F. M. Dekking. Fractal image coding: some mathematical remarks on its limits and its prospects. Research Report Faculty of Technical Mathematics and Informatics, Delft Univeristy of Technology, No 95, 1995.
We discuss both black and white and grey value image encoding with the classical schemes proposed by M. Barnsley, respectively A. Jacquin. For the black and white case we prove a Decollage Theorem from which one might deduce that the fractal coding of binary images is not feasible. For grey value images we 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 we 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 multiresolutionanaly sis.
@TechReport{Dekk95b,
Author = {Dekking, F. M.},
Title = {Fractal image coding: some mathematical remarks on its limits and its prospects},
Number = {95},
Institution = {Faculty of Technical Mathematics and Informatics, Delft Univeristy of Technology},
Year = {1995}
}