Advertisement

On the Manifold Structure of the Space of Brain Images

  • Samuel Gerber
  • Tolga Tasdizen
  • Sarang Joshi
  • Ross Whitaker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5761)

Abstract

This paper investigates an approach to model the space of brain images through a low-dimensional manifold. A data driven method to learn a manifold from a collections of brain images is proposed. We hypothesize that the space spanned by a set of brain images can be captured, to some approximation, by a low-dimensional manifold, i.e. a parametrization of the set of images. The approach builds on recent advances in manifold learning that allow to uncover nonlinear trends in data. We combine this manifold learning with distance measures between images that capture shape, in order to learn the underlying structure of a database of brain images. The proposed method is generative. New images can be created from the manifold parametrization and existing images can be projected onto the manifold. By measuring projection distance of a held out set of brain images we evaluate the fit of the proposed manifold model to the data and we can compute statistical properties of the data using this manifold structure. We demonstrate this technology on a database of 436 MR brain images.

Keywords

Brain Image Gaussian Mixture Model Reconstruction Error Ambient Space Manifold Structure 
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.

References

  1. 1.
    Woods, R.P., Dapretto, M., Sicotte, N.L., Toga, A.W., Mazziotta, J.C.: Creation and use of a talairach-compatible atlas for accurate, automated, nonlinear intersubject registration, and analysis of functional imaging data. Human Brain Mapping 8(2-3), 73–79 (1999)CrossRefGoogle Scholar
  2. 2.
    Blezek, D.J., Miller, J.V.: Atlas stratification. Medical Image Analysis 11(5) (2007)Google Scholar
  3. 3.
    Sabuncu, M.R., Balci, S.K., Golland, P.: Discovering modes of an image population through mixture modeling. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 381–389. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Zöllei, L., Learned-Miller, E.G., Grimson, W.E.L., Wells, W.M.: Efficient population registration of 3D data. In: Liu, Y., Jiang, T.-Z., Zhang, C. (eds.) CVBIA 2005. LNCS, vol. 3765, pp. 291–301. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Studholme, C., Cardenas, V.: A template free approach to volumetric spatial normalization of brain anatomy. Pattern Recogn. Lett. 25(10), 1191–1202 (2004)CrossRefGoogle Scholar
  6. 6.
    Ericsson, A., Aljabar, P., Rueckert, D.: Construction of a patient-specific atlas of the brain: Application to normal aging. In: ISBI, May 2008, pp. 480–483 (2008)Google Scholar
  7. 7.
    Lee, J.A., Verleysen, M.: Nonlinear Dimensionality Reduction. Springer, Heidelberg (2007)CrossRefzbMATHGoogle Scholar
  8. 8.
    Twining, C.J., Marsland, S.: Constructing an atlas for the diffeomorphism group of a compact manifold with boundary, with application to the analysis of image registrations. J. Comput. Appl. Math. 222(2), 411–428 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Davis, B.C., Fletcher, P.T., Bullitt, E., Joshi, S.: Population shape regression from random design data. In: ICCV (2007)Google Scholar
  10. 10.
    Christensen, G.E., Rabbitt, R.D., Miller, M.I.: Deformable Templates Using Large Deformation Kinematics. IEEE Transactions on Medical Imaging 5(10) (1996)Google Scholar
  11. 11.
    Dupuis, P., Grenander, U.: Variational problems on flows of diffeomorphisms for image matching. Q. Appl. Math. LVI(3), 587–600 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. IJCV 61(2), 139–157 (2005)CrossRefGoogle Scholar
  13. 13.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(550), 2319–2323 (2000)CrossRefGoogle Scholar
  14. 14.
    Lorenzen, P.J., Davis, B.C., Joshi, S.: Unbiased atlas formation via large deformations metric mapping. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 411–418. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Joshi, S., Davis, B., Jomier, M., Gerig, G.: Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage 23 (2004)Google Scholar
  16. 16.
    Avants, B., Gee, J.C.: Geodesic estimation for large deformation anatomical shape averaging and interpolation. NeuroImage 23(suppl. 1), S139–S150 (2004)CrossRefGoogle Scholar
  17. 17.
    Hill, D.L.G., Hajnal, J.V., Rueckert, D., Smith, S.M., Hartkens, T., McLeish, K.: A dynamic brain atlas. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2488, pp. 532–539. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Zhang, Q., Souvenir, R., Pless, R.: On manifold structure of cardiac mri data: Application to segmentation. In: CVPR 2006, pp. 1092–1098. IEEE, Los Alamitos (2006)Google Scholar
  19. 19.
    Rohde, G., Wang, W., Peng, T., Murphy, R.: Deformation-based nonlinear dimension reduction: Applications to nuclear morphometry, pp. 500–503 (May 2008)Google Scholar
  20. 20.
    Younes, L., Arrate, F., Miller, M.I.: Evolutions equations in computational anatomy. NeuroImage 45(1, suppl. 1), S40–S50 (2009)CrossRefGoogle Scholar
  21. 21.
    Hastie, T.: Principal curves and surfaces. Ph.D Dissertation (1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Samuel Gerber
    • 1
  • Tolga Tasdizen
    • 1
  • Sarang Joshi
    • 1
  • Ross Whitaker
    • 1
  1. 1.Scientific Computing and Imaging InstituteUniversity of UtahUSA

Personalised recommendations