Spatial Confidence Regions for Quantifying and Visualizing Registration Uncertainty

  • Takanori Watanabe
  • Clayton Scott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7359)

Abstract

For image registration to be applicable in a clinical setting, it is important to know the degree of uncertainty in the returned point-correspondences. In this paper, we propose a data-driven method that allows one to visualize and quantify the registration uncertainty through spatially adaptive confidence regions. The method applies to various parametric deformation models and to any choice of the similarity criterion. We adopt the B-spline model and the negative sum of squared differences for concreteness. At the heart of the proposed method is a novel shrinkage-based estimate of the distribution on deformation parameters. We present some empirical evaluations of the method in 2-D using images of the lung and liver, and the method generalizes to 3-D.

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References

  1. 1.
    Christensen, G.E., Geng, X., Kuhl, J.G., Bruss, J., Grabowski, T.J., Pirwani, I.A., Vannier, M.W., Allen, J.S., Damasio, H.: Introduction to the Non-rigid Image Registration Evaluation Project (NIREP). In: Pluim, J.P.W., Likar, B., Gerritsen, F.A. (eds.) WBIR 2006. LNCS, vol. 4057, pp. 128–135. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Chun, S.Y., Fessler, J.: A simple regularizer for B-spline nonrigid image registration that encourages local invertibility. IEEE J. Sel. Top. Sig. Proc. 3(1), 159–169 (2009); special Issue on Digital Image Processing Techniques for OncologyGoogle Scholar
  3. 3.
    Fitzpatrick, J.M., West, J.B.: The distribution of target registration error in rigid-body, point-based registration. IEEE Trans. Med. Imaging 20(9), 917–927 (2001)CrossRefGoogle Scholar
  4. 4.
    Golub, G.H., Van Loan, C.F.: Matrix computations, 3rd edn. Johns Hopkins University Press (1996)Google Scholar
  5. 5.
    Holden, M.: A review of geometric transformations for nonrigid body registration. IEEE Trans. Med. Imag. 27(1), 111–128 (2008)CrossRefGoogle 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., Unser, M.: Fast parametric elastic image registration. IEEE Transactions on Image Processing 12(11), 1427–1442 (2003)CrossRefGoogle Scholar
  8. 8.
    Kybic, J.: Bootstrap resampling for image registration uncertainty estimation without ground truth. IEEE Transactions on Image Processing 19(1), 64–73 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ledoit, O., Wolf, M.: Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection. Journal of Empirical Finance 10, 603–621 (2003)CrossRefGoogle Scholar
  10. 10.
    Risholm, P., Pieper, S., Samset, E., Wells III, 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, Part II. LNCS, vol. 6362, pp. 554–561. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Robinson, M.D., Milanfar, P.: Fundamental performance limits in image registration. IEEE Transactions on Image Processing 13(9), 1185–1199 (2004)CrossRefGoogle 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.
    Yetik, I.S., Nehorai, A.: Performance bounds on image registration. IEEE Transactions on Signal Processing 54(5), 1737–1749 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Takanori Watanabe
    • 1
  • Clayton Scott
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of MichiganAnn ArborUSA

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