Numerical Solution of Non-Linear Diffusion Equation in Image Blurring Using Two-Point EGSOR Iterative Method

Abstract

The non-linear diffusion equation is known to be a significant application in solving image processing issues. The equations provided the image filtering techniques that blurring the image without degrade the edge information which is also one of crucial study in computer vision. Nonetheless, an intense amount of computations is needed in filtering the image as the sizes that keep getting bigger. Along these lines, this paper constructs an analysis to speed up the required computation in solving the developed linear system with the faster iterative method, i.e. two-point Explicit Group Successive Over-Relaxation or known as 2-EGSOR. For the performances comparison, the standard Gauss-Seidel (GS), Successive Over-Relaxation (SOR) and 2-EGSOR iterative method will be set to produce almost the similar quality image of Jacobi iterative method measured by using percentage error of the overall pixels difference. Subsequently, it is discovered the 2-EGSOR offers faster approach to blur the image compared the others iterative methods with the least iterations and computational time.