Study On Fast Algorithms For Fractal Image Compression

Fractal image coding is a very promising image compression technique. Due to its novelty, high compression rate, resolution independence and fast decoding, the technique has received more interests from the researchers in the area of image processing, especially image compression over the past decade. However, it typically is very time-consuming to encode fractally an image, which limited its applications and development. Therefore, the author proposed several fast encoding algorithms, two of which are introdued in this dissertation. The main content of this dissertation is described as follows. Chapter 1 introduced simply the necessity of image compression and popular image compression methods, including fractal image compression. Chapter 2 first gave some basic mathematical knowledge, including measure space, fixed point theorem, collage theorem and Iterated Function System, and then outlined applications of fractal theory in image processing. Chapter 3 introduced the basic principle, algorithm analysis and simulation of baseline fractal image coding, and then outlined the origin and the development of fractal image coding. Chapter 4 proposed a fast encoding algorithm based on relative coefficient to improve the baseline fractal algorithm. The simulations show that, for the eight standard 256×256 test images with various complexities, the proposed algorithm can averagely accelerate the encoding process by about five times, while giving a little increase of the PSNR (peak signal-to-noise ratio) in comparison to the corresponding baseline fractal algorithm. Chapter 5 presented a fast encoding algorithm based on one-norm of normalised block Experiments demonstrate that, for three popular 512×512 test images, the proposed algorithm can averagely reduce the runtime by about 40 times while there is averagely the PSNR gain of 0.91dB, in comparison with the baseline fractal algorithm. Chapter 6 summarized the study in this dissertation.