A Relative Fractal Dimension Spectrum for a Perceptual Complexity Measure

W. Kinsner and R. Dansereau
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W. Kinsner: University of Manitoba, Canada
R. Dansereau: University of Manitoba, Canada

International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), 2008, vol. 2, issue 1, 73-86

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.

Date: 2008
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