Sub-Riemannian fast marching in SE(2)

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

doi:10.1007/978-3-319-25751-8_44

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 proceeding › Conference contribution › Academic › peer-review

13 Citations (Scopus)

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.

Original language	English
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	https://doi.org/10.1007/978-3-319-25751-8_44
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)
Publisher	Springer
Volume	9423

Conference

Conference	20th Iberoamerican Congress, CIARP 2015, November 9-12, 2015, Montevideo, Uruguay
Abbreviated title	CIARP 2015
Country	Uruguay
City	Montevideo
Period	9/11/15 → 12/11/15

Access to Document

10.1007/978-3-319-25751-8_44

http://www.bmia.bmt.tue.nl/people/RDuits/SE2FM.pdf

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Sanguinetti, G., Bekkers, E., Duits, R., Janssen, M. H. J., Mashtakov, A., & Mirebeau, J-M. (2015). Sub-Riemannian fast marching in SE(2). In A. Pardo, & J. Kittler (Eds.), Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings (pp. 366-374). (Lecture Notes in Computer Science (LNCS); Vol. 9423). Springer. https://doi.org/10.1007/978-3-319-25751-8_44

Sanguinetti, Gonzalo ; Bekkers, Erik ; Duits, Remco ; Janssen, Michael H.J. ; Mashtakov, Alexey ; Mirebeau, Jean-Marie. / Sub-Riemannian fast marching in SE(2). Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings. editor / A. Pardo ; J. Kittler. Cham : Springer, 2015. pp. 366-374 (Lecture Notes in Computer Science (LNCS)).

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abstract = "We propose a Fast Marching based implementation for com-puting sub-Riemanninan (SR) geodesics in the roto-translation groupSE(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 withextreme anisotropies is used to compute a SR-distance map as the so-lution of a corresponding eikonal equation. Subsequent backtracking onthe distance map gives the geodesics. To validate the method, we con-sider the uniform cost case in which exact formulas for SR-geodesics areknown and we show remarkable accuracy of the numerically computedSR-spheres. We also show a dramatic decrease in computational timewith respect to a previous PDE-based iterative approach. Regarding im-age analysis applications, we show the potential of considering these dataadaptive geodesics for a fully automated retinal vessel tree segmentation.",

author = "Gonzalo Sanguinetti and Erik Bekkers and Remco Duits and Janssen, {Michael H.J.} and Alexey Mashtakov and Jean-Marie Mirebeau",

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note = "20th Iberoamerican Congress, CIARP 2015, November 9-12, 2015, Montevideo, Uruguay : Congreso IberoAmericano de Reconocimiento de Patrones, CIARP 2015 ; Conference date: 09-11-2015 Through 12-11-2015",

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Sanguinetti, G, Bekkers, E , Duits, R, Janssen, MHJ, Mashtakov, A & Mirebeau, J-M 2015, Sub-Riemannian fast marching in SE(2). in A Pardo & J Kittler (eds), Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings. Lecture Notes in Computer Science (LNCS), vol. 9423, Springer, Cham, pp. 366-374, 20th Iberoamerican Congress, CIARP 2015, November 9-12, 2015, Montevideo, Uruguay, Montevideo, Uruguay, 9/11/15. https://doi.org/10.1007/978-3-319-25751-8_44

Sub-Riemannian fast marching in SE(2). / Sanguinetti, Gonzalo; Bekkers, Erik ; Duits, Remco; Janssen, Michael H.J.; Mashtakov, Alexey; Mirebeau, Jean-Marie.

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings. ed. / A. Pardo; J. Kittler. Cham : Springer, 2015. p. 366-374 (Lecture Notes in Computer Science (LNCS); Vol. 9423).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Sub-Riemannian fast marching in SE(2)

AU - Sanguinetti, Gonzalo

AU - Bekkers, Erik

AU - Duits, Remco

AU - Janssen, Michael H.J.

AU - Mashtakov, Alexey

AU - Mirebeau, Jean-Marie

PY - 2015/10/25

Y1 - 2015/10/25

N2 - We propose a Fast Marching based implementation for com-puting sub-Riemanninan (SR) geodesics in the roto-translation groupSE(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 withextreme anisotropies is used to compute a SR-distance map as the so-lution of a corresponding eikonal equation. Subsequent backtracking onthe distance map gives the geodesics. To validate the method, we con-sider the uniform cost case in which exact formulas for SR-geodesics areknown and we show remarkable accuracy of the numerically computedSR-spheres. We also show a dramatic decrease in computational timewith respect to a previous PDE-based iterative approach. Regarding im-age analysis applications, we show the potential of considering these dataadaptive geodesics for a fully automated retinal vessel tree segmentation.

AB - We propose a Fast Marching based implementation for com-puting sub-Riemanninan (SR) geodesics in the roto-translation groupSE(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 withextreme anisotropies is used to compute a SR-distance map as the so-lution of a corresponding eikonal equation. Subsequent backtracking onthe distance map gives the geodesics. To validate the method, we con-sider the uniform cost case in which exact formulas for SR-geodesics areknown and we show remarkable accuracy of the numerically computedSR-spheres. We also show a dramatic decrease in computational timewith respect to a previous PDE-based iterative approach. Regarding im-age analysis applications, we show the potential of considering these dataadaptive geodesics for a fully automated retinal vessel tree segmentation.

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DO - 10.1007/978-3-319-25751-8_44

M3 - Conference contribution

SN - 978-3-319-25750-1

T3 - Lecture Notes in Computer Science (LNCS)

SP - 366

EP - 374

BT - Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings

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PB - Springer

CY - Cham

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Y2 - 9 November 2015 through 12 November 2015

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Sanguinetti G, Bekkers E , Duits R, Janssen MHJ, Mashtakov A, Mirebeau J-M. Sub-Riemannian fast marching in SE(2). In Pardo A, Kittler J, editors, Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications : 20th Iberoamerican Congress, CIARP 2015, Montevideo, Uruguay, November 9-12, 2015 : Proceedings. Cham: Springer. 2015. p. 366-374. (Lecture Notes in Computer Science (LNCS)). https://doi.org/10.1007/978-3-319-25751-8_44