Adaptive tri-direction edge detection operators based on the spiral architecture

We present a general approach to the computation of adaptive tri-directional operators for use on hexagonal pixel-based images, based on the spiral architecture. We show that the use of Gaussian basis functions within the finite element method provides a framework for a systematic design procedure for operators that are adaptive to spiral neighbourhoods through the use of an explicit scale parameter. We evaluate the proposed operators using simulated hexagonal images and provide comparative results with the use of traditional rectangular operators.