Hamiltonian Fast Marching: A numerical solver for anisotropic and non-holonomic eikonal PDEs

Jean-Marie Mirebeau (1, 2) , Jorg Portegies (3)

1 CNRS - Centre National de la Recherche Scientifique
2 LMO - Laboratoire de Mathématiques d'Orsay
3 TU/e - Eindhoven University of Technology [Eindhoven]

We introduce a generalized Fast-Marching algorithm, able to compute paths globally minimizing a measure of length, defined w.r.t. a variety of metrics in dimension two to five. Our method applies in particular to arbitrary Riemannian metrics, and implements features such as second order accuracy, sensitivity analysis, and various stopping criteria. We also address the singular metrics associated with several non-holonomic control models, related with curvature penalization, such as the Reeds-Shepp's car with or without reverse gear, the Euler-Mumford elastica curves, and the Dubins car. Applications to image processing and to motion planning are demonstrated.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Jean-Marie Mirebeau, Jorg Portegies. Hamiltonian Fast Marching: A numerical solver for anisotropic and non-holonomic eikonal PDEs. Image Processing On Line, 2019, 9, pp.47-93. ⟨hal-01778322⟩