Emplicit-implicit Difference Numerical Method For PDE-based In Image Processing

The PDE-based method in image processing is an emerging field developed over the past decade, so studying its numerical solution method has important theoretical value and practical significance. The paper presents a new unconditional stability difference schemes--emplicit-implicit difference scheme for several kinds of classical PDE model of image processing:mean curvature motion model(MCM equation),nonlinear diffusion (P-M) model,total variation (TV) model,geodesic active contour (GAC) model. The stability of these schemes are analyzed by using linear stability analysis, and the stability proof is proposed, At last the computational efficiency of these schemes is discussed.Theoretical analysis and numerical experiments point that the emplicit-implicit difference scheme has the advantages of higher accuracy(second-order precision) and less computation, compared with the traditional emplicit method. When this difference scheme is used for image processing, the denoised or blurred image can be filtered more effectively and the efficiency of processing can be improved too. This method preserves the edge and detailed information. So the emplicit-implicit difference method is a feasible and efficient numerical scheme, which can be used in image denoising, image restoration and image segmentation.