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30 What is the state of fractal compression?




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This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.

30 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
(http://www.iterated.com/), 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://rtfm.mit.edu/pub/usenet/ .

One of the best online references for Fractal Compress is Yuval
Fisher's Fractal Image Encoding page
(http://inls.ucsd.edu/y/Fractals/) at the Institute for Nonlinear
Science, University for California, San Diego. It includes references
to papers, other WWW sites, software, and books about Fractal
Compression.

Three major research projects include:

Waterloo Montreal Verona Fractal Research Initiative
http://links.uwaterloo.ca/

Groupe FRACTALES
http://www-syntim.inria.fr/fractales/

Bath Scalable Video Software Mk 2
http://dmsun4.bath.ac.uk/bsv-mk2/

Several 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. Anson, "The Fractal Transform", Jones and
Bartlett, April, 1993. ISBN 0-86720-218-1. Without assuming a
great deal of technical knowledge, the authors explain the
workings of the Fractal Transform(TM).
3. 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.
4. Y. Fisher (Ed), "Fractal Image Compression: Theory and
Application". Springer Verlag, 1995.
5. Y. Fisher (Ed), "Fractal Image Encoding and Analysis: A NATO ASI
Series Book", Springer Verlag, New York, 1996 contains the
proceedings of the Fractal Image Encoding and Analysis Advanced
Study Institute held in Trondheim, Norway July 8-17, 1995. The
book is currently being produced.

Some introductary articles about fractal compression:

1. The October 1993 issue of Byte discussed fractal compression. You
can ftp sample code:
ftp://ftp.uu.net/published/byte/93oct/fractal.exe .
2. A Better Way to Compress Images," M.F. Barnsley and A.D. Sloan,
BYTE, pp. 215-223, January 1988.
3. "Fractal Image Compression," M.F. Barnsley, Notices of the
American Mathematical Society, pp. 657-662, June 1996.
(http://www.ams.org/publications/notices/199606/barnsley.html)
4. A. E. Jacquin, Image Coding Based on a Fractal Theory of Iterated
Contractive Image Transformation, "IEEE Transactions on Image
Processing", January 1992.
5. A "Hitchhiker's Guide to Fractal Compression" For Beginners by
E.R. Vrscay
ftp://links.uwaterloo.ca/pub/Fractals/Papers/Waterloo/vr95.ps.gz

Andreas Kassler wrote a Fractal Image Compression with WINDOWS package
for a Fractal Compression thesis. It is available at
http://www-vs.informatik.uni-ulm.de/Mitarbeiter/Kassler/papers.htm

Other references:

Fractal Compression Bibliography
http://www.dip.ee.uct.ac.za/imageproc/compression/fractal/fract
al.bib.html

Fractal Video Compression
http://inls.ucsd.edu/y/Fractals/Video/fracvideo.html

Many fractal image compression papers are available from
ftp://ftp.informatik.uni-freiburg.de/documents/papers/fractal

A review of the literature is in Guide.ps.gz.
ftp://ftp.informatik.uni-freiburg.de/documents/papers/fractal/R
EADME

 

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