Image Diffusion Variational Method

Image noise removal as the foundation of image segmentation and machine recognition is a classic field in image processing, and plays a very important role in the processing and analysis of medical images and satellite remote sensing image.Image diffusion can make the image smooth, and remove the noise. Recently, many scientists proposed the image diffusion method based on variational theory, the point of the method is protecting the edge when denoising. These methods are based on the first derivative of images intensity, names gradient. But these methods usually produce staircasing. In order to reduce the staircasing effect, this paper introduced variational diffusion models based on second order derivative. Meanwhile, the paper systematically analyses the protection or enhancement of edges, to instruct the designing of the regularization term. The paper's work includes:(1) Established the universal model based on first order derivation. Based on the concept of directional derivative, we deduces the Euler-lagrange equations, gradient decent equations, diffusion equations, and proposed Jacobi iterative scheme, Gauss-Seidel scheme and SOR scheme.(2)The paper deduced the conditions of forward diffusion and backward diffusion, edge protection and enhancement, to guide 2D models design.(3) Established image diffusion variational methods based on second derivative, and deduced the conditions of regularization term of forward diffusion and backward diffusion. Experimental results demonstrate their good performance in edge protection and staircasing reduction.