Which partition scheme for what image? Partitioned iterated function systems for fractal image compression

Fractal image compression is an area where we expect very high rates of compression as opposed to JPEG compression which produces high quality images at comparably low rates of compression1 in a reasonable amount of time. The success, in terms of compression ratio and image quality, of a fractal encoder lies in the choice of a partition scheme.; We will review a formal model for a Partition Iterated Function System (PIFS) encoder/decoder together with the necessary mathematical background. A description of a fractal tool follows. This tool implements the PIFS model and several partition schemes. It was written in C++ by Andrew Bernat (author of this thesis). Reasonable theoretical bounds on error and image quality for different partition schemes are difficult to obtain; empirical studies are the only alternative. The fractal tool serves this purpose. It can help to determine which kinds of partition schemes yield higher compression rates and larger signal-to-noise ratios (SNR) for particular images. We discuss this in the paper.; 1We will make precise the meaning of high and low.