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It is well-known that the minimum spanning tree (MST) is widely used in image segment, edge-preserving filtering, and stereo matching. However, the non-local (NL) filter based on the MST generally results in overly smooth images, since it ignores spatial affinity. In this paper, we propose a new spatial minimum spanning tree filter (SMSTF) to improve the performance of the NL filter by designing a spatial MST to avoid over-smoothing problems, by introducing recursive techniques to implement the filtering process. The SMSTF has the advantages that: (1) the kernel of our filter considers spatial affinity and similarity of intensity; (2) The size of the filter kernel is the entire image domain; (3) the complexity of the SMSTF is linear to the number of image pixels. For these reasons, our filter achieves excellent edge-preserving results. Extensive experiments demonstrate the versatility of the proposed method in a variety of image processing and computer vision tasks, including edge-preserving smoothing, stylization, colorization, and stereo matching.

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Efficiency and accuracy of semi-global matching (SGM) make it outperform many stereo matching algorithms and is widely used under challenging occasions. However, SGM only incorporates information along a scanline in each pass and lacks interaction between scanlines, resulting in streak artifacts in the disparity image. We introduce a local edge-aware filtering method to SGM to enhance the interaction of neighboring scanlines, since streak artifacts can be avoided. We use bilateral weights based on intensity similarity and spatial affinity between pixels to build connections among scanlines. In each pass, we recursively estimate the aggregated cost of SGM and compute the weighted average of aggregated costs for pixels in the orthogonal direction to obtain the output of our method along each scanline. As one-dimensional bilateral filtering is used in our method, the extra computation is linear to image resolution and label space, which is a small fraction of that needed by SGM. We present ablation studies using stereo pairs under both constrained and natural conditions to verify the effectiveness of our method. Extensive experiments on Middlebury and Karlsruhe Institute of Technology and Toyota Technology Institute datasets demonstrate that our method removes all streak artifacts, improves the quality of the disparity image, and outperforms many other non-local cost aggregation approaches.

The accuracy and speed of semi-global matching (SGM) make it widely used in many computer vision problems. However, SGM often struggles in dealing with pixels in the homogeneous regions and also suffers from streak artefacts for weak smoothness constraints. Meanwhile, we observe that the global method usually fails in occluded areas. The disparities for occluded pixels are typically the average of the disparity of nearby pixels. The local method can propagate the information into occluded pixels with a similar color. In this paper, we propose a novel, to the best of our knowledge, four-direction global matching with a cost volume update scheme to cope with textureless regions and occlusion. The proposed method makes two changes in the recursive formula: a) the computation process considers four visited nodes to enforce more smooth constraints; b) the recursive formula integrates cost filtering to propagate reliable information farther in nontextured regions. Thus, our method can inherit the speed of SGM, properly avoid streaking artefacts, and deal with the occluded pixel. Extensive experiments in stereo matching on Middlebury demonstrate that our method outperforms typical SGM-based cost aggregation approaches and other state-of-the-art local methods.