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Bilateral Regularization in Reproducing Kernel Hilbert Spaces for Discontinuity Preserving Image Registration

  • Christoph JudEmail author
  • Nadia Möri
  • Benedikt Bitterli
  • Philippe C. Cattin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10019)

Abstract

The registration of abdominal images is an increasing field in research and forms the basis for studying the dynamic motion of organs. Particularly challenging therein are organs which slide along each other. They require discontinuous transform mappings at the sliding boundaries to be accurately aligned. In this paper, we present a novel approach for discontinuity preserving image registration. We base our method on a sparse kernel machine (SKM), where reproducing kernel Hilbert spaces serve as transformation models. We introduce a bilateral regularization term, where neighboring transform parameters are considered jointly. This regularizer enforces a bias to homogeneous regions in the transform mapping and simultaneously preserves discontinuous magnitude changes of parameter vectors pointing in equal directions. We prove a representer theorem for the overall cost function including this bilateral regularizer in order to guarantee a finite dimensional solution. In addition, we build direction-dependent basis functions within the SKM framework in order to elongate the transformations along the potential sliding organ boundaries. In the experiments, we evaluate the registration results of our method on a 4DCT dataset and show superior registration performance of our method over the tested methods.

Keywords

Transformation Model Reproduce Kernel Hilbert Space Organ Boundary Target Registration Error Representer Theorem 
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.
    Gorbunova, V., Lo, P., Ashraf, H., Dirksen, A., Nielsen, M., de Bruijne, M.: Weight preserving image registration for monitoring disease progression in lung CT. In: Axel, L., Fichtinger, G., Metaxas, D., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 863–870. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Hofmann, T., Schölkopf, B., Smola, A.J.: Kernel methods in machine learning. Ann. Stat. 36, 1171–1220 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Jud, C., Möri, N., Cattin, P.C.: Sparse kernel machines for discontinuous registration. In: 7th International Workshop on Biomedical Image Registration (2016)Google Scholar
  4. 4.
    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
  5. 5.
    Kiriyanthan, S., Fundana, K., Majeed, T., Cattin, P.C.: A primal-dual approach for discontinuity preserving image registration through motion segmentation. Int. J. Comput. Math. Methods Med. (2016, in press)Google Scholar
  6. 6.
    Möri, N., Jud, C., Salomir, R., Cattin, P.C.: Leveraging respiratory organ motion for non-invasive tumor treatment devices: a feasibility study. Phys. Med. Biol. 61(11), 4247–4267 (2016)CrossRefGoogle Scholar
  7. 7.
    Paciorek, C.J., Schervish, M.J.: Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17(5), 483–506 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., 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
  10. 10.
    Schmidt-Richberg, A.: Sliding motion in image registration. Registration Methods for Pulmonary Image Analysis, pp. 65–78. Springer, Wiesbaden (2014)CrossRefGoogle Scholar
  11. 11.
    Sotiras, A., Davatzikos, C., Paragios, N.: Deformable medical image registration: a survey. IEEE Trans. Med. Imaging 32(7), 1153–1190 (2013)CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    Vandemeulebroucke, J., Sarrut, D., Clarysse, P.: The POPI-model, a point-validated pixel-based breathing thorax model. In: International Conference on the Use of Computers in Radiation Therapy, vol. 2, pp. 195–199 (2007)Google Scholar
  14. 14.
    Vishnevskiy, V., Gass, T., Székely, G., Goksel, O.: Total variation regularization of displacements in parametric image registration. In: Yoshida, H., Näppi, J.J., Saini, S. (eds.) ABDI 2014. LNCS, vol. 8676, pp. 211–220. Springer, Heidelberg (2014)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Christoph Jud
    • 1
    Email author
  • Nadia Möri
    • 1
  • Benedikt Bitterli
    • 1
  • Philippe C. Cattin
    • 1
  1. 1.Department of Biomedical EngineeringUniversity of BaselAllschwilSwitzerland

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