A Pyramidal Haar-Transform Implementation

  • Luigi Carrioli


The one-dimensional Haar functions set, used to built the homonymous transform, is defined in the interval (0,1) in this way:
$$\begin{gathered} \begin{array}{*{20}{c}} p \\ {HAR\left( {2 + n,x} \right) = } \end{array}\left[ {\begin{array}{*{20}{c}} {{2^{p/2}} for \frac{n}{{{2^p}}} \leqslant X < \frac{{\left( {n + 1/2} \right)}}{{{2^p}}}} \\ { - {2^{p/2}} for \frac{{\left( {n + 1/2} \right)}}{{{2^p}}} \leqslant X < \frac{{n + 1}}{{{2^p}}}} \\ {0 elsewhere} \end{array}} \right. \hfill \\ p = 1,2, \ldots n = 0,1, \ldots ,{2^p} - 1 \hfill \\ \end{gathered} $$


Digital Image Processing Integrate Technology Parallel Image Global Phase Processor Element 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G.E. Paglia: “Rappresentazione ed elaborazione numerica dei segnali (III parte)”, RIDIS, Universita di Pavia, 1981,Google Scholar
  2. 2.
    K.G. Beauchamp: “Walsh functions and their application”, Academic Press, 1975.Google Scholar
  3. 3.
    R.C. Gonzalez, P. Wintz: “Digital Image Processing”, Addison-Wesley, 1977.MATHGoogle Scholar
  4. 4.
    V. Cantoni, M. Ferretti, S. Levialdi, F. Maloberti: “A Pyramid Project using Integrated Technology”, in Integrated Technology for Parallel Image Processing, ed. Levialdi, Polignano workshop ( Italy ), June 1983, Academic Press.Google Scholar
  5. 5.
    V. Cantoni, M. Ferretti, S. Levialdi, R. Stefanelli: “Papia: Pyramidal Architecture for Parallel Image Analysis”, 7-th symposium on Computer Arithmetic, June 4-6 1985, Urbana, Illinois.Google Scholar
  6. 6.
    J.E. Shore: “A two dimensional Haar-like transform”, NRL Report 7472 AD 755433, 1973.Google Scholar
  7. 7.
    J. Lifermann: “Les methodes rapides de transformation du signal”, Masson et Cie, Paris, 1977.Google Scholar
  8. 8.
    N. Ahmed, K.R. Rao: “Orthogonal transforms for digital signal processing”, Springer-Verlag, Berlin, 1975.MATHGoogle Scholar
  9. 9.
    W.K. Pratt : “Digital image processing”, Wiley, N.Y., 1977.Google Scholar
  10. 10.
    H.F. Harmuth: “Transmission of information by orthogonal functions”, Springer-Verlag, Berlin, 1970.MATHGoogle Scholar
  11. A. Rosenfeld : “Multiresolution image representation”, Digital Image Analysis, Pitman Book 1983, S. Levialdi ed., 18–28.Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Luigi Carrioli
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaPavia UniversityPaviaItaly

Personalised recommendations