We consider a PDE framework for computing shortest paths for the 2D and 3D Reeds-Shepp car. We minimize a data-driven total-variation functional on position-and-orientation space, allowing only forward motion, to track complex elongated structures in images. We compute (quasi)-distance maps and (approximate) optimal sub-Finslerian/sub-Riemannian geodesics via Eikonal PDEs and gradient descent, with convergence results and comparison to exact solutions. We show benefits in: 1) vessel tracking in 2D medical images, 2) fiber tracking in DW-MRI-data.

This presentation is part of Minisymposium “MS69 - Anisotropic multi scale methods and biomedical imaging”
organized by: Davide Barbieri (Universidad Autonoma de Madrid) , Demetrio Labate (University of Houston) .

Authors:

Remco Duits (Technische Universiteit Eindhoven)

Jean-Marie Mirebeau (Université Paris-Sud - CNRS - Université Paris-Saclay )

Jorg Portegies (Eindhoven University of Technology)

Stephan Meesters (Eindhoven University of Technology)

Keywords:

(finsler geometry, multi-orientation image processing, nonlinear optimization, partial differential equation models, sub-riemannian geometry, vessel tracking)