Fast Hermite Projection Method

  • Andrey Krylov
  • Danil Korchagin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4141)

Abstract

Fast Hermite projection scheme for image processing and analysis is introduced. It is based on an expansion of image intensity function into a Fourier series using full orthonormal system of Hermite functions instead of trigonometric basis. Hermite functions are the eigenfunctions of the Fourier transform and they are computationally localized both in frequency and spatial domains in the contrast to the trigonometric functions. The acceleration of this expansion procedure is based on Gauss-Hermite quadrature scheme simplified by the replacement of Hermite associated weights and Hermite polynomials by an array of associated constants. This array of associated constants depends on the values of Hermite functions. Image database retrieval and image foveation applications based on 2D fast Hermite projection method have been considered. The proposed acceleration algorithm can be also efficiently used in Hermite transform method.

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References

  1. 1.
    Szego, G.: Orthogonal Polynomials, vol. 23. American Mathematical Society Colloquium Publications, NY (1959)Google Scholar
  2. 2.
    Martens, J.-B.: The Hermite Transform – Theory. IEEE Transactions on Acoustics, Speech and Signal Processing 38, 1595–1606 (1990)CrossRefMATHGoogle Scholar
  3. 3.
    Krylov, A., Kortchagine, D.: Projection filtering in image processing. In: Proceedings Int. Conference Graphicon 2000, Moscow, pp. 42–45 (2000)Google Scholar
  4. 4.
    Najafi, M., Krylov, A., Kortchagine, D.: Image deblocking with 2-D Hermite transform. In: Proceedings Int. Conference Graphicon 2003, Moscow, pp. 180–183 (2003)Google Scholar
  5. 5.
    Krylov, A., Kortchagine, D.: Hermite Foveation. In: Proceedings Int. Conference Graphicon 2004, Moscow, pp. 166–169 (2004)Google Scholar
  6. 6.
    Krylov, A.S., Kortchagine, D.N., Lukin, A.S.: Streaming Waveform Data Processing by Hermite Expansion for Text-Independent Speaker Indexing from Continuous Speech. In: Proceedings Int. Conference Graphicon 2002, Nizhny Novgorod, pp. 91–98 (2002)Google Scholar
  7. 7.
    Gabor, D.: Theory of Communication. J. IEE (London), part III 93(26), 429–457 (1946)Google Scholar
  8. 8.
    Bloom, J.A., Reed, T.R.: An Uncertainty Analysis of Some Real Functions for Image Processing Applications. In: Proceedings of ICIP 1997, pp. III-670–673 (1997)Google Scholar
  9. 9.
    Eberlein, W.F.: A New Method for Numerical Evaluation of the Fourier Transform. Journal of Mathematical Analysis and Application 65, 80–84 (1978)CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Krylov, V.I.: Numerical Integral Evaluation, pp. 116–147. Science, Moscow (1967)Google Scholar
  11. 11.
    Chang, E.-C., Mallat, S., Yap, C.: Wavelet Foveation. J. Applied and Computational Harmonic Analysis 9(3), 312–335 (2000)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andrey Krylov
    • 1
  • Danil Korchagin
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.European Organization for Nuclear ResearchGenevaSwitzerland

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