Approaches to decompose flat structuring element for fast overlapping search morphological algorithm

The fast morphological algorithm, overlapping search (OS) algorithm, recently proposed by Lam and Li (1998), can only be applied to a flat structuring element (FSE) whose 1D Euler-Poincare constants, N ⁽¹⁾(x) and N⁽¹⁾(y), at any x or y coordinate are equal to 1. Thus, an arbitrarily shaped structuring element must be decomposed to a set of constrained components before employing the fast algorithm. In the paper, a decomposition algorithm, based on line-scanning process, and an improved algorithm, based on conditionally maximal convex polygon (CMCP), are proposed to generalize the use of the overlapping search morphological algorithm for any arbitrary flat structuring element