Local Image Registration Uncertainty Estimation Using Polynomial Chaos Expansions

  • Gokhan GunayEmail author
  • Sebastian van der Voort
  • Manh Ha Luu
  • Adriaan Moelker
  • Stefan Klein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10883)


Most image registration methods involve multiple user-defined tuning parameters, such as regularization weights and smoothing parameters. Changing these tuning parameters leads to differences in the local deformation estimates that result from the registration algorithm. Uncertainty in the optimal value of the tuning parameters thus leads to uncertainty in the local deformation estimates. In this work, we propose a method to quantify this uncertainty using an efficient surrogate modeling approach based on polynomial chaos expansion. Given a specified distribution on each input tuning parameter, this approach requires only a few image registration runs to characterize the distribution of output deformation estimates at each voxel. In experiments on liver CT images, we evaluate the accuracy of the uncertainty estimate by comparing with a brute force Monte Carlo estimate. The results show that there is a negligible difference between estimates of Monte-Carlo simulation and the proposed method. The proposed method thus provides a good indication of the uncertainty in local deformation estimates due to uncertainty in the optimal setting of tuning parameters.


Image registration Uncertainty estimation Polynomial chaos expansion Surrogate modeling 


  1. 1.
    Blatman, G., Sudret, B.: Adaptive sparse polynomial chaos expansion based on least angle regression. J. Comput. Phys. 230(6), 2345–2367 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Crestaux, T., Matre, O.L., Martinez, J.M.: Polynomial chaos expansion for sensitivity analysis. Reliab. Eng. Syst. Saf. 94(7), 1161–1172 (2009)CrossRefGoogle Scholar
  3. 3.
    Gunay, G., Luu, M.H., Moelker, A., van Walsum, T., Klein, S.: Semiautomated registration of pre- and intraoperative CT for image-guided percutaneous liver tumor ablation interventions. Med. Phys. 44(7), 3718–3725 (2017)CrossRefGoogle Scholar
  4. 4.
    Gunay, G., van der Voort, S., Luu, M.H., Moelker, A., Klein, S.: Parameter sensitivity analysis in medical image registration algorithms using polynomial chaos expansions. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10433, pp. 335–343. Springer, Cham (2017). Scholar
  5. 5.
    Hu, C., Youn, B.D.: Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems. Struct. Multidiscip. Optim. 43(3), 419–442 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hub, M., Kessler, M.L., Karger, C.P.: A stochastic approach to estimate the uncertainty involved in B-spline image registration. IEEE Trans. Med. Imaging 28(11), 1708–1716 (2009)CrossRefGoogle Scholar
  7. 7.
    Kybic, J.: Bootstrap resampling for image registration uncertainty estimation without ground truth. IEEE Trans. Image Process. 19(1), 64–73 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Muenzing, S.E., van Ginneken, B., Murphy, K., Pluim, J.P.: Supervised quality assessment of medical image registration: application to intra-patient CT lung registration. Med. Image Anal. 16, 1521–1531 (2012)CrossRefGoogle Scholar
  9. 9.
    Perko, Z., Gilli, L., Lathouwers, D., Kloosterman, J.L.: Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis. J. Comput. Phys. 260, 54–84 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Perko, Z., van der Voort, S.R., van de Water, S., Hartman, C.M.H., Hoogeman, M., Lathouwers, D.: Fast and accurate sensitivity analysis of IMPT treatment plans using polynomial chaos expansion. Phys. Med. Biol. 61(12), 4646 (2016)CrossRefGoogle Scholar
  11. 11.
    Risholm, P., Pieper, S., Samset, E., Wells, W.M.: Summarizing and visualizing uncertainty in non-rigid registration. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010. LNCS, vol. 6362, pp. 554–561. Springer, Heidelberg (2010). Scholar
  12. 12.
    Simpson, I.J., Schnabel, J.A., Groves, A.R., Andersson, J.L., Woolrich, M.W.: Probabilistic inference of regularisation in non-rigid registration. NeuroImage 59(3), 2438–2451 (2012)CrossRefGoogle Scholar
  13. 13.
    Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55(1), 271–280 (2001)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Sokooti, H., Saygili, G., Glocker, B., Lelieveldt, B.P.F., Staring, M.: Accuracy estimation for medical image registration using regression forests. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9902, pp. 107–115. Springer, Cham (2016). Scholar
  15. 15.
    Sotiras, A., Davatzikos, C., Paragios, N.: Deformable medical image registration: a survey. IEEE Trans. Med. Imaging 32(7), 1153–1190 (2013)CrossRefGoogle Scholar
  16. 16.
    Staring, M., Klein, S., Pluim, J.P.W.: A rigidity penalty term for nonrigid registration. Med. Phys. 34(11), 4098–4108 (2007)CrossRefGoogle Scholar
  17. 17.
    Sudret, B.: Global sensitivity analysis using polynomial chaos expansions. Reliab. Eng. Syst. Saf. 93(7), 964–979 (2008)CrossRefGoogle Scholar
  18. 18.
    van der Voort, S., van de Water, S., Perk, Z., Heijmen, B., Lathouwers, D., Hoogeman, M.: Robustness recipes for minimax robust optimization in intensity modulated proton therapy for oropharyngeal cancer patients. Int. J. Radiat. Oncol. Biol. Phys. 95(1), 163–170 (2016)CrossRefGoogle Scholar
  19. 19.
    Wiener, N.: The homogeneous chaos. Am. J. Math. 60(4), 897–936 (1938)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Xiu, D., Karniadakis, G.E.: The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2), 619–644 (2002)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Gokhan Gunay
    • 1
    Email author
  • Sebastian van der Voort
    • 1
  • Manh Ha Luu
    • 1
  • Adriaan Moelker
    • 2
  • Stefan Klein
    • 1
  1. 1.Departments of Radiology and Medical Informatics, Biomedical Imaging Group RotterdamErasmus MCRotterdamThe Netherlands
  2. 2.Departments of Radiology and Nuclear MedicineErasmus MCRotterdamThe Netherlands

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