  Fractal image compression, Culik's image compression and zerotree prediction
coding of wavelet image decomposition coefficients succeed only because typical
images being compressed possess a significant degree of self-similarity.
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 of the present paper is to demonstrate these relations.
  The paper offers a plain-term interpretation of Culik's image compression, in
regular image processing terms, without resorting to finite state machines and
similar lofty language. The interpretation is shown to be algorithmically
related to an IFS fractal image compression method: an IFS can be exactly
transformed into Culik's image code. Using this transformation, we will prove
that in a self-similar (part of an) image any zero wavelet coefficient is the
root of a zerotree, or its branch.
  The paper discusses the zerotree coding of (wavelet/projection) coefficients
as a common predictor/corrector, applied vertically through different layers of
a multiresolutional decomposition, rather than within the same view. This
interpretation leads to an insight into the evolution of image compression
techniques: from a causal single-layer prediction, to non-causal same-view
predictions (wavelet decomposition among others) and to a causal cross-layer
prediction (zero-trees, Culik's method).
