Me. Montiel et al., IMAGE MANIPULATION USING M-FILTERS IN A PYRAMIDAL COMPUTER-MODEL, IEEE transactions on pattern analysis and machine intelligence, 17(11), 1995, pp. 1110-1115
This paper presents how morphological transformations can be related t
o representations of a set on different lattices. A hierarchical defin
ition of structuring element conveys to a class of multigrid transform
ations Psi(k) that handle changes on discrete representations of regio
ns. The transformations correspond to upward and downward processes in
a hierarchical structure. Based on multigrid transformations, requiri
ng O(log n) time is presented. The approach considers grey level regio
ns as sets and processes through a pyramid to carry out geometric mani
pulations. Extending the concept of boundary to cope with hierarchical
representations of a set, a second method which identifies the bounda
ries in an image is discussed.