Multi-directional filters designed from 1D prototypes

In this paper a design method based on spectral transformations is proposed for a particular class of 2D IIR filters, namely multi-directional filters. The design starts from an analog prototype with specified parameters. Applying an appropriate frequency transformation to the 1D transfer function, the desired 2D filter is directly obtained in a factorized form. The approach is mainly analytical but also uses numerical approximations and is simple, efficient and versatile. For two-directional filters, an example is given of extracting lines with two different orientations from a test image.