The mechanical competence of trabecular bone is a function of its apparent density and three‐dimensional (3D) distribution. Three‐dimensional structure is typically inferred from histomorphometry and stereology on a limited number of two‐dimensional anatomic sections. In this work 3D nuclear magnetic resonance (NMR) images of anisotropic trabecular bone from the distal radius were analyzed in terms of a series of new structural parameters which are obtainable at relatively crude resolution, i.e., in the presence of substantial partial volume blurring. Unlike typical feature extraction techniques requiring image segmentation, the method relies on spatial autocorrelation analysis, which is based on the probability of finding bone at specified locations. The structural parameters were measured from high‐resolution images (78×78×78 μm³ voxels) of 23 trabecular bone specimens from the distal radius. Maximum‐likelihood bone volume fractions (BVF) were calculated for each voxel and a resolution achievable in vivo (156×156×156 μm³ voxels) was simulated by averaging BVF's from neighboring voxels. The parameters derived from the low‐resolution images were found to account for 91% of the variation in Young's modulus. The results suggest that noninvasive assessment of the mechanical competence of trabecular bone in osteoporotic patients may be feasible.