Applications Of Fractal Coding In Image Processing

With the rapid development of multimedia communication technology, there is an urgent need for efficient image compression technology to meet people's daily life. Fractal image coding is a novel and promising image compression technology. Since Jacquin proposed the first block based fractal image coding algorithm, researchers worldwide have had a strong interest in the study. After many years'development, fractal image coding has been successfully applied in image compression as well as other image processing applications. In our research, the fractal image coding itself and its applications to other aspects of image processing are studied. The main contributions of the dissertation are as follows:(1) Research of the fast fractal image coding. Since the fractal encoding process is the first step of the fractal image coding, acceleration of fractal coding is the first issue to be resolved and the fast fractal coding algorithm based on feature vector's nearest search is a promising method. By analyzing the configuration of the image intensity, the definitions of structural information feature and correlation information feature are proposed. We can proof that the nearest neighbor search result for one range block in the feature space is a requirement for the best matched domain block. Experiments show that compared with similar fast fractal encoding algorithms, the proposed algorithm can provide better decoded image quality in the case of the same compression ratio and encoding time.(2) Hybrid image compression algorithm based on fast fractal coding. Fractal image coding algorithm has the potential of high compression ratio. If the size of the range block is bigger, the compression ratio will be higher. Firstly, the input image is segmented by the quadtree algorithm. By comparing the fast fractal image coding algorithm and the JPEG algorithm, we can see that the fast fractal image coding algorithm is suitable for the blocks of 32×32 and 16×16 pixels and the remain blocks of pixels can be coded by the JPEG algorithm. Experiments show that in the case of the same compression ratio, the proposed algorithm can obtain better decoded image quality. Lastly, the possibility of applying our algorithm in the practical applications is discussed.(3) Estimation of the decoded image quality in the fractal image coding. According to the collage theorem, we can only obtain the error limit of the decoded image from the collage error in the encoding process. Based on large amounts of experiments, we find that there exists a logarithmic relationship between the average collage error and the decoded image quality. Since the decoded image quality can be estimated by the average collage error, we can estimate the decoded image quality temporally in the fractal encoding process. For some images that are not suitable for fractal image coding, we can replace the fractal coding algorithm with other image compression methods without finishing the fractal encoding and decoding process completely.(4) Fractal coding used in other aspects of image processing except image compression. (ⅰ) Fractal image de-noising algorithm based on model constraint. Since the mean value will remain a constant for the local parts of the noisy image and restored image, the restored image quality can be further improved by the above constraint model. Experiments show that we can obtain better restored image quality. (ⅱ) Fractal image magnification based on no search lossless fractal image coding. Because of the resolution independence in the fractal decoding process, fractal image coding can be used to image magnification. Firstly, the no search fractal image coding is adopted to encode the low resolution image, then an error compensation vector is added to the block matching process in the fractal encoding and the collage error can be removed. According to the collage theorem, the fractal decoded image can be obtained losslessly. Lastly, the no search lossless fractal encoding algorithm is combined with some other existing fractal image magnification technique. Experiments show that the proposed algorithm can provide better performance than other similar fractal image magnification methods and the conventional ones. (ⅲ) Acceleration of the fractal image encoding and decoding process. Under some circumstances such as fractal image de-noising and fractal image magnification, the fractal encoding and decoding process will be completed continuously. Some useful information in the fractal encoding process can be used to help the fractal decoding process. We find that if the collage image is selected as the initial image, the fractal image decoding process can be completed in a shorter time.(5) Image quality assessment based on structural orientation information. The structural Similarity (SSIM) method can achieve better image assessment result compared with conventional Peak Signal to Noise Ratio (PSNR) method, but the structural information in SSIM is not completely extracted. In our research, the orientation information was further extracted and the Local Structural Orientation Similarity (LSOS) was proposed. Different frequencies of the image are assessed with LSOS and the results are summed with different weights. Experiments show that compared with other methods, the proposed method can be more consistent with the human visual system.