Implementation of the Explicit Group Iterative Method for Solving Image Blurring Problem using Non-Linear Diffusion Equations

Abstract

Diffusion equations have been known to solve various image processing problems. This study employs the diffusion equations as the partial difference equations (PDEs)-based image processing techniques for image blurring which also can be refer as the process of image smoothing. The solutions of diffusion equations were obtained using the iterative algorithms and thereafter applied in the image blurring processes. The images were blurred without destroying the crucial information of an image that need to be preserve such as sharp edges, lines and shapes as the diffusion occurs inside the image locations, where the images with different sizes were tested. In terms of performance comparison, the standard point Gauss-Seidel and two-point Explicit Group (2-EG) methods were considered to produce the same quality image of classical point iterative method which is Jacobi. The numerical results showed that 2-EG iterative method capable to smooth the inner region of the images faster compared to the standard point iterative method. It was shown that the 2-EG iterative method more efficient in reducing the number of iterations and computational time than the standard point iterative method.