Fractal image coding based on a theory of iterated contractive image transformations

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Abstract
The notion of fractal image compression arises from the fact that the iteration of simple deterministic mathematical procedures can generate images with infinitely intricate geometries, known as fracial images [2]. The purpose of research on fractal—based digital image coding is to solve the inverse problem of constraining this complexity to match the real—world complexity of real—world images. In this. paper, we propose a fractal image coding technique based on a mathematical theory of iterated transformations [1, 2, 3, 7] which encompasses deterministic fractal geometry. Initial results were reported in [7, 8]. The main characteristics of this technique are that (i) it is fractal in the sense that it approximates an original image by a fractal image, and (ii) it is a block—coding technique which relies on the assumption that image redundancy can be efficiently exploited through blockwise self—iransformabiliiy. We therefore refer to it as fracial block—coding. The coding—decoding system is based on the construction, for each original image given to encode, of a specific image transformation which, when iterated on any initial image, produces a sequence of images which converges to a fractal approximation of the original. We show how to design such coders, and thoroughly describe the implementation of a system for monochrome still images. Extremely promising coding results were obtained.

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