The New Graphic Description of the Haar Wavelet Transform

  • Piotr Porwik
  • Lisowska Agnieszka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3039)


The image processing and analysis based on the continuous or discrete image transforms are the classic processing technique. The image transforms are widely used in image filtering, data description, etc. The image transform theory is a well known area, but in many cases some transforms have particular properties which are not still investigated. This paper for the first time presents graphic dependences between parts of Haar and wavelets images. The extraction of image features immediately from spectral coefficients distribution has been shown. In this paper it has been presented that two-dimensional both, the Haar and wavelets functions products, can be treated as extractors of particular image features.


Discrete Cosine Transform Wavelet Transform Wavelet Decomposition Decomposition Level Wavelet Method 
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  1. 1.
    Addison, P.S., Watson, J.N., Feng, T.: Low-Oscillation Complex Wavelets. Journal of Sound and Vibration 254(4), 733–762 (2002)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Ahmed, N., Rao, K.R.: Orthogonal Transforms for Digital Signals Processing. Springer, Heidelberg (1975)Google Scholar
  3. 3.
    Castleman, K.R.: Digital Image Processing. Prentice-Hall, New Jersey (1996)Google Scholar
  4. 4.
    Daubechies, I.: Recent results in wavelet applications. Journal of Electronic Imaging 7(4), 719–724 (1998)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Drori, I., Lischinski, D.: Fast Multiresolution Image Operations in the Wavelet Domain. IEEE Transactions on Visualization and Computer Graphics 9(3), 395–411 (2003)CrossRefGoogle Scholar
  6. 6.
    Harmuth, H.F.: Sequence Theory. Foundations and applications. Academic Press, New York (1977)Google Scholar
  7. 7.
    Haar, A.: Zur Theorie der orthogonalen Functionsysteme. Math. Annal. (69), 331–371 (1910)Google Scholar
  8. 8.
    Jorgensen, P.: Matrix Factorizations, Algorithms, Wavelets. Notices of the American Mathematical Society 50(8), 880–894 (2003)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Lisowska, A.: Nonlinear Weighted Median Filters in Dyadic Decomposition of Images. Annales UMCS Informatica AI 1, 157–164 (2003)Google Scholar
  10. 10.
    Lisowska, A., Porwik, P.: New Extended Wavelet Method of 2D Signal Decomposition Based on Haar Transform. Mathematics and Computers in Simulation. Elsevier Journal (to appear)Google Scholar
  11. 11.
    Mallat, S.A.: Theory for Multiresolution Signal Decomposition: The Wavelet Representation. IEEE Trans. Pattern Analysis and Machine Intelligence 11Google Scholar
  12. 12.
    Walker, J.S.: Fourier Analysis and Wavelet Analysis. Notices of the American Mathematical Society 44(6), 658–670 (1997)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Piotr Porwik
    • 1
  • Lisowska Agnieszka
    • 2
  1. 1.Institute of InformaticsSilesian UniversitySosnowiecPoland
  2. 2.Institute of MathematicsSilesian UniversityKatowicePoland

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