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.
G. Sanguinetti—The research leading to the results of this article has received funding from the European Research Council under the (FP7/2007-2014-)ERC grant ag. no. 335555 and from (FP7-PEOPLE-2013-ITN)EU Marie-Curie ag. no. 607643.
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Sanguinetti, G., Bekkers, E., Duits, R., Janssen, M.H.J., Mashtakov, A., Mirebeau, JM. (2015). Sub-Riemannian Fast Marching in SE(2). In: Pardo, A., Kittler, J. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2015. Lecture Notes in Computer Science(), vol 9423. Springer, Cham. https://doi.org/10.1007/978-3-319-25751-8_44
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DOI: https://doi.org/10.1007/978-3-319-25751-8_44
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