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An Isotropic Minimal Path Based Framework for Segmentation and Quantification of Vascular Networks

  • Emmanuel CohenEmail author
  • Laurent D. Cohen
  • Thomas Deffieux
  • Mickael Tanter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10746)

Abstract

Minimal path approaches for image analysis aim to extract curves minimizing an energy functional. The energy of a path corresponds to its weighted curve length according to a relevant metric function. In this study, we design a binary isotropic metric model with the use of a Hessian-based vascular enhancement filter in order to extract geometrical features from vascular networks. We introduce a constrained keypoint search method able to extract subpixel vessel centrelines, diameters and bifurcations. Experiments on retinal images demonstrated that the proposed framework achieves similar even better segmentation performances as compared with methods using more sophisticated metric designs.

Notes

Acknowledgement

We would like to particularly thank Dr. Da Chen for his precious help and advice.

References

  1. 1.
    Attali, D., Boissonnat, J.D., Edelsbrunner, H.: Stability and computation of medial axes-a state-of-the-art report. In: Möller, T., Hamann, B., Russell, R.D. (eds.) Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. MATHVISUAL, pp. 109–125. Springer, Heidelberg (2009).  https://doi.org/10.1007/b106657_6 CrossRefGoogle Scholar
  2. 2.
    Bekkers, E.J., Duits, R., Mashtakov, A., Sanguinetti, G.R.: Data-driven sub-riemannian geodesics in SE(2). In: Aujol, J.-F., Nikolova, M., Papadakis, N. (eds.) SSVM 2015. LNCS, vol. 9087, pp. 613–625. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-18461-6_49 Google Scholar
  3. 3.
    Benmansour, F., Cohen, L.D.: Fast object segmentation by growing minimal paths from a single point on 2D or 3D images. J. Math. Imaging Vis. 33(2), 209–221 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Benmansour, F., Cohen, L.D.: Tubular structure segmentation based on minimal path method and anisotropic enhancement. Int. J. Comput. Vis. 92(2), 192–210 (2011)CrossRefGoogle Scholar
  5. 5.
    Bullitt, E., Gerig, G., Pizer, S.M., Lin, W., Aylward, S.R.: Measuring tortuosity of the intracerebral vasculature from mra images. IEEE Trans. Med. Imaging 22(9), 1163–1171 (2003)CrossRefGoogle Scholar
  6. 6.
    Chen, D., Cohen, L.D.: Piecewise geodesics for vessel centerline extraction and boundary delineation with application to retina segmentation. In: Aujol, J.-F., Nikolova, M., Papadakis, N. (eds.) SSVM 2015. LNCS, vol. 9087, pp. 270–281. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-18461-6_22 Google Scholar
  7. 7.
    Chen, D., Mirebeau, J.M., Cohen, L.D.: Vessel tree extraction using radius-lifted keypoints searching scheme and anisotropic fast marching method. J. Algorithms Comput. Technol. 10(4), 224–234 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cohen, E., Deffieux, T., Demené, C., Cohen, L.D., Tanter, M.: 3D vessel extraction in the rat brain from ultrasensitive doppler images. In: Gefen, A., Weihs, D. (eds.) Computer Methods in Biomechanics and Biomedical Engineering. LNB, pp. 81–91. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-59764-5_10 CrossRefGoogle Scholar
  9. 9.
    Cohen, E., Deffieux, T., Tiran, E., Demene, C., Cohen, L., Tanter, M.: Ultrasensitive doppler based neuronavigation system for preclinical brain imaging applications. In: 2016 IEEE International Ultrasonics Symposium (IUS), pp. 1–4. IEEE (2016)Google Scholar
  10. 10.
    Cohen, L.D., Kimmel, R.: Global minimum for active contour models: a minimal path approach. Int. J. Comput. Vision 24(1), 57–78 (1997)CrossRefGoogle Scholar
  11. 11.
    Crandall, M.G., Lions, P.L.: Viscosity solutions of hamilton-jacobi equations. Trans. Am. Math. Soc. 277(1), 1–42 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Demené, C.: Cartographie vasculaire et fonctionnelle du cerveau par échographie Doppler ultrarapide chez le petit animal et le nouveau-né. Ph.D. thesis, Paris 7 (2015)Google Scholar
  13. 13.
    Deschamps, T., Cohen, L.D.: Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Med. Image Anal. 5(4), 281–299 (2001)CrossRefGoogle Scholar
  14. 14.
    Frangi, A.F., Niessen, W.J., Vincken, K.L., Viergever, M.A.: Multiscale vessel enhancement filtering. In: Wells, W.M., Colchester, A., Delp, S. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 130–137. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0056195 CrossRefGoogle Scholar
  15. 15.
    Hart, W.E., Goldbaum, M., Côté, B., Kube, P., Nelson, M.R.: Measurement and classification of retinal vascular tortuosity. Int. J. Med. Inform. 53(2), 239–252 (1999)CrossRefGoogle Scholar
  16. 16.
    Jerman, T., Pernus, F., Likar, B., Spiclin, Z.: Enhancement of vascular structures in 3D and 2D angiographic images. IEEE Trans. Med. Imaging 35(9), 2107 (2016)CrossRefGoogle Scholar
  17. 17.
    Kaul, V., Yezzi, A., Tsai, Y.: Detecting curves with unknown endpoints and arbitrary topology using minimal paths. IEEE Trans. Pattern Anal. Mach. Intell. 34(10), 1952–1965 (2012)CrossRefGoogle Scholar
  18. 18.
    Law, M.W.K., Chung, A.C.S.: Three dimensional curvilinear structure detection using optimally oriented flux. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008. LNCS, vol. 5305, pp. 368–382. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-88693-8_27 CrossRefGoogle Scholar
  19. 19.
    Li, H., Yezzi, A., Cohen, L.: 3D multi-branch tubular surface and centerline extraction with 4D iterative key points. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5762, pp. 1042–1050. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-04271-3_126 CrossRefGoogle Scholar
  20. 20.
    Mirebeau, J.M.: Anisotropic fast-marching on cartesian grids using lattice basis reduction. SIAM J. Numer. Anal. 52(4), 1573–1599 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Peyré, G., Péchaud, M., Keriven, R., Cohen, L.D.: Geodesic methods in computer vision and graphics. Found. Trends® Comput. Graph. Vis. 5(3–4), 197–397 (2010)zbMATHGoogle Scholar
  22. 22.
    Rouy, E., Tourin, A.: A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal. 29(3), 867–884 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci. 93(4), 1591–1595 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, vol. 3. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  25. 25.
    Sofka, M., Stewart, C.V.: Retinal vessel centerline extraction using multiscale matched filters, confidence and edge measures. IEEE Trans. Med. Imaging 25(12), 1531–1546 (2006)CrossRefGoogle Scholar
  26. 26.
    Staal, J., Abramoff, M., Niemeijer, M., Viergever, M., van Ginneken, B.: Ridge based vessel segmentation in color images of the retina. IEEE Trans. Med. Imaging 23(4), 501–509 (2004)CrossRefGoogle Scholar
  27. 27.
    Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Autom. Control 40(9), 1528–1538 (1995)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Emmanuel Cohen
    • 1
    • 2
    Email author
  • Laurent D. Cohen
    • 1
  • Thomas Deffieux
    • 2
  • Mickael Tanter
    • 2
  1. 1.CEREMADE, PSL Research University, Université Paris Dauphine, CNRS, UMR 7534ParisFrance
  2. 2.Institut Langevin, PSL Research University, ESPCI ParisTech, CNRS, UMR 7587, INSERM U979ParisFrance

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