New Vector Field Regularization Techniques for Nonrigid Image Registration

  • Pascal Cathier
  • Nicholas Ayache
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2717)


The aim of this paper is to propose new linear isotropic regularization techniques for vector fields. In nonrigid registration, most of the regularization techniques treat independently each component of the deformation. However, real materials often have non-zero Poisson ratio, as a stress in one direction would affect the position of the material in every direction. This is especially true for near-incompressible materials such as brain tissue. Therefore, explicit modeling of this property is expected to produce more accurate registration results. In this paper, we propose a new family of isotropic quadratic energies that possess such cross-effects, and derive filters and splines for vector field regularization. Contrary to usual filters and splines (e.g Gaussian filters or thin plate splines), these ones are vectorial, and have parameters that enable them to control the strength of the interaction between coordinates. We show how they can be used for intensity- or landmark-based registration, and finally show how they mix when combining intensity- and landmark-based registration.


Impulse Response Fourier Domain Functional Derivative Thin Plate Spline Nonrigid Registration 
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.
    Cachier, P., Bardinet, E., Dormont, D., Pennec, X., Ayache, N.: Iconic Feature Based Nonrigid Registration: The PASHA Algorithm. CVIU — Special Issue on Nonrigid Registration (2003) (in Press)Google Scholar
  2. 2.
    Cachier, P., Mangin, J.-F., Pennec, X., Rivière, D., Papadopoulos-Orfanos, D., Régis, J., Ayache, N.: Multisubject Non-Rigid Registration of Brain MRI using Intensity and Geometric Features. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 734–742. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Davis, M.H., Khotanzad, A., Flamig, D.P., Harms, S.E.: A Physics-Based Coordinate Transformation for 3D Image Matching. IEEE Trans. on Medical Imaging 16(3), 317–328 (1997)CrossRefGoogle Scholar
  4. 4.
    Duchon, J.: Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces. RAIRO Analyse Numérique 10(12), 5–12 (1976)MathSciNetGoogle Scholar
  5. 5.
    Kannappan, P., Sahoo, P.K.: Rotation Invariant Separable Functions are Gaussian. SIAM J. on Math. Analysis 23(5), 1342–1351 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Lakes, R.: Foam Structures with a negative Poisson’s ratio. Science 235(4792), 1038–1040 (1987)CrossRefGoogle Scholar
  7. 7.
    Rey, D., Subsol, G., Delingette, H., Ayache, N.: Automatic Detection and Segmentation of Evolving Processes in 3D Medical Images: Application to Multiple Sclerosis. In: Kuba, A., Sámal, M., Todd-Pokropek, A. (eds.) IPMI 1999. LNCS, vol. 1613, pp. 154–167. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Rivière, D., Mangin, J.-F., Papadopoulos, D., Martinez, J.-M., Frouin, V., Régis, J.: Automatic recognition of cortical sulci using a congregation of neural networks. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 40–49. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Rohr, K., Fornefett, M., Stiehl, H.S.: Approximating Thin-Plate Splines for Elastic Registration: Integration of Landmark Errors and Orientation Attributes. In: Proc. of IPMI 1999, Visegrád, Hungary. LNCS, vol. 1613, pp. 252–265. Springer, Heidelberg (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Pascal Cathier
    • 1
  • Nicholas Ayache
    • 1
  1. 1.Epidaure, INRIA-SophiaFrance

Personalised recommendations