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Translation and rotation invariant method of Renyi dimension estimation

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  • Dlask, Martin
  • Kukal, Jaromir

Abstract

A fractal dimension is a non-integer characteristic that measures the space filling of an arbitrary set. The conventional methods usually provide a biased estimation of the fractal dimension, and therefore it is necessary to develop more complex methods for its estimation. A new characteristic based on the Parzen estimate formula is presented, and for the analysis of correlation dimension, a novel approach that employs the log-linear dependence of a modified Renyi entropy is used. The new formula for the Renyi entropy has been investigated both theoretically and experimentally on selected fractal sets.

Suggested Citation

  • Dlask, Martin & Kukal, Jaromir, 2018. "Translation and rotation invariant method of Renyi dimension estimation," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 536-541.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:536-541
    DOI: 10.1016/j.chaos.2018.07.030
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    References listed on IDEAS

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    1. Nie, Chun-Xiao, 2017. "Correlation dimension of financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 632-639.
    2. Dlask, Martin & Kukal, Jaromir, 2017. "Application of rotational spectrum for correlation dimension estimation," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 256-262.
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    Cited by:

    1. Dlask, Martin & Kukal, Jaromir, 2022. "Hurst exponent estimation of fractional surfaces for mammogram images analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

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