Measures of complexity for 3D image analysis of trabecular bone
Nonlinear Dynamics Group, Institute of Physics, University of Potsdam, 14415 Potsdam, Germany
2 Department of Biomaterials, Max-Planck-Institute of Colloids and Interfaces, 14424 Potsdam-Golm, Germany
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.
© EDP Sciences, Springer-Verlag, 2007