Implementation of Anisotropic Diffusion Filter Algorithm for Grayscale Images

Anisotropic diffusion is an advanced image processing technique specifically designed to smooth image noise while preserving important edge features. This algorithm fundamentally differs from traditional Gaussian filtering by intelligently controlling the diffusion process to avoid blurring crucial structural information in images. The core concept of this algorithm involves adjusting diffusion intensity based on local image gradients. In flat regions, the algorithm performs strong smoothing to eliminate noise, while in edge regions, it reduces diffusion intensity to protect edge sharpness. This adaptiveness enables the algorithm to identify and preserve significant image features. The implementation typically follows an iterative approach where each iteration calculates diffusion coefficients in four directions (up, down, left, right). These coefficients depend on the magnitude of local gradients - regions with smaller gradients receive larger diffusion coefficients, while edge areas with larger gradients correspond to smaller coefficients. Through multiple iterations, image noise is gradually eliminated while edges remain sharp. In code implementation, key steps include: 1. Gradient calculation using central differences or Sobel operators 2. Diffusion coefficient computation using exponential functions of gradient magnitude 3. Four-directional diffusion application with discrete approximations 4. Iterative updating of pixel values using time-step parameters This technique is particularly suitable for medical image processing, satellite image enhancement, and other applications requiring precise edge preservation. Compared to traditional linear filtering methods, anisotropic diffusion delivers higher-quality image processing results, albeit with relatively higher computational complexity.