Vector Median Filter (VMF) for Color Image Processing

The Vector Median Filter (VMF) is an image processing algorithm designed specifically for color images that accounts for the correlations between the three color channels. This algorithm operates by treating each pixel's RGB values as a vector in 3D space, then performing vector-based sorting within a defined neighborhood window. Instead of processing channels independently, VMF calculates distances between vectors using metrics like Euclidean or Manhattan distance, then selects the vector that minimizes the sum of distances to all other vectors in the neighborhood as the median output. In implementation, the filter typically involves: 1) Defining a sliding window (commonly 3×3 or 5×5 pixels), 2) Computing pairwise vector distances between the center pixel and its neighbors, 3) Sorting vectors based on their cumulative distance sums, and 4) Replacing the center pixel with the vector having the smallest cumulative distance. This approach preserves color edges and textures while effectively reducing noise, as it considers both individual pixel values and their spatial relationships. Key advantages include better preservation of color integrity compared to component-wise median filtering, and robust performance against impulse noise. Typical applications in image processing include digital photography enhancement, medical imaging, and satellite image restoration where color consistency is critical. The algorithm can be optimized using partial distance calculations and early termination techniques for real-time processing.