Asymmetric Difference Numerical Method For Image Processing Based On PDE

Image processing based on the partial differential equation(PDE) is an emerging interdisciplinary branch, and its study of numerical methods has important theoretical significance and practical value. This paper constructs a new unconditional stability difference schemes——asymmetric difference scheme for several kinds of classical model:mean curvature motion(MCM equation),affine morphological scale space(AMSS equation),nonlinear diffusion (P-M)model,total variation (TV)model,geodesic active contour (GAC)model, analyzes the stability of these schemes using linear stability analysis and proposes the stability proof, discusses the computational efficiency of these schemes.Theoretical analysis and numerical experiments show that, using the asymmetric difference scheme in image process, image can be smoothed better and improve the efficiency of denoising, maintain the edge information and enhances the segmentation speed. Compared with the existing methods, the asymmetric difference method is a feasible and efficient numerical scheme.