| Summary: | This thesis describes and investigates new methods for lossy image compression. The methods are based on the theory of Iterated Function Systems (IFS) which is a branch of deterministic fractal geometry. Iterated Function Systems have for some time promised to provide the basis for new image compression techniques which may challenge existing industrial standards. This thesis examines current fractal compression techniques and presents improvements which greatly increase their compression performance. The fractal compression methods rely on the assumption that image redundancy can be efficiently exploited by taking advantage of image self-similarity. Traditional fractal compression techniques have concentrated on using block-based transformations to encode image self-similarity. In this thesis alternative classes of transformations are investigated which can encode image self-similarity more efficiently. Two different fractal compression systems are presented. The first uses variable-size block-based transformations and the second region-based transformations, where the regions can be irregularly shaped segments of the image. With the block-based systems, exhaustive algorithms are used to generate the transformations. With the region-based transformations it is not practical to use exhaustive algorithms and so heuristic methods are investigated. The emphasis, however, is on improving the compression performance of fractal based encoders and not on reducing their computational complexity. The results of many experiments on synthetic and natural images are presented. The results show that the new algorithms achieve a doubling of compression ratio over traditional block-based algorithms at a similar decompressed image quality. The hierarchical block-based and region-based transformations can be more efficient in encoding the self-similarity found in the test images.
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