Hamiltonian fast marching: a numerical solver for anisotropic and non-holonomic eikonal PDEs

Jean Marie Mirebeau, Jorg Portegies

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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.

Originele taal-2Engels
Pagina's (van-tot)47-93
Aantal pagina's47
TijdschriftImage Processing On Line
Volume9
DOI's
StatusGepubliceerd - 1 jan 2019

Vingerafdruk

Hamiltonians
Railroad cars
Motion planning
Sensitivity analysis
Gears
Image processing

Citeer dit

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Hamiltonian fast marching : a numerical solver for anisotropic and non-holonomic eikonal PDEs. / Mirebeau, Jean Marie; Portegies, Jorg.

In: Image Processing On Line, Vol. 9, 01.01.2019, blz. 47-93.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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