Divided The Study Of Fractal Image Compression

Fractal image compression(FIC) is a new image coding method developed in recent ten years, and has been studied extensively. In chapter one, we mainly introduce the developmental history of fractal and the current research status of fractal image compression. In the following chapters, the theory and method of fractal image compression are studied.In this paper, the condition of compression transform is discussed, then theconception of xn-compression is presented, and a series of conclusions that checkif the transform is compression are obtained. Fractal image compression is based on the fixed-point theorem and the collage theorem proposed by M.Barnsley in 1988. In chapter three the extend collage theorem is presented which gives the control expression of the Hausdorff distance between two iterated images. On this basis, the error theorem is obtained which divides the Hausdorff distance between the original image and reconstructed image into two control parts. The fixed point of each contraction mapping is introduced, the fixed-point image(which is tiled by all the fixed points) is selected as an initial image when decoding, and is proved to be a good estimation of the attractor of the IFS. The experimental results show that a better reconstructed image can be got by few iterations at roughly the same compression ratio (CR).The block-based fractal image compression method has a low compression ratio, so simple region-based fractal image compression is introduced, then the competitive region-based fractal image compression method is presented. The experimental results show that the compression ratio is effectively improved at a similar PSNR value.Wavelet-fractal image compression has been received widely attention. In chapter five, pyramidal wavelet-fractal image compression is studied, sometheorems about it are obtained, then the coding methods are given, including the method of linear compression transform and the fast coding method of degree two polynomial compression transform. Simulation shows that the compression time is saved greatly when the same coding result is kept.