2 Rate / Distortion Performance of Fractal Transforms for Image Compression 2

We study the delity/compression performance of fractal image coding, and evaluate the merits or otherwise of a number of complexity options. We can rst of all choose a quantization scheme for the transmission of coeecients which limits the code alphabet, according to permissible degradations. This alphabet can then be entropy coded to eliminate redundancy so that the compression eeciency of a range of implementation options can be studied and related to objective and subjective measures of degradation. We nd rotations and reeections of little value. A limited degree of searching may be of beneet within image regions of high edge value, but in general more is gained by using a higher order fractal function than by searching. Fractal image coding works by contraction mapping of portions of images onto smaller image fragments, normally rectangular image blocks. The Iterated Transform Technique (ITT), published by Jacquin 1 used a low order grey scale mapping and incorporated searching to select the blocks whose mappings give lowest distortion measure. Monro's generalization of this process, 2 called the Bath Fractal Transform (BFT), demonstrated the trade-oo between higher order mappings and the searching of the image, with useful gains in delity achieved up to the biquadratic case.