ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa


Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2014, Vol. 11, No. 2, pp. 26-37

Scaling properties of digital images of Earth landscape

N.G. Makarenko1,2 , L.M. Karimova2 , O.N. Kruglun2 
1 Central Astronomical Observatory RAS, Saint-Petersburg, Russia
2 Institute for Information Science and Management Problems Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan
Properties of scale invariance are usually associated with power statistics in the distribution of samples. This invariance or scaling appears asymptotically as heavy-tails of some distributions or explicitly, as the laws of Pareto-type distribution of random variables. Power function retains its shape when zooming. This property is abstracted as a statistical self-similarity of the data samples or multifractality of the measure. A quantitative description of statistical self-similarity reduces to estimating the multifractal spectrum. There are two approaches to obtaining such estimates. The first is based on the microcanonical formalism and reduces to the calculation of local exponents Holder for suitable measures. Spectrum itself is then obtained using the histograms. The second approach is based on the canonical formalism and computing the moments of the partition function. In this case, the local behavior of the measures can describe the number of the moment and the time corresponding generalized Renyi dimensions. The transition to the adjoint Legendre variables leads to multifractal spectrum. It has long been observed that most of the high-contrast digital images of terrestrial landscapes have attributes of power statistics. In this paper, we estimate multifractal spectra for such images. The existence of such spectra allows to correctly apply the methods of multifractal segmentation to remote sensing images.
Keywords: power asymptotics, multifractality, Choquet capacities, data of remote sensing, statistics of heavy tails
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