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.
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IPOL - Image Processing On Line - http://ipol.im/
contact [email protected] - http://www.ipol.im/meta/contact/
news+feeds twitter @IPOL_journal - http://www.ipol.im/meta/feeds/
announces [email protected] - http://tools.ipol.im/mm/announce/
discussions [email protected] - http://tools.ipol.im/mm/discuss/
