| Image compression and coding are essentially important for the development of various multimedia services and telecommunication applications. Recent publications show a substantial increase in this area, in which many new ideas have been proposed. Fractal image compression is one of the most remarkable techniques because it opens up a refreshing new view to image coding. Since the early 1990s, fractal image compression has achieved obvious advances in the past decade. Fractal image compression is first proposed by Barnsley and is developed from the mathematical theory called Iterated Function Systems (IFS), which is an important branch of Fractal Geometry. 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. The fractal decoding is a relatively simple iteration procedure, in which the decoded image is approximated by iterating the contractive transformation denoted in the fractal code on an arbitrary initial image. Since the middle of 2001, the author has been doing a comprehensive literature search on the articles published in journals and conference proceedings, and technical reports on fractal image compression/coding and closely related subjects; specifically, papers published in IEEE/IEE journals and IEEE/IEE conference proceedings, which have resulted in more than 500 references at the time of this writing. Based on the most of these articles, the author explored many aspects of fractal image compression, in which some existing fractal encoding/decoding algorithms are improved and several new fractal encoding/decoding algorithms are proposed. Some of the algorithms improved/proposed by the author are summarized in this dissertation.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, baseline fractal coding, and so on.Chapter 2 introduces the necessary mathematical knowledges of fractal image coding, including metric space, fixed-point theorems, collage theorem and iterated function systems. In addition, the chapter outlines the applications of fractals to image processing as well.Chapter 3 describes the basic principle of fractal image coding, and gives the description and implementation of the baseline fractal coding algorithm, and discusses experimental results. Chapter 4 presents a literature survey of the current fractal coding for still grayscale image, but excluding color image and video coding research.The subsequent Chapter 5 - Chapter 7 introduce some of the fractal encoding/decoding algorithms improved/proposed recently by the author. Chapter 5 proposes a new scheme to improve the fractal image encoding in terms of image quality and encoding time. The improvement is achieved by using an adaptive codebook reduction strategy, i.e., by a priori exclusion of the codebook blocks which are unlikely to meet the constraint on contrast scaling factors. Experimental results demonstrated the effectiveness and efficiency of the proposed scheme; the decoded image quality (objective and subjective) has no degradation by contrast with that of the corresponding fractal algorithm, while the encoding time is significantly reduced (about 10 times).Chapter 6 presents two fast encoding algorithms for fractal image compression. The first is based on the cross traces of image blocks defined by the author and an explicit relationship that links the least square error to cross traces. A simulation on a 256×256 Lena image shows that, depending on the search window size, the proposed method can achieve not only lo...
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