Trabecular bone (TB) is a complex quasi-random network of interconnected struts and plates. TB constantly remodels to adapt dynamically to the stresses to which it is subjected (Wolff's Law). In osteoporosis, this dynamic equilibrium between bone formation and resorption is perturbed, leading to bone loss and structural deterioration, both increasing fracture risk. Bone's mechanical competence can only be partly explained by variations in bone mineral density, which led to the notion of bone structural quality. Previously, we developed digital topological analysis or DTA which classifies plates, rods, profiles, edges and junctions in a TB skeletal representation. Although the method has become quite popular, a major limitation is that DTA produces hard classifications only, failing to distinguish between narrow and wide plates. Here, we present a new method called volumetric topological analysis or VTA for quantification of regional topology in complex quasi-random TB networks. At each TB voxel, the method uniquely classifies the topology on the continuum between perfect plates and rods. Therefore, the method is capable of detecting early alterations of trabeculae from plates to rods according to the known etiology of osteoporotic bone loss. Here, novel ideas of geodesic distance transform, geodesic scale and feature propagation have been introduced and combined with DTA and fuzzy distance transform methods conceiving the new VTA technology. The method has been applied to MDCT and μCT images of a cadaveric distal tibia specimen and the results have been quantitatively evaluated. Specifically, intra- and inter-modality reproducibility of the method has been examined and the results are found very promising.