics

{\cal O}(N \ln N + N \ln \kappa({\cal M}))

Adaptive multiresolution analysis based on anisotropic triangulations

, where

Monotone and consistent discretization of the Monge-Ampère operator

N

Sub-Riemannian fast marching in SE(2)

is the discrete domain cardinality. The logarithmic dependency in the maximum anisotropy ratio

Minimal Geodesics Along Volume-Preserving Maps, Through Semidiscrete Optimal Transport

\kappa({\cal M})

Fast-Marching Methods for Curvature Penalized Shortest Paths

of the Riemannian metric allows us to handle extreme anisotropies for a limited numerical cost. We prove the convergence of the algorithm and illustrate its efficiency by numerical experiments. The algorithm relies on the computation at each grid point

A New Finsler Minimal Path Model with Curvature Penalization for Image Segmentation and Closed Contour Detection

z