A simple algorithm for decomposing convex structuring elements

A finite subset of Z² is called a structuring element. The paper presents a new and simple algorithm for decomposing a convex structuring element as a sequence of Minkowski additions of a minimum number of subsets of the elementary square (i.e., the 3×3 square centered at the origin). Besides its simplicity, the advantage of this algorithm over some known algorithms is that it generates a sequence of non necessarily convex subsets, which means subsets with smaller cardinality and consequently faster implementation of the corresponding dilations and erosions. The algorithm is based on algebraic and geometrical properties of Minkowski additions. Theoretical analysis of correctness and computational time complexity are also presented