MATLAB Code Implementation for Diffusion Equation

The following MATLAB code implements the diffusion equation, which can be applied to various image processing tasks including image smoothing, noise removal, filtering, and edge processing. The diffusion equation serves as a fundamental mathematical model that enables multiple image manipulation operations through partial differential equations. This implementation utilizes finite difference methods to approximate the diffusion process, typically employing convolution operations with Gaussian kernels or anisotropic diffusion filters. Key functions include gradient calculations for edge detection, iterative updating of pixel values based on diffusion coefficients, and parameter controls for diffusion strength and iteration counts. The code allows users to perform image smoothing by reducing high-frequency noise, implement denoising through selective diffusion processes, apply various filtering techniques, and enhance edge features using controlled diffusion mechanisms. Through this implementation, users can efficiently process images to meet diverse requirements, with adjustable parameters for controlling the degree of smoothing, noise reduction thresholds, and edge preservation characteristics. The code structure includes main diffusion functions, parameter configuration sections, and visualization components for result comparison.