Equivalence of mean intercept length and gradient fabric tensors – 3d study

In this study the relationship between the mean intercept length (MIL) method – the current standard histomorphometric method of assessing structural anisotropy and an alternative method of the gray-level structure tensor (GST) is investigated. Both methods are applied to a set of 25 three-dimensional binary μCT images of trabecular bone. It is shown that there is a very strong correlation between the logarithms of the principal values of the MIL and the GST fabric tensors (Pearson's coefficient of correlation higher than 0.98) and between the logarithms of the invariants of the MIL and the GST fabric tensors (Pearson's coefficient of correlation higher than 0.999). There is also a good correlation between the degree of anisotropy calculated from the MIL and from the GST tensors (Pearson's coefficient of correlation equal to 0.90). The principal anisotropy directions of the MIL and the GST fabric tensors coincide at the 5% significance level. Additionally, the performance of both methods is tested, based on a set of artificial structures with prescribed orientations.