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11b: What is the state of fractal compression?


This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by others.

11b: What is the state of fractal compression?

Fractal compression is quite controversial, with some people claiming
it doesn't work well, and others claiming it works wonderfully. The basic
idea behind fractal image compression is to express the image as an iterated
function system (IFS). The image can then be displayed quickly and
zooming will generate infinite levels of (synthetic) fractal detail. The
problem is how to efficiently generate the IFS from the image.

Barnsley, who invented fractal image compression, has a patent on fractal
compression techniques (4,941,193). Barnsley's company, Iterated Systems
Inc, has a line of products including a Windows viewer, compressor,
magnifier program, and hardware assist board.

Fractal compression is covered in detail in the comp.compression FAQ file
(See "compression-FAQ"). Ftp: ftp://rtfm.mit.edu/pub/usenet/

Three books describing fractal image compression are:

1. M. Barnsley, _Fractals Everywhere_, Academic Press Inc., 1988. ISBN 0-
12-079062-9. This is an excellent text book on fractals. This is probably
the best book for learning about the math underpinning fractals. It is also a
good source for new fractal types.

2. M. Barnsley and L. Hurd, _Fractal Image Compression_, Jones and
Bartlett. ISBN 0-86720-457-5. This book explores the science of the fractal
transform in depth. The authors begin with a foundation in information
theory and present the technical background for fractal image compression.
In so doing, they explain the detailed workings of the fractal transform.
Algorithms are illustrated using source code in C.
3. Y. Fisher (Ed), _Fractal Image Compression: Theory and Application_.
Springer Verlag, 1995.

The October 1993 issue of Byte discussed fractal compression. You can ftp
sample code: ftp.uu.net:/published/byte/93oct/fractal.exe .

An introductory paper is:

1. A. E. Jacquin, Image Coding Based on a Fractal Theory of Iterated
Contractive Image Transformation, _IEEE Transactions on Image
Processing_, January 1992.

A fractal decompression demo program is available by anonymous ftp:
lyapunov.ucsd.edu:/pub/inls-ucsd/fractal-2.0 [].

Another MS-DOS compression demonstration program is available by
anonymous ftp: ftp://lyapunov.ucsd.edu/pub/ .

A site with information on fractal compression is
ftp://legendre.ucsd.edu/pub/Research/ . On the WWW you can access
file://legendre.ucsd.edu/pub/Research/Fisher/fractal.html .

Many fractal image compression papers are available from
ftp.informatik.uni-freiburg.de:/documents/papers/fractal [].
A review of the literature is in Guide.ps.gz. See the README
file for an overview of the available documents.

Other references:

http://dip1.ee.uct.ac.za/fractal.bib.html "Fractal Compression

http://inls.ucsd.edu/y/Fractals/ Fractal Compression (Yuval Fisher )


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