Minimal Combinatorial Maps for analyzing 3D Data (bibtex)
by Thomas Illetschko
Abstract:
Combinatorial maps and irregular pyramids based on combinatorial maps for 2D data have been studied in great detail. It has been shown that this concept is advantageous for many applications in the field of image processing and pattern recognition by providing means to store information of the topological relation of the represented data. While the concept of combinatorial maps has been defined for any dimension, most of the studies concentrated on the representation of two dimensional data and only few results exist regarding higher dimensions. This report studies the properties of combinatorial maps for 3D data. Especially collapsing an initial map of the volumetric data by applying contraction and removal operations to produce a minimal representation while preserving the topological relations is presented in this report. Formal conditions for applying these operations as well as the minimal configurations of the topological relations found in volumetric data are presented in this report and means for discriminating and identifying these minimal configurations using pseudo elements are introduced.
Reference:
Minimal Combinatorial Maps for analyzing 3D Data (Thomas Illetschko), Technical report, PRIP, TU Wien, 2006.
Bibtex Entry:
@TechReport{TR110,
  author =	 "Thomas Illetschko",
  title =	 "Minimal Combinatorial Maps for analyzing 3D Data",
  institution =	 "PRIP, TU Wien",
  number =	 "PRIP-TR-110",
  year =	 "2006",
  url =		 "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr110.pdf",
  abstract =	 "Combinatorial maps and irregular pyramids based on
                  combinatorial maps for 2D data have been studied in
                  great detail. It has been shown that this concept is
                  advantageous for many applications in the field of
                  image processing and pattern recognition by
                  providing means to store information of the
                  topological relation of the represented data. While
                  the concept of combinatorial maps has been defined
                  for any dimension, most of the studies concentrated
                  on the representation of two dimensional data and
                  only few results exist regarding higher
                  dimensions. This report studies the properties of
                  combinatorial maps for 3D data. Especially
                  collapsing an initial map of the volumetric data by
                  applying contraction and removal operations to
                  produce a minimal representation while preserving
                  the topological relations is presented in this
                  report. Formal conditions for applying these
                  operations as well as the minimal configurations of
                  the topological relations found in volumetric data
                  are presented in this report and means for
                  discriminating and identifying these minimal
                  configurations using pseudo elements are
                  introduced.",
}
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