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Weighted median, in the form of either solver or filter, has been employed in a wide range of computer vision solutions for its beneficial properties in sparsity representation. But it is hard to be accelerated due to the spatially varying weight and the median property. We propose a few efficient schemes to reduce computation complexity from O(r2) to O(r) where r is the kernel size. Our contribution is on a new joint-histogram representation, median tracking, and a new data structure that enables fast data access. The effectiveness of these schemes is demonstrated on optical flow estimation, stereo matching, structure-texture separation, image filtering, to name a few. The running time is largely shortened from several minutes to less than 1 second. The source code is provided in the project website.

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