Mean Curvature Motion And The Nonlinear Diffusion Equation Numerical Methods And Applied Research

Mean curvature motion and nonlinear diffusion filtering play an important role in image processing and computer vision. The paper focuses on researching the numerical schemes and the utility of mean curvature motion and nonlinear diffusion filtering.About the mean curvature motion, the most common method is the level set method at present. The advantage of this method is topology-independent, but its efficiency is poor. In this paper, we perform the level set method with an additive operator splitting (AOS) scheme, which is used in nonlinear diffusion filtering. And the efficiency can be improved.About the numerical schemes of nonlinear diffusion filtering, the most useful and efficient scheme is the additive operator splitting scheme proposed by J. weickert. The scheme is unconditionally stable and large time step is permitted in iteration. But the AOS scheme is limited in its accuracy to first order in time. Therefore we realize a new scheme which is second order in time and the gain in accuracy is noticeable.Due to the nonlinear diffusion equation------Perona & Malik equation (P & M equation) proposed by Perona and Malik, nonlinear diffusion filtering is widely used in image processing. There are two shortcomings when such filter is used for image denoising: single speckle is reserved after filtering and noise at edges cannot be eliminated successfully. To overcome these problems, in this paper we proposed a new diffusion model. We introduce the curvature as a new control factor into the nonlinear diffusion equation. The experimental results show that it performs better than the Perona & Malik Model in image denoising.