Texture Image Segmentation Based On Non-local Mumford-Shah Model

Image segmentation is of importance in image analysis,computer vision,etc..It is the basis of object detection and recognition,image retrieval,scene analysis,medical image analysis,video surveillance and so on.The task of image segmentation is to divide the image into different regions according to various image features.Variational method based on edges,regions,statistical information,and prior shapes has become one of the predominant methods of image segmentation.However,since because the texture is difficult to express,there are still many difficulties in variational image segmentation based on texture features.Recently,the non-local operator and non-local variational model in the field of image restoration have laid a good foundation for texture image denoising and inpainting.This thesis extends the related concepts to the research of texture image variational segmentation.The main work and innovation are as follows:1.A non-local Mumford-Shah-TV model for grayscale texture image segmentation is proposed.In the field of variational image processing,the Mumford-Shah model with nonlocal operators can segment texture image components,but the boundaries of objects have errors.As the TV(Total Variation)model based on local operator has the advantage of image structural character expression.In this thesis,a combined non-local Mumford-Shah-TV model under variational framework making use of the properties of TV(total variation)regularizer and non-local operators is proposed.The new model improves the accuracy of boundaries segmentation in grayscale texture image.2.A non-local Mumford-Shah-MTV(MSM)model for color texture image segmentation is proposed.Since the variational model of color image must consider the coupling effect of multilayer images at edges,the non-local MSM model of grayscale texture image segmentation cannot directly be extended to color texture image segmentation.Based on the non-local variational segmentation model of grayscale texture image,non-local MSM model is proposed combined with the multi-channel TV term of color image.The proposed model achieves accurate segmentation of color texture image at edges.3.The ADMM algorithm for the proposed model is designed.Because of the TV and MTV items in the model,the direct variational solution will lead to complex nonlinear curvature,resulting in low efficiency of differential discrete calculation.Alternating direction method of multipliers is designed for the proposed model by introducing auxiliary variables,Lagrange multipliers and penalty parameters to decompose the original problems into a series of optimization sub problems.Finally,to improve the computational efficiency by using simple Gauss-Seidel iteration and generalized soft threshold formula.Finally,comparisons with the existing models by numerous experiments show that the proposed texture image segmentation models have higher accuracy and better edge preservation.The works here can be extended to the multi-phase segmentation problem easily.