Computation of Curvature Penalized Shortest Paths via the Fast Marching Algorithm MS38

Motivated by applications to motion planning and image segmentation, we consider paths models with a data-driven cost and a curvature penalization, such as the Euler/Mumford elasticas or the Reeds-Shepp car. Our strategy for computing paths of minimal energy involves a dimension lifting in $R^d x S^{d-1}$, d=2,3, and a strongly anisotropic approximation of the singular metric underlying the model. The relevant eikonal equation is then numerically solved by a variant of the Fast-Marching algorithm.

This presentation is part of Minisymposium “MS38 - Geometry-driven anisotropic approaches for imaging problems
organized by: Luca Calatroni (CMAP, École Polytechnique CNRS) , Dario Prandi (CNRS - L2S, CentraleSupélec) , Valentina Franceschi (INRIA Paris) .

Jean-Marie Mirebeau (Université Paris-Sud - CNRS - Université Paris-Saclay )
image segmentation, partial differential equation models