3D Point Correspondence by Minimum Description Length in Feature Space

  • Jiun-Hung Chen
  • Ke Colin Zheng
  • Linda G. Shapiro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)


Finding point correspondences plays an important role in automatically building statistical shape models from a training set of 3D surfaces. For the point correspondence problem, Davies et al. [1] proposed a minimum-description-length-based objective function to balance the training errors and generalization ability. A recent evaluation study [2] that compares several well-known 3D point correspondence methods for modeling purposes shows that the MDL-based approach [1] is the best method.

We adapt the MDL-based objective function for a feature space that can exploit nonlinear properties in point correspondences, and propose an efficient optimization method to minimize the objective function directly in the feature space, given that the inner product of any vector pair can be computed in the feature space. We further employ a Mercer kernel [3] to define the feature space implicitly. A key aspect of our proposed framework is the generalization of the MDL-based objective function to kernel principal component analysis (KPCA) [4] spaces and the design of a gradient-descent approach to minimize such an objective function. We compare the generalized MDL objective function on KPCA spaces with the original one and evaluate their abilities in terms of reconstruction errors and specificity. From our experimental results on different sets of 3D shapes of human body organs, the proposed method performs significantly better than the original method.


Feature Space Reconstruction Error Minimum Description Length Kernel Parameter Kernel Principal Component Analysis 
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.


  1. 1.
    Davies, R., Twining, C., Cootes, T., Waterton, J., Taylor, C.: A minimum description length approach to statistical shape modeling. IEEE TMI 21(5), 525–537 (2002)Google Scholar
  2. 2.
    Styner, M., Rajamani, K., Nolte, L.P., Zsemlye, G., Szekely, G., Taylor, C., Davies, R.H.: Evaluation of 3d correspondence methods for model building. In: IPMI, pp. 63–75 (2003)Google Scholar
  3. 3.
    Vapnik, V.: The Nature of Statisticl Learning Theory. Springer, New York (1995)Google Scholar
  4. 4.
    Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10(5), 1299–1319 (1998)CrossRefGoogle Scholar
  5. 5.
    Davies, R., Twining, C., Taylor, C.: Statistical Models of Shape: Optimisation and Evaluation. Springer Publishing Company, Heidelberg (2008)zbMATHGoogle Scholar
  6. 6.
    Heimann, T., Meinzer, H.P.: Statistical shape models for 3d medical image segmentation: A review. Medical Image Analysis 13(4), 543–563 (2009)CrossRefGoogle Scholar
  7. 7.
    Styner, M., Oguz, I., Heimann, T., Gerig, G.: Minimum description length with local geometry. In: ISBI 2008, pp. 1283–1286 (2008)Google Scholar
  8. 8.
    Corouge, I., Gouttard, S., Gerig, G.: Towards a shape model of white matter fiber bundles using diffusion tensor mri. In: ISBI 2004, vol. 1, pp. 344–347 (2004)Google Scholar
  9. 9.
    Heimann, T., Wolf, I., Williams, T.G., Meinzer, H.P.: 3d active shape models using gradient descent optimization of description length. In: IPMI, pp. 566–577 (2005)Google Scholar
  10. 10.
    Heimann, T., Oguz, I., Wolf, I., Styner, M., Meinzer, H.: Implementing the automatic generation of 3d statistical shape models with itk. In: Open Science Workshop at MICCAII (2006)Google Scholar
  11. 11.
    Romdhani, S., Gong, S., Psarrou, R.: A multi-view nonlinear active shape model using kernel pca. In: BMVC, pp. 483–492 (1999)Google Scholar
  12. 12.
    Twining, C.J., Taylor, C.J.: Kernel principal component analysis and the construction of non-linear active shape models. In: BMVC, pp. 23–32 (2001)Google Scholar
  13. 13.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. PAMI 24, 509–522 (2002)Google Scholar
  14. 14.
    Brechbühler, C., Gerig, G., Kübler, O.: Parametrization of closed surfaces for 3-d shape description. CVIU 61(2), 154–170 (1995)Google Scholar
  15. 15.
    Wang, Y., Chiang, M., Thompson, P.: Mutual informationbased 3d surface matching with applications to face recognition and brain mapping. In: ICCV 2005, vol. 1, pp. 527–534 (2005)Google Scholar
  16. 16.
    Thodberg, H.H.: Minimum description length shape and appearance models. In: IPMI, pp. 51–62 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jiun-Hung Chen
    • 1
  • Ke Colin Zheng
    • 2
  • Linda G. Shapiro
    • 1
  1. 1.Computer Science and EngineeringUniversity of WashingtonSeattle
  2. 2.Microsoft Corporation 

Personalised recommendations