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

摘要

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.