Design of 2D recursive filters with double-directional selectivity

This paper proposes an analytic design method for 2D recursive filters, with double-directional orientation-selective frequency response. The method relies on a zero-phase prototype filter which is transformed using a frequency mapping specific to fan-shaped filters. The proposed technique does not involve the bilinear transform, which introduces distortions and requires various corrections, such as pre-warping, which complicates the design. Instead, several variable substitutions and efficient approximations are used, in order to obtain a rational expression of the frequency mapping. Finally the 2D filter coefficients are obtained, and the resulted filters are partially separable. The advantage of analytic design is the possibility of filter directional tuning, since filter matrices depend explicitly on specified parameters. They find applications in image processing and pattern recognition, like simultaneously detecting lines with two orientations from an image, as simulation results show.