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A Relative Fractal Dimension Spectrum for a Perceptual Complexity Measure

A Relative Fractal Dimension Spectrum for a Perceptual Complexity Measure

W. Kinsner, R. Dansereau
Copyright: © 2008 |Volume: 2 |Issue: 1 |Pages: 14
ISSN: 1557-3958|EISSN: 1557-3966|ISSN: 1557-3958|EISBN13: 9781615201952|EISSN: 1557-3966|DOI: 10.4018/jcini.2008010106
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MLA

Kinsner, W., and R. Dansereau. "A Relative Fractal Dimension Spectrum for a Perceptual Complexity Measure." IJCINI vol.2, no.1 2008: pp.73-86. http://doi.org/10.4018/jcini.2008010106

APA

Kinsner, W. & Dansereau, R. (2008). A Relative Fractal Dimension Spectrum for a Perceptual Complexity Measure. International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), 2(1), 73-86. http://doi.org/10.4018/jcini.2008010106

Chicago

Kinsner, W., and R. Dansereau. "A Relative Fractal Dimension Spectrum for a Perceptual Complexity Measure," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI) 2, no.1: 73-86. http://doi.org/10.4018/jcini.2008010106

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Abstract

This article presents a derivation of a new relative fractal dimension spectrum, DRq, to measure the dissimilarity between two finite probability distributions originating from various signals. This measure is an extension of the Kullback-Leibler (KL) distance and the Rényi fractal dimension spectrum, Dq. Like the KL distance, DRq determines the dissimilarity between two probability distibutions X and Y of the same size, but does it at different scales, while the scalar KL distance is a single-scale measure. Like the Rényi fractal dimension spectrum, the DRq is also a bounded vectorial measure obtained at different scales and for different moment orders, q. However, unlike the Dq, all the elements of the new DRq become zero when X and Y are the same. Experimental results show that this objective measure is consistent with the subjective mean-opinion-score (MOS) when evaluating the perceptual quality of images reconstructed after their compression. Thus, it could also be used in other areas of cognitive informatics.

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