MORPHOLOGICAL STRUCTURING ELEMENT DECOMPOSITION: IMPLEMENTATION AND COMPARISON

Structuring element decomposition is used to reduce computation time in performing morphological image processing operations by breaking down a structuring element into simpler components. This paper classifies decomposition algorithms into two broad categories, namely morphological combination and set theoretic combination classes. Two important structuring element decomposition methods, the tree search and arbitrary shape decomposition algorithms, are discussed and their performances are compared using a series of different structuring element shapes. We found that the tree search decomposition algorithm is restricted to mainly symmetric and convex structuring elements, and its computation time for performing a morphological operation grows exponentially with the size of the element used, whereas the arbitrary shape decomposition algorithm performs the same operation in linear time, and can deal with any structuring element shape.