Circuits, Systems, and Signal Processing

, Volume 37, Issue 9, pp 4015–4033 | Cite as

Fast and Stable Computation of the Charlier Moments and Their Inverses Using Digital Filters and Image Block Representation

  • Hicham KarmouniEmail author
  • Abdeslam Hmimid
  • Tarik Jahid
  • Mhamed Sayyouri
  • Hassan Qjidaa
  • Abdellah Rezzouk


In this paper, we suggest a new method of fast and stable calculation of the discrete orthogonal moments of Charlier and their inverses. This method is meant to accelerate the computation time and improve the quality of images reconstruction. In this method, we have combined two main concepts. The first concept is the digital filters based on the Z-transform to accelerate the calculation process of the discrete orthogonal moments of Charlier. The second concept is the partitioning of the image into a set of blocks of fixed sizes where each block is processed independently. The significant reduction in the image space during partitioning makes it possible to represent the minute details of the image with only low orders of Charlier’s discrete orthogonal moments, which ensures the digital stability during the processing of the image. In order to demonstrate the efficiency, stability, and precision of our method compared to other existing methods, some simulations have been performed on different types of binary images and gray images with and without noise.


Charlier moments Digital filters Z-transform Lapped block-based method 


  1. 1.
    N.A. Abu, S.L. Wong, H. Rahmalan, S. Sahib, Fast and efficient 4 \(\times \) 4 Tchebichef moment image compression. Majlesi J. Electr. Eng. 4(314), 37–45 (2010)Google Scholar
  2. 2.
    H. El Fadili, K. Zenkouar, H. Qjidaa, Lapped block image analysis via the method of Legendre moments. EURASIP J. Appl. Signal Process. 2003(9), 902–913 (2003)Google Scholar
  3. 3.
    J. Flusser, T. Suk, B. Zitová, Moments and Moment Invariants in Pattern Recognition (Wiley, Chichester, 2009)CrossRefzbMATHGoogle Scholar
  4. 4.
    M. Hatamian, A real-time two-dimensional moment generating algorithm and its single chip implementation. IEEE Trans. Acoust. Speech Signal Process. 34(3), 546–553 (1986)CrossRefGoogle Scholar
  5. 5.
    A. Hmimid, M. Sayyouri, H. Qjidaa, Image classification using a new set of separable two-dimensional discrete orthogonal invariant moments. J. Electron. Imag. 23(1), 013026 (2014)CrossRefzbMATHGoogle Scholar
  6. 6.
    A. Hmimid, M. Sayyouri, H. Qjidaa, Fast computation of separable two-dimensional discrete invariant moments for image classification. Pattern Recogn. 48, 509–521 (2015)CrossRefzbMATHGoogle Scholar
  7. 7.
    B. Honarvar, J. Flusser, Fast computation of Krawtchouk moments. Inf. Sci. 288(20), 73–86 (2014)CrossRefzbMATHGoogle Scholar
  8. 8.
    B. Honarvar, R. Paramesran, A new formulation of geometric moments from lower output values of digital filters. J. Circ. Syst. Comput. 23(04), 1450055 (2014)CrossRefGoogle Scholar
  9. 9.
    B. Honarvar, R. Paramesran, C.-L. Lim, The fast recursive computation of Tchebichef moment and its inverse transform based on Z-transform. Digit. Signal Process. 23(5), 1738–1746 (2013)CrossRefGoogle Scholar
  10. 10.
    H.S. Hsu, Moment preserving edge detection and its application to image data compression. Opt. Eng. 32, 1596–1608 (1993)CrossRefGoogle Scholar
  11. 11.
  12. 12.
    M.K. Hu, Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory 8(2), 179–187 (1962)CrossRefzbMATHGoogle Scholar
  13. 13.
    R. Mukundan, S.H. Ong, P.A. Lee, Image analysis by Tchebichef moments. IEEE Trans. Image Process. 10(9), 1357–1364 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    G.A. Papakostas, E.G. Karakasis, D.E. Koulouriotis, Accurate and speedy computation of image Legendre moments for computer vision applications. Image Vis. Comput. 28(3), 414–423 (2010)CrossRefGoogle Scholar
  15. 15.
    M. Sayyouri, A. Hmimid, H. Qjidaa, A fast computation of novel set of Meixner invariant moments for image analysis. Circ. Syst. Signal Process. 2014, 1–26 (2014). zbMATHGoogle Scholar
  16. 16.
    M. Sayyouri, A. Hmimid, H. Qjidaa, Image analysis using separable discrete moments of Charlier–Hahn. Multimed. Tools Appl. 75(1), 547–571 (2014)CrossRefzbMATHGoogle Scholar
  17. 17.
    I.M. Spiliotis, B.G. Mertzios, Real-time computation of two-dimensional moments on binary images using image block representation. IEEE Trans. Image Process. 7(11), 1609–1615 (1998)CrossRefGoogle Scholar
  18. 18.
    M.R. Teague, Image analysis via the general theory of moments. J. Opt. Soc. Am. 70(8), 920–930 (1980)MathSciNetCrossRefGoogle Scholar
  19. 19.
    X.Y. Wang, P.P. Niu, H.Y. Yang, C.P. Wang, A.L. Wang, A new robust color image watermarking using local quaternion exponent moments. Inf. Sci. 277, 731–754 (2014)CrossRefGoogle Scholar
  20. 20.
    G. Wang, S. Wang, Recursive computation of Tchebichef moment and its inverse transform. Pattern Recognit. 39(1), 47–56 (2006)CrossRefGoogle Scholar
  21. 21.
    W.-H. Wong, W.-C. Siu, Improved digital filter structure for fast moments computation. IEE Proc. Vis. Image Signal Process. 146(2), 73–79 (1999)CrossRefGoogle Scholar
  22. 22.
    P.T. Yap, R. Paramesra, S.H. Ong, Image analysis by Krawtchouk moments. IEEE Trans. Image Process. 12(11), 1367–1377 (2003)MathSciNetCrossRefGoogle Scholar
  23. 23.
    P.T. Yap, P. Raveendran, S.H. Ong, Image analysis using Hahn moments. IEEE Trans. Pattern Anal. Mach. Int. 29(11), 2057–2062 (2007)CrossRefGoogle Scholar
  24. 24.
    Y. Zhang, S. Wang, Pathological brain detection based on wavelet entropy and Hu moment invariants. Bio. Med. Mater. Eng. 26, 1283–1290 (2015)CrossRefGoogle Scholar
  25. 25.
    H. Zhu, M. Liu, H. Shu, H. Zhang, L. Luo, General form for obtaining discrete orthogonal moments. IET Image Process. 4(5), 335–352 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Hicham Karmouni
    • 1
    Email author
  • Abdeslam Hmimid
    • 1
  • Tarik Jahid
    • 1
  • Mhamed Sayyouri
    • 2
  • Hassan Qjidaa
    • 1
  • Abdellah Rezzouk
    • 3
  1. 1.CED-ST, STIC, Laboratory of Electronic Signals and Systems of Information LESSI, Faculty of Science Dhar El MahrezUniversity Sidi Mohamed Ben Abdellah- FezFesMorocco
  2. 2.Laboratoire des Sciences de l’Ingénieur pour l’Energie, Ecole Nationale des Sciences Appliquées d’El JadidaUniversité Chouaïb DoukkaliEL Jadida PlateauMorocco
  3. 3.CED-ST, SMPI, Laboratory of Solid Physics LPS, Faculty of Science Dhar El MahrezUniversity Sidi Mohamed Ben Abdellah- FezFesMorocco

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