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Non-parametric Discrete Registration with Convex Optimisation

  • Mattias P. Heinrich
  • Bartlomiej W. Papież
  • Julia A. Schnabel
  • Heinz Handels
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8545)

Abstract

Deformable image registration is an important step in medical image analysis. It enables an automatic labelling of anatomical structures using atlas-based segmentation, motion compensation and multi-modal fusion. The use of discrete optimisation approaches has recently attracted a lot attention for mainly two reasons. First, they are able to find an approximate global optimum of the registration cost function and can avoid false local optima. Second, they do not require a derivative of the similarity metric, which increases their flexibility. However, the necessary quantisation of the deformation space causes a very large number of degrees of freedom with a high computational complexity. To deal with this, previous work has focussed on parametric transformation models. In this work, we present an efficient non-parametric discrete registration method using a filter-based similarity cost aggregation and a decomposition of similarity and regularisation term into two convex optimisation steps. This approach enables non-parametric registration with billions of degrees of freedom with computation times of less than a minute. We apply our method to two different common medical image registration tasks, intra-patient 4D-CT lung motion estimation and inter-subject MRI brain registration for segmentation propagation. We show improvements on current state-of-the-art performance both in terms of accuracy and computation time.

Keywords

Image Registration Convex Optimisation Global Regularisation Target Registration Error Cost Aggregation 
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.

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References

  1. 1.
    Avants, B.B., Tustison, N.J., Song, G., Cook, P.A., Klein, A., Gee, J.C.: A reproducible evaluation of ANTs similarity metric performance in brain image registration. Neuroimage 54(3), 2033–2044 (2011)CrossRefGoogle Scholar
  2. 2.
    Cachier, P., Bardinet, E., Dormont, D., Pennec, X., Ayache, N.: Iconic feature based nonrigid registration: The PASHA algorithm. Comput. Vis. Image Underst. 89(2-3), 272–298 (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Castillo, R., Castillo, E., Guerra, R., Johnson, V.E., McPhail, T., Garg, A.K., Guerrero, T.: A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets. Phys. Med. Biol. 54(7), 1849 (2009)CrossRefGoogle Scholar
  4. 4.
    Caviness Jr., V.S., Meyer, J., Makris, N., Kennedy, D.N.: MRI-based Topographic Parcellation of Human Neocortex: An Anatomically Specified Method with Estimate of Reliability. Journal of Cognitive Neuroscience 8(6), 566–587 (1996)CrossRefGoogle Scholar
  5. 5.
    Chambolle, A.: An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20(1-2), 89–97 (2004)MathSciNetGoogle Scholar
  6. 6.
    Christensen, G.E., Johnson, H.J.: Consistent Image Registration. IEEE Trans. Med. Imag. 20(7), 568–582 (2001)CrossRefGoogle Scholar
  7. 7.
    Glocker, B., Komodakis, N., Tziritas, G., Navab, N., Paragios, N.: Dense image registration through MRFs and efficient linear programming. Med. Imag. Anal. 12(6), 731–741 (2008)CrossRefGoogle Scholar
  8. 8.
    Heinrich, M.P., Jenkinson, M., Papież, B.W., Brady, M., Schnabel, J.A.: Towards Realtime Multimodal Fusion for Image-Guided Interventions Using Self-Similarities. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part I. LNCS, vol. 8149, pp. 187–194. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Heinrich, M.P., Jenkinson, M., Brady, M., Schnabel, J.A.: MRF-based Deformable Registration and Ventilation Estimation of Lung CT. IEEE Trans. Med. Imag. 32(7), 1239–1248 (2013)CrossRefGoogle Scholar
  10. 10.
    Heinrich, M.P.: Deformable lung registration for pulmonary image analysis of MRI and CT scans. University of Oxford (2013)Google Scholar
  11. 11.
    Hermann, S., Werner, R.: High Accuracy Optical Flow for 3D Medical Image Registration Using the Census Cost Function. In: Klette, R., Rivera, M., Satoh, S. (eds.) PSIVT 2013. LNCS, vol. 8333, pp. 23–35. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  12. 12.
    Hosni, A., Rhemann, C., Bleyer, M., Rother, C., Gelautz, M.: Fast Cost-Volume Filtering for Visual Correspondence and Beyond. IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 504–511 (2013)CrossRefGoogle Scholar
  13. 13.
    Klein, A., et al.: Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration. Neuroimage 46(3), 786–802 (2008)CrossRefGoogle Scholar
  14. 14.
    Lewis, J.P.: Fast normalized cross-correlation. Vision Interface 10(1), 120–123 (1995)Google Scholar
  15. 15.
    Lorenzi, M., Ayache, N., Frisoni, G.B., Pennec, X.: LCC-Demons: a robust and accurate diffeomorphic registration algorithm. NeuroImage 81, 470–483 (2013)CrossRefGoogle Scholar
  16. 16.
    Papież, B.W., Heinrich, M.P., Risser, L., Schnabel, J.A.: Complex Lung Motion Estimation via Adaptive Bilateral Filtering of the Deformation Field. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part III. LNCS, vol. 8151, pp. 25–32. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  17. 17.
    Popuri, K., Cobzas, D., Jägersand, M.: A Variational Formulation for Discrete Registration. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part III. LNCS, vol. 8151, pp. 187–194. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  18. 18.
    Rühaak, J., Heldmann, S., Kipshagen, T., Fischer, B.: Highly Accurate Fast Lung CT Registration. In: Ourselin, S., Haynor, D.R. (eds.) SPIE Medical Imaging, pp. 1–9 (2013)Google Scholar
  19. 19.
    Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. Int. J. Comput. Vision 47(1), 7–42 (2002)CrossRefzbMATHGoogle Scholar
  20. 20.
    So, R.W.K., Tang, T.W.H., Chung, A.C.S.: Non-rigid image registration of brain magnetic resonance images using graph-cuts. Pattern Recognition 44(10-11), 2450–2467 (2011)CrossRefGoogle Scholar
  21. 21.
    Sotiras, A., Davatzikos, C., Paragios, N.: Deformable Medical Image Registration: A Survey. IEEE Trans. Med. Imag. 32(7), 1153–1190 (2013)CrossRefGoogle Scholar
  22. 22.
    Steinbrücker, F., Pock, T., Cremers, D.: Large displacement optical flow computation without warping. In: ICCV 2009, pp. 1609–1614 (2009)Google Scholar
  23. 23.
    Veksler, O.: Fast Variable Window for Stereo Correspondence using Integral Images. In: CVPR 2003, pp. 1–6 (2003)Google Scholar
  24. 24.
    Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic demons: Efficient non-parametric image registration. NeuroImage 45(1), 61–72 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mattias P. Heinrich
    • 1
  • Bartlomiej W. Papież
    • 2
  • Julia A. Schnabel
    • 2
  • Heinz Handels
    • 1
  1. 1.Institute of Medical InformaticsUniversity of LübeckGermany
  2. 2.Institute of Biomedical Engineering, Department of EngineeringUniversity of OxfordUK

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