T. Bedford, F. M. Dekking, M. S. Keane. Fractal image coding techniques and contraction operators. Nieuw Arch. Wisk. (4), 10(3):185-218, 1992.
Michael Barnsley and his coworkers have recently popularised the idea of using fractals to achieve compression of the data in an image (for example, a TV picture or a satellite photograph). The intuitive idea is very appealing: Since many images contain complex fractal-like objects, an efficient way of encoding the image will try to describle these objects as frctals rather than approximating them in "smooth" ways. Barnsley and Sloan [3] wrote an article for a popular computing journal in which a method for fractal coding was loosely described, a number of "coded" pictures were shown, and the astonishing claim was made that compression rates of 1:10 000 are possible using their techniques. Since then Barnsley and Sloan have been granted a US patent [4] on "Methods and apparatus for image compression by iterated function system". In this paper we shall discuss some of the problems involved with any implementation of Barnsley's coding methods. We also discuss an alternative fractal coding technique due to Jacquin ([15], [17]), which was developed as a part of his PhD thesis under Barnsley at Georgia Institute of technology. Much of the work described in this article was carried out during a cooperative project between Delft University of Technology and Philips Research Laborarories, Eindhoven. The authors would like to thank M. Breeuwer, G. Jansen, R. H. P. Janssen, P. van Otterloo, and D. van Schooneveld for their contributions to the project.
@article{BeDeKe92,
Author = {Bedford, T. and Dekking, F. M. and Keane, M. S.},
Title = {Fractal image coding techniques and contraction operators},
Journal = {Nieuw Arch. Wisk. (4)},
Volume = {10},
Number = {3},
Pages = {185--218},
Year = {1992}
}