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The accurate diagnosis of osteoporosis has gained increasing importance due to the aging of our society. Areal bone mineral density (BMD) measured by dual-energy X-ray absorptiometry (DXA) is an established criterion in the diagnosis of osteoporosis. This measure, however, is limited by its two-dimensionality. This work presents a method to reconstruct both the 3D bone shape and 3D BMD distribution of the proximal femur from a single DXA image used in clinical routine. A statistical model of the combined shape and BMD distribution is presented, together with a method for its construction from a set of quantitative computed tomography (QCT) scans. A reconstruction is acquired in an intensity based 3D-2D registration process whereby an instance of the model is found that maximizes the similarity between its projection and the DXA image. Reconstruction experiments were performed on the DXA images of 30 subjects, with a model constructed from a database of QCT scans of 85 subjects. The accuracy was evaluated by comparing the reconstructions with the same subject QCT scans. The method presented here can potentially improve the diagnosis of osteoporosis and fracture risk assessment from the low radiation dose and low cost DXA devices currently used in clinical routine.