author = {Luc {B}run and Walter Kropatsch}, title = {Dual Contractions of Combinatorial Maps}, institution = {Institute of Computer Aided Design}, year = 1999, number = 54, url = {article:=ftp://www.prip.tuwien.ac.at/pub/publications/trs/tr54.ps.gz}, theme = {hierarchical}, address = {Vienna University of Technology, lstr. 3/1832,A-1040 Vienna AUSTRIA}, month = {January}, url = { http://www.prip.tuwien.ac.at/}, abstract = " 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."