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Dual Contractions of Combinatorial Maps

Luc Brun &
Walter Kropatsch.
This paper presents a new formalism for irregular
pyramids based on combinatorial maps. The
combinatorial map formalism allows us to encode a
planar graph thanks to two permutations encoding the
edges and the vertices of the graph.The combinatorial
map formalism encode explicitly the orientation of the
planar graph. This last property is useful to describe
the partitions of an image which May be considered as
a subset of the oriented plane IR^2. This new
constraint allows us to design interesting properties
for irregular pyramids. Finally the combinatorial
formalism allows us to encode efficiently the graph
transformations used in irregular pyramids.