Fractal Image Coding: Some Mathematical Remarks on Its Limits and Its Prospects

摘要

The authors discuss both black and white and grey value image encoding with theclassical schemes proposed by M. Barnsley, respectively A. Jacquin. For the black and white case they prove a Decollage Theorem from which one might deduce that the fractal coding of binary images is not feasible. For grey value images the authors take a close look at the different metrics in which collages are made. From this one might deduce that the mathematical basis for this type of coding is somewhat smaller than usually assumed. Finally they propose a time reduction of the domain pool search by an analysis of the grey value pyramid associated to an image. This naturally leads to the introduction of martingales, which offer a new viewpoint to multiresolution analysis.