A Unified Approach to Shape Model Fitting and Non-rigid Registration

  • Marcel Lüthi
  • Christoph Jud
  • Thomas Vetter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8184)


Non-rigid registration and shape model fitting are the central problems in any shape modeling pipeline. Even though the goal is in both problems to establishing point-to-point correspondence between two objects, their algorithmic treatment is usually very different. In this paper we present an approach that allows us to treat both problems in a unified algorithmic framework. We use the well known formulation of non-rigid registration as the problem of fitting a Gaussian process model, whose covariance function favors smooth deformations. We compute a low rank approximation of the Gaussian process using the Nyström method, which allows us to formulate it as a parametric fitting problem of the same form as shape model fitting. Besides simplifying the modeling pipeline, our approach also lets us naturally combine shape model fitting and non-rigid registration, in order to reduce the bias in statistical model fitting, or to make registration more robust. As our experiments on 3D surfaces and 3D CT images show, the method leads to a registration accuracy that is comparable to standard registration methods.


Covariance Function Gaussian Process Image Registration Shape Model Reproduce Kernel Hilbert Space 
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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  1. 1.
    Blanz, V., Vetter, T.: A morphable model for the synthesis of 3D faces. In: SIGGRAPH 1999: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp. 187–194. ACM Press (1999)Google Scholar
  2. 2.
    Christensen, G.E., Miller, M.I., Vannier, M.W., Grenander, U.: Individualizing neuro-anatomical atlases using a massively parallel computer. Computer 29(1), 32–38 (1996)CrossRefGoogle Scholar
  3. 3.
    Cootes, T.F., Taylor, C.J.: Combining point distribution models with shape models based on finite element analysis. Image and Vision Computing 13(5) (1995)Google Scholar
  4. 4.
    Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics 56(4), 617–694 (1998)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hein, M., Bousquet, O.: Kernels, associated structures and generalizations. Max-Planck-Institut fuer biologische Kybernetik, Technical Report (2004)Google Scholar
  6. 6.
    Klein, S., Staring, M., Pluim, J.P.: Evaluation of optimization methods for nonrigid medical image registration using mutual information and b-splines. IEEE Transactions on Image Processing 16(12), 2879–2890 (2007)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lüthi, M., Jud, C., Vetter, T.: Using landmarks as a deformation prior for hybrid image registration. Pattern Recognition, 196–205 (2011)Google Scholar
  8. 8.
    Lüthi, M., Blanc, R., Albrecht, T., Gass, T., Goksel, O., Büchler, P., Kistler, M., Bousleiman, H., Reyes, M., Cattin, P.C., et al.: Statismo-a framework for pca based statistical models (2012)Google Scholar
  9. 9.
    Opfer, R.: Multiscale kernels. Advances in Computational Mathematics 25(4), 357–380 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Paysan, P., Knothe, R., Amberg, B., Romdhani, S., Vetter, T.: A 3D face model for pose and illumination invariant face recognition. In: Advanced Video and Signal Based Surveillance 2009, pp. 296–301 (2009)Google Scholar
  11. 11.
    Rasmussen, C.E., Williams, C.K.: Gaussian processes for machine learning. Springer (2006)Google Scholar
  12. 12.
    Rueckert, D., Frangi, A.F., Schnabel, J.A.: Automatic construction of 3D statistical deformation models using non-rigid registration. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 77–84. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Schölkopf, B., Steinke, F., Blanz, V.: Object correspondence as a machine learning problem. In: ICML 2005: Proceedings of the 22nd International Conference on Machine Learning, pp. 776–783. ACM Press, New York (2005)Google Scholar
  14. 14.
    Thirion, J.P.: Image matching as a diffusion process: an analogy with Maxwell’s demons. Medical Image Analysis 2(3), 243–260 (1998)CrossRefGoogle Scholar
  15. 15.
    Wahba, G.: Spline models for observational data. Society for Industrial Mathematics (1990)Google Scholar
  16. 16.
    Wang, Y., Staib, L.H.: Boundary finding with prior shape and smoothness models. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(7) (2000)Google Scholar
  17. 17.
    Wang, Y., Staib, L.H.: Physical model-based non-rigid registration incorporating statistical shape information. Medical Image Analysis 4(1), 7–20 (2000)CrossRefGoogle Scholar
  18. 18.
    Xue, Z., Shen, D., Davatzikos, C.: Statistical representation of high-dimensional deformation fields with application to statistically constrained 3D warping. Medical Image Analysis 10(5), 740–751 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Marcel Lüthi
    • 1
  • Christoph Jud
    • 1
  • Thomas Vetter
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of BaselSwitzerland

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