Binary Structuring Elements Decomposition Based on an Improved Recursive Dilation-Union Model and RSAPSO Method

This paper proposed an improved approach to decompose structuring elements of an arbitrary shape. For the model of this method, we use an improved dilation-union model, adding a new termination criterion, as the sum of 3-by-3 matrix should be less than 5. Next for the algorithm of this method, we introduced in the restarted simulated annealing particle swarm optimization method. The experiments demonstrate that our method can find better results than Park's method, Anelli's method, Shih's SGA method, and Zhang's MFSGA method. Besides, our method gave the best decomposition tree of different SE shapes including “ship,” “car,” “heart,” “umbrella,” “vase,” “tree,” “cat,” “V,” “bomb,” and “cup.”