An image pyramid with morphological operators

The aim of this research is to obtain a morphological pyramid with the aid of alternating sequential filters. The authors establish a relationship between alternating sequential filters and the morphological sampling theorem developed by R. Haralick et al. (1987). An alternative proof for opening and closing in the sampled and unsampled domain using the basis functions is shown. This decomposition is then used to show the relationship of the compound mapping opening-closing in the sampled and unsampled domain. An upper and a lower bound for the above relationships are presented. Under certain circumstances, an equivalence is shown for opening-closing between the sampled and the unsampled domain. An extension to more complicated algorithms using union of openings and intersection of closings is also proposed