Orientation-selective digital filters based on 1D prototypes

In this paper we propose a simple analytical design method for 2D digital filters with an orientation-selective frequency response. This method relies on a 1D IIR prototype filter, whose shape is identical with the cross-section of the oriented filter to be designed. We determine a 1D to 2D complex transformation which leads to a 2D oriented filter through simple substitution in each factor of the transfer function. The design method ensures the stability of the resulting 2D IIR filter, provided the prototype is also stable. We also present a simpler particular case, namely a zero-phase oriented filter, and a full design for given specifications is presented. Simulation results are finally given, to illustrate the detection of straight lines with a given orientation from an image, using the 2D oriented filter.