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Studies on many dense correspondence tasks in the field of computer vision attempt to find spatially smooth results. A typical way to solve these problems is by smoothing the matching costs using edge-preserving filters. However, local filters generate locally optimal results, in that they only take the costs over a small support window into account, and non-local filters based on a minimum spanning tree (MST) tend to overuse the piece-wise constant assumption. In this paper, we propose a linear time non-local cost aggregation method based on two complementary spatial tree structures. The geodesic distances in both the spatial and intensity spaces along the tree structures are used to evaluate the similarity of pixels, and the final aggregated cost is the sum of the outputs from these two trees. The filtering output of a pixel on each tree can be obtained by recursively aggregating the costs along eight sub-trees with linear time complexity. The only difference between the filtering procedures on these two spatial tree structures is the order of the filtering. Experimental results in optical flow estimation and stereo matching on the Middlebury and KITTI datasets demonstrate the effectiveness and efficiency of our method. It turns out that our method outperforms typical non-local filters based on the MST in cost aggregation. Moreover, a comparison of handcrafted features and deep features learned by convolutional neural networks (CNNs) in calculating the matching cost is also provided. The code will be available soon. [ABSTRACT FROM AUTHOR]

High efficiency and accuracy of semi-global matching (SGM) make it widely used in many stereo vision applications. However, SGM not only struggles in dealing with pixels in homogeneous area, but also suffers from streak artifacts. In this paper, we propose a novel omni-directional SGM (OmniSGM) with a cost volume update scheme to aggregate costs from paths along all directions and to encourage reliable information to propagate across entire image. Specifically, we perform SGM along four tree structures, namely trees in the left, right, top and bottom of root node, and then fuse the outputs to obtain final result. The contributions of pixels on each tree can be recursively computed from leaf nodes to root node, ensuring our method has linear time computational complexity. Moreover, An iterative cost volume update scheme is proposed using aggregated cost in the last pass to enhance the robustness of initial matching cost. Thus, useful information is more likely to propagate in a long distance to handle the ambiguities in low textural area. Finally, we present an efficient strategy to propagate disparities of stable pixels along the minimum spanning tree (MST) for disparity refinement. Extensive experiments in stereo matching on Middlebury and KITTI datasets demonstrate that our method outperforms typical traditional SGM-based cost aggregation methods. [ABSTRACT FROM AUTHOR]