The Haar-wavelet transform in digital image processing: its status and achievements

• Autorzy: Porwik, P. , Lisowska, A.
• Języki publikacji: EN

Abstrakty

EN

Image processing and analysis based on continuous or discrete image transforms are classic techniques. The image transforms are widely used in image filtering, data description, etc. Nowadays, wavelet theorems make up very popular methods of image processing, denoising and compression. Considering that Haar functions are the simplest wavelets, these forms are 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 have not been investigated yet. This paper presents graphic dependences between parts of Haar and wavelets spectra for the first time. It also presents a method of image analysis by means of the wavelet-Haar spectrum. Some properties of the Haar and wavelet spectrum are investigated. Extraction of image features directly from spectral coefficients distribution is presented. The paper shows that two-dimensional products of both Haar and wavelet functions can be treated as exstractors of particular image features. Furthermore, it is also shown that some coefficients from both the spectra are proportional, which simplifies computations and analyses to some degree.

Słowa kluczowe

EN

wavelets; Haar transform; multiresolution

• Czasopismo: Machine Graphics and Vision
• Rocznik: 2004
• Tom: Vol. 13, No. 1/2
• Strony: 79-98
• Opis fizyczny: Bibliogr. 50 poz., il., wykr.

Twórcy

autor

Porwik, P.

• Institute of Informatics, University of Silesia, ul. Będzińska 39, 41-200 Sosnowiec, Poland,

autor

Lisowska, A.

• Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland,

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