Star length distribution: a volume-based concept for the characterization of structural anisotropy

Determination and quantification of anisotropy is of great interest in research fields dealing with physical structures or surface textures. In this paper, a volume-based method is presented, which essentially determines the mean object length in a certain direction for a typical point within a structure or texture. The mean object lengths for all orientations together form the so-called star length distribution (SLD). The validity and the accuracy of the SLD method are investigated, and illustrated by applying it to trabecular bone. By using a line sampling algorithm, the relation with other anisotropy measures could be studied analytically. Preliminary tests suggest that with SLD a more exact description of the mechanical properties of porous structures may be obtained than with other anisotropy measures. However, due to possible secondary orientations that become apparent with SLD, a fabric tensor must be of rank higher than two in order to properly describe an orthogonal structure mathematically.