Top-Hat Filtering Program with Eight-Directional PM Diffusion Algorithm

The program has been expanded to maintain core concepts while incorporating additional technical details. PMK_8.m implements an eight-directional Perona-Malik diffusion equation, which utilizes gradient-based diffusion coefficients to control smoothing intensity. The algorithm examines pixel variations across eight distinct directions (0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°) to adaptively smooth homogeneous regions while preserving edge structures. Beyond this primary function, users can consult internal documentation headers for descriptions of auxiliary functions handling boundary conditions, gradient calculations, and diffusion parameter optimization. The diffusion equation approach excels in image denoising by maintaining strong edge preservation through nonlinear diffusion processes, while effectively smoothing areas with minimal color variations using spatially-adaptive filtering techniques. Implementation typically involves iterative updates of pixel values based on directional gradient magnitudes and conduction coefficients.