A simple model for image self-similarity and the possible use of mutual information

In general, images possess a considerable degree of affine self-similarity, that is, their subblocks are well approximated by a number of other subblocks with the help of affine greyscale transformations. In this paper, we introduce a quite simple, yet formal mathematical model of such affine self-similarity. The traditional measure of approximation is the L
²
norm. We also explore the use of mutual information as a measure of similarity between image subblocks. Finally we examine a simple mutual information-based method of fractal image coding.