Twice Decomposition of Morphological Structuring Elements

In image processing based on mathematical morphology, we got used to decompose large and complex morphological structuring element into small and simple ones in order to decrease the computational complexity. In this paper, we propose a novel algorithm for the decomposition of two dimensional structures and it is proved valid and more efficient. Motivated by the decomposition of wavelet basis, we decompose the two dimensional structuring elements twice and replace them by two one-dimensional structuring elements. The proposed method not only decreases the computational complexity from O(n²) to O(n) for every pixel but also puts forward a convenient way to implement morphological transforms with simple hardware or in a parallel fashion.