Optimum linear approximation of the Euclidean norm to speed up vector median filtering

For reducing impulsive noise without degrading image contours, median filtering is a powerful tool. In multiband images, as for example color images or vector field obtained by optic flow computation, a vector median filter can be used. Vector median filters are defined on the basis of a suitable distance, the best performing distance being the Euclidean. The Euclidean distance is computed by using the Euclidean norm which is quite demanding from the point of view of computation given that a square root is required. An optimal piecewise linear approximation of the Euclidean norm is presented which is applied to vector median filtering