Osteoporosis is bone disease which leads to low bone mass and the deterioration of the bone micro-architecture. Rarefied bone structures are more susceptible to fractures which are the worst complications of osteoporosis. Bone mineral density is considered to be the standard technique for predicting the bone strength and the effects of drug therapy. However, other properties of the bone like the trabecular structure and connectivity may also contribute. Here, we analyze μ-CT tomographic images for a sample of 151 specimens taken from human vertebrae in vitro. Using the local structural characterization of the bone trabecular network given by isotropic and anisotropic scaling indices, we generate structural decompositions of the μ-CT image and quantify the resulting patterns applying topological measures, namely the Minkowski Functionals (MF). The values of the MF are then used to assess the biomechanical properties of trabecular bone via a correlation analysis. Biomechanical properties were quantified by the maximum compressive strength calculated in an uniaxial compression test. We compare our results with those obtained using standard global histomorphometric parameters and the bone fraction BV/TV . Results obtained using structural decompositions obtained from anisotropic scaling indices were superior to those given by isotropic scaling indices. The highest correlation coefficient (r = 0.72) was better than those obtained for the standard global histomorphometric parameters and only comparable with the one given by BV/TV. Our results suggest that plate-like and dense column-like structures aligned along the direction of the external force play a relevant role for the prediction of bone strength.