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 (Corresponding author)
, Finn M. Sherry
, Tos T.J.M. Berendschot
, Remco Duits

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

1 Citation (Scopus)

25 Downloads (Pure)

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.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision
Subtitle of host publication	10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II
Editors	Tatiana A. Bubba, Romina Gaburro, Silvia Gazzola, Kostas Papafitsoros, Marcelo Pereyra, Carola-Bibiane Schönlieb
Place of Publication	Cham
Publisher	Springer
Chapter	II
Pages	192-204
Number of pages	13
ISBN (Electronic)	978-3-031-92369-2
ISBN (Print)	978-3-031-92368-5
DOIs	https://doi.org/10.1007/978-3-031-92369-2_15
Publication status	Published - 17 May 2025
Event	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 - Dartington, United Kingdom Duration: 18 May 2025 → 22 May 2025

Publication series

Name	Lecture Notes in Computer Science
Volume	15668
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025
Abbreviated title	SSVM 2025
Country/Territory	United Kingdom
City	Dartington
Period	18/05/25 → 22/05/25

Funding

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.

Keywords

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

Access to Document

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

pdfFinal published version, 1.58 MBLicence: TAVERNE

https://arxiv.org/abs/2504.03388v1Licence: Unspecified

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, Dartington, UK, May 18–22, 2025, Proceedings, Part II (pp. 192-204). (Lecture Notes in Computer Science; Vol. 15668). Springer. 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, Dartington, UK, May 18–22, 2025, Proceedings, Part II. editor / Tatiana A. Bubba ; Romina Gaburro ; Silvia Gazzola ; Kostas Papafitsoros ; Marcelo Pereyra ; Carola-Bibiane Schönlieb. Cham : Springer, 2025. pp. 192-204 (Lecture Notes in Computer Science).

@inproceedings{4bd5c888cc47442f8922d6415d839043,

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{\texttimes}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",

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booktitle = "Scale Space and Variational Methods in Computer Vision",

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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, Dartington, UK, May 18–22, 2025, Proceedings, Part II. Lecture Notes in Computer Science, vol. 15668, Springer, Cham, pp. 192-204, 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025, 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. (Corresponding author); Sherry, Finn M.; Berendschot, Tos T.J.M. et al.
Scale Space and Variational Methods in Computer Vision: 10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II. ed. / Tatiana A. Bubba; Romina Gaburro; Silvia Gazzola; Kostas Papafitsoros; Marcelo Pereyra; Carola-Bibiane Schönlieb. Cham: Springer, 2025. p. 192-204 (Lecture Notes in Computer Science; Vol. 15668).

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

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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.

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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, Dartington, UK, May 18–22, 2025, Proceedings, Part II. Cham: Springer. 2025. p. 192-204. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-92369-2_15

Crossing-Preserving Geodesic Tracking on Spherical Images

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