Recursive fan-type filter design from 1D analog transfer functions

In this paper a new design method for a class of 2D IIR fan-type filters based on spectral transformations is proposed. The design starts from an analog prototype filter with specified parameters and whose transfer function is factorized into biquads. Applying an appropriate frequency transformation to the 1D transfer function, the desired 2D filter is directly obtained in a factorized form as well. The approach is mainly analytical but also uses numerical approximations and is simple, efficient and versatile. These fan-type filters can also be regarded as components of directional filter banks. Using the determined frequency transformation, two-directional selective filters are obtained as well. Design examples are provided and simulation results are shown, for an application in medical image processing, namely the detection of blood vessels with a specified orientation from angiography images. For two-directional filters, an example is given of extracting lines with two different orientations from a test image.