Algorithm for decomposition of binary morphological convex structuring elements based on periodic lines

This paper presents a new and simple algorithm for decomposing a convex structuring element into dilations of periodic lines with a union of a residue component. The algorithm proposed in this paper is based on the boundaries of convex structuring elements and the properties of dilations. Besides simplicity of the algorithm, the advantage of the method is that periodic lines possess a faster implementation of the corresponding dilations and erosions. The examples of optimal decomposition demonstrate that the algorithm offers a low complexity of morphological operators. The results indicate that the present decomposition algorithm is more robust when compared with other algorithms.