The Effectiveness of the Finite Differences Method on Physical and Medical Images Based on a Heat Diffusion Equation

Abstract

Abstract In this paper, we study the influence of applying the well-known finite differences method on medical and physical images. These images will be used as coefficients in the steps of the solution after the images being imported and converted to arrays. The aim of the study is to show and analyze the changes that could happen to images for the sake of an enhancement. Experiments of one dimension and two dimensions will be illustrated by applying the explicit and the implicit methods using MATLAB to explain the way of how these methods affect images. Furthermore, we will study and measure the quality of the proposed images in each phase of the experiments using statistical metrics such as PSNR (Peak Signal to Noise Ratio), MSE (Mean Squared Error), MD (Maximum Difference) and some other statistical metrics.