Fully Connected Guided Image Filtering

This paper presents a linear time fully connected guided filter by introducing the minimum spanning tree (MST) to the guided filter (GF). Since the intensity based filtering kernel of GF is apt to overly smooth edges and the fixed-shape local box support region adopted by GF is not geometric-adaptive, our filter introduces an extra spatial term, the tree similarity, to the filtering kernel of GF and substitutes the box window with the implicit support region by establishing all-pairs-connections among pixels in the image and assigning the spatial-intensity-aware similarity to these connections. The adaptive implicit support region composed by the pixels with large kernel weights in the entire image domain has a big advantage over the predefined local box window in presenting the structure of an image for the reason that: 1, MST can efficiently present the structure of an image; 2, the kernel weight of our filter considers the tree distance defined on the MST. Due to these reasons, our filter achieves better edge-preserving results. We demonstrate the strength of the proposed filter in several applications. Experimental results show that our method produces better results than state-of-the-art methods.