Vessel tracking via sub-riemannian geodesics on the projective line bundle

E.J. Bekkers, R. Duits, A. Mashtakov, Y. Sachkov

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

5 Citations (Scopus)
2 Downloads (Pure)


We study a data-driven sub-Riemannian (SR) curve optimization model for connecting local orientations in orientation lifts of images. Our model lives on the projective line bundle R2 × P1, with P1 = S1/~ with identification of antipodal points. It extends previous cortical models for contour perception on R2 × P1 to the data-driven case. We provide a complete (mainly numerical) analysis of the dynamics of the 1st Maxwell-set with growing radii of SR-spheres, revealing the cut-locus. Furthermore, a comparison of the cusp-surface in R2 × P1 to its counterpart in R2 × S1 of a previous model, reveals a general and strong reduction of cusps in spatial projections of geodesics. Numerical solutions of the model are obtained by a single wavefront propagation method relying on a simple extension of existing anisotropic fast-marching or iterative morphological scale space methods. Experiments show that the projective line bundle structure greatly reduces the presence of cusps. Another advantage of including R2 × P1 instead of R2 × S1 in the wavefront propagation is reduction of computational time.

Original languageEnglish
Title of host publicationGeometric Science of Information
Subtitle of host publicationThird International Conference, GSI, 2017 Paris, France, November 7-9, 2017: proceedings
EditorsF. Nielsen, F. Barbaresco
Place of PublicationCham
Number of pages9
ISBN (Electronic)978-3-319-68445-1
ISBN (Print)978-3-319-68444-4
Publication statusPublished - 2017
Event3rd International Conference on Geometric Science of Information, GSI 2017 - Paris, France
Duration: 7 Nov 20179 Nov 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd International Conference on Geometric Science of Information, GSI 2017


  • Projective line bundle
  • Sub-Riemannian geodesic
  • Tracking


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