Crossing-Preserving Geodesic Tracking on Spherical Images

Nicky J. van den Berg; Finn M. Sherry; Tos T.J.M. Berendschot; Remco Duits

doi:10.1007/978-3-031-92369-2_15

Crossing-Preserving Geodesic Tracking on Spherical Images

Nicky J. van den Berg^*, Finn M. Sherry, Tos T.J.M. Berendschot, Remco Duits

^*Corresponding author for this work

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

Abstract

In image analysis one often encounters spherical images, for instance in retinal imaging. The behavior of the vessels in the retina is an indicator of several diseases. To automate disease diagnosis using retinal images, it is necessary to develop an algorithm that automatically identifies and tracks vessels. To deal with crossings due to projected blood vessels in the image it is common to lift retinal images to the space of planar positions and orientations M<inf>2</inf>:=R<sup>2</sup>×S<sup>1</sup>. This implicitly assumes that the flat image accurately represents the geometry of the retina. As the eyeball is a sphere (and not a plane), we propose to compute the cusp-free, crossing-preserving geodesics in the space of spherical positions and orientations W<inf>2</inf> on wide-field images. We clarify how to relate both manifolds and compare the calculated geodesics. The results show clear advantages of crossing-preserving tracking in W<inf>2</inf> over non-crossing-preserving tracking in W<inf>2</inf> and are comparable to tracking results in M<inf>2</inf>.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings
Editors	Tatiana A. Bubba, Romina Gaburro, Silvia Gazzola, Kostas Papafitsoros, Marcelo Pereyra, Carola-Bibiane Schönlieb
Publisher	Springer Verlag
Pages	192-204
Number of pages	13
Volume	15668 LNCS
ISBN (Print)	9783031923685
DOIs	https://doi.org/10.1007/978-3-031-92369-2_15
Publication status	Published - 1 Jan 2025
Event	10th International Conference on Scale Space and Variational Methods in Computer Vision - Dartington, United Kingdom Duration: 18 May 2025 → 22 May 2025 Conference number: 10 https://sites.google.com/view/ssvm-2025/home-page

Publication series

Series	Lecture Notes in Computer Science
Volume	15668 LNCS
ISSN	0302-9743

Conference

Conference	10th International Conference on Scale Space and Variational Methods in Computer Vision
Abbreviated title	SSVM 2025
Country/Territory	United Kingdom
City	Dartington
Period	18/05/25 → 22/05/25
Internet address	https://sites.google.com/view/ssvm-2025/home-page

Keywords

Geodesic Tracking
Retinal Imaging
Spherical Images
Sub-Riemannian Geometry
Vascular Tree Tracking

Access to Document

10.1007/978-3-031-92369-2_15

Cite this

van den Berg, N. J., Sherry, F. M., Berendschot, T. T. J. M., & Duits, R. (2025). Crossing-Preserving Geodesic Tracking on Spherical Images. In T. A. Bubba, R. Gaburro, S. Gazzola, K. Papafitsoros, M. Pereyra, & C.-B. Schönlieb (Eds.), Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings (Vol. 15668 LNCS, pp. 192-204). Springer Verlag. https://doi.org/10.1007/978-3-031-92369-2_15

van den Berg, Nicky J. ; Sherry, Finn M. ; Berendschot, Tos T.J.M. et al. / Crossing-Preserving Geodesic Tracking on Spherical Images. Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. editor / Tatiana A. Bubba ; Romina Gaburro ; Silvia Gazzola ; Kostas Papafitsoros ; Marcelo Pereyra ; Carola-Bibiane Schönlieb. Vol. 15668 LNCS Springer Verlag, 2025. pp. 192-204 (Lecture Notes in Computer Science, Vol. 15668 LNCS).

@inproceedings{5f498c9253ba4a25902f218bd371700f,

title = "Crossing-Preserving Geodesic Tracking on Spherical Images",

abstract = "In image analysis one often encounters spherical images, for instance in retinal imaging. The behavior of the vessels in the retina is an indicator of several diseases. To automate disease diagnosis using retinal images, it is necessary to develop an algorithm that automatically identifies and tracks vessels. To deal with crossings due to projected blood vessels in the image it is common to lift retinal images to the space of planar positions and orientations M2:=R2×S1. This implicitly assumes that the flat image accurately represents the geometry of the retina. As the eyeball is a sphere (and not a plane), we propose to compute the cusp-free, crossing-preserving geodesics in the space of spherical positions and orientations W2 on wide-field images. We clarify how to relate both manifolds and compare the calculated geodesics. The results show clear advantages of crossing-preserving tracking in W2 over non-crossing-preserving tracking in W2 and are comparable to tracking results in M2.",

keywords = "Geodesic Tracking, Retinal Imaging, Spherical Images, Sub-Riemannian Geometry, Vascular Tree Tracking",

author = "{van den Berg}, {Nicky J.} and Sherry, {Finn M.} and Berendschot, {Tos T.J.M.} and Remco Duits",

note = "Funding Information: We gratefully acknowledge the Dutch Foundation of Science NWO for its financial support by Talent Programme VICI 2020 Exact Sciences (Duits, Geometric learning for Image Analysis, VI.C 202-031). We thank the students of the modeling week project \u201CGeodesic Tracking of Blood Vessels in Wide-Field Retinal Images\u201D for preliminary experimental results. Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 ; Conference date: 18-05-2025 Through 22-05-2025",

year = "2025",

month = jan,

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doi = "10.1007/978-3-031-92369-2_15",

language = "English",

isbn = "9783031923685",

volume = "15668 LNCS",

series = "Lecture Notes in Computer Science",

publisher = "Springer Verlag",

pages = "192--204",

editor = "Bubba, {Tatiana A.} and Romina Gaburro and Silvia Gazzola and Kostas Papafitsoros and Marcelo Pereyra and Carola-Bibiane Sch{\"o}nlieb",

booktitle = "Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings",

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van den Berg, NJ, Sherry, FM, Berendschot, TTJM & Duits, R 2025, Crossing-Preserving Geodesic Tracking on Spherical Images. in TA Bubba, R Gaburro, S Gazzola, K Papafitsoros, M Pereyra & C-B Schönlieb (eds), Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. vol. 15668 LNCS, Springer Verlag, Lecture Notes in Computer Science, vol. 15668 LNCS, pp. 192-204, 10th International Conference on Scale Space and Variational Methods in Computer Vision, Dartington, United Kingdom, 18/05/25. https://doi.org/10.1007/978-3-031-92369-2_15

Crossing-Preserving Geodesic Tracking on Spherical Images. / van den Berg, Nicky J.; Sherry, Finn M.; Berendschot, Tos T.J.M. et al.
Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. ed. / Tatiana A. Bubba; Romina Gaburro; Silvia Gazzola; Kostas Papafitsoros; Marcelo Pereyra; Carola-Bibiane Schönlieb. Vol. 15668 LNCS Springer Verlag, 2025. p. 192-204 (Lecture Notes in Computer Science, Vol. 15668 LNCS).

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

TY - GEN

T1 - Crossing-Preserving Geodesic Tracking on Spherical Images

AU - van den Berg, Nicky J.

AU - Sherry, Finn M.

AU - Berendschot, Tos T.J.M.

AU - Duits, Remco

N1 - Conference code: 10

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Y1 - 2025/1/1

N2 - In image analysis one often encounters spherical images, for instance in retinal imaging. The behavior of the vessels in the retina is an indicator of several diseases. To automate disease diagnosis using retinal images, it is necessary to develop an algorithm that automatically identifies and tracks vessels. To deal with crossings due to projected blood vessels in the image it is common to lift retinal images to the space of planar positions and orientations M2:=R2×S1. This implicitly assumes that the flat image accurately represents the geometry of the retina. As the eyeball is a sphere (and not a plane), we propose to compute the cusp-free, crossing-preserving geodesics in the space of spherical positions and orientations W2 on wide-field images. We clarify how to relate both manifolds and compare the calculated geodesics. The results show clear advantages of crossing-preserving tracking in W2 over non-crossing-preserving tracking in W2 and are comparable to tracking results in M2.

AB - In image analysis one often encounters spherical images, for instance in retinal imaging. The behavior of the vessels in the retina is an indicator of several diseases. To automate disease diagnosis using retinal images, it is necessary to develop an algorithm that automatically identifies and tracks vessels. To deal with crossings due to projected blood vessels in the image it is common to lift retinal images to the space of planar positions and orientations M2:=R2×S1. This implicitly assumes that the flat image accurately represents the geometry of the retina. As the eyeball is a sphere (and not a plane), we propose to compute the cusp-free, crossing-preserving geodesics in the space of spherical positions and orientations W2 on wide-field images. We clarify how to relate both manifolds and compare the calculated geodesics. The results show clear advantages of crossing-preserving tracking in W2 over non-crossing-preserving tracking in W2 and are comparable to tracking results in M2.

KW - Geodesic Tracking

KW - Retinal Imaging

KW - Spherical Images

KW - Sub-Riemannian Geometry

KW - Vascular Tree Tracking

U2 - 10.1007/978-3-031-92369-2_15

DO - 10.1007/978-3-031-92369-2_15

M3 - Conference article in proceeding

SN - 9783031923685

VL - 15668 LNCS

T3 - Lecture Notes in Computer Science

SP - 192

EP - 204

BT - Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings

A2 - Bubba, Tatiana A.

A2 - Gaburro, Romina

A2 - Gazzola, Silvia

A2 - Papafitsoros, Kostas

A2 - Pereyra, Marcelo

A2 - Schönlieb, Carola-Bibiane

PB - Springer Verlag

T2 - 10th International Conference on Scale Space and Variational Methods in Computer Vision

Y2 - 18 May 2025 through 22 May 2025

ER -

van den Berg NJ, Sherry FM, Berendschot TTJM, Duits R. Crossing-Preserving Geodesic Tracking on Spherical Images. In Bubba TA, Gaburro R, Gazzola S, Papafitsoros K, Pereyra M, Schönlieb CB, editors, Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. Vol. 15668 LNCS. Springer Verlag. 2025. p. 192-204. (Lecture Notes in Computer Science, Vol. 15668 LNCS). doi: 10.1007/978-3-031-92369-2_15

Crossing-Preserving Geodesic Tracking on Spherical Images

Abstract

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Keywords

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