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, nite-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 e ects of nitewidth windows. To address this problem, We introduce a new set of lters, moment lters. Due to their recursiveness in the Fourier and spatial domains, these lters allow the e ects of nite-width windows and foreshortening to be explicitly analyzed and eliminated.