The quantitative characterization of tissue probes as visualized by CT or MR is of great interest in many fields of
medical image analysis. A proper quantification of the information content in such images can be realized by calculating
well-suited texture measures, which are able to capture the main characteristics of the image structures under study.
Using test images showing the complex trabecular structure of the inner bone of a healthy and osteoporotic patient we
propose and apply a novel statistical framework, with which one can systematically assess the sensitivity of the chosen
texture measures to higher order correlations (HOCs), i.e. correlations not being captured by linear methods like the
power spectrum. To this end, so-called surrogate images are generated, in which the linear properties are preserved,
while parts or all higher order correlations are wiped out. This is achieved by dedicated Fourier phase shuffling
techniques. We compare three commonly used classes of texture measures, namely spherical Mexican hat wavelets
(SMHW), Minkowski functionals (MF) and scaling indices (SIM). While the SMHW yield only very poor sensitivity to
HOCs in both cases, the MF and SIM could detect the HOCs very well with significance up to S = 320σ (MF) and S =
150σ (SIM). The relative performance of the MF and SIM differed significantly for the healthy and osteoporotic bone.
Thus, MF and SIM are preferable for a proper quantification of the bone structure. They depict complementary aspects
of it and thus should both be used for characterising the trabecular bone.