Further analysis of the nearest neighbor median filter(NNMF) is carried out. It is proved that the NNMF has the threshold decomposition property and the stacking property. Using these properties, it is formally shown that the NNMF is a subclass of the weighted median filter(WMF), and the weight coefficients of the equivalent WMF are derived. It is shown that the NNMF is more efficient than the equivalent WMF from the viewpoint of computational complexity. Two theorems about the effect of repeated operations of NNMF are proved. These theorems are described in the style of dealing with local configurations of image. Moreover, hardware implementations of the NNMF are presented.
Median filters, Nearest neighbor median filter, Weighted median filter, Threshold decomposition, Theoretical analysis, Hardware implementation