Fractal image compression is a technique based on the representation of an image by a contractive transform, on the space of images, for which the fixed point is close to the original image. This broad principle encompasses a very wide variety of coding schemes, many of which have been explored in the rapidly growing body of published research. While certain theoretical aspects of this representation are well established, relatively little attention has been given to the construction of a coherent underlying image model that would justify its use. Most purely fractal-based schemes are not competitive with the current state of the art, but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success. This review represents a survey of the most significant advances, both practical and theoretical, since the publication of Jacquin's (1990) original fractal coding scheme.
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