Inverse and approximation problem for two-dimensional fractal sets
The geometry of fractals is rich enough that they have extensively been used to model natural phenomena and images. Iterated function systems (IFS) theory provides a convenient way to describe and classify deterministic fractals in the form of a recursive definition. As a result, it is conceivable t...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 3(1994), 6 vom: 15., Seite 802-20 |
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| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1994
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Journal Article |
| Zusammenfassung: | The geometry of fractals is rich enough that they have extensively been used to model natural phenomena and images. Iterated function systems (IFS) theory provides a convenient way to describe and classify deterministic fractals in the form of a recursive definition. As a result, it is conceivable to develop image representation schemes based on the IFS parameters that correspond to a given fractal image. In this paper, we consider two distinct problems: an inverse problem and an approximation problem. The inverse problem involves finding the IFS parameters of a signal that is exactly generated via an IFS. We make use of the wavelet transform and of the image moments to solve the inverse problem. The approximation problem involves finding a fractal IFS-generated image whose moments match, either exactly or in a mean squared error sense, a range of moments of the original image. The approximating measures are generated by an IFS model of a special form and provide a general basis for the approximation of arbitrary images. Experimental results verifying our approach will be presented |
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| Beschreibung: | Date Completed 02.10.2012 Date Revised 25.02.2008 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1057-7149 |