Approximating image filters with box filters

Box filters have been used to speed up many computation-intensive operations in Image Processing and Computer Vision. They have the advantage of being fast to compute, but their adoption has been hampered by the fact that they present serious restrictions to filter construction. This paper relaxes these restrictions by presenting a method for automatically approximating an arbitrary 2-D filter by a box filter. To develop our method, we first formulate the approximation as a minimization problem and show that it is possible to find a closed form solution to a subset of the parameters of the box filter. To solve for the remaining parameters of the approximation, we develop two algorithms: Exhaustive Search for small filters and Directed Search for large filters. Experimental results show the validity of the proposed method.