Dual Contraction of Combinatorial Maps (bibtex)
by Luc Brun, Walter Kropatsch
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 $R^2$. 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.
Reference:
Dual Contraction of Combinatorial Maps (Luc Brun, Walter Kropatsch), Technical report, PRIP, TU Wien, 1999.
Bibtex Entry:
@TechReport{TR054,
  author =	 "Luc Brun and Walter Kropatsch",
  institution =	 "PRIP, TU Wien",
  number =	 "PRIP-TR-054",
  title =	 "Dual {C}ontraction of {C}ombinatorial {M}aps",
  year =	 "1999",
  url =		 "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr54.ps.gz",
  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 $R^2$. 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. ",
}
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