Sub-Riemannian fast marching in SE(2)

Gonzalo Sanguinetti, Erik Bekkers, Remco Duits, Michael H.J. Janssen, Alexey Mashtakov, Jean-Marie Mirebeau

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

13 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationProgress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings
EditorsA. Pardo, J. Kittler
Place of PublicationCham
Number of pages8
ISBN (Electronic) 978-3-319-25751-8
ISBN (Print)978-3-319-25750-1
Publication statusPublished - 25 Oct 2015
Event20th Iberoamerican Congress, CIARP 2015, November 9-12, 2015, Montevideo, Uruguay: Congreso IberoAmericano de Reconocimiento de Patrones - Montevideo, Uruguay
Duration: 9 Nov 201512 Nov 2015

Publication series

NameLecture Notes in Computer Science (LNCS)


Conference20th Iberoamerican Congress, CIARP 2015, November 9-12, 2015, Montevideo, Uruguay
Abbreviated titleCIARP 2015


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