Alternating sequential filters and multiresolution morphology

Important concepts of the morphological sampling theorem and distance relationships are highlighted. Two representations are stated based on the kernels of morphological mappings, one as the union of erosions, the other as the intersection of dilations. A subset of this representation, namely basis functions, is used. An alternative proof for some of the theorems of R. Haralick et al. (Proc. IEEE First Conference on Computer Vision, London, 1987) using basis functions is shown. This decomposition is used to show the relationship of opening-closing in the sampled and unsampled domains