Parallel Line Grouping and Irregular Curve Pyramids (bibtex)
by Walter G. Kropatsch, Dieter Willersinn
Abstract:
Parallel lines are important features for object recognition by grouping. Regular 2x2/2 curve pyramids are hierarchical symbolic representations of curves that can be constructed and processed in logarithmic time. The rigidity of the regular structure causes an unstable, shift variant representation of parallel lines. In order to usefully apply the concept of the curve pyramid on grouping problems, the shift variance problem had to be overcome by extending the concept to irregular pyramids. These have a structure that adapts to the image data by deriving control information from curve relations. The algorithm that builds the irregular curve pyramid by deriving higher levels of abstraction from a set of relations goes far beyond merely solving the shift variance problem. It can reduce the computational complexity in comparable applications where all possible combinations of parts have to be checked in order to reassemble complex objects.
Reference:
Parallel Line Grouping and Irregular Curve Pyramids (Walter G. Kropatsch, Dieter Willersinn), Technical report, PRIP, TU Wien, 1994.
Bibtex Entry:
@TechReport{TR022,
  author =	 "Walter G. Kropatsch and Dieter Willersinn",
  institution =	 "PRIP, TU Wien",
  number =	 "PRIP-TR-022",
  title =	 "Parallel {L}ine {G}rouping and {I}rregular {C}urve
                  {P}yramids",
  year =	 "1994",
  url =		 "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr22.ps.gz",
  abstract =	 "Parallel lines are important features for object
                  recognition by grouping. Regular 2x2/2 curve
                  pyramids are hierarchical symbolic representations
                  of curves that can be constructed and processed in
                  logarithmic time. The rigidity of the regular
                  structure causes an unstable, shift variant
                  representation of parallel lines. In order to
                  usefully apply the concept of the curve pyramid on
                  grouping problems, the shift variance problem had to
                  be overcome by extending the concept to irregular
                  pyramids. These have a structure that adapts to the
                  image data by deriving control information from
                  curve relations. The algorithm that builds the
                  irregular curve pyramid by deriving higher levels of
                  abstraction from a set of relations goes far beyond
                  merely solving the shift variance problem. It can
                  reduce the computational complexity in comparable
                  applications where all possible combinations of
                  parts have to be checked in order to reassemble
                  complex objects.",
}
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