Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective

 

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dc.contributor.advisor De Jager, Gerhard en_ZA
dc.contributor.author Wohlberg, Brendt en_ZA
dc.date.accessioned 2014-11-10T08:54:59Z
dc.date.available 2014-11-10T08:54:59Z
dc.date.issued 1996 en_ZA
dc.identifier.citation Wohlberg, B. 1996. Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/9475
dc.description Bibliography: p. 208-225. en_ZA
dc.description.abstract Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Electrical Engineering en_ZA
dc.title Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective en_ZA
dc.type Doctoral Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Engineering and the Built Environment
dc.publisher.department Department of Electrical Engineering en_ZA
dc.type.qualificationlevel Doctoral
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Wohlberg, B. (1996). <i>Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering. Retrieved from http://hdl.handle.net/11427/9475 en_ZA
dc.identifier.chicagocitation Wohlberg, Brendt. <i>"Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering, 1996. http://hdl.handle.net/11427/9475 en_ZA
dc.identifier.vancouvercitation Wohlberg B. Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Electrical Engineering, 1996 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/9475 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Wohlberg, Brendt AB - Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques. DA - 1996 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1996 T1 - Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective TI - Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective UR - http://hdl.handle.net/11427/9475 ER - en_ZA


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