Morphological structuring image decomposition

Two major structuring element decomposition techniques are compared, and the superiority of the two pixel decomposition techniques over the cellular decomposition technique is shown in terms of the number of pipeline stages. As for the general structuring function decomposition, to the authors´ knowledge, there is no efficient algorithm that has been found. The difficulty can be overcome by using an adequate representation of the general gray-scale structuring function. Representing a gray-scale image as a specific 3-D set, i.e. an umbra, makes it easier to shift all morphological theorems from the binary domain to the gray-scale domain; however, a direct umbra representation is not appropriate for the general gray-scale structuring function decomposition. The authors also provide a morphologically realizable representation and decomposition for the general gray-scale structuring function and show recursive algorithms which are pipelineable for efficiently performing gray-scale morphological operations