Iterated Function Systems; A Direct Discrete Approach with Pyramids (bibtex)
by Michael A. Neuhauser, Irene J. Leitgeb
Abstract:
Iterated Function Systems (IFS) are sets of contractive transformations. They define a unique attractor which can be interpreted as a binary image. Since IFS with few transformations can generate very complex images, they can be used for image compression. The difficulty lies in finding an IFS that approximates a given image well; this is known as the inverse problem. We show a new way of computing the discrete attractor of an IFS directly for a specific screen resolution. The run time efficiency of this algorithm is improved by the use of image pyramids. Furthermore, some ideas for approaching the inverse problem from a new direction are presented. We discuss the 1D case with the intention of using the so gained experience in 2D.
Reference:
Iterated Function Systems; A Direct Discrete Approach with Pyramids (Michael A. Neuhauser, Irene J. Leitgeb), Technical report, PRIP, TU Wien, 1992.
Bibtex Entry:
@TechReport{PP-Neuhauser92a,
  author =	 "Michael A. Neuhauser and Irene J. Leitgeb",
  institution =	 "PRIP, TU Wien",
  number =	 "PRIP-TR-013",
  title =	 "Iterated {F}unction {S}ystems; {A} {D}irect
                  {D}iscrete {A}pproach with {P}yramids",
  year =	 "1992",
  url =		 "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr13.ps.gz",
  abstract =	 "Iterated Function Systems (IFS) are sets of
                  contractive transformations. They define a unique
                  attractor which can be interpreted as a binary
                  image. Since IFS with few transformations can
                  generate very complex images, they can be used for
                  image compression. The difficulty lies in finding an
                  IFS that approximates a given image well; this is
                  known as the inverse problem. We show a new way of
                  computing the discrete attractor of an IFS directly
                  for a specific screen resolution. The run time
                  efficiency of this algorithm is improved by the use
                  of image pyramids. Furthermore, some ideas for
                  approaching the inverse problem from a new direction
                  are presented. We discuss the 1D case with the
                  intention of using the so gained experience in 2D.",
}
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