On the inverse problem of fractal compression

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

On the inverse problem of fractal compression

Files

hartenstein_232562.pdf(2.03 MB)

Date

2001

Authors

Hartenstein, Hannes

Ruhl, Matthias

Saupe, Dietmar

Vrscay, Edward R.

Publication type

Contribution to a collection

Published in

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

Abstract

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.

Subject (DDC)

004 Computer Science

Cite This

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, 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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