Image coding based on a fractal theory of iterated contractive image transfort-nations

The conception of digital image coding techniques is of great interest in various areas concerned with the storage or transmission of images. For the past few years, there has been a tendency to combine different classical coding techniques in order to obtain greater coding efficiency. In this paper, we propose an independent and novel approach to image coding, based on a fractal theory of iterated transformations. The main characteristics of this approach are that i) it relies on the assumption that image redundancy can be efficiently exploited through self-transformability on a block-wise basis, and ii) it approximates an original image by a fractal image. We, therefore, refer to our approach as fractal block coding. The coding-decoding system is based on the construction, for an original image to encode, of a specific image transformation-a fractal code-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 a system for the coding of monochrome digital images at rates in the range of 0.5-1.0 b/pixel. Our fractal block coder has performance comparable to state-of-the-art vector quantizers, with which it shares some aspects. Extremely promising coding results are obtained.