Image processing using elliptically-shaped filters

This paper proposes an analytical design method for a class of 2D filters, namely elliptical-shaped zero-phase filters. These include as a particular case the circularly-symmetric filters, and also the orientation-selective filters with a narrow frequency response along a direction in the frequency plane specified by a given angle. These filters are based on zero-phase low-pass 1D prototypes. We consider here maximally-flat filters which introduce minimum errors in the pass-band, and also very selective prototypes. Using specific frequency transformations the desired 2D filters are obtained, which are very efficient and preserve the properties of their 1D counterparts. Simulation results on some test images are provided.