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{TR013,
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 = "https://www.prip.tuwien.ac.at/pripfiles/trs/tr13.pdf",
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.",
}