Erik J Bekkers


Assistant professor at University of Amsterdam

Vessel Tracking via Sub-Riemannian Geodesics on ℝ2×P1

Results

This page contains the results of our vessel tracking experiments on retinal image patches using a sub-Riemannian geometry. We compared the model on SE(2) with the proposed model on the projective line bundle PT(R2). Details are described in the paper.

  • The main article [1] can be found here.
  • A .zip file containing snapshots of all the results can be found here. The same color coding is used as in the article (Fig. 4):
    • Green: SE(2) geodesic connecting the seed with the sink with forward arrival direction.
    • Red-Dashed: SE(2) geodesic connecting the seed with the sink with backward arrival direction.
    • Blue: PT(R2) geodesic connecting the seed with optimal arrival direction.

PT(R2) results

Figure: Data-adaptive SR geodesics in SE(2) (in green and red-dashed) compared to SR geodesics in PT(ℝ2) (in blue). For the SE(2) case we specify antipodal boundary conditions since the correct initial and end directions are not known a priori.

References

  1. E. J. Bekkers, R. Duits, A. P. Mashtakov, and Y. L. Sachkov. "Vessel Tracking via Sub-Riemannian Geodesics on the Projective Line Bundle". In: International Conference on Geometric Science of Information. Springer, 2017, pp. 773-781.