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.