Anti-aliasing of gray-scale/color/outline images: Looking through the lens of numerical approaches for PDE-based models

Abstract

Down-sampling in the process of saving and transferring images often leads to the appearance of jaggies or step like edges in the objects of images where they should be smooth to seem natural. The application of blurring filters for the purpose of anti-aliasing images seems inappropriate since it leaves a blurring effect that destroys the edges in a way that they become indistinguishable. In 2012 Ziou and Horé proposed a novel partial differential equation (PDE) in which anti-aliased images efficiently. However, solving this equation as it is severely nonlinear and defined in a large domain due to the size of images is a challenging problem. In this paper, we propose a new numerical method that is based on a combination of iterative operator splitting (IOS) technique with Gaussian radial basis functions (RBFs) method for solving this equation in an efficient way. The proposed method converts the problem to several one-dimensional linear problems that are solved in smaller sizes to overcome the large domain of the problem. The Crank-Nicolson method is applied for the discretization of the time dimension. The proposed method is tested on different gray-scale, color, and outline images to illustrate the efficiency of the proposed method visually and numerically in the section of numerical results.