Image Denoising And Segmentation Based On Wavelet Shrinkage And Anisotropic Diffusion And Their Equivalence

Digital Image Processing is an integrative borderline science, which integrates whole of math, computer science, electronics and informatics. It plays a great role in the field of astronautics, medical science, industry and military. Image denoising and image segmentation are hot-point problems that are researched in image processing field. Wavelet analysis and the method based on partial differential equation are two kinds of effective methods. The effects of image denoising and image segmentation determine whether subsequent processing succeeds or not.Wavelet Shrinkage is an effective method of image denoising, and the multiresolution analysis of wavelet is a classic method of image segmentation. The linear diffusion and anisotropic diffusion based on partial differential equation implement the denoising by diffusing the input image. Active contour model is a classical image segmentation method based on partial differential equation. Wavelet shrinkage has denoising capability of adapting to frequency localizaion, and anisotropic diffusion has denoising capability of adapting to spatial localization. Research on the relationship between wavelet shrinkage and anisotropic diffusion, and finding a new method that combines the advantages of them are significant to image denoising and image segmentation.At the present time, the equivalence between HAAR wavelet shrinkage and total variation (TV) diffusion under some conditions has been proved. In this thesis, in the first place, one hybrid method that combines the wavelet shrinkage and anisotropic diffusion is researched. Secondly, the equivalence between wavelet shrinkage and anisotropic diffusion is researched, and the equivalent conditions are derived. Based on the equivalence, the anisotropic wavelet shrinkage method is proposed, which is used on image denoising and image segmentation. The main contributions of this research are as follows:1. Two low-order diffusions, PM diffusion and TV diffusion, are introduced. Thus low-order method is influenced by noise easily, and the staircase effects appear in the diffused results. Module of Gaussian curvature can be used to describe the roughness of image. The energy functional of image is defined. The gradient descent method is used to solve the functional. The high-order anisotropic diffusion based on Gaussian curvature is derived. To solve the problems about the results which are easily polluted by noises existing in low-order diffusion. Combined wavelet shrinkage, as a result, the high-order wavelet shrinkage based on Gaussian curvature is proposed.2. The basic theory and discrete form of PM diffusion and high-order anisotropic diffusion based on directional curvature are discussed. Based on the discrete form, the equivalence between HAAR wavelet shrinkage and the two diffusions is proposed, the equivalent conditions is derived. The theory and discrete form of general 2-order anisotropic diffusion is researched then, one equivalent framework between HAAR wavelet shrinkage and general 2-order anisotropic diffusion is proposed under conditions of 2-dimensional discrete forms.3. Wavelet analysis selects different wavelet function according to constructing principle of wavelet function, and different wavelet is attained. Wavelet analysis is implemented by applying the different wavelet function. In the thesis, according to the analytic form of wavelet shrinkage, combined the analytic form of anisotropic diffusion, one equivalent form between wavelet shrinkage and anisotropic diffusion is proposed, thus the equation that wavelet shrinkage function and diffused function meet is derived. 4. Wavelet shrinkage has nice capability of frequency localization, and anisotropic diffusion has nice capability of spatial localizaion. In the thesis, the wavelet shrinkage and anisotropic diffusion are combined. Based on the equivalence between wavelet shrinkage and anisotropic diffusion, it can be concluded that new methods can be obtained that have the advantages of above two methods. The new method includes the anisotropic wavelet shrinkage image denoising method and multi-resolution anisotropic wavelet shrinkage image segmentation method.