Synthesis and Applications of Oriented Gaussian FIR Filters

An analytical design procedure is proposed for 2D Gaussian orientation-selective FIR filters, based on a frequency transformation applied to a Gaussian prototype. The synthesis starts from a Gaussian filter with specified selectivity with a frequency response approximated as a factored trigonometric polynomial. An efficient frequency mapping is derived and applied to each factor, leading to the desired oriented filter, whose transfer function finally results in matrix form. The 2D filters have a correct shape, with good linearity, a low ripple and negligible distortions. Several design examples for imposed specifications are provided, and also applications in directional filtering are shown, proving the filter capabilities.