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.

众所周知，最小生成树（MST）广泛用于图像分段，边缘保留滤波和立体匹配。但是，基于MST的非本地（NL）滤镜通常会导致图像过于平滑，因为它忽略了空间亲和力。在本文中，我们提出了一种新的空间最小生成树滤波器（SMSTF），通过设计空间MST以避免过度平滑问题，并引入递归技术来实现滤波过程，从而提高NL滤波器的性能。SMSTF的优点是：（1）我们过滤器的内核考虑了空间亲和力和强度相似性；（2）过滤器内核的大小是整个图像域；（3）SMSTF的复杂度与图像像素数成线性关系。由于这些原因，我们的滤光片可获得出色的边缘保留效果。