A. E. Jacquin. Image coding based on a fractal theory of iterated contractive Markov operators, Part I: Theoretical Foundation. Research Report Georgia Institute of Technology, No 91389, 1989.
An extension of classical results about iterated sequences and fixed points of contractive transformations is developed. We give results about the existence and construction of non-wandering points and attracting sets with arbitrarily small diameter for contractive transformations defined in pseudometric spaces of abstract objects. We present the inverse problem of constraining a transformation to have an attracting set which contains an original object given a priori. We apply these results in the specific framework of a space of Borel measures-our mathematical models for monochrome images. In such a space, we propose two distance functions, and describe a class of contractive transformations-called Markov operators-defined consistently with a partition of the support of the measures. These theoretical results are then shown to provide a foundation for the design of a new generation of block coding systems for digital images.
@TechReport{Jacq89a,
Author = {Jacquin, A. E.},
Title = {Image coding based on a fractal theory of iterated contractive Markov operators, Part I: Theoretical Foundation},
Number = {91389},
Institution = {Georgia Institute of Technology},
Year = {1989}
}