On the design of two-dimensional polar separable filters

In this paper we present a new approach to the design of polar separable 2D filters. The novelty lies in the existence of an analytic description of the filter in both domains, the spatial and the frequency domain. That means no numeric optimisation becomes necessary and derivatives of the filters can be computed analytically. The method is based on a series of Poisson filters, which is interpreted in terms of a z-transform. The resulting radial filters are then combined with spherical harmonics. We show several examples, among these a new 2D quadrature filter.