Guided filter

Edge-preserving smoothing image filter A guided filter is an edge-preserving smoothing image filter. As with a bilateral filter, it can filter out noise or texture while retaining sharp edges. Comparison Compared to the bilateral filter, the guided image filter has two advantages: bilateral filters have high computational complexity, while the guided image filter uses simpler calculations with linear computational complexity. Bilateral filters sometimes include unwanted gradient reversal artifacts and cause image distortion. The guided image filter is based on linear combination, making the output image consistent with the gradient direction of the guidance image, preventing gradient reversal. Definition One key assumption of the guided filter is that the relation between guidance I {\displaystyle I} and the filtering output q {\displaystyle q} is linear. Suppose that q {\displaystyle q} is a linear transformation of I {\displaystyle I} in a window ω k {\displaystyle \omega _{k}} centered at the pixel k {\displaystyle k} . In order to determine the linear coefficient ( a k , b k ) {\displaystyle (a_{k},b_{k})} , constraints from the filtering input p {\displaystyle p} are required