Sub-window median-like filter in constant time
Daiki Isono, Xiaohua Zhang, Wenbo Jiang, Yuelan Xin · 2020
Due to its simplicity, median filter is a very famous and useful tool in the fields such as image processing and computer graphics. Median filter is mainly for eliminating irrelevant details, especially removing salt-and- pepper noises in image. It has the ability to preserve structural edges compared with box filter and Gaussian filter, however, this ability is very limited. When the radius of filter window becomes larger, the edge-preserving ability also becomes very weak. In this paper, we propose a median-like filter that removes small details including salt-and-pepper noises in image while having stronger edge-preserving ability than classical median filter. The filter computes the output at the observed pixel using 8 sub-windows and a full window. Among these windows, 4 of them are built on the 4 quadrants respectively, other 4 of them are on left, right, top, and bottom half planes. All of these sub-windows contain the observed pixel. Moreover, since medians are computed from histograms, we update column histograms and kernel histograms by simple subtraction and addition operations to accelerate the filtering. The computational complexity of the proposed median-like filter is independent of window size and thus is in constant time. A SSIM (Structural SIMilarity) evaluation demonstrates that the proposed median-like filter performs well.