On the Fast Modification of the Vector Median Filter

A new filtering approach designed to eliminate impulsive noise in color images, while preserving fine image details is presented in this paper. The comparison shows that the new filter outperforms the VMF, as well as other standard procedures used in color image processing for the elimination of impulsive noise. 1 Vector Median Filter Noise reduction is an important step in many color image processing applications. The most popular nonlinear, multichannel filters are based on the ordering of vectors in a predefined filter window. The output of these filters is defined as the lowest ranked vector according to a specific ordering technique [1-13]. Let F(x) represent a multichannel image and let W be a window of finite size n. The noisy image vectors inside the window are denoted as Fj , j = 0, 1, . . . , n − 1 . If the distance between two vectors Fi,Fj is denoted as ρ(Fi,Fj) then the scalar quantity Ri = ∑n−1 j=0 ρ(Fi,Fj) is the distance associated with the noisy vector Fi in W . An ordering of the Ri ’s implies the same ordering to the corresponding vectors Fi into a sequence F(0),F(1), . . . ,F(n−1) . Nonlinear ranked type multichannel estimators define the vector F(0) as the filter output, which is called a Vector Median Filter (VMF) if the L1 metric is used. The output of the VMF is the pixel Fk ∈W for which the following condition is satisfied: n−1 ∑