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Statistical analysis of digital images of periodic fibrous structures using generalized Hurst exponent distributions

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  • Blachowicz, Tomasz
  • Ehrmann, Andrea
  • Domino, Krzysztof

Abstract

Distinction of diverse two-dimensional periodic structures can be based on a large number of methods and parameters, while the quantitative description of differences between similar samples is usually difficult. This article aims, by the use of statistical random walk in a generalized q-order dimensional space, at introducing a methodology to qualify the networked structures on the basis of exemplary textile samples. The presented results were obtained at 1-bit monochromatic maps obtained from optical microscopic pictures. Significant features of samples were represented by the obtained distributions of Hurst exponents and Shannon entropy calculations.

Suggested Citation

  • Blachowicz, Tomasz & Ehrmann, Andrea & Domino, Krzysztof, 2016. "Statistical analysis of digital images of periodic fibrous structures using generalized Hurst exponent distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 167-177.
    • Handle: RePEc:eee:phsmap:v:452:y:2016:i:c:p:167-177
    DOI: 10.1016/j.physa.2016.02.013
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    References listed on IDEAS

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    1. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    2. Blachowicz, T. & Cwikiel, K. & Binkowski, M. & Zghidi, H., 2015. "Analysis of the three-dimensional TGS crystal spatial inhomogeneity of the fractal structure," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 185-190.
    3. Chan, Ngai Hang & Chen, Song Xi & Peng, Liang & Yu, Cindy L., 2009. "Empirical Likelihood Methods Based on Characteristic Functions With Applications to Lévy Processes," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1621-1630.
    4. Xi-Yuan Qian & Ya-Min Liu & Zhi-Qiang Jiang & Boris Podobnik & Wei-Xing Zhou & H. Eugene Stanley, 2015. "Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces," Papers 1504.02435, arXiv.org, revised Apr 2015.
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    Cited by:

    1. Lotfalinezhad, Hamze & Maleki, Ali, 2020. "TTA, a new approach to estimate Hurst exponent with less estimation error and computational time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    2. Lifeng Wu & Xiaohui Gao & Yan Chen, 2019. "Memory Property of Grey Accumulation Generation Sequence," Complexity, Hindawi, vol. 2019, pages 1-10, July.

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