Circular IIR Filter Design and Applications in Biomedical Image Analysis

This work presents an analytical design method for a category of two-dimensional IIR filters, specifically with circular symmetry, which have useful applications in image processing. The design is based on efficient digital elliptic filters, used as 1D prototypes, to which some complex frequency transformations are applied; this allows to obtain directly a factored form of the transfer function for the 2D circularly-symmetric filter. The design procedure involves some accurate approximations, but no global optimization algorithm. As a result, the 2D filter matrices are derived. The filter has the advantage of being adjustable, as its bandwidth is determined by a parameter which appears in the filter coefficients. The designed 2D filters have an accurate circular shape, exhibiting very low distortions even near the margins of the frequency plane, and are efficient, of high selectivity and relatively low order. The designed filters can be used as a bank of circular filters, useful in a multi-resolution analysis of an image. To prove their filtering capabilities, simulation results are provided for circular filtering of a biomedical image, namely a retina angiogram.