Sub-Riemannian geodesics in SO(3) with application to vessel tracking in spherical images of retina
- Authors: Mashtakov A.P.1, Duits R.2, Sachkov Y.L.1, Bekkers E.2, Beschastnyi I.Y.3
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Affiliations:
- Program Systems Institute of RAS, Yaroslavl Region
- Eindhoven University of Technology
- International School for Advanced Studies
- Issue: Vol 95, No 2 (2017)
- Pages: 168-171
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224955
- DOI: https://doi.org/10.1134/S1064562417020181
- ID: 224955
Cite item
Abstract
In order to detect vessel locations in spherical images of retina we consider the problem of minimizing the functional \(\int\limits_0^l {\mathfrak{C}\left( {\gamma \left( s \right)} \right)\sqrt {{\xi ^2} + k_g^2\left( s \right)} ds}\) for a curve γ on a sphere with fixed boundary points and directions. The total length l is free, s denotes the spherical arclength, and kg denotes the geodesic curvature of γ. Here the smooth external cost C ≥ δ > 0 is obtained from spherical data. We lift this problem to the sub-Riemannian (SR) problem in Lie group SO(3) and propose numerical solution to this problem with consequent comparison to exact solution in the case C = 1. An experiment of vessel tracking in a spherical image of the retina shows a benefit of using SO(3) geodesics.
About the authors
A. P. Mashtakov
Program Systems Institute of RAS, Yaroslavl Region
Author for correspondence.
Email: alexey.mashtakov@gmail.com
Russian Federation, Pereslavl-Zalessky, 152021
Remco Duits
Eindhoven University of Technology
Email: alexey.mashtakov@gmail.com
Netherlands, Eindhoven
Yu. L. Sachkov
Program Systems Institute of RAS, Yaroslavl Region
Email: alexey.mashtakov@gmail.com
Russian Federation, Pereslavl-Zalessky, 152021
Erik Bekkers
Eindhoven University of Technology
Email: alexey.mashtakov@gmail.com
Netherlands, Eindhoven
I. Yu. Beschastnyi
International School for Advanced Studies
Email: alexey.mashtakov@gmail.com
Italy, Trieste