Non-rigid Image Registration Using Gaussian Mixture Models

  • Sangeetha Somayajula
  • Anand A. Joshi
  • Richard M. Leahy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7359)


Non-rigid mutual information (MI) based image registration is prone to converge to local optima due to Parzen or histogram based density estimation used in conjunction with estimation of a high dimensional deformation field. We describe an approach for non-rigid registration that uses the log-likelihood of the target image given the deformed template as a similarity metric, wherein the distribution is modeled using a Gaussian mixture model (GMM). Using GMMs reduces the density estimation step to that of estimating the parameters of the GMM, thus being more computationally efficient and requiring fewer number of samples for accurate estimation. We compare the performance of our approach (GMM-Cond) with that of MI with Parzen density estimation (Parzen-MI), on inter-subject and inter-modality (CT to MR) mouse images. Mouse image registration is challenging because of the presence of a rigid skeleton within non-rigid soft tissue, and due to major shape and posture variability in inter-subject registration. The results show that GMM-Cond has higher registration accuracy than Parzen-MI in terms of sum of squared difference in intensity and dice coefficients of overall and skeletal overlap. The GMM-Cond approach is a general approach that can be considered a semi-parametric approximation to MI based registration, and can be used an alternative to MI for high dimensional non-rigid registration.


Mutual Information Gaussian Mixture Model Joint Density Template Image Rigid Registration 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ashburner, J., Friston, K.: Nonlinear spatial normalization using basis functions. Human Brain Mapping 7(4), 254–266 (1999)CrossRefGoogle Scholar
  2. 2.
    Ashburner, J., Friston, K.J.: Unified segmentation. NeuroImage 26(3), 839–851 (2005)CrossRefGoogle Scholar
  3. 3.
    Baiker, M., Staring, M., Löwik, C.W.G.M., Reiber, J.H.C., Lelieveldt, B.P.F.: Automated Registration of Whole-Body Follow-Up MicroCT Data of Mice. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 516–523. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Silverman, B.W.: Density estimation for Statistics and Data analysis. Chapman and Hall (1986)Google Scholar
  5. 5.
    D’Agostino, E., Maes, F., Vandermeulen, D., Suetens, P.: A viscous fluid model for multimodal non-rigid image registration using mutual information. Medical Image Analysis 7(4), 565–575 (2003)CrossRefGoogle Scholar
  6. 6.
    Zhang, J., Rangarajan, A.: Bayesian multimodality non-rigid image registration via conditional density estimation. In: Information Proc. in Med. Imaging, pp. 499–511 (2003)Google Scholar
  7. 7.
    Krum, W., Griffin, L.D., Hill, D.L.G.: Non-rigid image registration: Theory and practice. Br. Journ. Radiol. 1(77), S140–S153 (2004)Google Scholar
  8. 8.
    Leventon, M.E., Grimson, W.E.L.: Multi-modal Volume Registration Using Joint Intensity Distributions. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 1057–1066. Springer, Heidelberg (1998)Google Scholar
  9. 9.
    MacLachlan, G., Peel, D.: Finite Mixture Models. Wiley (2000)Google Scholar
  10. 10.
    Kovacevic, N., Hamarneh, G., Henkelman, M.: Anatomically Guided Registration of Whole Body Mouse MR Images. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003. LNCS, vol. 2879, pp. 870–877. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Papademetris, X., Dione, D.P., Dobrucki, L.W., Staib, L.H., Sinusas, A.J.: Articulated Rigid Registration for Serial Lower-Limb Mouse Imaging. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005, Part II. LNCS, vol. 3750, pp. 919–926. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Pohl, K.M., Fisher, J., Grimson, W.E.L., Kikinis, R., Wells, W.M.: A Bayesian model for joint segmentation and registration. NeuroImage 31(1), 228–239 (2006)CrossRefGoogle Scholar
  13. 13.
    Roche, A., Malandain, G., Ayache, N., Prima, S.: Towards a Better Comprehension of Similarity Measures Used in Medical Image Registration. In: Taylor, C., Colchester, A. (eds.) MICCAI 1999. LNCS, vol. 1679, pp. 555–566. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  14. 14.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley (2001)Google Scholar
  15. 15.
    Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L., Leach, M.O., Hawkes, D.J.: Nonrigid registration using free-form deformations: application to breast mr images. IEEE Trans. Med. Imaging 18(8), 712–721 (1999)CrossRefGoogle Scholar
  16. 16.
    Shattuck, D.W., Sandor-Leahy, S.R., Schaper, K.A., Rottenberg, D.A., Leahy, R.M.: Magnetic resonance image tissue classification using a partial volume model. NeuroImage 13(5), 856–876 (2001)CrossRefGoogle Scholar
  17. 17.
    Somayajula, S., Joshi, A.A., Leahy, R.M.: Mutual information based non-rigid mouse registration using a scale-space approach. In: 5th IEEE Intl. Symposium on Biomedical Imaging, pp. 1147–1150 (2008)Google Scholar
  18. 18.
    Van de Sompel, D., Brady, M.: Regularising limited view tomography using anatomical reference images and information theoretic similarity metrics. Medical Image Analysis 16(1), 278–300 (2012)CrossRefGoogle Scholar
  19. 19.
    Wang, H., Stout, D., Chatziioannou, A.: Estimation of mouse organ locations through registration of a statistical mouse atlas with micro-ct images. IEEE Transactions on Medical Imaging 31(1), 88–102 (2012)CrossRefGoogle Scholar
  20. 20.
    Woods, R.P., Grafton, S.T., Watson, J.D.G., Sicotte, N.L., Mazziotta, J.C.: Automated image registration: I. General methods and intrasubject, intramodality validation. Journal of Computed Assisted Tomography 22, 139–152 (1998)CrossRefGoogle Scholar
  21. 21.
    Wells, W., Viola, P., Atsumi, H., Nakajima, S., Nakajima, S., Kikinis, R.: Multimodal volume registration by maximization of mutual information. Med. Image Analysis 1(1), 35–51 (1996)CrossRefGoogle Scholar
  22. 22.
    Li, X., Peterson, T.E., Gore, J.C., Dawant, B.M.: Automatic Inter-subject Registration of Whole Body Images. In: Pluim, J.P.W., Likar, B., Gerritsen, F.A. (eds.) WBIR 2006. LNCS, vol. 4057, pp. 18–25. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  23. 23.
    Zöllei, L., Jenkinson, M., Timoner, S.J., Wells, W.M.: A Marginalized MAP Approach and EM Optimization for Pair-Wise Registration. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 662–674. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sangeetha Somayajula
    • 1
  • Anand A. Joshi
    • 2
  • Richard M. Leahy
    • 2
  1. 1.Dept. of Informatics ITMerck Research LaboratoriesBostonUSA
  2. 2.Signal and Image Processing InstituteUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations