Image Coding Based On Fractal Dimension And Wavelet

With the development of computer application such as Internet communications, digital libraries and long-distance medical diagnostic system, the memory storage and data transmission become the most important problem. To reduce memory storage and transmission time, image compression appears to be very important. Nowadays, fractal image compression has received much appreciation because of its characteristic of fast decoding and resolution-independent. However, the traditional algorithms still suffer from a high encoding time. With the main purpose of gaining an image compression technique that has fast coding speed and good decoding image quality, by analyzing the distribution of the coefficients after wavelet transformation, the paper proposed a new fractal coding method based on fractal dimension and wavelet transformation.In chapter one and two, the basic principles and methodologies for image compression are introduced. Then the mathematical foundation and the coding principle for fractal image compression and wavelet transform coding are expatiated, and the LIFS fractal image compression scheme proposed by Jacquin is discussed in detail.In chapter three, first of all, the fractal dimension and several kinds of its calculation methods are expatiated. Then, based on the characteristics of wavelet transform and fractal dimension, a new technique--feature vector fractal image compression is proposed. In this technique, image blocks are partitioned into different frequency segments after wavelet transform, and the domain blocks are clustered using the feature vectors composed of the fractal dimensions of those frequency segments, then the range blocks are searched only in the cluster. In this way, the encoding time is largely reduced.On the one hand, in the fractal image encoding the pool of domain blocks generally involves a large amount of domain blocks, but there are small parts of the domain blocks that can take part in the encoding. On the other hand, because the energy concentrates on the coefficients of low frequency subband after wavelet transformation, the low frequency subband contains more original information than the similar images. Hence, in chapter four, combined with traditional quad-tree image compression method, an algorithm of quad-tree image compression based on fractal dimension is proposed. This algorithm replaces the similar image with low-frequency image of wavelet transformation in order to sample the domain block, and it also reduces the size of the domain pool using the fractal dimension value of each domain block, which speed up the searching and encoding process.From the results of the experiments, by taking full advantage of the characters of image, our algorithm yields a higher encoding speed than the traditional Jacquin method or traditional quad-tree imagecompression scheme.