DECOMPOSITION OF ARBITRARILY-SHAPED MORPHOLOGICAL STRUCTURING ELEMENTS

For image processing systems that have a limited size of region of sup port, say 3 x 3, direct implementation of morphological operations by a structuring element larger than the prefixed size is impossible. The decomposition of morphological operations by a large structuring elem ent into a sequence of recursive operations, each using a smaller stru cturing element, enables the implementation of large morphological ope rations. In this paper, we present the decomposition of arbitrarily sh aped (convex or concave) structuring elements into 3 x 3 elements, opt imized with respect to the number of 3 x 3 elements. The decomposition is based on the concept of factorization of a structuring element int o its prime factors. For a given structuring element, all its correspo nding 3 x 3 prime concave factors are first determined. From the set o f the prime factors, the decomposability of the structuring element is then established, and subsequently the structuring element is decompo sed into a smallest possible set of 3 x 3 elements. Examples of optima l decomposition and structuring elements that are not decomposable are presented.