Image Enhancement Using Diffusion Filtering

This text describes an approach to implement image enhancement using diffusion filtering. The process begins with Gaussian filtering preprocessing, which helps reduce noise in the image through convolution with a Gaussian kernel typically implemented using functions like imgaussfilt() in MATLAB or GaussianBlur() in OpenCV. Next, we compute the image gradient using operators such as Sobel or Prewitt filters, which helps identify edges and intensity variations in the image through partial derivative calculations in x and y directions. Subsequently, we calculate the structural tensor and diffusion tensor - the structural tensor characterizes local image structure using outer products of gradients, while the diffusion tensor guides the anisotropic diffusion process based on eigenanalysis of the structural tensor. We then perform numerical discretization using finite difference methods to make the diffusion equation computable, implementing schemes like explicit or semi-implicit discretization with appropriate time stepping. Finally, we develop enhancement evaluation code incorporating metrics such as PSNR (Peak Signal-to-Noise Ratio), SSIM (Structural Similarity Index), or visual quality assessment to quantitatively measure the effectiveness of our image enhancement method. Through these systematic steps, we can effectively enhance images while gaining deeper understanding of image features and structures.