Image compression with iterated function systems, finite automata and zerotrees: grand unification

The paper deals with analysis, generalizations and unifications of the latest group of powerful image compression techniques: fractal image compression with iterated function systems (IFS), Culik's compression with finite automata and Shapiro's embedded coding of wavelet coefficients using zerotrees. All three techniques achieve premium results by exploiting properties of self-similarity of typical images. In more precise terms, they all rely on the fact that parts of image representations at different resolutions may in some sense be similar. Therefore, a higher-resolution representation may be rather accurately predicted from a low-resolution one. This is a unifying, common concept of these seemingly dissimilar compression techniques, which may not be apparent due to particular terminologies each of the methods uses. Besides the common concept, these methods turn out to be even more tightly related, to the point of algorithmical reducibility of one technique to another. The goal is to demonstrate these relations.