Basis matrix representation of morphological filters with N-dimensional structuring elements

In this paper, we present a basis matrix representation of grayscale morphological filters in N-dimensions. A procedure is proposed to derive the basis matrix and the block basis matrix (BBM) from an N-dimensional grayscale structuring element (GSE). It is shown that both opening and closing with arbitrary N-dimensional GSE can be accomplished by a local matrix operation using the basis matrix. Furthermore, these basis matrix representations are extended to the efficient implementation of open-closing (OC) and close-opening (CO) using the BBM.