Fractal Image Compression
Fractals are geometric objects that are exactly self-similar and have a
fractional (Hausdorff) dimension. Consequently, they contain an infinite
amount of detail. However, they can be described by a very simple rule and
so their infinite complexity can be coded into a simple formula. Now this
is compression! Since many 'real' objects exhibit some sort of
self-similarity (on certain ranges of scales at least), fractals can be
used to generate real-looking objects (eg. clouds and leaves) as well as
to encode 'real' images.
To find out a bit more about fractal image compression, go to the
W2003 lecture notes Feb 3. To see some examples
of fractal image compression, go to the Fractal image compression page.
References:
- Fractal Image Compression
by Y. Fischer,
in Appendix A of Chaos and Fractals: New
Frontiers of Science H.-O Peitgen, H. Jurgens, D. Saupe, Springer-Verlag, 1992.
- Fractal Image Compression. Theory and Application, Yuval
Fisher, editor. Springer-Verlag, 1995.
- Waterloo Fractal
Compression Project at the University of Waterloo (http://links.uwaterloo.ca).
- Fractal and Wavelet Image Compression Techniques, Stephen Welstead,
SPIE Optical Engineering Press, 1999.
General references on fractals:
- "Chaos and Fractals. New Frontiers in Science", by H.-O. Peitgen, H.
Jurgens, and D. Saupe. Springer-Verlag, 1992.
- "Fractals Everywhere", by Michael Barnsley. Academic Press, 1993 (second ed.)
- My lecture notes
To use some software for drawing fractals, go to the
Software page.
Some programs that domonstrate fractal image compression; see
Andrew Dagleish's and Farhad Sadaghaini's projects in 2001.