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ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa
CURRENT PROBLEMS IN REMOTE SENSING OF THE EARTH FROM SPACE

  

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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References:

  1. Berenson B. Zhivopiscy ital'janskogo Vozrozhdenija (Painters of the Italian Renaissance), Moscow: B.S.G.Press, 2006, 559 p.
  2. Knjazeva I.S., Makarenko N.G. Mul'tifraktal'nyj analiz izobrazhenij (Multifractal analysis of images), Izvestiya vuzov. Prikladnaja Nelinejnaja Dinamika, 2009, Vol. 4, pp. 85-99.
  3. Korolenko P.V., Maganova M.S., Mesnjankin A.V. Novacionnye metody analiza stohasticheskih processov i struktur v optike. Fraktal'nye i mul'tifraktal'nye metody, vejvlet-preobrazovanija (Innovatory methods of analysis of stochastic processes and structures in optics. Fractal and multifractal methods, wavelet transform) Moscow: MGU, 2004, 82 p.
  4. Makarenko N.G. Geometrija izobrazhenij (Geometry of images), Nejroinformatika 2009. Lekcii po nejroinformatike, Moscow: MIFI, 2009, pp. 89-125.
  5. Makarenko N.G., Kruglun O.A., Makarenko I.N., Karimova L.M. Mul'tifraktal'naja segmentacija dannyh distancionnogo zondirovanija (Multifractal segmentation of remote sensing data.), Issledovanie Zemli iz Kosmosa, 2008, No. 3, pp. 18-26.
  6. Pesin Ya.B. Teorija razmernosti i dinamicheskie sistemy: sovremennyj vzgljad i prilozhenija (Dimension theory in dynamical systems: Contemporary views and applications) Moscow-Izhevsk: IKI, 2002, 404 p.
  7. Rauschenbach B. V. Prostranstvennye postroenija v zhivopisi. Ocherk osnovnyh metodov (Spatial construction in painting. Basic methods), Moscow: NAUKA, 1980, 286 p.
  8. Abry P., Wendt H., Jaffard S. When Van Gogh meets Mandelbrot: Multifractal Classification of Painting’s Texture, Signal Processing, 2013, Vol. 93, pp. 554–572.
  9. Arneodo A., Decoster N., Kestener P., Roux S.G. A Wavelet-based method for multifractal image analysis: from Theoretical Concepts to Experimental Applications, Advances in Imaging and Electron Physics, 2003, Vol. 126, pp. 1-92.
  10. Chhabra A. B., Jensen R. V. Direct determination of the f (α) singularity spectrum, Phys.Rev. Lett, 1989, Vol. 62, pp. 1327-1330.
  11. Chainais P. Infinitely Divisible Cascades to Model the Statistics of Natural Images, IEEE Transact. on Pattern Analysis and Machine Intelligence, 2007, Vol. 29, No. 12, pp. 1-15.
  12. Chainais P., Kœnig E., Delouille V., Hochedez J-F. Virtual super resolution of textured images using multifractal stochastic processes, J. of Mathem. Imaging and Vision, 2011, Vol. 39, pp. 28-44.
  13. Falconer K. Techniques in fractal geometry, John Wiley & Sons, 1997, 256 p.
  14. Field D.J. Relations between the statistics of natural images and the response properties of cortical cells, J. Opt. Soc. Am. A., 1987, Vol. 4, pp. 2379-2394.
  15. Field D.J. What the statistics of natural images tell us about visual coding, Human Vision, Visual Procsssing and Digital Display, 1989, Vol. 1077, pp. 269-276.
  16. Harte D. Multifractals: Theory and Applications, Chapman & Hall/CRC, 2001, 248 p.
  17. Laughlin S. B., Matching coding scenes to enhance efficiency, In: Physical and Biological Processing of Images, Springer, Berlin, 1983, pp. 42-72.
  18. Lee A. B., Pedersen K. S., Mumford D. The Nonlinear Statistics of High-Contrast Patches in Natural Images, Intern. J. of Comp.Vis., 2003, Vol. 54, pp. 83–103.
  19. Marr D. Vision, MIT Press, 2010, 403 p.
  20. Mumford D., Desolneux A. Pattern Theory. The Stochastic Analysis of Real-World Signals, A K Peters, Ltd., Natick, Massachusetts, 2010, 400 p.
  21. Nevado A., Turiel A., Parga N. Scene dependence of the non-gaussian scaling properties of natural images, Network: Computation in Neural Systems, 2000, Vol. 11, pp. 131–152.
  22. Rudermant D.L. The statistics of natural images, Network: Computation in Neural Systems, 1994, Vol. 5, pp. 517-548.
  23. Turiel A., Mato G., Parga N. The self-similarity properties of natural images resemble those of turbulent flows, Phys. Rev. Lett., 1998, Vol. 80(5), pp. 1098-1101.
  24. Turiel A., Isern-Fontanet J, Garcia-Ladona E, Font J. Multifractal Method for the Instantaneous Evaluation of the Stream Function in Geophysical Flows, Phys. Rev. Lett., 2005, Vol. 95, pp. 104502.
  25. Turiel A., Nieves V., Garcia-Ladona E., Font J., Rio M.-H., Larnicol G. The multifractal structure of satellite sea surface temperature maps can be used to obtain global maps of streamlines, Ocean Sci., 2009, Vol. 5, pp. 447–460.
  26. Wendt H., Rouxa St. G., Jaffard St., Abry P. Wavelet leaders and bootstrap for multifractal analysis of images, Signal Proces., 2009, Vol. 89, pp. 1100-1114.
  27. Wendt H., Abry P., Jaffard S., Hui Ji. Wavelet leader multifractal analysis for texture classification, IEEE Int. Conf. on Image Processing, Cairo, Egypt, 2009, pp. 3829-3832.
  28. Xu Y., Ji H., Fermüller C. Viewpoint invariant texture description using fractal analysis, Intern. J. of Computer Vision, 2009, Vol. 83 (1), pp. 85-100.