Approximate orientation steerability based on angular Gaussians

Junctions are significant features in images with intensity variation that exhibits multiple orientations. This makes the detection and characterization of junctions a challenging problem. The characterization of junctions would ideally be given by the response of a filter at every orientation. This can be achieved by the principle of steerability that enables the decomposition of a filter into a linear combination of basis functions. However, current steerability approaches suffer from the consequences of the uncertainty principle: in order to achieve high resolution in orientation they need a large number of basis filters increasing, thus, the computational complexity. Furthermore, these functions have usually a wide support which only accentuates the computational burden. We propose a novel alternative to current steerability approaches. It is based on utilizing a set of polar separable filters with small support to sample orientation information. The orientation signature is then obtained by interpolating orientation samples using Gaussian functions with small support. Compared with current steerability techniques our approach achieves a higher orientation resolution with a lower complexity. In addition, we build a polar pyramid to characterize junctions of arbitrary inherent orientation scales.