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Design Procedure for 2D Gaussian Anisotropic Filters

This paper proposes an analytical design method for a class of 2D anisotropic filters, with a directional frequency response, specified by a given orientation angle. These filters have a Gaussian shape in a vertical section and a relatively straight, linear shape in a horizontal section, parallel with the frequency plane. The design starts from a Gaussian prototype with a specified selectivity, to which successive frequency transformations are applied, yielding the transfer function in matrix form of the 2D anisotropic filter with a desired selectivity and orientation. The filter is quite efficient and adjustable, being specified by parameters which appear explicitly in the filter matrices, and allow for adjusting independently their selectivity and orientation. The resulted filters have an accurate shape of the frequency response, high directional selectivity and relatively low order. Moreover, an advantage of this analytical approach is that the filter transfer function results in a parametric, factored form, which allows efficient implementation and easy tunability.