Fractal compression

Fractal image representation may be described mathematically as an iterated function system (IFS).

A simple approach[2] for doing so is the following partitioned iterated function system (PIFS): In the second step, it is important to find a similar block so that the IFS accurately represents the input image, so a sufficient number of candidate blocks for Di need to be considered.

This bottleneck of searching for similar blocks is why PIFS fractal encoding is much slower than for example DCT and wavelet based image representation.

[3] Other researchers attempt to find algorithms to automatically encode an arbitrary image as RIFS (recurrent iterated function systems) or global IFS, rather than PIFS; and algorithms for fractal video compression including motion compensation and three dimensional iterated function systems.

While this asymmetry has so far made it impractical for real time applications, when video is archived for distribution from disk storage or file downloads fractal compression becomes more competitive.

[14][15][16] Since the interpolation cannot reverse Shannon entropy however, it ends up sharpening the image by adding random instead of meaningful detail.

Michael Barnsley and Alan Sloan formed Iterated Systems Inc.[21] in 1987 which was granted over 20 additional patents related to fractal compression.

To date the most successful use of still fractal image compression is by Microsoft in its Encarta multimedia encyclopedia,[24] also under license.

The redistribution of the "decompressor DLL" provided by the ColorBox III SDK was governed by restrictive per-disk or year-by-year licensing regimes for proprietary software vendors and by a discretionary scheme that entailed the promotion of the Iterated Systems products for certain classes of other users.

In 1994 SoftVideo was licensed to Spectrum Holobyte for use in its CD-ROM games including Falcon Gold and Star Trek: The Next Generation A Final Unity.

[26] In 1996, Iterated Systems Inc. announced[27] an alliance with the Mitsubishi Corporation to market ClearVideo to their Japanese customers.

Two firms, Total Multimedia Inc. and Dimension, both claim to own or have the exclusive licence to Iterated's video technology, but neither has yet released a working product.

[29] In summary, it is a simple quadtree block-copying system with neither the bandwidth efficiency nor PSNR quality of traditional DCT-based codecs.

[41][42] Femtosoft developed an implementation of fractal image compression in Object Pascal and Java.