Low-cost junction characterization using polar averaging filters

Junction characterization is a very important task since junctions are multi-scalar and multi-oriented structures. In order to deal with complex junctions an algorithm must exhibit a high orientational selectivity. The resulting computational burden can be attenuated by applying the concept of steerability. The response of a filter at an arbitrary orientation or scale can be approximated from the responses of a finite set of so-called basis filters. As this basis filter set resembles a bandwidth in Fourier space the uncertainty principle is applicable: High orientational selectivity can only be achieved by a huge number of basis filters and high computational complexity. In this paper we present an alternative approach to alleviate this computational burden. The proposed filters encode a local polar transformation and a cascade of 2D-averaging and 1D-differentiating with first derivatives of Gaussians. The smaller support and the dimension reduction in the convolution achieves the best trade-off between computational complexity and orientational selectivity