Hamiltonian Fast Marching: A Numerical Solver for Anisotropic and Non-Holonomic Eikonal PDEs
Jean-Marie Mirebeau, Jorg Portegies
→ BibTeX
@article{ipol.2019.227,
    title   = {{Hamiltonian Fast Marching: A Numerical Solver for Anisotropic and Non-Holonomic Eikonal PDEs}},
    author  = {Mirebeau, Jean-Marie and Portegies, Jorg},
    journal = {{Image Processing On Line}},
    volume  = {9},
    pages   = {47--93},
    year    = {2019},
    doi     = {10.5201/ipol.2019.227},
}
% if your bibliography style doesn't support doi fields:
    note    = {\url{https://doi.org/10.5201/ipol.2019.227}}
published
2019-02-24
reference
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

Communicated by Bertrand Kerautret
Demo edited by Bertrand Kerautret

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.

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