FRACTAL IMAGE-CODING - A REVIEW

Specific classes of Fractals can be used for Digital Image Compression or Coding. For such an application, the general problem statement is the following. Given any original discrete image specified by an array of pixels, how can a computer construct a fractal image-the coded image-which is both visually close to the original one, and has a digital representation which requires fewer bits than the original image. In this paper, we describe art approach to image coding based on a fractal theory of iterated contractive transformations defined piecewise. The main characteristics of this approach are that: i) it relies on the assumption that image redundancy can be efficiently captured and exploited through piecewise self-transformability on a block-wise basis, and ii) it approximates an original image by a fractal image, obtained from a finite number of iterations of an image transformation called a fractal code. We refer to this approach as Fractal Block Coding. The general coding-decoding system is based on the construction, for an original image to encode, 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 at the decoder, produces a sequence of images which converges to a fractal approximation of the original. The fractal code consists of a description of both an image partition and a contractive image transformation defined as a list of parent and child block transformations, each specified by a small set of quantized parameters. We describe the design of such a system for the encoding of monochrome digital images at rates below 1 b/pixel, without any entropy coding of the parameters of the fractal code. We also present novel ideas and extensions from the work of a number of researchers which has appeared since the publication of the fractal block coding work of the author.