Study On Several Issues About Variation Models Of Image Processing

Image is an important medium for human to acquire and transmit information, which plays an important role in the era of network information. Image processing is a developing rapidly interdisciplinary field in information science and engineering, and it has a very important position and application value in the society and life. Variation model is a mathematical model to solve the functional extremum (maximum or minimum). The variation model is featured with a variety of forms, flexible structures and efficient operation performance, etc. The variation-based image processing model established in the early 1990s is a kind of important mathematic tools in the field of digital image processing, which has attracted wide attention of foreign and domestic scholars.There are several key points such as image denoising, image inpainting and image segmentation in image processing. In addition, poor adaptive performance, "staircase effect" in smooth region and other inadequacies also exist in the image processing. Owing to them, this dissertation studies the characteristics and significance of the variation model and puts forward the improvement ideas and methods. The main contents of this dissertation are as follows.(1) In the study about variation model of image denoising, the image denoising algorithm based on the smooth ROF model is proposed for the regularization term indifferentiable issues in the Rudin-Osher-Fatemi model. By modifying the regularization term in the ROF model, this algorithm not only can break away from the Courant-Friedrichs-Lewy condition, but also has the feature of global convergence. By solving the smooth ROF model with the Primal-Dual method, each iteration update corresponds to a primitive variable and a dual variable. Compared with the time marching method and fixed point method, this method has a better stability and efficiency in performance. The experimental results show that when appropriate smoothing parameter is selected, the model proposed can effectively reduce the "staircase effect" in the smooth area of the image and can protect the edge region of the image.(2) In the study about variation model of image inpainting, more reasonable potential function is used to put forward an improved image inpainting algorithm based on variation model after the analysis of the total variation model. The algorithm only diffuses on the image edges rather than in the gradient direction so as to keep the image edges. If there are noises in the image to be repaired, image denoising can be conducted in the outside of the information loss area, which can protect the image important characteristics while avoiding the "staircase effect". Secondly, An image inpainting algorithm based on convex Mumford-Shah model is proposed for the tedious solving process of Mumford-Shah model. The proposed algorithm fully cares the different diffusion abilities of quadratic norm and total variation norm in the image texture region and smooth area, which can avoid solving the curve length item, and numerical solution is conducted to the model with the Split-Bregman algorithm. The experimental results show that the algorithm has a higher computing efficiency, and can keep the curve smoothness of image edges.(3) In the study about variation model of image segmentation, an image segmentation algorithm based on constraint Mumford-Shah model is proposed to solve the computation complexity of Mumford-Shah model. By modifying the length item of the Mumford-Shah model, this algorithm coverts the nonconvex Mumford-Shah model into a convex optimization problem, and constraints the pixel values of the image in a fixed range. Then alternating direction method of multipliers is used to solve the model. After getting the smoothing solution of the model, the K-means clustering method is used for image segmentation, which has achieved the synchronization of smooth and segmentation, improved the operation efficiency and has the performance of the adaptive multiple segmentation. Then, considering that the coefficient matrix of convex Mumford-Shah model is a random matrix, and that the computation efficiency of alternating direction method of multipliers will lower, the image segmentation algorithm based on inexact alternating direction method is put forward. This algorithm not only can process the additive noise and the image segmentation problem under the fuzzy background, but also can deal with the image segmentation problem under random sampling background. Notably, if the phase number of image segmentation is changed, the image smooth solution is not necessary to be recalculated, which is more convenient for application. The experimental results show that the algorithm can handle the image segmentation problem of degraded image, and has a higher segmentation precision.