The standard finite difference scheme(forward difference approximation for time derivative and central difference approximations for spatial derivatives)for fourth-order nonlinear diffusion filter allows very small ti...The standard finite difference scheme(forward difference approximation for time derivative and central difference approximations for spatial derivatives)for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results.The alternating directional implicit(ADI)splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size.In this paper,we develop 3×3 stencils for the approximation of second-order spatial derivatives based on the finite pointset method.We then make use of these stencils for approximating the fourth-order partial differential equation.We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme,without compromising on the quality of the filtered image.Further,we demonstrate through numerical simulations that the proposed scheme is more efficient,in obtaining quality filtered image,than an ADI splitting scheme.展开更多
文摘The standard finite difference scheme(forward difference approximation for time derivative and central difference approximations for spatial derivatives)for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results.The alternating directional implicit(ADI)splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size.In this paper,we develop 3×3 stencils for the approximation of second-order spatial derivatives based on the finite pointset method.We then make use of these stencils for approximating the fourth-order partial differential equation.We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme,without compromising on the quality of the filtered image.Further,we demonstrate through numerical simulations that the proposed scheme is more efficient,in obtaining quality filtered image,than an ADI splitting scheme.
