Osteoporosis, characterized by low bone mineral density (BMD) and micro-architectural deterioration of trabecular bone (TB), increases risk of fractures associated with substantial morbidity, mortality, and financial costs. A quantitative measure of TB micro-architecture with high reproducibility, large between-subjects variability and strong association with bone strength that may be computed via in vivo imaging would be an important indicator of bone quality for clinical trials evaluating fracture risks under different clinical conditions. Previously, the notion of tensor scale (t-scale) was introduced using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. Here, we develop a new 3-D t-scale algorithm for fuzzy objects and investigate its application to compute quantitative measures characterizing TB micro-architecture acquired by in vivo multi-row detector CT (MD-CT) imaging. Specifically, new measures characterizing individual trabeculae on the continuum of a perfect plate and a perfect rod and their orientation are directly computed in a volumetric BMD representation of a TB network. Reproducibility of these measures is evaluated using repeat MD-CT scans and also by comparing their correlation between MD-CT and micro-CT imaging. Experimental results have demonstrated that the t-scale-based TB micro-architectural measures are highly reproducible with strong association of their values at MD-CT and micro-CT resolutions. Results of an experimental mechanical study have proved these measures' ability to predict TB's bone strength.