Globally Optimal Active Contours, Sequential Monte Carlo and On-Line Learning for Vessel Segmentation

  • Charles Florin
  • Nikos Paragios
  • Jim Williams
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3953)


In this paper we propose a Particle Filter-based propagation approach for the segmentation of vascular structures in 3D volumes. Because of pathologies and inhomogeneities, many deterministic methods fail to segment certain types of vessel. Statistical methods represent the solution using a probability density function (pdf). This pdf does not only indicate the best possible solution, but also valuable information about the solution’s variance. Particle Filters are used to learn the variations of direction and appearance of the vessel as the segmentation goes. These variations are used in turn in the particle filters framework to control the perturbations introduced in the Sampling Importance Resampling step (SIR). For the segmentation itself, successive planes of the vessel are modeled as states of a Particle Filter. Such states consist of the orientation, position and appearance (in statistical terms) of the vessel. The shape of the vessel and subsequently the particles pdf are recovered using globally active contours, implemented using circular shortest paths by branch and bound [1] that guarantees the global optimal solution. Promising results on the segmentation of coronary arteries demonstrate the potential of the proposed approach.


Gaussian Mixture Model Particle Filter Active Contour Deformable Model Minimal Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Appleton, B., Sun, C.: Circular shortest paths by branch and bound.  36(11), 2513–2520 (November 2003)Google Scholar
  2. 2.
    Avants, B., Williams, J.: An adaptive minimal path generation technique for vessel tracking in cta/ce-mra volume images. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 707–716. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Cañero, C., Radeva, P.: Vesselness enhancement diffusion. Pattern Recognition Letters 24(16), 3141–3151 (2003)CrossRefGoogle Scholar
  4. 4.
    Caselles, V., Catté, F., Coll, B., Dibos, F.: A geometric model for active contours in image processing. Numerische Mathematik 66(1), 1–31 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Deschamps, T., Cohen, L.D.: Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Medical Image Analysis 5(4), 281–299 (2001)CrossRefGoogle Scholar
  6. 6.
    Descoteaux, M., Collins, L., Siddiqi, K.: Geometric Flows for Segmenting Vasculature in MRI: Theory and Validation. In: Medical Imaging Computing and Computer-Assisted Intervention, pp. 500–507 (2004)Google Scholar
  7. 7.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Doucet, A., de Freitas, J., Gordon, N.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001)zbMATHGoogle Scholar
  9. 9.
    Duda, R., Hart, P.: Pattern Classification and Scene Analysis. John Wiley and Sons, Chichester (1973)zbMATHGoogle Scholar
  10. 10.
    Fearnhead, P., Clifford, P.: Online inference for well-log data. Journal of the Royal Statistical Society 65, 887–899 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Figueiredo, M., Leitao, J.: A nonsmoothing approach to the estimation of of vessel controus in angiograms. IEEE Transactions on Medical Imaging 14, 162–172 (1995)CrossRefGoogle Scholar
  12. 12.
    Frangi, A., Niessen, W., Nederkoorn, P., Elgersma, O., Viergever, M.: Three-dimensional model-based stenosis quantification of the carotid arteries from contrast-enhanced MR angiography. In: Mathematical Methods in Biomedical Image Analysis, pp. 110–118 (2000)Google Scholar
  13. 13.
    Gordon, N.: Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation. IEE Proceedings 140, 107–113 (1993)Google Scholar
  14. 14.
    Gordon, N.: On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing 10, 197–208 (2000)CrossRefGoogle Scholar
  15. 15.
    Gordon, N.: A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking. IEEE Transactions on Signal Processing 50, 174–188 (2002)CrossRefGoogle Scholar
  16. 16.
    Hart, M., Holley, L.: A method of Automated Coronary Artery Trackin in Unsubtracted Angiograms. IEEE Computers in Cardiology, 93–96 (1993)Google Scholar
  17. 17.
    Isard, M., Blake, A.: Contour Tracking by Stochastic Propagation of Conditional Density. In: European Conference on Computer Vision, vol. I, pp. 343–356 (1996)Google Scholar
  18. 18.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active Contour Models. In: IEEE International Conference in Computer Vision, pp. 261–268 (1987)Google Scholar
  19. 19.
    Krissian, K., Malandain, G., Ayache, N., Vaillant, R., Trousset, Y.: Model based detection of tubular structures in 3d images. Computer Vision and Image Understanding 80, 130–171 (2000)zbMATHCrossRefGoogle Scholar
  20. 20.
    Lorigo, L., Faugeras, O., Grimson, E., Keriven, R., Kikinis, R., Nabavi, A., Westin, C.: Codimension-Two Geodesic Active Controus for the Segmentation of Tubular Structures. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. I: 444–451 (2000)Google Scholar
  21. 21.
    Malladi, R., Sethian, J.: A Real-Time Algorithm for Medical Shape Recovery. In: International Conference on Computer Vision, pp. 304–310 (1998)Google Scholar
  22. 22.
    Nain, D., Yezzi, A., Turk, G.: Vessel Segmentation Using a Shape Driven Flow. In: Medical Imaging Copmuting and Computer-Assisted Intervention (2004)Google Scholar
  23. 23.
    O’Donnell, T., Boult, T., Fang, X., Gupta, A.: The Extruded Generalized Cylider: A Deformable Model for Object Recovery. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 174–181 (1994)Google Scholar
  24. 24.
    Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  25. 25.
    Petrocelli, R., Manbeck, K., Elion, J.: Three Dimentional Structue Recognition in Digital Angiograms using Gauss-Markov Models. IEEE Computers in Radiology, 101–104 (1993)Google Scholar
  26. 26.
    Rueckert, D., Burger, P., Forbat, S., Mohiadin, R., Yang, G.: Automatic Tracking of the Aorta in Cardiovascular MR images using Deformable Models. IEEE Transactions on Medical Imaging 16, 581–590 (1997)CrossRefGoogle Scholar
  27. 27.
    Sato, Y., Nakajima, S., Atsumi, H., Koller, T., Gerig, G., Yoshida, S., Kikinis, R.: 3D Multiscale line filter for segmentation and visualization of curvilinear structures in medical images. In: Conference on Computer Vision, Virtual Reality and Robotics in Medicine and Media Robotics and Computer-Assisted Surgery, pp. 213–222 (1997)Google Scholar
  28. 28.
    Sethian, J.: A Review of the Theory, Algorithms, and Applications of Level Set Methods for Propagating Interfaces, pp. 487–499. Cambridge University Press, Cambridge (1995)Google Scholar
  29. 29.
    Sorantin, E., Halmai, C., Erbohelyi, B., Palagyi, K., Nyul, K., Olle, K., Geiger, B., Lindbichler, F., Friedrich, G., Kiesler, K.: Spiral-CT-based assesment of Tracheal Stenoses using 3D Skeletonization. IEEE Transactions on Medical Imaging 21, 263–273 (2002)CrossRefGoogle Scholar
  30. 30.
    Toyama, K., Blake, A.: Probabilistic Tracking in a Metric Space. In: IEEE International Conference in Computer Vision, pp. 50–59 (2001)Google Scholar
  31. 31.
    Vasilevskiy, A., Siddiqi, K.: Flux Maximizing Geometric Flows. In: IEEE International Conference in Computer Vision, pp. I: 149–154 (2001)Google Scholar
  32. 32.
    West, W.: Modelling with mixtures. In: Bernardo, J., Berger, J., Dawid, A., Smith, A. (eds.) Bayesian Statistics. Clarendon Press (1993)Google Scholar
  33. 33.
    Yim, P., Choyke, P., Summers, R.: Grayscale Skeletonization of Small Vessels inMagnetic Resonance Angiography. IEEE Transactions on Medical Imaging 19, 568–576 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Charles Florin
    • 1
  • Nikos Paragios
    • 2
  • Jim Williams
    • 1
  1. 1.Imaging & Visualization DepartmentSiemens Corporate ResearchPrincetonUSA
  2. 2.Grande Voie des VignesMAS – Ecole Centrale de ParisChatenay-Malabry CedexFrance

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