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

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

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Abstract

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
PublisherSpringer
Pages773-781
Number of pages9
ISBN (Electronic)978-3-319-68445-1
ISBN (Print)978-3-319-68444-4
DOIs
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)
Volume10589 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Conference on Geometric Science of Information, GSI 2017
CountryFrance
CityParis
Period7/11/179/11/17

Keywords

  • Projective line bundle
  • Sub-Riemannian geodesic
  • Tracking

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  • Cite this

    Bekkers, E. J., Duits, R., Mashtakov, A., & Sachkov, Y. (2017). Vessel tracking via sub-riemannian geodesics on the projective line bundle. In F. Nielsen, & F. Barbaresco (Eds.), Geometric Science of Information : Third International Conference, GSI, 2017 Paris, France, November 7-9, 2017: proceedings (pp. 773-781). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10589 LNCS). Springer. https://doi.org/10.1007/978-3-319-68445-1_89