A Localized Statistical Motion Model as a Reproducing Kernel for Non-rigid Image Registration

  • Christoph JudEmail author
  • Alina Giger
  • Robin Sandkühler
  • Philippe C. Cattin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10434)


Thoracic image registration forms the basis for many applications as for example respiratory motion estimation and physiological investigations of the lung. Although clear motion patterns are shared among different subjects, such as the diaphragm moving in superior and inferior direction, in current image registration methods such basic prior knowledge is not considered. In this paper, we propose a novel approach for integrating a statistical motion model (SMM) into a parametric non-rigid registration framework. We formulate the SMM as a reproducing kernel and integrate it into a kernel machine for image registration. Since empirical samples are rare and statistical models built from small sample size are usually over-restrictive we localize the SMM by damping spatial long-range correlations and reduce the model bias by adding generic transformations to the SMM. As an example, we show our methods applicability on the example of the Dirlab 4DCT lung images where we build leave-one-out models for estimating the respiratory motion.


Statistical motion model Image registration 


  1. 1.
    Castillo, E., Castillo, R., Martinez, J., Shenoy, M., Guerrero, T.: Four-dimensional deformable image registration using trajectory modeling. Phys. Med. Biol. 55(1), 305 (2009)CrossRefGoogle Scholar
  2. 2.
    Chen, M., Lu, W., Chen, Q., Ruchala, K.J., Olivera, G.H.: A simple fixed-point approach to invert a deformation field. Med. Phys. 35(1), 81–88 (2008)CrossRefGoogle Scholar
  3. 3.
    Ehrhardt, J., Werner, R., Schmidt-Richberg, A., Handels, H.: Statistical modeling of 4D respiratory lung motion using diffeomorphic image registration. IEEE Trans. Med. Imaging 30(2), 251–265 (2011)CrossRefGoogle Scholar
  4. 4.
    Hofmann, T., Schölkopf, B., Smola, A.J.: Kernel methods in machine learning. Ann. Stat. 36, 1171–1220 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jud, C., Möri, N., Bitterli, B., Cattin, P.C.: Bilateral regularization in reproducing kernel Hilbert spaces for discontinuity preserving image registration. In: Wang, L., Adeli, E., Wang, Q., Shi, Y., Suk, H.-I. (eds.) MLMI 2016. LNCS, vol. 10019, pp. 10–17. Springer, Cham (2016). doi: 10.1007/978-3-319-47157-0_2CrossRefGoogle Scholar
  6. 6.
    Jud, C., Möri, N., Cattin, P.C.: Sparse kernel machines for discontinuous registration and nonstationary regularization. In: Proceedings of the International Workshop on Biomedical Image Registration, pp. 9–16 (2016)Google Scholar
  7. 7.
    Jud, C., Preiswerk, F., Cattin, P.C.: Respiratory motion compensation with topology independent surrogates. In: Workshop on Imaging and Computer Assistance in Radiation Therapy (2015)Google Scholar
  8. 8.
    Lüthi, M., Jud, C., Vetter, T.: A unified approach to shape model fitting and non-rigid registration. In: Wu, G., Zhang, D., Shen, D., Yan, P., Suzuki, K., Wang, F. (eds.) MLMI 2013. LNCS, vol. 8184, pp. 66–73. Springer, Cham (2013). doi: 10.1007/978-3-319-02267-3_9CrossRefGoogle Scholar
  9. 9.
    Pace, D.F., Aylward, S.R., Niethammer, M.: A locally adaptive regularization based on anisotropic diffusion for deformable image registration of sliding organs. IEEE Trans. Med. Imaging 32(11), 2114–2126 (2013)CrossRefGoogle Scholar
  10. 10.
    Polyak, B.T., Juditsky, A.B.: Acceleration of stochastic approximation by averaging. SIAM J. Control Optim. 30(4), 838–855 (1992)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Preiswerk, F., De Luca, V., Arnold, P., Celicanin, Z., Petrusca, L., Tanner, C., Bieri, O., Salomir, R., Cattin, P.C.: Model-guided respiratory organ motion prediction of the liver from 2D ultrasound. Med. Image Anal. 18(5), 740–751 (2014)CrossRefGoogle Scholar
  12. 12.
    Preston, J.S., Joshi, S., Whitaker, R.: Deformation estimation with automatic sliding boundary computation. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9902, pp. 72–80. Springer, Cham (2016). doi: 10.1007/978-3-319-46726-9_9CrossRefGoogle Scholar
  13. 13.
    Risser, L., Vialard, F.X., Baluwala, H.Y., Schnabel, J.A.: Piecewise-diffeomorphic image registration: application to the motion estimation between 3D CT lung images with sliding conditions. Med. Image Anal. 17(2), 182–193 (2013)CrossRefGoogle Scholar
  14. 14.
    Shi, W., Jantsch, M., Aljabar, P., Pizarro, L., Bai, W., Wang, H.: ORegan, D., Zhuang, X., Rueckert, D.: Temporal sparse free-form deformations. Med. Image Anal. 17(7), 779–789 (2013)CrossRefGoogle Scholar
  15. 15.
    Vishnevskiy, V., Gass, T., Szekely, G., Tanner, C., Goksel, O.: Isotropic total variation regularization of displacements in parametric image registration. IEEE Trans. Med. Imaging 36, 385–395 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Christoph Jud
    • 1
    Email author
  • Alina Giger
    • 1
  • Robin Sandkühler
    • 1
  • Philippe C. Cattin
    • 1
  1. 1.Department of Biomedical EngineeringUniversity of BaselAllschwilSwitzerland

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