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Lacunarity exponent and Moran index: A complementary methodology to analyze AFM images and its application to chitosan films

Author

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  • Pinto, Erveton P.
  • Pires, Marcelo A.
  • Matos, Robert S.
  • Zamora, Robert R.M.
  • Menezes, Rodrigo P.
  • Araújo, Raquel S.
  • de Souza, Tiago M.

Abstract

In this work, we developed new scripts to calculate the lacunarity exponent and Moran’s index of Atomic Force Microscopy (AFM) images. The lacunarity exponent was estimated by combining the Otsu binarization and gliding-box algorithm, and Moran index was introduced to evaluate the surfaces’ spatial autocorrelation. Developed scripts were first validated using numerical simulation of self-similar fractal and self-affine isotropic surfaces. Then, we successfully synthesized chitosan films with different glycerol concentrations and used the lacunarity and Moran’s index for a thorough characterization. The validation of the proposed scripts using simulated Sierpinski Carpets and 3D artificial surfaces showed promising potential for analyzing AFM images. Finally, the methodology application to AFM images of chitosan films suggested that lacunarity analysis and Moran index determination could complement thin films’ quality processing control.

Suggested Citation

  • Pinto, Erveton P. & Pires, Marcelo A. & Matos, Robert S. & Zamora, Robert R.M. & Menezes, Rodrigo P. & Araújo, Raquel S. & de Souza, Tiago M., 2021. "Lacunarity exponent and Moran index: A complementary methodology to analyze AFM images and its application to chitosan films," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    • Handle: RePEc:eee:phsmap:v:581:y:2021:i:c:s0378437121004659
    DOI: 10.1016/j.physa.2021.126192
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    References listed on IDEAS

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    1. Yanguang Chen, 2013. "New Approaches for Calculating Moran’s Index of Spatial Autocorrelation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
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    6. Nasehnejad, Maryam & Nabiyouni, G. & Gholipour Shahraki, Mehran, 2018. "Thin film growth by 3D multi-particle diffusion limited aggregation model: Anomalous roughening and fractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 135-147.
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