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 is the principal researcher who has worked on fractal compression (1988), and he holds several patents on the technology. The most widely known practical fractal compression algorithm was invented by Arnaud Jacquin in 1991, although Barnsley and Alan Sloan took out the patent (US. 5,065,447) on this method also. 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. The patent issue may have been a problem, and fractal compression is much slower to compress than JPEG. (JPEG decompression takes about the same time as fractal decompression). Also, the improved compression ratio may have been an illusion. Fractal compression only has a large advantage over JPEG at low image quality levels, 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.
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 highly non-trivial. 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. 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. According to [1], fractal image compression is sardonically known as the "graduate student algorithm": lock a graduate student in a room with a computer until s/he has solved your problem.
Today fractal compression seems to be even less relevant, with wavelet compression outperforming it in most applications for those willing to accept the patent situation. JPEG is still widely used.
