  Image smoothing is a fundamental task in signal processing. For such task,
box filter is well-known. However, box filter can not keep some features of the
signal, such as edges, corners and the jump in the step function. In this
paper, we present a one-sided box filter that can smooth the signal but keep
the discontinuous features in the signal. More specifically, we perform box
filter on eight one-sided windows, leading to a one-sided box filter that can
preserve corners and edges. Our filter inherits the constant $O(1)$
computational complexity of the original box filter with respect to the window
size and also the linear $O(N)$ computational complexity with respect to the
total number of samples. We performance several experiments to show the
efficiency and effectiveness of this filter. We further compare our filter with
other the-state-of-the-art edge preserving methods. Our filter can be deployed
in a large range of applications where the classical box filter is adopted.
