Steerable wedge filters

Steerable filters, as developed by Freeman and Adelson (1991), are a class of rotation-invariant linear operators that may be used to analyze local orientation patterns in imagery. The most common examples of such operators are directional derivatives of Gaussians and their 2D Hilbert transforms. The inherent symmetry of these filters produces an orientation response that is periodic with period π, even when the underlying image structure does not have such symmetry. This problem may be alleviated by reconsidering the full class of steerable filters. We develop a family of even- and odd-symmetric steerable filters that have a spatially asymmetric “wedge-like” shape and are optimally localized in their orientation response. Unlike the original steerable filters, these filters are not based on directional derivatives and the Hilbert transform relationship is imposed on their angular components. We demonstrate the ability of these filters to properly represent oriented structures