A fast algorithm for morphological operations with flat structuring element

Flat structuring elements are commonly used in morphological operations. In this paper, a fast algorithm employing the result of previous searching area, which is determined by a domain-selection method, is proposed. It is applicable to structuring elements conforming to a constraint that its one-dimensional (1-D) Euler-Poincare constants, N^{(1/)(x) and N}sup (1/)(y), at any x- or y-coordinate must be equal to 1. The proposed algorithm is compared with three other methods, namely threshold linear convolution of Kisacanin and Schonfeld (KS), structuring element decomposition of Shih and Mitchell (SM), and fast implementation of Wang and He (WH), in terms of the theoretical expected number of comparisons and experimental computation time. It is found that the proposed algorithm requires less computation time than KS and SM methods for nearly all sizes of square, octagon, and rhombus structuring elements, except for the size of 3×3. In addition, it is also more time efficient than the WH method, except for the square structuring element