Image Diffusion Of Energy Variational Method

Image restoration is a major field of image processing.Denoising and inpainting are the main projects of image restoration.Image diffusion based on variational methods and PDEs is one of the basic methods of image restoration.The basic idea of variational methods is take the question as calculation of the minimum of a functional.And then,we get the numerical solution through solving the PDEs which are derived from the energy functional.Image diffusion technique is discussed in this paper,Several aspects are introduced as follows:First,a hybrid variational image diffusion model using gradient and divergence is presented in this paper to reduce staircasing during image diffusion with edge preserving or enhancement.For the design of smooth terms in diffusion model, forward and backward diffusion conditions for one dimension model based on first and second derivatives are derived first,which are extended to two dimension image space. Second,we propose a dual method for solving TV minimization problems.The new method eliminates the numerical problems of singularity caused by the non-differentiability of the objective function through a dual variable,and yields a de-noised image which is independent of any artificial perturbation,and thus,should be a more precise solution to the problem.Third,the classic variational image diffusion models are extended to image diffusion on implicit surface by means of intrinsic image gradients defined on implicit surface expressed by zero level set function,and a generic variational level set model for nonlinear image diffusion on implicit surface are presented. Forth,take Charbonnier model,generalized TV model,P-M model as examples.Some numerical examples are given to show their capabilities of forward/backward diffusion and edge preserving/enhancement.