Research On Fractal Image Compression

Fractal image coding is a very promising compression technique. It has been paid great attention because of its novelty, high compression rate, resolution independence and rapid decoding. This paper mainly studies the basic theory of fractal and fractal image compression methods. Firstly, the article reviewed the basic principles and methodologies for image compression. Then we introduce the principles of fractal geometry and the mathematical foundation necessary for fractal image compression. After that the LIFS fractal image compression scheme proposed by Jacquin is discussed in detail. Finally two new methods of fractal image compression are proposed after some discussion. Experiment results show that these algorithms and methods are useful and valid.The main contributions of this dissertation are as follows:(1) Introduce the classical fractal image compression method proposed by Fisher, then propose a new algorithm based on Fisher's method, so named the Hierarchical Matching Encoding Scheme (HMES). Firstly there are no rotations and flips on domain blocks in this method, which compress the domain pool consequently. Secondly a hierarchical classification matching scheme is proposed to classify the domain blocks more reasonably. Experimental results on standard gray scale image show that the hierarchical classification matching scheme yields much better performance over other classification matching scheme.(2) A multi-dimensional fractal image compression is presented. In this method we adopt several domain pools of different sizes other than the traditional domain pool. The size of the domain blocks are twice, three times, four times, five times of the ranges separately. In the matching process, the search is conducted in each domain pool. Experimental results show that this method has advantage over Fisher's algorithm; it reduces the encoding time while the compression ratio and PSNR are both increased.