# Optimal Paths for Variants of the 2D and 3D Reeds–Shepp Car with Applications in Image Analysis

@article{Duits2018OptimalPF,
title={Optimal Paths for Variants of the 2D and 3D Reeds–Shepp Car with Applications in Image Analysis},
author={Remco Duits and Stephan P. L. Meesters and Jean-Marie Mirebeau and Jorg M. Portegies},
journal={Journal of Mathematical Imaging and Vision},
year={2018},
volume={60},
pages={816 - 848}
}
• Published 19 December 2016
• Computer Science
• Journal of Mathematical Imaging and Vision
We present a PDE-based approach for finding optimal paths for the Reeds–Shepp car. In our model we minimize a (data-driven) functional involving both curvature and length penalization, with several generalizations. Our approach encompasses the two- and three-dimensional variants of this model, state-dependent costs, and moreover, the possibility of removing the reverse gear of the vehicle. We prove both global and local controllability results of the models. Via eikonal equations on the…

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