Directional filtering in edge detection

Two-dimensional (2-D) edge detection can be performed by applying a suitably selected optimal edge half-filter in n directions. Computationally, such a two-dimensional n-directional filter can be represented by a pair of real masks, that is, by one complex-number matrix, regardless of the number of filtering directions, n: Specific calculations of the edge strength were conducted using a 2-D tridirectional filter based on a Petrou–Kittler one-dimensional (1-D) detector optimized for the ramp edges, which are characteristic of posterior eye capsule images that were used here as a test set. In applications to image segmentation, tridirectional filtering results in co-occurrence arrays of low dimensionality.