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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) .