[IPOL announce] new article: Hamiltonian Fast Marching: A Numerical Solver for Anisotropic and Non-Holonomic Eikonal PDEs

[announcements about the IPOL journal]

A new article is available in IPOL: http://www.ipol.im/pub/art/2019/227/

Jean-Marie Mirebeau, and Jorg Portegies,
Hamiltonian Fast Marching: A Numerical Solver for Anisotropic and 
Non-Holonomic Eikonal PDEs,
Image Processing On Line, 9 (2019), pp. 47–93.
https://doi.org/10.5201/ipol.2019.227

Abstract
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 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.