Wedge Filters Designed From 1D Digital Prototypes

Abstract

This work proposes an efficient analytic method for designing a class of 2D filters useful in image processing, namely wedge-shaped filters, which can be considered components of a directional filter bank. The design starts from a 1D digital filter prototype transfer function. Using accurate approximations and specific frequency mappings, first an unilateral, half-plane filter with a given orientation is obtained. Using two such unilateral 2D filters with imposed orientation angles, a desired directional wedge filter is derived, with specified orientation and aperture angles. Its transfer function results directly in a factored form, which is an advantage in implementation. The resulted wedge filter is parametric and tunable, since the specified parameters occur in the final matrix form of the filter transfer function.