Analysis of Dynamic Processes by Statistical Moments of High Orders

  • Stanislava Šimberová
  • Tomáš Suk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8258)


We present a new approach to image analysis in temporal sequence of images (data cube). Our method is based on high-order statistical moments (skewness and kurtosis) giving interesting information about a dynamic event in the temporal sequence. The moments enable precise determination of the ”turning points” in the temporal sequence of images. The moment’s curves are analyzed by continuous complex Morlet wavelet that leads to the description of quasi-periodic processes in the investigated event as a time sequence of local spectra. These local spectra are compared with Fourier spectrum. We experimentally illustrate the performance on the real data from astronomical observations.


Statistical moments Frequency analysis Fourier and wavelet transformations Dynamic processes 


  1. 1.
    Dudewicz, E.J., Mishra, S.N.: Modern Mathematical Statistics. Wiley and Sons, New York (1988)zbMATHGoogle Scholar
  2. 2.
    Flusser, J., Suk, T., Zitová, B.: Moments and Moment Invariants in Pattern Recognition. Wiley, Chichester (2009)CrossRefzbMATHGoogle Scholar
  3. 3.
    Coles, P., Jones, B.: A lognormal model for the cosmological mass distribution. Monthly Notices of the Royal Astronomical Society 248, 1–13 (1991)Google Scholar
  4. 4.
    Burkhart, B., Falceta-Gonçalves, D., Kowal, G., Lazarian, A.: Density Studies of MHD Interstellar Turbulence: Statistical Moments, Correlations and Bispectrum. Astronomical Journal 693, 250–266 (2009)Google Scholar
  5. 5.
    Takada, M., Jain, B.: The kurtosis of the cosmic shear field. Monthly Notices of the Royal Astronomical Society 337, 875–894 (2002)CrossRefGoogle Scholar
  6. 6.
    Pain, J.C., Gilleron, F., Bauche, J., Bauche-Arnoult, C.: Effect of third- and fourth-order moments on the modeling of unresolved transition arrays. High Energy Density Physics 5, 294–301 (2009)CrossRefGoogle Scholar
  7. 7.
    Grossi, M., Branchini, E., Dolag, K., Matarrese, S., Moscardini, L.: The mass density field in simulated non-Gaussian scenarios. Monthly Notices of the Royal Astronomical Society 390, 438–446 (2008)CrossRefGoogle Scholar
  8. 8.
    Nita, G.M., Gary, D.E.: The generalized spectral kurtosis estimator. Monthly Notices of the Royal Astronomical Society 406, L60–L64 (2010)Google Scholar
  9. 9.
    Nita, G.M., Gary, D.E.: Statistics of the Spectral Kurtosis Estimator. Publications of the Astronomical Society 122, 595–607 (2010)CrossRefGoogle Scholar
  10. 10.
    Alipour, N., Safari, H., Innes, D.E.: An Automatic Detection Method for Extreme-ultraviolet Dimmings Associated with Small-scale Eruption. Astronomical Journal 746, 12 (2012)Google Scholar
  11. 11.
    Marr, D., Hildreth, E.: Theory of edge detection. Proceedings of the Royal Society of London. Series B, Biological Sciences 207(1167), 187–217 (1980)CrossRefGoogle Scholar
  12. 12.
    Li, H.: Complex Morlet wavelet amplitude and phase map based bearing fault diagnosis. In: Proceedings of the 8th World Congress on Intelligent Control and Automation, pp. 6923–6926. IEEE (July 2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stanislava Šimberová
    • 1
  • Tomáš Suk
    • 2
  1. 1.Astronomical InstituteAcademy of Sciences of the Czech RepublicOndřejovCzech Republic
  2. 2.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPrague 8Czech Republic

Personalised recommendations