A Static SMC Sampler on Shapes for the Automated Segmentation of Aortic Calcifications

  • Kersten Petersen
  • Mads Nielsen
  • Sami S. Brandt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6314)


In this paper, we propose a sampling-based shape segmentation method that builds upon a global shape and a local appearance model. It is suited for challenging problems where there is high uncertainty about the correct solution due to a low signal-to-noise ratio, clutter, occlusions or an erroneous model. Our method suits for segmentation tasks where the number of objects is not known a priori, or where the object of interest is invisible and can only be inferred from other objects in the image. The method was inspired by shape particle filtering from de Bruijne and Nielsen, but shows substantial improvements to it. The principal contributions of this paper are as follows: (i) We introduce statistically motivated importance weights that lead to better performance and facilitate the application to new problems. (ii) We adapt the static sequential Monte Carlo (SMC) algorithm to the problem of image segmentation, where the algorithm proves to sample efficiently from high-dimensional static spaces. (iii) We evaluate the static SMC sampler on shapes on a medical problem of high relevance: the automated quantification of aortic calcifications on X-ray radiographs for the prognosis and diagnosis of cardiovascular disease and mortality. Our results suggest that the static SMC sampler on shapes is more generic, robust, and accurate than shape particle filtering, while being computationally equally costly.


Shape Particle Shape Model Automate Segmentation Importance Weight Target Distribution 
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.
    Breiman, L.: Random forests. Machine Learning 45(1), 5–32 (2001)zbMATHCrossRefGoogle Scholar
  2. 2.
    Brejl, M., Sonka, M.: Object localization and border detection criteria design in edge-based image segmentation: Automated learning from examples. IEEE Trans. Med. Imaging 19(10), 973–985 (2000)CrossRefGoogle Scholar
  3. 3.
    de Bruijne, M.: Shape particle guided tissue classification. In: Golland, P., Rueckert, D. (eds.) MMBIA (2006)Google Scholar
  4. 4.
    de Bruijne, M., Nielsen, M.: Image segmentation by shape particle filtering. In: ICPR 2004, vol. 3, pp. 722–725 (2004)Google Scholar
  5. 5.
    de Bruijne, M., Nielsen, M.: Shape particle filtering for image segmentation. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 168–175. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    de Bruijne, M., Nielsen, M.: Multi-object segmentation using shape particles. In: IPMI, pp. 762–773 (2005)Google Scholar
  7. 7.
    Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models—their training and application. Comput. Vis. Image Underst. 61(1), 38–59 (1995)CrossRefGoogle Scholar
  8. 8.
    Del Moral, P., Doucet, A., Jasra, A.: Sequential monte carlo samplers. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68(3), 411–436 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Deutscher, J., Blake, A., Reid, I.: Articulated body motion capture by annealed particle filtering. In: Proc. IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 126–133 (August 2002)Google Scholar
  10. 10.
    Douc, R., Cappe, O.: Comparison of resampling schemes for particle filtering. In: Pan, Y., Chen, D.-x., Guo, M., Cao, J., Dongarra, J. (eds.) ISPA 2005. LNCS, vol. 3758, pp. 64–69. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Doucet, A., de Freitas, N., Gordon, N.: Sequential Monte Carlo methods in practice. Springer, New York (2001)zbMATHGoogle Scholar
  12. 12.
    Fan, A.C.: Curve Sampling and Geometric Conditional Simulation. PhD thesis, Massachussetts Institute of Technology (February 2008)Google Scholar
  13. 13.
    Hansson, M., Brandt, S., Gudmundsson, P.: Bayesian probability maps for evaluation of cardiac ultrasound data. In: PMMIA (2009)Google Scholar
  14. 14.
    Hansson, M., Brandt, S., Gudmundsson, P., Lindgren, F.: Evaluation of cardiac ultrasound data by bayesian probability maps. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Kuno, Y., Wang, J., Pajarola, R., Lindstrom, P., Hinkenjann, A., Encarnação, M.L., Silva, C.T., Coming, D. (eds.) ISVC 2009. LNCS, vol. 5876, pp. 1073–1084. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Johansen, A.M., Del Moral, P., Doucet, A.: Sequential monte carlo samplers for rare events. Technical report, University of Cambridge, Department of Engineering, Trumpington (2005)Google Scholar
  16. 16.
    Kervrann, C., Heitz, F.: A hierarchical markov modeling approach for the segmentation and tracking of deformable shapes. Graphical Models and Image Processing 60(3), 173–195 (1998)CrossRefGoogle Scholar
  17. 17.
    Neal, R.M.: Annealed importance sampling. Statistics and Computing 11(2), 125–139 (2001)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Roberts, M.G., Cootes, T.F., Adams, J.E.: Robust active appearance models with iteratively rescaled kernels. In: Proc. BMVC, vol. 1, pp. 302–311 (2007)Google Scholar
  19. 19.
    Roberts, M.G., Cootes, T.F., Pacheco, E., Oh, T., Adams, J.E.: Segmentation of lumbar vertebrae using part-based graphs and active appearance models. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5762, pp. 1017–1024. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Smyth, P.P., Taylor, C.J., Adams, J.E.: Automatic measurement of vertebral shape using active shape models. In: Image and Vision Computing, pp. 705–714. BMVA Press (1996)Google Scholar
  21. 21.
    Wilson, P., Kauppila, L., O’Donnell, C., Kiel, D., Hannan, M., Polak, J., Cupples, L.: Abdominal aortic calcific deposits are an important predictor of vascular morbidity and mortality. Circulation (103), 1529–1534 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kersten Petersen
    • 1
  • Mads Nielsen
    • 1
    • 2
  • Sami S. Brandt
    • 2
  1. 1.Department of Computer ScienceUniversity of CopenhagenDenmark
  2. 2.Synarc Imaging TechnologiesDenmark

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