  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.
