Fractal image compression

Abstract

Image compression techniques based on fractals have been developed in the last few years and may promise better compression performance. Fractal image compression techniques are being developed due to the recognition that fractals can describe natural scenes better than shapes of traditional geometry. This paper describes principle and common techniques of fractal image compression. Mathematical foundations for fract image compression techniques are presented first. Then three main fractal image compression techniques are discussed. The first and most important technique is based on iterated function systems (IFS): images are compressed into compact IFS codes at encoding stage, and fractal images are generated to approximate the original image at the decoding stage. The second technique is segment-based coding: images are segmented according to the fractal dimension and these segments are coded efficiently using properties of the human visual system. The third technique is yardstick coding which is similar to DPCM and subsampling with subsequent interpolation. But it was inspired by the fractal geometry on measuring the length of a curve using a yardstick.