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Helmut Ahammer1, Nikolaus Sabathiel1, Martin A Reiss1

  • 1Institute of Biophysics, Centre of Physiological Medicine, Medical University of Graz, Graz A-8010, Austria.

Chaos (Woodbury, N.Y.)
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Area of Science:

  • Image analysis and fractal geometry.

Background:

  • Fractal dimensions quantify data complexity, with Higuchi's algorithm being a reliable 1D method.
  • Extending fractal dimension estimation to 2D digital images is a significant research need.

Purpose of the Study:

  • To propose and evaluate several 2D generalized Higuchi algorithms for digital image analysis.
  • To compare these new algorithms against existing pseudo-2D methods and other established techniques.

Main Methods:

  • Development of novel 2D generalization algorithms for Higuchi's fractal dimension estimation.
  • Testing algorithms on artificially generated grayscale and RGB color images.
  • Comparative analysis with pseudo-2D generalizations, Fourier, and Blanket methods.

Main Results:

  • The proposed 2D generalized Higuchi algorithms demonstrate high robustness in image analysis.
  • Differences between the proposed 2D generalizations and pseudo-2D methods were found to be minimal.
  • The study validates the applicability of generalized Higuchi algorithms for 2D data.

Conclusions:

  • The developed 2D Higuchi algorithms are effective and robust for analyzing digital images.
  • The proposed methods offer a reliable extension of 1D fractal analysis to 2D image data.
  • Further research can explore these algorithms for diverse image processing applications.