Sub-Riemannian geodesics in SO(3) with application to vessel tracking in spherical images of retina
- 作者: Mashtakov A.1, Duits R.2, Sachkov Y.1, Bekkers E.2, Beschastnyi I.3
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隶属关系:
- Program Systems Institute of RAS, Yaroslavl Region
- Eindhoven University of Technology
- International School for Advanced Studies
- 期: 卷 95, 编号 2 (2017)
- 页面: 168-171
- 栏目: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224955
- DOI: https://doi.org/10.1134/S1064562417020181
- ID: 224955
如何引用文章
详细
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.
作者简介
A. Mashtakov
Program Systems Institute of RAS, Yaroslavl Region
编辑信件的主要联系方式.
Email: alexey.mashtakov@gmail.com
俄罗斯联邦, Pereslavl-Zalessky, 152021
Remco Duits
Eindhoven University of Technology
Email: alexey.mashtakov@gmail.com
荷兰, Eindhoven
Yu. Sachkov
Program Systems Institute of RAS, Yaroslavl Region
Email: alexey.mashtakov@gmail.com
俄罗斯联邦, Pereslavl-Zalessky, 152021
Erik Bekkers
Eindhoven University of Technology
Email: alexey.mashtakov@gmail.com
荷兰, Eindhoven
I. Beschastnyi
International School for Advanced Studies
Email: alexey.mashtakov@gmail.com
意大利, Trieste