Iberoamerican Congress on Pattern Recognition

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications pp 366-374 | Cite as

Sub-Riemannian Fast Marching in SE(2)

  • Gonzalo Sanguinetti
  • Erik Bekkers
  • Remco Duits
  • Michiel H. J. Janssen
  • Alexey Mashtakov
  • Jean-Marie Mirebeau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9423)

Abstract

We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the image data. The key ingredient is a Riemannian approximation of the SR-metric. Then, a state of the art Fast Marching solver that is able to deal with extreme anisotropies is used to compute a SR-distance map as the solution of a corresponding eikonal equation. Subsequent backtracking on the distance map gives the geodesics. To validate the method, we consider the uniform cost case in which exact formulas for SR-geodesics are known and we show remarkable accuracy of the numerically computed SR-spheres. We also show a dramatic decrease in computational time with respect to a previous PDE-based iterative approach. Regarding image analysis applications, we show the potential of considering these data adaptive geodesics for a fully automated retinal vessel tree segmentation.

Keywords

Roto-translation group Sub-riemannian Fast marching 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Gonzalo Sanguinetti
    • 1
  • Erik Bekkers
    • 2
  • Remco Duits
    • 1
    • 2
  • Michiel H. J. Janssen
    • 1
  • Alexey Mashtakov
    • 2
  • Jean-Marie Mirebeau
    • 3
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.Laboratory Ceremade, CNRSUniversity Paris-DauphineParisFrance

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