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Efficient Kernel Density Estimation Of Shape And Intensity Priors For Level Set Segmentation

  • Daniel Cremers
  • Mikael Rousson
Part of the Topics in Biomedical Engineering. International Book Series book series (ITBE)

We propose a nonlinear statistical shape model for level set segmentation that can be efficiently implemented. Given a set of training shapes, we perform a kernel density estimation in the low-dimensional subspace spanned by the training shapes. In this way, we are able to combine an accurate model of the statistical shape distribution with efficient optimization in a finite-dimensional subspace. In a Bayesian inference framework, we integrate the nonlinear shape model with a nonparametric intensity model and a set of pose parameters that are estimated in a more direct data-driven manner than in previously proposed level set methods. Quantitative results show superior performance (regarding runtime and segmentation accuracy) of the proposed nonparametric shape prior over existing approaches.

Keywords

Kernel Density Active Contour Kernel Density Estimation Statistical Shape Segmentation Accuracy 
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.

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9 References

  1. 1.
    Dervieux A, Thomasset F. 1979. A finite element method for the simulation of Rayleigh- Taylor instability. In Approximation methods for Navier-Stokes problems, pp. 145-158. Ed R Rautmann. Berlin: Springer.Google Scholar
  2. 2.
    Osher SJ, Sethian JA. 1988. Front propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12-49.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Caselles V, Catt é F, Coll T, Dibos F. 1993. A geometric model for active contours in image processing. Num Math 66:1-31.MATHCrossRefGoogle Scholar
  4. 4.
    Malladi R, Sethian JA, Vemuri BC. 1994. A topology independent shape modeling scheme. In Proceedings of the SPIE conference on geometric methods in computer vision, Vol. 2031, pp. 246-258. Bellingham, WA: SPIE.Google Scholar
  5. 5.
    Kichenassamy S, Kumar A, Olver PJ, Tannenbaum A, Yezzi AJ. 1995. Gradient flows and geometric active contour models. In Proceedings of the fifth international conference computer vision (ICCV’95), pp. 810-815. Washington, DC: IEEE Computer Society.CrossRefGoogle Scholar
  6. 6.
    Leventon M, Grimson W, Faugeras O. 2000. Statistical shape influence in geodesic active contours. In Proceedings of the IEEE international conference on computer vision and pattern recognition (CVPR), Vol. 1, pp. 316-323. Washington, DC: IEEE Computer Society.Google Scholar
  7. 7.
    Tsai A, Yezzi AJ, Willsky AS. 2003. A shape-based approach to the segmentation of medical imagery using level sets. IEEE Trans Med Imaging, 22(2):137-154.CrossRefGoogle Scholar
  8. 8.
    Cremers D, Osher SJ, Soatto S. 2006. Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. Int J Comput Vision. 69(3):335-351.CrossRefGoogle Scholar
  9. 9.
    Rousson M, Paragios N, Deriche R. 2004. Implicit active shape models for 3d segmentation in MRI imaging. In Proceedings of the international conference on medical image computing and computer-assisted intervention (MICCAI 2000). Lecture notes in computer science, Vol. 2217, pp. 209-216. New York: Springer.Google Scholar
  10. 10.
    Dam EB, Fletcher PT, Pizer S, Tracton G, Rosenman J. 2004. Prostate shape modeling based on principal geodesic analysis bootstrapping. In Proceedings of the international conference on medical image computing and computer-assisted intervention (MICCAI 2003). Lecture notes in computer science, Vol. 2217, pp. 1008-1016. New York: Springer.Google Scholar
  11. 11.
    Freedman D, Radke RJ, Zhang T, Jeong Y, Lovelock DM, Chen GT. 2005. Model-based seg- mentation of medical imagery by matching distributions. IEEE Trans Med Imaging 24(3):281-292.CrossRefGoogle Scholar
  12. 12.
    Rosenblatt F. 1956. Remarks on some nonparametric estimates of a density function. Ann Math Stat 27:832-837.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Silverman BW. 1992. Density estimation for statistics and data analysis. London: Chapman and Hall.Google Scholar
  14. 14.
    Paragios N, Deriche R. 2002. Geodesic active regions and level set methods for supervised texture segmentation. Int J Comput Vision 46(3):223-247.MATHCrossRefGoogle Scholar
  15. 15.
    Chan LA Vese TF. 2001. Active contours without edges. IEEE Trans Med Imaging, 10(2):266-277.Google Scholar
  16. 16.
    Rousson, M., Cremers, D., 2005. Efficient Kernel Density Estimation of Shape and Intensity Priors for Level Set Segmentation, International conference on medical image computing and computed-assisted intervention (MICCAI 2005), 2: 757-764.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Daniel Cremers
    • 1
  • Mikael Rousson
    • 2
  1. 1.Department of Computer ScienceUniversity of BonnGermany
  2. 2.Department of Imaging and VisualizationSiemens Corporate ResearchPrincetonUSA

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