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Practical 2D signal decomposition design based on Haar-wavelet transform

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Języki publikacji
EN
Abstrakty
EN
The image processing and analysis bused on the continuous or discrete image transforms ate classic processing techniques. The image transforms are widely used in image filtering, data description, etc. Nowadays the wavelet theorems are modern methods of image processing and particularly compression. Considering that the Haar functions are the simplest wavelets, these forms are often used in many methods of discrete image transforms and processing. The image transform theory is a well known area characterized by a precise mathematical background, but in many cases some transforms have particular properties which are not still investigated. This paper presents the new method of image analysis by means of the wavelet-Haar spectrum. Presented method allows us to calculate wavelet-Haar spectral coefficients faster than the classical fast wavelets approach. Some properties of the Haar and wavelets spectrum have been investigated. The extraction of image features immediatelv 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 he treated as extractors of particular image features.
Rocznik
Strony
61--82
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
  • Institute of Informatics, Silesian University, ul. Będzińska 39, 41-200 Sosnowiec, Poland
autor
  • Institute of Mathematics, Silesian University, ul. Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] Ahmed N. and Rao K.R.: Orthogonal Transforms for Digital Signals Processing. Springer-Verlag. Berlin, Heidelberg. (1975).
  • [2] Bhaskaran V., Konstantinides K.: Image and video compression standards: algorithms and architectures. Kluwer, Boston. (1995).
  • [3] Castleman K.R.: Digital Image Processing. Prentice-Hall. New Jersey. (1996).
  • [4] Creusere C.D.: A new method of robust image compression based on the embedded zerotree wavelet algorithm. IEEE Trans. Image Processing, vol. 6, pp. 1436-1442. (1997).
  • [5] Daubechies I.: Ten lectures on wavelets. Philadelphia PA. SIAM (1992).
  • [6] Gröchenig K., Madych W. R.: Multiresolution Analysis, Haar bases and self-similar tilings of Rⁿ, IEEE Trans. Inf. Theory, 38 (2), pp. 556-568. (1992).
  • [7] Harmuth H.F.: Sequency Theory. Foundations and applications. Academic Press. New York (1977).
  • [8] Mallat S.: A Theory for Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 11, No.7, pp. 674-693. (1989).
  • [9] Pratt W. K.: Digital Image Processing. John Wiley and Sons, New York, (1978).
  • [10] Rudin W.: Functional Analysis, McGraw-Hill, New York. (1973).
  • [11] Stollniz EJ., DeRose T.D., Salesin D.H.: Wavelets for Computer Graphics: A Primer, Part 1. IEEE Computer Graphics and Applications, pp. 76-84 (1995).
  • [12] Walker J. S. Fourier Analysis and Wavelet Analysis. Notices of the American Mathematical Society. Vol. 44, No 6, pp. 658-670. (1997).
  • [13] Wavelets and their Applications in Computer Graphics. SIGGRAPH’95. Course Notes. University of British Columbia. (1995).
  • [14] Wojtaszczyk P., A: Mathematical Introduction to Wavelets. Cambridge University Press, Cambridge. (1997).
  • [15] Yankowitz D., Bruckstein A.M.: A New Method for Image Segmentation. Computer Vision, Graphics and Image Processing, pp. 82-95. No 46/1. (1989).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0027-0072
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