Junction Characterization Using Polar Pyramid

Abstract

In this paper we present a new approach in characterizing gray-value junctions. Due to the multiple intrinsic orientations present in junctions the response of a filter is needed at every orientation. As a rotation of the filter would considerably increase the computational burden alternative techniques like filter steerability have been proposed. Steerability relies in interpolating the response at an arbitrary orientation from the responses of some basis filters. Unfortunately, current steerability approaches suffer from the consequences of the uncertainty principle: In order to achieve high selectivity in orientation they need a huge number of basis filters increasing, thus, the computational complexity.

The new approach presented here achieves a higher orientational selectivity with a lower complexity. We consider the local polar map of the neighborhood of a junction where the new coordinates are the radius and the angle. Finding the gray-value transitions of a junction can be interpreted as ID edge detection. Hence, the orientational selectivity problem can be attacked by applying a pyramidal scheme. It is well known that it is always possible to reconstruct a signal using the sampling kernel as an interpolation function. Therefore, our approach can also steer the response of a Gaussian derivative to every orientation. The total algorithmic complexity encompasses the small support 2D-filtering for polar mapping and radial smoothing plus an ID-differentiation.