Study On Algorithms For Fast Fractal Image Coding Technology

Image compression and coding are essentially important for the development of various multimedia services and telecommunication applications. Nowly the most algorithms for image compression and coding are proposed based on the correlation of the near image pixels and so their compression ratioes are not big. In fact, not only the near pixels are correlated but also the distant pixels are commonly correlated in an image. The fractal image coding regards the image as a fractal and gains the goal of compression by the self-correlation in the various dimention in a natural imge and then initiates a new idea in the range of image coding.Fractal image compression was first proposed by Barnsley in the latter of 1980s and was developed from the mathematical theory called Iterated Function Systems . In this technique, an image is usually represented by a contractive affine transformation, for which the reconstructed image is its fixed point and approximate to the original image. The fractal code of the image consists of the parameters of the contractive transformation. Thus, encoding an image by fractal techniques consists of finding an appropriate contractive transformation whose fixed point is the best possible approximation of the original image. But ,Barsley's fractal compression method suffers from too long coding time and need manual operation with high techniques for the operators. So it has no practicality. Barsley's student named Jacquin proposed a method of fractal compression based on image tiles' partition in 1990. The method makes an image into some fixed tiles instead of Barsley's method based on the image content. And then the method gains auto-coding by computers and boosts the process of the fractal image coding.But, Jacquin's coding method has some short because it has much computation and coding time. The method tries to look for the best mathed domain block for every range block in an image. Namely , the method need to search in the codepool for every contractive affine transformation and all domain blocks need to compare with any rang block and computer the mean square error. The paper proposes some improved algorithm from two factors by aiming at the lack of Jacquin's algorithm—the algorithm based on codebook reduction and the algoritnm based on correlation coefficients, the algorithm based on codebook reduction is achieved by a priori exclusion of the codebook blocks which are unlikely to meet the constraint on contrast scaling factorsand then markedly reduce the number of computation and the coding time while the decoding image has hardly been degraded. For the algoritnm based on correlation coefficients, we replace making the MSE minimum by making the correlation coefficient maximum awording off computering the constract scaling factors and intensity factors before computering MSE. And combining the algorithm based on codebook reduction, we obviously improve the performance of coding while the decoding image's PSNR even has increased a little. At last, A new algorithm for fast fractal image decoding based on adjusted contrast factors which are adjusted through setting some thresholds for the codebook is proposed based on the baseline algorithm. The experiment results show the algorithm can gain a higher quality of decoding image after the first iteration decoding than the baseline fractal decoding and accelerate obviously the process of converging in contrast to the baseline fractal decoding with a less degradation of decoded image.