Statistics of natural images using hash fractal image compression

This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in CompSysTech '03 Proceedings of the 4th international conference conference on Computer systems and technologies: e-Learning, http://dx.doi.org/10.1145/973620.973661.
Natural images form very small subset of all images. In spite of the fact, the direct computation of their block densities is not possible. On the other hand, the existence of various successful image compression methods, in particularly, the fractal compression, indicates that the compression somehow is able to capture and use at least part of the natural image statistics. In this work we show how hash based fractal image compression can be used to derive quite precise the entropies of 4 × 4 patches of the natural images. We state that the probability density in first order factorize to the probability densities of the contrast, the brightness and the index of the codebook blocks.