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An Inhomogeneous Multi-resolution Regularization Concept for Discontinuity Preserving Image Registration

  • Christoph JudEmail author
  • Robin Sandkühler
  • Philippe C. Cattin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10883)

Abstract

Sliding organs pose challenges in the registration of dynamic medical images because the smoothness criterion which is commonly assumed over the whole image domain does not apply at the sliding interfaces. In this case, image registration methods have to cope with local discontinuities in the correspondence map. We present a new registration methodology based on a multi-resolution transformation model which is defined as a directed acyclic graph. The graph’s edges connect consecutive resolution levels enabling to inhomogeneously pass displacements through to higher levels. Thus, they are well suited to cope with local discontinuities while aiming at smooth correspondence maps. We introduce three regularization terms which operate on the graph. A total variation term ensuring discontinuity preserving smoothness, a sparsity term on zero edge-weights to prevent trivial solutions and a term which prefers transformations which are explained in lower resolution levels. For an early proof of concept we analyze the registration performance of our method on synthetic 2D data and on a 2D slice of the POPI model.

References

  1. 1.
    Bajcsy, R., Kovačič, S.: Multiresolution elastic matching. Comput. Vis. Graph. Image Process. 46(1), 1–21 (1989)CrossRefGoogle Scholar
  2. 2.
    Heinrich, M.P., Jenkinson, M., Brady, M., Schnabel, J.A.: MRF-based deformable registration and ventilation estimation of lung CT. IEEE Trans. Med. Imaging 32(7), 1239–1248 (2013)CrossRefGoogle Scholar
  3. 3.
    Jud, C., Möri, N., Cattin, P.C.: Sparse kernel machines for discontinuous registration and nonstationary regularization. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pp. 9–16 (2016)Google Scholar
  4. 4.
    Jud, C., Sandkühler, R., Möri, N., Cattin, P.C.: Directional Averages for motion segmentation in discontinuity preserving image registration. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10433, pp. 249–256. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66182-7_29CrossRefGoogle Scholar
  5. 5.
    Kiriyanthan, S., Fundana, K., Majeed, T., Cattin, P.C.: Discontinuity preserving image registration through motion segmentation: a primal-dual approach. Comput. Math. Methods Med. 2016, 20 (2016). Article ID 9504949MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lester, H., Arridge, S.R.: A survey of hierarchical non-linear medical image registration. Pattern Recogn. 32(1), 129–149 (1999)CrossRefGoogle Scholar
  7. 7.
    Mendonca, M.W.: Multilevel Optimization: convergence theory, algorithms and application to derivative-free optimization. Ph.D. thesis, Phd thesis, Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium (2009)Google Scholar
  8. 8.
    Modersitzki, J.: Numerical Methods for Image Registration. Oxford University Press on Demand, Oxford (2004)Google 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.
    Papież, B.W., Heinrich, M.P., Fehrenbach, J., Risser, L., Schnabel, J.A.: An implicit sliding-motion preserving regularisation via bilateral filtering for deformable image registration. Med. Image Anal. 18(8), 1299–1311 (2014)CrossRefGoogle Scholar
  11. 11.
    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).  https://doi.org/10.1007/978-3-319-46726-9_9CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    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
  14. 14.
    Schmidt-Richberg, A., Werner, R., Handels, H., Ehrhardt, J.: Estimation of slipping organ motion by registration with direction-dependent regularization. Med. Image Anal. 16(1), 150–159 (2012)CrossRefGoogle Scholar
  15. 15.
    von Siebenthal, M., Szekely, G., Gamper, U., Boesiger, P., Lomax, A., Cattin, P.: 4D MR imaging of respiratory organ motion and its variability. Phys. Med. Biol. 52(6), 1547 (2007)CrossRefGoogle Scholar
  16. 16.
    Sotiras, A., Davatzikos, C., Paragios, N.: Deformable medical image registration: a survey. IEEE Trans. Med. Imaging 32(7), 1153–1190 (2013)CrossRefGoogle Scholar
  17. 17.
    Sun, W., Niessen, W.J., van Stralen, M., Klein, S.: Simultaneous multiresolution strategies for nonrigid image registration. IEEE Trans. Image Process. 22(12), 4905–4917 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Thirion, J.P.: Image matching as a diffusion process: an analogy with Maxwell’s demons. Med. Image Anal. 2(3), 243–260 (1998)CrossRefGoogle Scholar
  19. 19.
    Van Stralen, M., Pluim, J.P.: Optimal discrete multi-resolution deformable image registration. In: Proceedings of the Sixth IEEE International Conference on Symposium on Biomedical Imaging: From Nano to Macro, pp. 947–950. IEEE Press (2009)Google Scholar
  20. 20.
    Vandemeulebroucke, J., Sarrut, D., Clarysse, P., et al.: The POPI-model, a point-validated pixel-based breathing thorax model. In: XVth International Conference on the Use of Computers in Radiation Therapy (ICCR), vol. 2, pp. 195–199 (2007)Google Scholar
  21. 21.
    Viergever, M.A., Maintz, J.A., Klein, S., Murphy, K., Staring, M., Pluim, J.P.: A survey of medical image registration-under review. Med. Image Anal. 33, 140–144 (2016)CrossRefGoogle Scholar
  22. 22.
    Vishnevskiy, V., Gass, T., Székely, G., Goksel, O.: Total variation regularization of displacements in parametric image registration. In: Yoshida, H., Näppi, J., Saini, S. (eds.) Abdominal Imaging. Computational and Clinical Applications. ABD-MICCAI 2014. Lecture Notes in Computer Science, vol. 8676. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-13692-9_20Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

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

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