@inproceedings{760b95511cb64908ae3430fedccbc38f,
title = "Data-driven sub-Riemannian geodesics in SE(2)",
abstract = "We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group SE(2)=R2¿S1 with a metric tensor depending on a smooth external cost C:SE(2)¿[d,1] , d>0 , computed from image data. The method consists of a first step where geodesically equidistant surfaces are computed as a viscosity solution of a Hamilton-Jacobi-Bellman (HJB) system derived via Pontryagin{\textquoteright}s Maximum Principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. We show that our method produces geodesically equidistant surfaces. For C=1 we show that our method produces the global minimizers, and comparison with exact solutions shows a remarkable accuracy of the SR-spheres/geodesics. Finally, trackings in synthetic and retinal images show the potential of including the SR-geometry. Keywords: Roto-translation group; Hamilton-Jacobi equations; Vessel tracking; Sub-riemannian geometry; Morphological scale spaces",
author = "E.J. Bekkers and R. Duits and A. Mashtakov and G.R. Sanguinetti",
year = "2015",
doi = "10.1007/978-3-319-18461-6_49",
language = "English",
isbn = "978-3-319-18460-9",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "613--625",
editor = "J.-F. Aujol and M. Nikolova and N. Papadakis",
booktitle = "Scale Space and Variational Methods in Computer Vision (5th International Conference, SSVM 2015, L{\`e}ge-Cap Ferret, France, May 31-June 4, 2015, Proceedings)",
address = "Germany",
}