Image Segmentation Methods And Algorithms Based On Total Variation Model

Image segmentation recently becomes an important research topic in the feld of imageprocessing. Our main work is based on the T V1g Lmodel and the MS model andthen propose some efcient numerical methods to solve them. The main results of thisdissertation are arranged as follows:In the frst chapter, we list some symbols and their defnitions which will be usedin this paper. We also give the basic knowledge of some related models and numericalmethods such as the total variational model, optimization theory, the B-M algorithm andthe Chambolle algorithm, the primal-dual method, etc.In the second chapter, we propose the semi-implicit gradient descent method (Cham-bolle’s method) and the augmented Lagrangian method to solve the T Vg L1model inorder to overcome its numerical difculties due to the non-diferentiablity. We also deducethat the semi-implicit gradient descent method can be regarded as the special form of theBM method and then prove the convergence of the proposed algorithm.In the third chapter, based on the MS segmentation model, we propose to use theprojected algorithm for solving it. Some numerical experiments show that this methodhas faster convergence speed than Chambolle algorithm as well as good noise resistance.This master thesis is funded by the project of Science and Technology Agency,Henan province.(No.132300410150).