Design and applications of 2D directional filters based on frequency transformations

We present a new approach to the design of 2D recursive filters, with a directionally-selective frequency response. Two analytical design methods are proposed, based on digital prototype filters and complex frequency transformations, determined using rational approximations and the bilinear transform. Design examples are presented for given specifications. The resulted filters are efficient, of low complexity and relatively high selectivity. They find useful applications in image processing, like detecting lines with a given orientation from an image.