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It is challenging to extend the support region of state-of-the-art local edge-preserving filtering approaches to the entire input image on account of huge memory cost and heavy computational burden. In this paper, we propose an O(N) time recursive non-local edge-aware filter. A novel graph and a linear time algorithm are presented to effectively propagate information across the entire image. In this graph, information is propagated along all directions to avoid visual artifacts. Both the intensity similarity and the spatial affinity are utilized to estimate the similarity of neighboring pixels, and the distance of any two pixels is the length of the path between these two pixels on a binary tree. Specifically, the input image is filtered at four directions, namely left-to-right, right-to-left, top-to-bottom and bottom-to-top. In each pass, the un-normalized output and the normalization constant of the root node are computed recursively from leaf nodes to the root node on a binary tree in linear time. The filtering output is the average of the outputs for these four directions. A comparison with other non-local edge-aware filters is presented to show the advantages of our approach. Extensive experiments demonstrate that our recursive non-local edge-preserving filter is effective in a variety of computer vision and image processing applications, including edge-aware filtering, detail enhancement, stylization, and stereo matching. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]