###
Construction of Combinatorial Pyramids

Luc Brun &
Walter Kropatsch.
Irregular pyramids are made of a stack of successively
reduced graphs embedded in the plane. Each vertex of a reduced graph
corresponds to a connected set of vertices in the level below. One
connected set of vertices reduced into a single vertex at the above
level is called the reduction window of this vertex. In the same
way, a connected set of vertices in the base level graph reduced to
a single vertex at a given level is called the receptive field of
this vertex. The graphs used in the pyramid May be region adjacency
graphs, dual graphs or combinatorial maps. This last type of
pyramids are called Combinatorial Pyramids. Compared to usual graph
data structures, combinatorial maps encode one graph and its dual
within a same formalism and offer an explicit encoding of the
orientation of edges around vertices. This paper describes the
construction scheme of a Combinatorial Pyramid. We also provide a
constructive definition of the notions of reduction windows and
receptive fields within the Combinatorial Pyramid framework.