Fast Fractal Image Compression

One primary problem we are confronted with in information age is to effectively store and transmit huge amounts of digital images. This casts increasing the urgency to develop new compression algorithms with high performance. Some popular international standards such as JPEG, MPEG and H.26X are not so perfect and still need to be improved. This is especially true for the grayscale images commonly used in medical areas. Fractal image encoding is one of the competitive schemes in recent research.Focusing on fractal image compression, this dissertation probes intensively into the encoding of grayscale images and sequence images. The main contributions are as follows:1. A fast fractal compression method based on wavelet decomposition is proposed. This algorithm is mainly implemented in two aspects. Firstly, according to the ununiform distribution of the energy in subbands in wavelet transform domain, the low frequency region, where most energy concentrates, is encoded with traditional fractal encoding method. Secondly, with the similarity of subband image among different channels after wavelet decomposition, we have introduced a local optimal search mechanism, instead of global one, to gain the whole image's fractal codes after suitably rescaling the parameters in low frequency regions. The encoding procedure speeds up greatly while preserving the compression ratio and the quality of the reconstructed image. The dissymmetry between the encoding and decoding process has also been improved dramatically.2. Study also goes deep into some classification based fractal encoding schemes. Taking into account the shortcomings of the hard clustering problem, in which the category number needs to be pre-specified, we aim to modify the fractal image coding algorithm by using Optimal Fuzzy Clustering (OFC) method. Firstly the Linde-Buzo-Gray (LEG) algorithm is realized to get a rough cluster of domain blocks, then optimal category with small computational cost is automatically obtained with the algorithm presented above. Less encoding time is achieved through soft clustering of the domain blocks and classification search. The simulation results show that our algorithm is superior to those fast encoding schemes reported recently.3. Fractal compression of sequence image has also been studied. A fast algorithm is presented in this dissertation. It's based on the principle of OFC which has been effectively used in still grayscale image compression. The correlation between adjacent images is fully used to organize the domain pool and the coding efficiency is improved greatly.