Digital Transforms in Handwriting Recognition

  • Giovanni Dimauro
Conference paper
Part of the NATO ASI Series book series (volume 124)


Digital transforms have been intensively used in the field of pattern recognition with the advance of computers. In the field of handwriting recognition, applications of such mathematical transformations ranges from character and numeral recognition, to word recognition and signature verification. This tutorial presents the fundamentals of digital transforms and their use in handwriting recognition. The tutorial is divided into three parts. The first part deals with the fundamental concepts and an overview of digital transforms. The second part deals with the implementation of digital transforms. Specifically the Discrete Fourier Transform (DFT) is explained in detail. Some computational aspects of the DFT are evaluated and some algorithms for Fast Fourier Transform are presented. In particular the “Radix-2 FFT” algorithms are discussed in detail. In the last part of the tutorial, some applications are presented: the DFT represents one of the most powerful tools for plane curve analysis and recognition. This is useful in handwriting recognition where the major information for the description and the classification of the pattern can be found in its boundary. Furthermore, Fourier Transform allows accurate analysis of plane curves and it was recently used for an experimental observation of human behaviour in recognizing handwritten characters. The results of such experiment pose suggestive questions about human ability in handwriting recognition which are now on the frontiers of the research in this field: How does man recognize handwritten pattern? Which features of a pattern are the most important for its recognition process? What about ambiguous patterns and their properties and about human recognition of ambiguous patterns? How could be automatically treated ambiguous patterns?


Discrete Fourier Tranform Phase Factor Plane Curf Fourier Descriptor Handwriting Recognition 
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.
    S. Impedovo, Introduzione all’ Analisi Spettrale ed Algoritmi “FFT”, Bari. Adriatica Editrice, 1987.Google Scholar
  2. 2.
    I. J. Good, A New Finite Series for Legendre Polynomials, Proc. Camb. Phil. Soc., 51, 385–388, 1958.CrossRefMathSciNetGoogle Scholar
  3. 3.
    A. N. Kolmogorov, S. V. Fomin, Elementi di Teoria delle Funzioni e di Analisi Funzionale, Mosca: Edizioni MIR, 1980, pp. 398–399.Google Scholar
  4. 4.
    L. R. Rabiner, B. Gold, Theory and Applications of Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1975.Google Scholar
  5. 5.
    J. W. Cooley, P. A. W. Lewis, P. D. Welch, The Fast Fourier Transform, Proc. IEEE, 55, 1675–1677, October 1967.Google Scholar
  6. 6.
    J. W. Cooley, P. A. W. Lewis, P. D. Welch, The Fast Fourier Transform and its Applications, IEEE Transaction and Education, 12 (1), March 1969.Google Scholar
  7. 7.
    S. Winograd, On Computing the Discrete Fourier Transform, Mathematics of computation, 32, 175–199, 1978.MATHMathSciNetGoogle Scholar
  8. 8.
    H. J. Nussbaumer, Digital Filtering Using Complex Marsenne Transform, IBM Journal of Res. and Dev., 20(5), 498–504, Sept. 1976.CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    J. H. McClellan, C. M. Rader, Number Theory in Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1979.MATHGoogle Scholar
  10. 10.
    A. V. Oppenheim, R. V. Schafer, Digital Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1975.MATHGoogle Scholar
  11. 11.
    B. A. Blesser, T. Kuklinsky, R.J. Shillman, Empirical tests for feature extraction selection based on a psychological theory of character recognition, Pattern Recognition, 8, 77–85, 1976.MATHGoogle Scholar
  12. 12.
    S. Impedovo, G. Dimauro, G. Pirlo, Ambiguity in the recognition process: some considerations on human variable behaviour, in From Pixels to Features III — Frontiers in Handwriting Recognition, S. Impedovo and J.-C. Simon (eds.), Elsevier, 1992.Google Scholar
  13. 13.
    M. Castellano, G. Dimauro, S. Impedovo, G. Pirlo, Ambiguous Patterns: Investigation on their properties, in Progress in Image Analysis and Processing, Edited by V. Cantoni, World Scientific, 1989.Google Scholar
  14. 14.
    R. Legault, C.Y. Suen, C. Nadal, Classification of Confusing Handwritten Numerals by Human Subjects, First IWFHR, Montreal, Canada, April 1990.Google Scholar
  15. 15.
    C.Y. Suen, P. Ahmed, Computer recognition of totally unconstrained handwritten zip codes, International Journal of Pattern Recognition and Artificial Intelligence, Word Scientific, 1(1), 1–15, 1987.Google Scholar
  16. 16.
    D. Dutta Majumder et Al., How to quantify shape distance for 2-D regions, Proc. of 7th ICPR, Montreal, Canada, pp. 72-74, 1984.Google Scholar
  17. 17.
    S. Impedovo, B. Marangelli, A.M. Fanelli, A Fourier descriptor set for recognizing nonstylized numerals, IEEE Trans. Syst. Man and Cybern., SMC 8–8, 640–645, Aug. 1978.Google Scholar
  18. 18.
    E. Person, K.S. Fu, Shape discrimination using Fourier descriptors, IEEE Trans. Syst. Man and Cybern., SMC 7–3, 170–179, Mar. 1977.CrossRefGoogle Scholar
  19. 19.
    C.T. Zahn et Al., Fourier descriptors for plane closed curve, IEEE Trans. Comp., C21–3, 269–281, Mar. 1972.CrossRefMathSciNetGoogle Scholar
  20. 20.
    A. Krzyzak, S.Y. Lueng, C.Y. Suen, Reconstruction of two dimensional patterns by Fourier descriptors, 9-th ICPR, Rome, Italy, pp. 555-558, Nov. 1988.Google Scholar
  21. 21.
    S. Impedovo, N. Abbattista, Hand-written numeral recognition; the organization degree measurement, Proc. 6th ICPR, Munich, Germany, pp. 40-43, Oct. 1982.Google Scholar
  22. 22.
    S. Impedovo, Power pattern-resolution in human vision — some consideration on the handwritten numeral resolution, Proc. SPIE, vol.548 — Appl. of Art. Intell. II, Washington, USA, pp. 263-268, 1985.Google Scholar
  23. 23.
    S. Impedovo, G. Dimauro, An interactive system for the selection of handwritten numeral classes, Proc. of 10th ICPR, Atlantic City, USA, pp. 563-566, 1990.Google Scholar
  24. 24.
    H. Samet, Region representation: quadtrees from binary arrays, Computer Graphics and Image Processing, May 1980, pp. 88-93.Google Scholar
  25. 25.
    HERMIA: An Heterogeneus and Reconfigurable Machine for Image Analysis, MVA IAPR Workshop on Machine Vision Applications, Tokyo, pp. 397–400, Nov. 28-30, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Giovanni Dimauro
    • 1
  1. 1.Dipartimento di InformaticaUniversità degli Studi di BariBariItaly

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