Fast algorithms for grayscale morphological operations

This paper presents efficient real time implementation methods for grayscale composite (opening and closing) function processing (FP) systems. The proposed method is based on a matrix representation of the composite FP system using a basis matrix. However, the straightforward implementation of the FP opening and closing has a complexity of O(N²), where N is the size of the structuring element. In order to improve the computational efficiency of the proposed implementation method, we present a recursive algorithm based on redundancy of the basis matrix and input matrices. It is shown that, with the proposed scheme, both opening and closing can be determined by 2N - 2 additions and 2N - 2 comparisons.