We discuss the basic concepts of Mathematical Morphology on the 
classical context of binary images and also on the abstract context 
of complete lattices. In particular, we present an estrategy to construct 
dilation and erosion morphological operators on sup-generated complete 
lattices.
Next, we present multi-triangulation, a mesh representation based on 
variable resolution meshes. To this representation, we show that we can 
associate a sup-generated complete lattice. On this lattice, we see how to 
define the dilation and erosion operators that reproduce a given sequence 
of local refinements and simplifications in a multi-triangulation. 
Finally, we show how to represent a given image using a 
multi-triangulation and, by constructing dilation operators 
on the sup-generated complete lattice associated to this 
multi-triangulation, we obtain sequences of images leading 
progressively to the given image.