OSBF: One-Sided Box Filter for Edge-Preserving Image Processing

Box filter is well-known for the image smoothing task, thanks to its effectiveness and computation efficiency. However, it can NOT preserve edges. In contrast, edge-preserving methods can NOT achieve the high computation performance as the box filter. To tackle this issue, in this paper, we present a one-sided box filter that can preserve edges much better than the box filter. Meanwhile, it has a similar high computation performance as the box filter. More specifically, we perform the box filter on nine one-sided local windows, and then select the most possible candidate as the result. Such selection imposes the non-linearity, which preserves the edges and corners. Several numerical experiments are conducted to confirm this edge-preserving property. At the same time, it has a similar computation performance as the box filter. It inherits the constant computation complexity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(1)$ </tex-math></inline-formula> and the linear complexity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N)$ </tex-math></inline-formula> from the box filter with respect to the window size and the total number of pixels, respectively. We numerically confirm that this filter is the fastest method among the edge-preserving methods, including the classical and the state of the art approaches. It is at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10 \times $ </tex-math></inline-formula> faster than other edge-preserving methods. Thanks to the edge-preserving property and the high computation performance, the proposed one-sided box filter can be deployed in a large range of applications where the edge-preserving and high performance is required, such as real-time video processing, augmented reality and view synthesis.