Formulation and Evaluation of Variational Curve Matching with Prior Constraints

  • Brian Avants
  • James Gee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2717)


This work explores a priori constraints based on human landmarking for defining the parameters of a variational curve registration algorithm. The result is a method for designing variational energies that adjust the optimization process over the solution domain such that features which are salient in the human decision-making process are used. The application here is locating correspondence of corpora callosa that agree with expert user data. General principles that guide our particular application are first stated. These principles involve the definition of a generic variational problem and an associated optimization algorithm, given here for the case of matching curves. A small set of specific similarity criterion for curves is then defined. The ability of each feature to find correspondences that relate to human decisions is individually tested. Following the results of this study, a Maximum a Posteriori (MAP) automatic landmarking and correspondence method is developed. The probabilities associated with the MAP estimates are also used to define variational weights that vary over the solution’s domain. These methods are both evaluated with respect to known correspondences and inter-user variability.


Variational Energy Prior Weight Active Shape Model Descriptor Function Curve Match 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cootes, T.F., Taylor, C.J., Graham, J.: Active shape models - their training and application. Computer Vision and Image Understanding 60, 38–59 (1995)CrossRefGoogle Scholar
  2. 2.
    Leventon, M., Grimson, E., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Proc. IEEE Conf. Comp. Vision and Patt. Recog., pp. 4–11 (2000)Google Scholar
  3. 3.
    Davies, R., Cootes, T., Waterton, J., Taylor, C.J.: An efficient method for constructing optimal statistical shape models. Medical Image Computing and Computer Assisted Intervention, 57–65 (2001)Google Scholar
  4. 4.
    Sebastian, T., Klein, P., Kimia, B., Crisco, J.: Constructing 2D curve atlases. Mathematical Methods in Biomedical Image Analysis, 70–77 (2000)Google Scholar
  5. 5.
    Younes, L.: Computable elastic distance between shapes. SIAM J. Appl. Math. 58, 565–586 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Tagare, H.D., O’Shea, D., Rangarajan, A.: A geometric criterion for shape based non-rigid correspondence. In: Fifth Intl. Conf. on Computer Vision, pp. 434–439 (1995)Google Scholar
  7. 7.
    Geiger, D., Liu, T., Kohn, R.: Representation and self-similarity of shapes. IEEE Trans. Pattern Analysis and Machine Intelligence 25, 86–99 (2003)CrossRefGoogle Scholar
  8. 8.
    Liu, T., Geiger, D.: Approximate tree matching and shape similarity. International Conference on Computer Vision, 456–462 (1999)Google Scholar
  9. 9.
    Avants, B., Gee, J.C.: Continuous curve matching with scale-space curvature and extrema-based scale selection. In: Griffin, L. (ed.) Scale-Space Theories in Computer Vision. LNCS. Springer, Heidelberg (2003) (in press)Google Scholar
  10. 10.
    Dubb, A., Avants, B., Gur, R., Gee, J.C.: Shape characterization of the corpus callosum in Schizophrenia using template deformation. In: Kikinis, R. (ed.) Medical Image Computing and Computer-Assisted Intervention, pp. 381–388. Springer, Heidelberg (2002)Google Scholar
  11. 11.
    Mokhtarian, F., Mackworth, A.: Scale-based description and recognition of planar curves and two-dimensional shapes. IEEE Trans. Pattern Analysis and Machine Intelligence 8, 34–44 (1986)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Brian Avants
    • 1
  • James Gee
    • 1
  1. 1.Departments of Bioengineering and RadiologyUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations