Fractal image coding: a review

An approach to image coding based on a fractal theory of iterated contractive transformations defined piecewise is described. The main characteristics of this approach are that it relies on the assumption that image redundancy can be efficiently captured and exploited through piecewise self-transformability on a block-wise basis, and it approximates an original image by a fractal image, obtained from a finite number of iterations of an image transformation called a fractal code. This approach is referred to as fractal block coding. The general coding-decoding system is based on the construction, for an image to be encoded, of a fractal code-a contractive image transformation for which the original image is an approximate fixed point-which, when applied iteratively on any initial image of the decoder, produces a sequence of images which converges to a fractal approximation of the original. The design of a system for the encoding of monochrome digital images at rates below 1 b/pixel is described. Ideas and extensions from the work of other researchers are presented