Design of 2D parametric filters for directional Gaussian smoothing

This paper proposes an analytical design method for a class of 2D recursive filters, namely filters for directional (anisotropic) Gaussian smoothing. These filters have a Gaussian shape in a vertical section and an elliptical shape in a horizontal section, parallel with the frequency plane, with a specified orientation angle. The design is based on decomposing the frequency response into three simple Gaussian components along the frequency axes and diagonal. For each component the transfer function is found applying an efficient pre-warping before using the bilinear transform, which allows obtaining filters with very little distortions. Finally the filter matrices are obtained. The filter is adjustable in the sense that it is specified by parameters which appear explicitly in the filter coefficients.