Constant Time Weighted Median Filtering for Stereo Matching and Beyond

Despite the continuous advances in local stereo matching for years, most efforts are on developing robust cost computation and aggregation methods. Little attention has been seriously paid to the disparity refinement. In this work, we study weighted median filtering for disparity refinement. We discover that with this refinement, even the simple box filter aggregation achieves comparable accuracy with various sophisticated aggregation methods (with the same refinement). This is due to the nice weighted median filtering properties of removing outlier error while respecting edges/structures. This reveals that the previously overlooked refinement can be at least as crucial as aggregation. We also develop the first constant time algorithm for the previously time-consuming weighted median filter. This makes the simple combination ``box aggregation + weighted median'' an attractive solution in practice for both speed and accuracy. As a byproduct, the fast weighted median filtering unleashes its potential in other applications that were hampered by high complexities. We show its superiority in various applications such as depth up sampling, clip-art JPEG artifact removal, and image stylization.