Research On Some Fast Fractal Image Encoding Method

In this paper, based on the fractal theory which is the kernel of the non-linear theory, some fast fractal image encoding method has been studied as follows:(1) Fractal image compression is a nonsymmetrical coding method, while encoding is the most consuming part while decoding time is quite short. The long time of the baseline method is essentially spent on the search for the best-match block in a large domain pool and such drawback renders it impractical for real time application. In this paper, adjacent search method is utilized to reduce the searching space, and speed up the fractal image compression. With the technique, the encoding speed is 300 times faster than that of conventional full search method, and outperforms precedes to the recently published spatial correlation algorithm by Truong et al. in terms of encoding time while the quality of the retrieved image is almost the same.(2) In this paper, speed-up fractal image compression with DCT (discrete cosine transform) classifier is proposed. During the encoding process, using the edge properties of image, the given image is first partitioned into some blocks based on the binary tree. At same time all blocks of the image are defined three classes, which are Smooth class, Diagonal/sub-diagonal edge and Horizontal/vertical edge class, only according to the lowest horizontal and vertical DCT coefficients of the given block. Then each range block searches the best match in the corresponding domain class. Since the searching space is reduced and the classification operation is simple and computationally efficient, the encoding speed is improved and the quality of the decoded image is preserved. The thresholds of the classifier are adaptively determined so as to guarantee the stable speedup. Experiments show that comparing with full search method, the proposed method reduced the encoding time greatly, and obtained rather good retrieved image, meanwhile, achieved the stable speedup ratio.(3) Image texture is an important content in image analysis and processing which can be used to describe the extent of irregular surface. The fractal dimension in fractal theory can be used to describe the image texture, and it is the same with the human visual system. The higher the fractal dimension is, the rougher the surface of the corresponding graph is, and vice versa. Therefore in this paper a fast fractal encoding method based on fractal dimension is proposed. During the encoding process, using the fractal dimension of the image, all blocks of the given image first are defined into three classes. Then each range block searches the best match in the corresponding class. The method is based on differential box counting which is chosen for texture analysis exactly. Since the searching space is reduced and the classification operation is simple and computationally efficient, the encoding speed is improved and the quality of the decoded image is preserved. Experiments show that comparing with full search method, the proposed method reduced the encoding time greatly, and obtained rather good retrieved image, meanwhile, achieved the stable speedup ratio.