A Study On Image Compression Based On Fractal Method

The fractal theory is a very active branch in modern mathematics and non-lineal science. Recently,it has played an increasingly important role in image processing and analysis. As a new method for image compression, fractal image compression has some desirable advantages such as high compression ratio, fast decoding speed and image resolution independent of the decoded image. However, the long coding time of this method becomes the main problem for the fractal image compression to be efficient and utilizable.The main reason for the slow speed of fractal image coding is that it takes too much time to look for the best matching domain blocks. Therefore, it is necessary to reduce the searching scope and improve the searching technique to quicken the coding speed. In addition, the best matching domain blocks must be in the searching scope.This paper mainly studies the approach of fractal image coding, and presents a new image coding method, improved fractal image coding approach based on quadtree partition. On the basis of the theory of image compression and fractal, the mathematical foundations and general algorithm of the fractal image compression, the fractal coding parameters are studied on emphasis. By analyzing the factors that affect the speed of fractal image coding, such as MSE, the contrast scaling(s), the variance of domain blocks (Var(D)), the variance of range blocks(Var(R)) and their relationships, some work has been done to improve the approach based on quadtree partition. First, two parameters, the threshold of flat block(ε) and the threshold of permitted code book(η), are added to the algorithm to control the encoding speed and the decoded image quality. Second, the luminance of the flat range blocks whose Variance is less thanεis replaced with its average, avoiding searching the matching block from the code book. Third, the domain blocks whose Variance is smaller thanηare removed from the permitted code book, which further reduces the searching scope and improves the encoding speed. Finally, experiments have shown that it can accelerate the speed of coding greatly compared with the original approach of fractal image coding in similar PSNR and compression ratio.