Study On Image Compression Based On Fractal Theory

With the development of multimedia technology and the increase of communication requirement, image coding has become one of the key technologies on which the digital society depends. Fractal image coding is a very promising image compression technique. It has been receiving more attention in research over the past decade because of its novelty, high compression rate, resolution independence and fast decoding; however, it requres a very long encoding time. The dissertation thus proposed a new fractal coding algorithm to accelerate encoding process. The main contents described in this dissertation are as follows: Chapter 1 is the introduction, which consists of an overview of several well-known image compression techniques, such as predictive coding, transform coding, vector quantization, wavelet coding, baseline fractal coding, and so on. Chapter 2 introduces the necessary mathematical knowledge of fractal image coding, including metric space, Banach's fixed-point theorem, collage theorem and iterated function systems (IFS). Chapter 3 describes the basic principle of fractal image coding, gives the description and implementation of the baseline fractal coding algorithm, and discusses experimental results. Chapter 4 presents a survey on the current literatures of fractal image coding for still grayscale image, especially wavelet-fractal image coding. Chapter 5 is the key part, in which the author proposed a fast fractal encoding algorithm based on the shape-feature of an image block, which is defined by the author. The proposed algorithm converted the range-domain matching problem to the nearest neighbors search problem in the sense of shape feature. The search space is reduced greatly, so the encoding time is considerably less than that of the baseline fractal encoding algorithm. Chapter 6 gives the conclusions and the direction of the author's future research.