Research Of Algorithms In Image Processing Based On Fractal And Wavelet Theory

Image denoising and segmentation are important in the area of image processing. Many people have done lots of researches deeply and presented relevant methods, many of which are successful. However, many improvements are still needed in order to match the concrete requirements of applications.Fractal and wavelet are new theories in mathematics. These theories have been applied in many subjects, including image processing. The combination between them is based on their close relationship. In fractal, local characters are researched in order to make sure entire characters; in the theory of wavelet, some systematic methods are used, which are about dependency between part and whole. In image processing, many approaches about wavelet are successful, and fractal has much potential although it is just in the beginning. It is a hopeful area for us to combine these theories and to use these.This thesis starts with the basic theories of fractal and wavelet, introduces their relationship, and then discusses their applications in image segmentation and image denoising. In image segmentation, this thesis provides an approach based on fractal and wavelet analysis, which is in order to solve the issues of region-based segmentation in high-resolution remote sensing sea images. In the approach, a new method based on differential box counting is presented. In image denoising, a model of correlation dimension is used, and the ways to analyze wavelet packet coefficients by the model are discussed. For some images in which natural objects are main, a new method is presented, which can control the decomposition order of wavelet packet transform adaptively according to the status of noise. Relevant experiments have been analyzed, which prove that these theories and methods are useful.