Rsearch Of Image Decomposition Based On Mumford-Shah Model And G Space

In recent years, the partial differential equations in image processing has been widely used . At the same time, the application of image decomposition based on partial differential equations has obtain more attention of reserchers . The basic idea of image decomposition is that a given image f can be decomposed into two components u which is the main component and v which is the texture and noise components , equaling f = u+v. At present , the models of image decomposition based on partial differential equations are mainly TV - L~2 model , TV - G model,MS - L~2 model and MS - G model . The paper mainly study the image decomposition model of MS - G. The MS - G model combines the advangtage of Mumford-Shah ( M - S) model and G space , that is it say , the M - S model maintains the smoothless of the non-edge pixels and avoids the staircase effect ; G space well characterizes the texture . The main work contains:1. Introduce the development of partial differential equations ,the classic models of partial differential equations , the derived methods of partial differential equations and the application in image decomposition ; and summary the advantage of partial differential equations ,and the idea of modeling based on three different theories including multi-scale theory , variatinal theory ,and curves and surfaces theory .2. Study the basis of theoretical of variational partial differential equation . Introduce the basic concepts an lemmas of partial differential equation , variational methods and finite difference method . The variation method provides theoretical framework for the mathematical model of image processing , and makes it become an well-posed problem which can ensure the solutions of equations existence ,uniqueness and regularity .3. Focuses on application of the image decomposition model of MS - G. In the influence of Iteration times, parameters ofλ,μ,αandρare analysed , and they chose proper values through the experience of experiments . Hu invariant moments and the feature parameters of GLCM (Gray Level Co-occurrence Matrix) which are Entropy , Angular Second Moment , Correlation , Inverse Difference Moment and Variance respectively describe the cartoon image (or edges image)and texture image . Moreover, combing both is used to image recognition . A new identification of image object based on image decomposition was proposed , and it is proved feasible through the experiments.