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{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 = "ftp://ftp.prip.tuwien.ac.at/pub/publications/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.", }

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