Shape Recognition Via an a Contrario Model for Size Functions

  • Andrea Cerri
  • Daniela Giorgi
  • Pablo Musé
  • Frédéric Sur
  • Federico Tomassini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4142)


Shape recognition methods are often based on feature comparison. When features are of different natures, combining the value of distances or (dis-)similarity measures is not easy since each feature has its own amount of variability. Statistical models are therefore needed. This article proposes a statistical method, namely an a contrario method, to merge features derived from several families of size functions. This merging is usually achieved through a touchy normalizing of the distances. The proposed model consists in building a probability measure. It leads to a global shape recognition method dedicated to perceptual similarities.


False Alarm Background Model Perceptual Information Size Function Fourier Descriptor 
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.


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  1. 1.
    Zahn, C., Roskies, R.: Fourier descriptors for plane closed curves. IEEE Transactions on Computers C-21(3), 269–281 (1972)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Dudani, S., Breeding, K., McGhee, R.: Aircraft identification by moment invariants. IEEE Transactions on Computers 26(1), 39–46 (1977)CrossRefGoogle Scholar
  3. 3.
    Monasse, P.: Contrast invariant image registration. In: Proceedings of International Conference on Acoustics, Speech and Signal Processing, Phoenix, Arizona, USA, vol. 6, pp. 3221–3224 (1999)Google Scholar
  4. 4.
    Hu, M.: Visual pattern recognition by moments invariants. IRE Transactions on Information Theory 8, 179–187 (1962)Google Scholar
  5. 5.
    Khalil, M., Bayoumi, M.: A dyadic wavelet affine invariant function for 2d shape recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(10) (2001)Google Scholar
  6. 6.
    Mokhtarian, F., Mackworth, A.: A theory of multiscale, curvature-based shape representation for planar curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(8), 789–805 (1992)CrossRefGoogle Scholar
  7. 7.
    Alvarez, L., Mazorra, L., Santana, F.: Geometric invariant shape representations using morphological multiscale analysis and applications to shape representation. Journal of Mathematical Imaging and Vision 18(2), 145–168 (2002)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Sclaroff, S., Pentland, A.: Modal matching for correspondence and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(6), 545–561 (1995)CrossRefGoogle Scholar
  9. 9.
    Verri, A., Uras, C., Frosini, P., Ferri, M.: On the use of size functions for shape analysis. Biological Cybernetics 70, 99–107 (1993)MATHCrossRefGoogle Scholar
  10. 10.
    Cerri, A., Ferri, M., Giorgi, D.: A new framework for trademark retrieval based on size functions. In: Proceedings of International Conference on Vision, Video and Graphics, Heriot Watt University, Edinburgh, pp. 167–172 (2005)Google Scholar
  11. 11.
    Frosini, P., Landi, C.: Size functions and formal series. Applicable Algebra in Engineering Communication and Computing 12, 327–349 (2001)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Verri, A., Uras, C.: Invariant size functions. In: Mundy, J., Zisserman, A., Forsyth, D. (eds.) Application of Invariance in Computer Vision, pp. 215–234. Springer, Heidelberg (1994)Google Scholar
  13. 13.
    Desolneux, A., Moisan, L., Morel, J.M.: Computational Gestalt Theory. Lecture Notes in Mathematics. Springer, Heidelberg (to appear, 2006)Google Scholar
  14. 14.
    Lowe, D.: Perceptual Organization and Visual Recognition. Kluwer Academic Publishers, Dordrecht (1985)Google Scholar
  15. 15.
    Moisan, L., Stival, B.: A probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix. International Journal of Computer Vision 57(3), 201–218 (2004)CrossRefGoogle Scholar
  16. 16.
    Desolneux, A., Moisan, L., Morel, J.M.: Edge detection by Helmholtz principle. Journal of Mathematical Imaging and Vision 14(3), 271–284 (2001)MATHCrossRefGoogle Scholar
  17. 17.
    Musé, P., Sur, F., Cao, F., Gousseau, Y., Morel, J.M.: An a contrario decision method for shape element recognition. International Journal of Computer Vision (to appear, 2006)Google Scholar
  18. 18.
    Sebastian, T.B., Klein, P.N., Kimia, B.B.: Shock-based indexing into large shape databases. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 731–746. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Salton, G., McGill, M.J.: Introduction to modern information retrieval. McGraw-Hill, New York (1983)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andrea Cerri
    • 1
  • Daniela Giorgi
    • 1
  • Pablo Musé
    • 2
  • Frédéric Sur
    • 3
  • Federico Tomassini
    • 1
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Centre de Mathématiques et de Leurs ApplicationsÉcole Normale Supérieure de CachanCachanFrance
  3. 3.Loria & INPL, LoriaVandoeuvre-lès-NancyFrance

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