8 March 2002 Wavelet packet decompositions of texture images: analysis of cost functions, filter influences, and image models
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Abstract
This work investigates the wavelet packet transforms and its abilities to efficiently represent images. We are interested in the image compression approach of image processing. The wavelet packet basis selection algorithm finds spatial frequency resonance in the image. The different decomposition trees that represents the optimal basis for the triplet image, cost function and filter gives us a feeling of chaos but for compression applications it doesn't matter that there is no typical tree for a particular image or that there is no strong trend for a certain type of tree in combination with a fixed filter or fixed cost function. The most important measure in image coding applications is believed to be the cost for coding the transform coefficients, it is even more important than the cost for choosing the optimal basis. When measuring the cost for coding the coefficient matrix we realize that we are free to choose a cost function that gives us a nice decomposition tree together with a good filter. We simulate the coding cost by estimate the entropy of the coefficient matrix. Results are presented from tests where the images from the Brodatz texture set have been decomposed with different filters and different cost functions and we also present calculations of the decision rule to split or not to split the subband. With the knowledge of the mean and variance of the input signal, we can calculate the typical decomposition tree for the signal using different image models.
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Anna Linderhed, Anna Linderhed, } "Wavelet packet decompositions of texture images: analysis of cost functions, filter influences, and image models", Proc. SPIE 4738, Wavelet and Independent Component Analysis Applications IX, (8 March 2002); doi: 10.1117/12.458773; https://doi.org/10.1117/12.458773
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