Image Restoration And Image Segmentation Based On Total Variation-type Regularization

Image restoration and segmentation occupy an important position in the field of image processing,which are the premise of subsequent image processing.However,the image we acquired will be influenced by external factors such as noise or blur,and makes weakened in the boundary information and regional features.It will affect the quality of subsequent image work.Therefore,an effective restoration or segmentation model has important research value.Based on these,the main research work of this thesis is as follows:In order to effectively maintain the structural characteristics of the restored image,this thesis proposes a surface regularization model by transforming the two-dimensional image into a three-dimensional surface problem in the sense of Riemannian manifold.Since the model is formally equivalent to the smooth and convex ROF model,we can transform it into the saddle point problem by using the conjugate function,and propose two different primal-dual methods to solve the problem.At the same time,the rationality of the model and the convergence of the algorithm are also analyzed theoretically.The rationality of the model and the robustness of the algorithm are verified by the final numerical comparison.By combining the classical GAC model with the C-V model,a new segmentation model is proposed in this thesis.In the model,by coupling the gradient operator and the edge detection matrix with different weight features,and the local structural features of the image can be effectively characterized,so that the quality of image segmentation can be improved.Since the model is a non-smooth problem with separable structure,the alternating direction multiplier method and gradient descent method are used to solve the problem.Finally,numerical comparison verifies the validity of the proposed model.