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On the inverse problem of fractal compression

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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

@incollection{Hartenstein2001inver-23256, title={On the inverse problem of fractal compression}, year={2001}, isbn={3-540-41290-5}, address={Berlin [u.a.]}, publisher={Springer}, 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.} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Hartenstein, Hannes</dc:creator> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <dc:contributor>Saupe, Dietmar</dc:contributor> <dspace:isPartOfCollection rdf:resource=""/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:rights>terms-of-use</dc:rights> <dc:date rdf:datatype="">2013-05-28T09:55:22Z</dc:date> <dc:contributor>Ruhl, Matthias</dc:contributor> <dcterms:issued>2001</dcterms:issued> <dcterms:isPartOf rdf:resource=""/> <dcterms:hasPart rdf:resource=""/> <dc:contributor>Hartenstein, Hannes</dc:contributor> <bibo:uri rdf:resource=""/> <dc:creator>Ruhl, Matthias</dc:creator> <dc:language>eng</dc:language> <dc:contributor>Vrscay, Edward R.</dc:contributor> <dc:creator>Vrscay, Edward R.</dc:creator> <dcterms:title>On the inverse problem of fractal compression</dcterms:title> <dspace:hasBitstream rdf:resource=""/> <dcterms:available rdf:datatype="">2013-05-28T09:55:22Z</dcterms:available> <dc:creator>Saupe, Dietmar</dc:creator> <dcterms:bibliographicCitation>Ergodic theory, analysis and efficient simulation of dynamical Systems / Bernold Fiedler (ed.). - Berlin [u.a.] : Springer, 2001. - S. 617-647. - ISBN 3-540-41290-5</dcterms:bibliographicCitation> <dcterms:rights rdf:resource=""/> </rdf:Description> </rdf:RDF>

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