Graph-theoretical analysis of the fractal transform

A part of a fractal code is an assignment of a domain block to every range block. The assignment is used to construct the dependence graph of a fractal code. The vertices of the graph represent the range blocks. Two vertices z and y are connected by a directed edge from y to x if the range block y is overlapped, fully or partially, by the domain block assigned to the range block x. An algorithm to analyze the structure of the dependence graph is presented. The exposed structure of the graph can be used for three different purposes. The first one is convergence analysis: the affine transformations linking domain and range blocks can be classified into those that affect convergence and those that do not. The second one is decoding time reduction: certain range blocks can be reconstructed in a non-iterative way. The third one is improving upon collage coding: the affine transformations for some range blocks can be optimized based on the domain blocks extracted from the reconstructed rather than the original image.