Moment filters for high precision computation of focus and stereo

Many low level visual computation problems such as focus, stereo, etc. can be formulated as problems of extracting one or more parameters of a non-stationary transformation between two images. Because of the non-stationary nature, finite-width windows are widely used in various algorithms to extract spatially local information from images. While the choice of window width has a very profound impact on the quality of results of algorithms, there has been no quantitative way to measure or eliminate the negative effects of finite width windows. To address this problem, we introduce a new set of filters, moment filters. Due to their recursiveness in the Fourier and spatial domains, these filters allow the effects of finite-width windows and fore-shortening to be explicitly analyzed and eliminated.