Iterierte Funktionensysteme - Das eindimensionale inverse Problem (bibtex)

by Irene J. Leitgeb

Abstract:

Since images of natural objects often have fractal features, Iterated Function Systems (IFS) seem quite suited for their representation in computers. A further reason to use IFS is their low requirements of memory. An IFS is a set of contractive functions that defines a fractal attractor; this attractor can be interpreted as a binary image. First of all, an explanation of IFS and the inverse problem will be given in this work, followed by an outline of existing approaches to the solution of the inverse problem. A brief introduction to the mathematical basis of IFS will then be given. Then an algorithm is presented that is based upon existing discretisation of transformations of an IFS and algorithms that find a discrete attractor of an IFS. The algorithm solves the inverse problem in the 1D case. It uses the ratio of the length of the black and the white connected components of an attractor which is invariant under the transformations of an IFS. In the discrete case an interval can be defined for this ratio. This information is used to find possible transformations. In consideration of sampling effects, the algorithm tries then to find the parameters for each possible transformation if they exist.

Reference:

Iterierte Funktionensysteme - Das eindimensionale inverse Problem (Irene J. Leitgeb), Technical report, PRIP, TU WIEN, 1993.

Bibtex Entry:

@TechReport{TR023, author = "Irene J. Leitgeb", institution = "PRIP, TU WIEN", number = "PRIP-TR-023", title = "Iterierte {F}unktionensysteme - {D}as eindimensionale inverse {P}roblem", year = "1993", url = "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr23.pdf", abstract = "Since images of natural objects often have fractal features, Iterated Function Systems (IFS) seem quite suited for their representation in computers. A further reason to use IFS is their low requirements of memory. An IFS is a set of contractive functions that defines a fractal attractor; this attractor can be interpreted as a binary image. First of all, an explanation of IFS and the inverse problem will be given in this work, followed by an outline of existing approaches to the solution of the inverse problem. A brief introduction to the mathematical basis of IFS will then be given. Then an algorithm is presented that is based upon existing discretisation of transformations of an IFS and algorithms that find a discrete attractor of an IFS. The algorithm solves the inverse problem in the 1D case. It uses the ratio of the length of the black and the white connected components of an attractor which is invariant under the transformations of an IFS. In the discrete case an interval can be defined for this ratio. This information is used to find possible transformations. In consideration of sampling effects, the algorithm tries then to find the parameters for each possible transformation if they exist.", }

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