Study On Image Restoration Models Based On PDE And Image Enhancement And Segmentation Algrithms

Digital image processing, which is connected with engineering, computer science, information science, statistics, physics, chemistry, biology, medicine, and social science, becomes an indispensable tool for scientific research and social production. In the current stage, image processing approaches can be divided mainly into three categories, i.e., stochastic modeling, wavelet theory, and partial differential equations. In this thesis, partial differential equations, image restoration, image enhancement and cluster segmentation are discussed.The main work can be summarized as follows:1. The heat equation performs equal diffusions in the gradient and the tangent direction, which can strongly smooth important character of the inputted image while de-noising. In order to better preserving the characteristic of an image, an improved diffusion model is proposed. Based on the classical heat diffusion model, a diffusion function is introduced in the gradient direction, which can make the diffusion occur according to the characteristic of an image. The new model has the ability of denoising and inpainting. Experiments show the effectiveness of the proposed model.2. Diffusion takes place only in the gradient direction for directional diffusion, and the smoothing degree is the same in every region. Focusing on avoiding this weakness, an improved directional diffusion model is proposed. In this proposed model, a diffusion function is introduced and the modulus of gradient is substituted by the modulus of a wavelet transform, which gives the results that the newly introduced model could preserve edges better and has strong ability to resist noise. The experimental results show improvements of the proposed model.3. Based on the classical TV model, nonlinear and linear weighted variation algorithms are put forward. In the nonlinear weighted variation model, a weight function is introduced in the regularization term of the TV model, which gives results that the new model can preserve the texture characteristics and the edge information better while removing noise. The linear model induces diffusion through pretreatment of the noised image, which reduces the computational effort. Compared with the TV model, the experimental results show improvements of both the proposed models. 4. Three image denoising models based on wavelet and partial differential equation are given. Of all these models the regularization terms are improved by different functions, and the features of noise in the wavelet domain are considered. Experiments show the proposed models have better ability to preserve edges.5. Considered the advantages of using L1 norm as a measure of the fidelity term in total variation, three models for image de-noising are developed based on the TV- L1 model. In the first proposed model, the modulus of gradient is substituted by the modulus of wavelet transform, which gives the results that the new model can preserve edges better and has stronger ability resisting noise. In the second one, the regularization term is modified; considering the features of noise in the wavelet domain, we propose the third model to reduce the computational complexity. The last model is presented based on the character of the multi-resolution analysis of wavelet transform.6. This paper proposed a contrast adaptive clip histogram equation algorithm based on the traditional contrast limited adaptive histogram equation algorithm. It can adaptively adjust the clip coefficient according to the standard deviation of each sub-images. Incorporating the contrast adaptive clip with the weighted-average histogram equation, this paper put forward another improved histogram equation algorithm which is called contrast adaptive clip weighted-average histogram equation. Experimental results show that the new algorithms produce remarkable enhancement effect on contrast unbalanced images and that it can effectively control the brightness of the inputted images while balancing the contrast and improve the quality of the inputted images.7.Firstly, aiming at overcoming the shortcomings of the K-means algorithm that it is sensitive to the initial state and converges to a local minimal, this paper puts forward an improved K-means algorithm based on density estimation and distance optimization and applies the improved algorithm on color image clustering analysis. This algorithm is stable and computationally less complex than the traditional K-means algorithm. Secondly, another human perceptual color clustering algorithm is proposed by integrating the median-cut algorithm. The new algorithm can well preserve the main colors of the original image and the clustering distortion is less than that of the median-cut algorithm.