The European Physical Journal Special Topics

, Volume 143, Issue 1, pp 109–116 | Cite as

Measures of complexity for 3D image analysis of trabecular bone

  • N. Marwan
  • P. Saparin
  • J. Kurths


Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.


Bone Loss Trabecular Bone European Physical Journal Special Topic Proximal Tibia Characteristic Length Scale 
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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • N. Marwan
    • 1
  • P. Saparin
    • 2
  • J. Kurths
    • 1
  1. 1.Nonlinear Dynamics Group, Institute of Physics, University of PotsdamPotsdamGermany
  2. 2.Department of BiomaterialsMax-Planck-Institute of Colloids and InterfacesPotsdam-GolmGermany

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