Orientation-selective 2D recursive filter design based on frequency transformations

In this paper we approach the design of a class of 2D recursive filters, with an orientation-selective frequency response. We propose an analytical design method based on a given 1D digital prototype filter and a complex frequency transformation which is separable and is determined using Pade or Chebyshev-Pade approximations and the bilinear transform. We also present separately a method for designing zero-phase oriented filters, which are very useful due to the absence of phase distortions. Some design examples are presented for given specifications. The resulted filters are very efficient, being at the same time of low complexity and relatively high selectivity. These filters may find useful applications in image processing, like detecting lines with a given orientation from an image, as we show through simulation results.