Decomposition of geometric-shaped structuring elements using morphological transformations on binary images

A unified technique to simplify the decomposition of various types of big geometric-shaped structuring elements into dilations of smaller structuring components by the use of a mathematical transformation is presented. The method can be applied to all types of ID gray-scale structuring elements to decompose them into dilations of smaller structuring components. The desired morphological erosion and dilation are equivalent to a simple inverse transformation over the result of operations on the transformed decomposable structuring elements. A strategy to decompose a large cyclic cosine structuring element is described. A technique for decomposing a two-dimensional convex structuring element into one-dimensional elements is also developed.<>