Research On The Color Image Processing Model,Based On Geometric Characteristics Of Anisotropic Diffusion Equation

In this research I propose a new effective method for color image denoising.The idea bases on the geometric nature of preserved image structure and features.I consider anisotropic,nonlinear,inhomogeneous diffusion filtering with three models for eigenvalues,that take advantage of the information about image structure,obtained from common partial derivative analysis,and therefore smooth noise without blurring even thinnest features.Two theoretical mathematical models,that obtain denoised image by the means of energy functional,or solving diffusion PDE Neumann boundary problem,both base on a strong theory,that is explained in details in this research.Numerical experiments have shown that the proposed method is highly effective for moderate levels of noise,and it's capacity to preserve structure is strong in comparison to existing methods in the field.I discuss the proposed model from two points of view: first is the minimization of the energy functional,and the second is anisotropic diffusion PDE problem.In chapter two there have been proven that the energy minimization problem is well-posed,moreover,solution satisfy strong comparison principle.In chapter three there have been proven that the diffusion PDE problem also has a unique solution,which satisfies weak comparison principle.Furthermore,the convergence to the stationary point,mean invariance principle,and extremum principles are satisfied for both these problems,which provides us with the opportunity to build a numerical scheme with guaranteed convergence properties.The numerical experiments have eventually provided highly satisfactory effects,that are: the denoising effect is not disintegrated by the smearing or blurring for moderate noise level,which is especially significant for thin features and small details of the image,therefore it may find application in investigative applications or any other that claim accuracy in the details as its number one priority.Moreover,the proposed model outperforms a number of famous color image denoising models from the literature.As a conclusion,the original purpose of the proposed model,which was to build an efficient numerical filtering program,that can be used in medical,military or civil problems,is successfully reached.