Arbitrary Gaussian Filtering with 25 Additions and 5 Multiplications per Pixel

Summed area tables, also known as integral images, allow image averaging to be performed very efficiently at a small fixed cost per pixel, independent of averaging filter size. Repeated filtering with averaging filters can be used to approximate Gaussian filtering. Thus a good approximation to Gaussian filtering can be achieved at a fixed cost per pixel independent of filter size. This note describes how to determine the averaging filters that one needs to approximate a Gaussian with a specified standard deviation. The use of difference of Gaussians to construct bandpass filters is also analysed.