Adaptive linear combination of weighted medians

In our previous literature¹, we proposed a class of nonlinear filters whose output is given by a linear combination of weighted medians (LCWM) of the input sequence. We showed that, unlike the median type filters having the lowpass response, the LCWM filters consisting of weighted median subfilters can not only suppress both Gaussian noise and impulsive noise effectively, but also offer various frequency characteristics including lowpass, bandpass, and highpass responses. In an attempt to improve the performance of LCWM filters, we propose an adaptive LCWM (ALCWM) filter which consists of directional weighted median subfilters with different geometric structures. The weighting factor of each subfilter is adaptively determined using the similarity between the directional subwindow and the local geometric image features of interest. It is shown experimentally that the ALCWM filter performs better than the aforementioned filters including the median and the LCWM filters in preserving more details.