@TechReport{TR035,
  author =	 "Walter G. Kropatsch",
  institution =	 "PRIP, TU Wien",
  number =	 "PRIP-TR-035",
  title =	 "Building {I}rregular {P}yramids by {D}ual {G}raph
                  {C}ontraction",
  year =	 "1994",
  url =		 "https://www.prip.tuwien.ac.at/pripfiles/trs/tr35.pdf",
  abstract =	 "Many image analysis tasks lead to or make use of
                  graph structures that are related through the
                  analysis process with the planar layout of a digital
                  image. This paper presents a theory that allows to
                  build different types of hierarchies on top of such
                  image graphs. The theory is based on the properties
                  of a pair of dual image graphs that the reduction
                  process should preserve, e.g. the structure of a
                  particular input graph. The reduction process is
                  controlled by decimation parameters, i.e. a selected
                  subset of vertices, called survivors, and a selected
                  subset of the graph's edges, the parent-child
                  connections. It is formally shown that two phases of
                  contractions transform a dual image graph to a dual
                  image graph built by the surviving vertices. Phase
                  one operates on the original (neighborhood) graph
                  and eliminates all non-surviving vertices. Phase two
                  operates on the dual (face) graph and eliminates all
                  degenerated faces that have been created in phase
                  one. The resulting graph preserves the structure of
                  the survivors, it is minimal and unique with respect
                  to the selected decimation parameters. The result is
                  compared with two modified specifications, the one
                  already in use for building stochastic and adaptive
                  irregular pyramids.",
}