Fast directional correlation on the sphere with steerable filters

Abstract: A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order \(O(L^5)\), where \(2L\) stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals and filters considered.