Theoretical Research And Application Of Digital Image Texture Extraction

With the fast development of the computer technology, the processing technology ofdigital image is widely used. Image decomposition, image denoising and imagesegmentation have become the research focus of the image processing. In recent years,image decomposition which based on partial differential equations is widely used in thefield of image processing and achieved great results, Such as the military, remote sensing,weather, and communications, medical and so on. This article will focus on imagedecomposition based on partial differential equations. Its main idea is to construct anappropriate variational model, then gain the corresponding variational partial differentialequations, and finally used the mathematic number methods to optimize the objectivefunction.The main works of this thesis are as follows:Firstly, we proposed three new image decomposition models by using dual method,based on image decomposition model of L.Rudin、 S.Osher and E.Fatemi, imagedecomposition model of L.Vese and S.Osher, and image decomposition model of S. Osher,A.Sole and L.Vese. Those proposed models overcome the inconsistency on numericalsimulation theoretically. Experimenter results show that our models work effetely.Secondly, for noisy image decomposition, not only need to extract the texture, but alsoneed to remove noise. This paper proposed a new variational model by taking advantagesof the texture detecting function to detecting texture, so that the noisy image decomposes“structure+texture+noise“. The existence and uniqueness of the solution are proved, andthe numerical simulation shows that the model can achieve good decomposition effect.Finally, Based on the above model, a new model for noisy image decomposition isproposed by using dual method, which gets a better “structure+texture+noise”decomposition results. And then the existence of the solution is proved. The numericalsimulation shows that the proposed model can gain a better “structure+texture+noise “.