Affine and Deformable Registration Based on Polynomial Expansion

  • Gunnar Farnebäck
  • Carl-Fredrik Westin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4190)


This paper presents a registration framework based on the polynomial expansion transform. The idea of polynomial expansion is that the image is locally approximated by polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the polynomial expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data.


Quadratic Polynomial Registration Algorithm Polynomial Expansion Deformable Registration Probabilistic Atlas 


  1. 1.
    Mazziotta, J.C., Toga, A.W., Evans, A.C., Fox, P., Lancaster, J.L.: A probabilistic atlas of the human brain: Theory and rationale for its development. Neuroimage 2(2), 89–101 (1995)CrossRefGoogle Scholar
  2. 2.
    Thompson, P.M., Toga, A.W.: Detection, visualization and animation of abnormal anatomic structure with a deformable probabilistic atlas based on random vector field transformations. Medical Image Analysis 1(4), 271–294 (1997)CrossRefGoogle Scholar
  3. 3.
    Grenander, U., Miller, M.: Computational anatomy: an emerging discipline. Q. Appl. Math. 56(4), 617–694 (1998)MATHMathSciNetGoogle Scholar
  4. 4.
    Guimond, A., Meunier, J., Thirion, J.P.: Average brain models: a convergence study. Comput. Vision Imag. Understand. 77(2), 192–210 (2000)CrossRefGoogle Scholar
  5. 5.
    Knutsson, H., Westin, C.F.: Normalized and differential convolution: Methods for interpolation and filtering of incomplete and uncertain data. In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, New York City, USA, pp. 515–523. IEEE, Los Alamitos (1993)CrossRefGoogle Scholar
  6. 6.
    Farnebäck, G.: Polynomial Expansion for Orientation and Motion Estimation. PhD thesis, Linköping University, SE-581 83 Linköping, Sweden, Dissertation No. 790 (2002) ISBN 91-7373-475-6Google Scholar
  7. 7.
    ITK: The Insight Segmentation and Registration Toolkit,

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gunnar Farnebäck
    • 1
  • Carl-Fredrik Westin
    • 1
  1. 1.Department of RadiologyBrigham and Womens’ Hospital, Harvard Medical SchoolBostonUSA

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