Fractal approximation of image blocks

Abstract

A method for block coding of images based on a least squares fractal approximation by a self-affine system (SAS) is presented. The computational cost of the approximation is linear in the number of pixels in the image. The approximation to a rectangularly tiled block involves evaluating various low-order moments over the block, and solving a system of four linear equations for each tile. The method is applied to a standard test image and the effects of various optimizations are shown. A quantitative comparison with the adaptive discrete cosine transform at 8:1 compression is made. The fidelity of the fractal method shows promise and its greater speed and simplicity compared to other fractal transforms suggest immediate applications such as interactive browsing of remote image archives or image representation in multimedia systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>