A new approach to vector median filtering based on space filling curves

The availability of a wide set of multidimensional information sources in different application fields (e.g., color cameras, multispectral remote sensing imagery devices, etc.) is the basis for the interest of image processing research on extensions of scalar nonlinear filtering approaches to multidimensional data filtering. A new approach to multidimensional median filtering is presented. The method is structured into two steps. Absolute sorting of the vectorial space based on Peano space filling curves is proposed as a preliminary step in order to map vectorial data onto an appropriate one-dimensional (1-D) space. Then, a scalar median filtering operation is applied. The main advantage of the proposed approach is the computational efficiency of the absolute sorting step, which makes the method globally faster than existing median filtering techniques. This is particularly important when dealing with a large amount of data (e.g., image sequences). Presented results also show that the filtering performances of the proposed approach are comparable with those of vector median filters presented in the literature.