Steerable Filtering Using Novel Circular Harmonic Functions with Application to Edge Detection

In this paper, we perform approximate steering of the elongated 2D Hermite-Gauss functions with respect to rotations and provide a compact analytical expressions for the related basis functions. A special notation introduced here considerably simplifies the derivation and unifies the cases of even and odd indices. The proposed filters are applied to edge detection. Quantitative analysis shows a performance increase of about 12.5% in terms of the Pratt´s figure of merit with respect to the well-established Gaussian gradient proposed by Canny.