Investigation of the mechanism for median image filtering in computer systems and special purpose networks

A successful solution to solve an impulse noise is to use median filtration proposed by John Tuke in 1971 for the analysis of economic processes. It should be noticed that median filtration is a heuristic processing method, its algorithm is not a mathematical solution to a strictly formulated problem. Therefore, the researchers pay much attention to the analysis of the image effectiveness processing on its basis and comparison with other methods. When applying a median filter, each image pixel is sequentially processed. For median filtration, a two-dimensional window (filter aperture) is used, usually has a central symmetry, with its center located at the current filtration point. The dimensions of the aperture are among the parameters that are optimized in the process of analyzing the algorithm efficiency. Image pixels, that appear within the window, form a working sample of the current step. However median filtering smoothens the image borders to a lesser degree than any linear filtering. The mechanism of this phenomenon is very simple and is as follows. Assume that the filter aperture is near the boundary separating the light and image's dark areas, with its center located in the dark area. Then, most likely, the work sample will contain more elements with small brightness values, and, consequently, the median will be among those elements of the work sample that match this area of the image. The situation changes to the opposite, if the aperture center is shifted to the region of higher brightness. But this means the presence of sensitivity in the median filter to brightness variations.