Research Of Mumford-Shah Segmentation Model Based On Variational PDE Method

Image segmentation is the basis for advanced image processing, such as image under-standing and recogintion, which is an important branch of image analysis and computer visualization. Therefore, image segmentation has a considerable attention in both theo-retical research and practical applications field. Along with the expansion of the scope of human activities, the application field of image segmentation will be continuously ex-panded. Consequently, image segmentation will play a role of inestimable importance.Mumford-Shah (M-S) model is one of the classicical image segmentation models, which attracts extensive attention of many scholars both at home and abroad. In this paper, we propose two novel two-phase and mutilphase segmentation methods based on the Chan-Vese (C-V) model and the piecewise constant M-S model, respectively. Then the related problems are studied and discussed.In this paper, we first introduce the research purpose and significance of image segmentation, the existing typical image segmentation methods, and the related theory knowledge such as variational method and gradient descent method. Then we introduce two new segmentation methods in detail. Firstly, we improve the typical C-V model by employing the information of edge and compute mean values of backgrounds and fore-grounds by using the K-means clustering method. Following from the framework of the primal dual scheme, we give the equivalence form of the proposed model and use the semi-implict gradient method to solve it. Experiments on some synthetic and natural images indicate the efficiency and robustness of the proposed segmentation method. Secondly, We adopt a primal-dual approach for global minimization of the piecewise constant M-S model combined with preprocessing techniques to segment the piecewise constant images with blur and noise. Before segmentation, the input image is deblurred and denoised to some extent by preprocessing method. Then we perform the segmentation of the image which has been preprocessed. Experiments and results analyzing indicate that the new proposed method is effective. Finally, main work and the direction of further research are summarized in this paper.This master thesis is supported by the project of Science and Technology Agency, Henan province (No.132300410150) and the National Natural Science Fund (No.U1304610).