Optimising computation of hexagonal differential gradient edge detector

It has recently been found that a hexagonal differential gradient operator can be considerably more efficient than the corresponding (Sobel) operator operating in a square lattice. The author shows that in the hexagonal case it is unnecessary to employ masks for directions other than 0 degrees or 90 degrees , and that in general greater efficiency can be achieved using x and y component masks: if these are used, computational savings can be made by using the standard vector component formulas for calculating intensity gradient and edge orientation.