Analytical design methods for directional Gaussian 2D FIR filters

This paper proposes two analytical design methods in the frequency domain for directional Gaussian 2D FIR filters, with a straight directional or an elliptically-shaped frequency response and with a specified selectivity and orientation in the frequency plane. One method relies on the substitution of a frequency mapping into the factored polynomial approximation of the Gaussian, while the other one is based on decomposing the frequency response into Gaussian components along three properly chosen directions in the frequency plane. The frequency response of the 2D directional filter results directly in a factored form, which is a major advantage in implementation. The filters are accurate, efficient and they eliminate the necessity of interpolation. With the mapping substitution method, they result also adjustable in orientation and aspect ratio. Several design examples are given for various specifications, and simulation results of directional filtering on test images are provided, to prove their applicability in image processing.