Dual Contraction of Combinatorial Maps

Pattern Recognition and Image Processing Group Institute of Computer Aided Automation Vienna University of Technology Treitlstr. 3/1832 A-1040 Vienna AUSTRIA Phone: +43 (1) 58801-18351 Fax: +43 (1) 5054668 E-mail: [email protected], [email protected] URL: http://www.prip.tuwien.ac.at/ PRIP-TR-54 January 29, 1999 Dual Contraction of Combinatorial Maps Luc Brun and Walter Kropatsch1 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 IR2. This new constraint allows us to design interesting properties for irregular pyramids. Finally the combinatorial formalism allows us to encode e ciently the graph transformations used in irregular pyramids.