Lamia Ben Youssef, Faouzi Ghorbel


The general principle of a matching algorithm is to optimize a criterion that furnishes a measure of the similarity between two images for a given space of geometrical transformations. In this work, we propose a framework based on a similarity measure – the generalized correlation – built in a systematic way from the links between a features space and a group of transformations modeled by an action group. Using results from representation theory, we can extend the correlation function to any homogeneous space with a transitively acting group. When the generalized Fourier transform exists, the group-based correlation can be expressed in a spectral space and it becomes possible to implement fast algorithms for its computation. Two important examples in the field of image processing are then detailed: the similarity group (rotation and scaling) on gray-level shapes from 2D images and the 3D rigid motion group (rotation and translation) followed by a plan projection.


  1. Ballard, D. (1981). Generalizing the hough transform to detect arbitrary shapes. Pattern Recognition, 13(2):111122.
  2. Ben Youssef, L. (2004). Corrélation sur les Groupes pour l'Analyse des Formes et l'Estimation du Mouvement, Application aux Images Sonar. Phd thesis, Univ. de Bordeaux 3. in french.
  3. Brown, L. G. (1992). A survey of image registration techniques. ACM Computing Surveys, 24(4):325-376.
  4. Cox, D., Little, J., and O'Shea, D. (1996). Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer- Verlag.
  5. Derrode, S. and Ghorbel, F. (2001). Robust and efficient Fourier-Mellin transform approximations for graylevel image reconstruction and complete invariant description. Computer Vision and Image understanding, 33(1):57-78.
  6. Gauthier, J., Bornard, G., and Silbermann, M. (1991). Motions and pattern analysis : Harmonic analysis en motion groups and their homogeneous spaces. IEEE trans. on Systems, Man, and Cybernetics, 21(1):159- 172.
  7. Ghorbel, F. (1994). A complete invariant description for gray-level images by the harmonic analysis approach. Pattern Recognition Letters, 15:1043-1051.
  8. Miller, M. and Younes, L. (2001). Group actions, homeomorphisms, and matching: A general framework. J. of Computer Vision, 41(1):6184.
  9. M.J. Swain, D. B. (1991). Color indexing. Internat. J. Comput. Vision, 7(1):1132.
  10. Pintsov, D. (1989). Invariant pattern recognition, symmetry, and Radon transforms. J. of the Optical Society of America A, 6(10):1544-1554.
  11. Rubinstein, J., Segman, J., and Zeevi, Y. (1991). Recognition of distorted patterns by invariance kernels. Pattern Recognition, 24(10):959-967.
  12. Segman, J. (1992). Fourier cross correlation and invariance transformation for an optimal recognition of functions deformed by affine groups. J. of the Optical Society of America A, 9:895-902.
  13. Segman, J. and Zeevi, Y. (1993). Image analysis by wavelettype transforms: Group theoretic approach. Mathematical Imaging and Vision, 3(1):51-77.
  14. S.X. Liao, M. P. (1996). On image analysis by moments. IEEE Trans. Pattern Anal. Machine Intell, 18(3):254266.
  15. Turski, J. (2004). Geometric Fourier analysis on the conformal camera for active vision. Society for industrial and applied mlathematics, 46(2):230-255.
  16. Y. Lamdan, H. W. (1988). Geometric hashing: a general and efficient model-based recognition scheme. Proc. ICCV, page 238249.
  17. Zitovà, B. and Flusser, J. (2003). Image registration methods: a survey. Image and Vision Computing, 21:977- 1000.

Paper Citation

in Harvard Style

Ben Youssef L. and Ghorbel F. (2006). IMAGE “GROUP-REGISTRATION” BASED ON REPRESENTATION THEORY . In Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, ISBN 972-8865-40-6, pages 317-322. DOI: 10.5220/0001373903170322

in Bibtex Style

author={Lamia Ben Youssef and Faouzi Ghorbel},
booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,},

in EndNote Style

JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,
SN - 972-8865-40-6
AU - Ben Youssef L.
AU - Ghorbel F.
PY - 2006
SP - 317
EP - 322
DO - 10.5220/0001373903170322