Abstract: In this paper, we present a family of circular or square optimal polynomial filters for prefiltering two-dimensional polygons and images. The criterion of designing polynomial filters is to maximize the energy concentration within a period of the spectra of the filters. The filters are nonnegative and can have arbitrary radius and order. For a given radius, the filters converge very fast when the order increases, making low-order filters suffice for high-quality prefiltering. With polynomial filters, it is convenient to evaluate the integral over the parts of polygons within the filter mask with closed-form solutions, or generate look-up tables quickly via analytic evaluation. The experiments demonstrate the excellent anti-aliasing performance of our polynomial filters.