Computing Homology Group Generators of Images Using Irregular Graph Pyramids (bibtex)
by Samuel Peltier, Adrian Ion, Yll Haxhimusa, Walter G. Kropatsch
Abstract:
We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure i.e. an irregular graph pyramid. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on the top level of the pyramid, since the number of cells is small, and a top down process is then used to deduce homology generators in any level of the pyramid, including the base level i.e. the initial image. We show that the new method produces valid homology generators and present some experimental results. In this report we also show that the generators of the first homology groups of a 2D image, computed with this pyramid based method always fit on the borders of the regions.
Reference:
Computing Homology Group Generators of Images Using Irregular Graph Pyramids (Samuel Peltier, Adrian Ion, Yll Haxhimusa, Walter G. Kropatsch), Technical report, PRIP, TU Wien, 2006.
Bibtex Entry:
@TechReport{TR111,
  author =	 "Samuel Peltier and Adrian Ion and Yll Haxhimusa and Walter G. Kropatsch",
  title =	 "Computing Homology Group Generators of Images Using Irregular Graph Pyramids",
  institution =	 "PRIP, TU Wien",
  number =	 "PRIP-TR-111",
  year =	 "2006",
  url =		 "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr111.pdf",
  abstract =	 "We introduce a method for computing homology groups and their
   generators of a 2D image, using a hierarchical structure i.e. an irregular graph
   pyramid. Instead of computing homology generators in the base where the number of
   entities (cells) is large, we first reduce the number of cells by a graph pyramid.
   Then homology generators are computed efficiently on the top level of the pyramid,
   since the number of cells is small, and a top down process is then used to deduce
   homology generators in any level of the pyramid, including the base level i.e. the
   initial image. We show that the new method produces valid homology generators and 
   present some experimental results. In this report we also show that the generators 
   of the first homology groups of a 2D image, computed with this pyramid based method 
   always fit on the borders of the regions.",
}
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