Research On Image Compression Based On Fractal Theory

In the society with highly developed information technology, a vast amount of information data must be used in the form of image. People are constantly looking for new and better ways to obtain higher compression ratio. Fractal image compression has great potential in image storage and image transmission because of its high-resolution reconstructed images and high compression ratio. But the calculation of similarity between a range block and a domain block in the encoding step is very complex and time-consuming. To overcome this problem, several encoding techniques have been presented in this paper.(1) Because of various problems existing in the traditional fractal image compression algorithm, such as too long compression time, many mathematical tools are used in combination with fractal theory in order to get better compression results. For instance, the wavelet transformation and the discrete cosine transform are widely applied to image compression. In this paper, several typical hybrid image compression methods are implemented. Then, the impact of key parameters on the overall compression performance is analyzed. Based on these analysis, several improvement methods are given in this paper.(2) A new method using plane fitting to decide whether a domain block is similar enough to a given range block is proposed. First, three coefficients are computed for describing each range and domain block. Then, the best-matched one for every range block is obtained by analyzing the relation between their coefficients. Experimental results show that the proposed method can shorten encoding time markedly, while the retrieved image quality is still acceptable. In the decoding step, a kind of simple line fitting on block boundaries is used to reduce blocking effects. At the same time, the proposed method can also achieve high compression ratio.(3) A new gray image compression method is presented based on the one-dimensional cellular automata. In the theory of cellular automata, a large number of cells can combine to form a complex dynamic system by interactions between cells. Since images can be seen as a set of binary data, cellular automata can be used to simulate images. When some appropriate parameters are calculated, we need to store only these parameters as the compression code of image, thereby achieving a high compression ratio. Through the experimental results and performance analysises, we can see that the computing process of the proposed method is simple and easy to implement. Moreover, the peak signal to noise ratio and the decompressing rate are both at a high level.