Based On Higher Order Spectral Characteristics Of The Image Fractal Coding

The fractal image compression technology was proposed by American mathematician Barnsley and Sloan in 1987. At present , fractal image compression technology has become a new orientation in the image compression field. In fractal compression, an image is usually represented by a contractive affine transformation , the fractal decoding is a relatively simple iteration procedure, in which the decoding image is approximated by iterating the contractive transformation on an arbitrary initial image.In this paper, several speeding methods based on feature classification were deeply analyzed , then a new approach of fractal coding based on high-order spectrum of image was proposed. The encoder firstly used the adaptive quad-tree partition to obtain range blocks, secondly computed the high-order spectrum of the image block which size was larger than 4×4. Constructing lower dimension k-d tree data structure to store the orthogonal projective vectors extracted from high-order spectrum of the image block, the nearest neighbor searching algorithm based on pre-quantization of fractal parameter was used to obtain fractal code quickly. Comparing with traditional method the simulation results under Visual C++ evidently illuminated that the new method can improve the PSNR , compression ratio and compression time cost .The main research work and the achievement obtained include the following contents:1. A new method to gain characteristic vector of the image for lower dimension was proposed. This conveniently supplied the nearest neighbor search algorithm. The search time was reduced rapidly because of lower dimension and using the high-spectrum of the image.2. A full search scheme was adopted other than local search in some classification method. The fidelity of decoding image was improved.3. To get the best match image block, the encoder use nearest neighbor searching algorithm based on pre-quantization of transform parameter to obtain fractal code. Intensive computation of encoding was reduced very much.4. Instead of storing the data point of image in a k-d tree leave node, we store only the identity of the subimage which contains the corresponding domain block and its position and other parameter. In this way the memory requirement is substantially reduced.