On the inverse problem of fractal compression

Hartenstein, Hannes; Ruhl, Matthias; Saupe, Dietmar; Vrscay, Edward R.

On the inverse problem of fractal compression

Dateien

hartenstein_232562.pdfGröße: 2.03 MBDownloads: 339

Datum

2001

Autor:innen

Hartenstein, Hannes

Ruhl, Matthias

Saupe, Dietmar

Vrscay, Edward R.

Publikationstyp

Beitrag zu einem Sammelband

Publikationsstatus

Published

Erschienen in

FIEDLER, Bernold, ed.. Ergodic theory, analysis and efficient simulation of dynamical Systems. Berlin [u.a.]: Springer, 2001, pp. 617-647. ISBN 3-540-41290-5

Zusammenfassung

The inverse problem of fractal compression amounts to determining a contractive operator such that the corresponding fixed point approximates a given target function. The standard method based on the collage coding strategy is known to represent a suboptimal method. Why does one not search for optimal fractal codes? We will prove that optimal fractal coding, when considered as a discrete optimization problem, constitutes an NP-hard problem, i.e., it cannot be solved in a practical amount of time. Nevertheless, when the fractal code parameters are allowed to vary continuously, we show that one is able to improve on collage coding by fine-tuning some of the fractal code parameters with the help of differential methods. The differentiability of the attractor as a function of its luminance parameters is established. We also comment on the approximating behaviour of collage coding, state a lower bound for the optimal attractor error, and outline an annealing scheme for improved fractal coding.

Fachgebiet (DDC)

004 Informatik

Zitieren

ISO 690

HARTENSTEIN, Hannes, Matthias RUHL, Dietmar SAUPE, Edward R. VRSCAY, 2001. On the inverse problem of fractal compression. In: FIEDLER, Bernold, ed.. Ergodic theory, analysis and efficient simulation of dynamical Systems. Berlin [u.a.]: Springer, 2001, pp. 617-647. ISBN 3-540-41290-5

BibTex

@incollection{Hartenstein2001inver-23256,
  year={2001},
  title={On the inverse problem of fractal compression},
  isbn={3-540-41290-5},
  publisher={Springer},
  address={Berlin [u.a.]},
  booktitle={Ergodic theory, analysis and efficient simulation of dynamical Systems},
  pages={617--647},
  editor={Fiedler, Bernold},
  author={Hartenstein, Hannes and Ruhl, Matthias and Saupe, Dietmar and Vrscay, Edward R.}
}

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