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

Mathematical morphology which is based on geometric shape, provides an approach to the processing and analysis of digital images. Several widely-used geometric-shaped structuring elements can be used to explore the shape characteristics of an object. A unified technique is presented 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. Hence, 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 is also presented to decompose a large cyclic cosine structuring element. The technique of decomposing a two-dimensional (2D) convex structuring element into one-dimensional (1D) ones is also developed.