Imposing Total Variation Prior Into Guided Filter

Guided filter is a popular filter thanks to its effectiveness in edge preserving and computation efficiency. On the other hand, total variation is a popular prior thanks to its mathematical properties. In this paper, we impose the total variation prior into guided filter, leading to a novel Total Variation Guided Filter (TVGF) that has both advantages from guided filter and total variation prior. First, TVGF has a closed-form expression and also a linear computation complexity. Our experiment confirms that TVGF is 1300+ times faster than traditional iterative solvers for total variation models. Second, thanks to the total variation, TVGF preserves edges better than the original guided filter and leads to much less artifacts. TVGF is also two times faster than the guided filter. We theoretically derive the TVGF and numerically confirm its effectiveness and efficiency. TVGF can be used in a large range of edge-aware applications, such as image smoothing, dehazing, depth estimation and optical flow estimation.