Fractal compression

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Fractal compression is a lossy compression method used to compress images using fractals. The method is best suited for photographs of natural scenes (trees, mountains, ferns, clouds). The fractal compression technique relies on the fact that in certain images, parts of the image resemble other parts of the same image.

Michael Barnsley led development of fractal compression in 1987, and holds several patents on the technology.^[1] The most widely known practical fractal compression algorithm was invented by Barnsley and Alan Sloan (U.S. Patent 5,065,447 ). Barnsley's graduate student Arnaud Jacquin implemented the algorithm in software for his Ph.D. thesis in 1989.^[2]All methods are based on the fractal transform using iterated function systems.

Fractal compression appeared to be a promising technology in the late 1980s, when in some circumstances it appeared to compress much better than JPEG, its main competitor at that time. However, fractal compression never achieved widespread use. Fractal compression is much, much slower to compress and much slower to decompress than JPEG. Furthermore, its patents were not widely licensed. Also, the improved compression ratio is an illusion^{[citation needed]}. Fractal compression only has a large advantage over JPEG at low image quality levels^{[citation needed]}, which is usually undesirable. The claim that fractal compressed images, when enlarged beyond their original size, looked better than similarly enlarged JPEG images seems also to have been an irrelevant distinction^{[citation needed]}.

It has also turned out that the most impressive examples of fractal compression require considerable human intervention: the process of generating an image from its fractal representation is easy to automate, but reversing the procedure to generate an optimal fractal representation of an image is very difficult. Most real-world images have heterogeneous mathematical properties; for instance a photograph in which mountains and clouds and trees might be represented by several classes of fractal representation; automated recognition of which class works best for which part of the image is a difficult problem in AI. Although Barnsley's collage theorem proves that for a large class of real-world images, compact fractal representations must exist; it does not provide a general-purpose algorithm for the construction of such representations. In practice, to achieve high image quality with compression ratios that significantly exceed those of JPEG requires significant amounts of human effort..