Fast Almost-Gaussian Filtering

Image averaging can be performed very efficiently using either separable moving average filters or by using summed area tables, also known as integral images. Both these methods allow averaging to be performed at a small fixed cost per pixel, independent of the 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 paper describes how to determine the averaging filters that one needs to approximate a Gaussian with a specified standard deviation. The design of bandpass filters from the difference of Gaussians is also analysed. It is shown that difference of Gaussian bandpass filters share some of the attributes of log-Gabor filters in that they have a relatively symmetric transfer function when viewed on a logarithmic frequency scale and can be constructed with large bandwidths.