Study On Image Processing Of Wavelet And Fractal Based

Wavelet is one of the most outstanding techniques in image processing, and fractal signal processing is a new analysis method developed in past two decades. A study of combining those two methods of signal processing and applying them to image processing is the topic of this thesis. The main contribution can be summarized as follows:1. On the basic of understanding wavelet theory and fractal signal processing theory, we particularly analyze the relation among those theories, and combine those fashion signal processing methods and apply them to image processing.2. Based on the characteristic of wavelet and fractal an algorithm of image compression using wavelet transform and fractal quadtree is presented. This algorithm combine time domain's fractal quadtree compression method with wavelet transform compression method. The results show that the algorithm approach might be able to improve vision effection because wavelet transform is used to enhance image's self-similar used by fractal method.3. Based on chaotic property, an improved algorithm of wavelet watermarking is proposed. The random sequence acted as watermark is generated using chaotic function model. Since the chaotic random sequence is sensitive to initial value, different random sequence causes different watermark, which makes digital watermark unique. The embedded watermark is robust to compression and noise addition.4. The document image segmentation is very useful for printing, faxing and such data processing. In this paper, an algorithm is developed for segmenting and classifying document image. Feature used for classification is based on the histogram distribution pattern of different image classes. The important attribute of the algorithm is using wavelet correlation image to enhance raw image's pattern, so the classification accuracy is improved.5. A novel multifractal analysis approach to the problem of image edge detection is proposed in this paper. Based on the singularity value of each pixel and its relative height, that is given by computing spectra associated with different kinds of capacities denned from gray levels, edge information of image is gotten according to the modified multifractal spectrum. Our experiment show that in several cases, the approach gives at least as good results as the classical ones, it's effective for edge detection and giving the eminent and detailed edge information of the image. The preliminary results show that the multifractal analysis approach might be able to build a bridge between edge detection and region extraction.6. To our best knowledge, we are the first in China to denoise SAR(Synthetic Aperture Radar) image by processing based on multifractal analysis. The multifractal spectrum of theoriginal signal is different from that of noise. We use this difference to denoise SAR image. Essentially, our method focuses on adjusting the Holder exponent a of multifractal spectrum. After much simulation research, we find that a should be adjusted to 1.72-1.73. This manipulation leads to a smooth and denoised image while preserving the relative strength of the singularities (for instance, edges or textures) in the image.