Efficient 2-D Gray-Scale Dilations and Erosions with Arbitrary Flat Structuring Elements

An efficient algorithm is presented for the computation of gray-scale morphological operations with 2-D structuring elements (S.E.). The required computing time is independent of the image content and of the number of gray levels used. For circular S.E.s, it always outperforms the only existing comparable method, which was proposed earlier, by a factor between 1.8 and 8.6, depending on the image type. So far, filtering using multiple S.E.s is always done by performing the operator for each size and shape of the S.E. separately. With our method filtering with multiple S.E.s can be performed by a single operator for a reduced computational cost per size or shape, which makes this method more suitable for use in granulometries, dilation-erosion scale spaces, and template matching using the hit-or-miss transform.