Flat structuring elements are commonly used in morphologicalnoperations. In this paper, a fast algorithm employing the result ofnprevious searching area, which is determined by a domain-selectionnmethod, is proposed. It is applicable to structuring elements conformingnto a constraint that its one-dimensional (1-D) Euler-Poincare constants,nN(1/)(x) and Nsup (1/)(y), at any x- or y-coordinate must benequal to 1. The proposed algorithm is compared with three other methods,nnamely threshold linear convolution of Kisacanin and Schonfeld (KS),nstructuring element decomposition of Shih and Mitchell (SM), and fastnimplementation of Wang and He (WH), in terms of the theoretical expectednnumber of comparisons and experimental computation time. It is foundnthat the proposed algorithm requires less computation time than KS andnSM methods for nearly all sizes of square, octagon, and rhombusnstructuring elements, except for the size of 3×3. In addition, itnis also more time efficient than the WH method, except for the squarenstructuring element
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