Abstract
We propose a Fast Marching based implementation for com-
puting 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 so-
lution of a corresponding eikonal equation. Subsequent backtracking on
the distance map gives the geodesics. To validate the method, we con-
sider 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 im-
age analysis applications, we show the potential of considering these data
adaptive geodesics for a fully automated retinal vessel tree segmentation.
puting 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 so-
lution of a corresponding eikonal equation. Subsequent backtracking on
the distance map gives the geodesics. To validate the method, we con-
sider 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 im-
age analysis applications, we show the potential of considering these data
adaptive geodesics for a fully automated retinal vessel tree segmentation.
Original language | English |
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Title of host publication | Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings |
Editors | A. Pardo, J. Kittler |
Place of Publication | Cham |
Publisher | Springer |
Pages | 366-374 |
Number of pages | 8 |
ISBN (Electronic) | 978-3-319-25751-8 |
ISBN (Print) | 978-3-319-25750-1 |
DOIs | |
Publication status | Published - 25 Oct 2015 |
Event | 20th Iberoamerican Congress, CIARP 2015, November 9-12, 2015, Montevideo, Uruguay: Congreso IberoAmericano de Reconocimiento de Patrones - Montevideo, Uruguay Duration: 9 Nov 2015 → 12 Nov 2015 |
Publication series
Name | Lecture Notes in Computer Science (LNCS) |
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Publisher | Springer |
Volume | 9423 |
Conference
Conference | 20th Iberoamerican Congress, CIARP 2015, November 9-12, 2015, Montevideo, Uruguay |
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Abbreviated title | CIARP 2015 |
Country/Territory | Uruguay |
City | Montevideo |
Period | 9/11/15 → 12/11/15 |