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

For reducing impulsive noise without degrading image contours, median ltering is a powerful tool. In multi-band images, as for example color images or vector eld obtained by optic ow computation, a vector median lter can be used. Vector median lters are deened on the basis of a suitable distance, the best performing distance being the euclidean. 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. In this paper an optimal piece{wise linear approximation of the euclidean norm is presented which is applied to vector median ltering.