An Efficient Vector Median Filter Computation

The vector median filter(VMF) is a useful and common tool for noise removal in color image processing[HPP04,PV00,AHN90]. The drawback of the approach in its general form is the high computational cost. Indeed it takes O(n×m×ms) distance evaluations for computing the filter response, where ms ist the mask size and n×m the dimension of the image. In this contribution we propose a general algorithmic optimization framework for reducing the complexity to O(n × m × ms). We discuss the dependency of the VMF on the distance measure and demonstrate that for the square Euclidian distance, the VMF becomes a vector near-mean filter with just O(n × m × ms) distance evaluations.