  We propose a method for estimating the bone mineral density (BMD) from a
plain x-ray image. Dual-energy X-ray absorptiometry (DXA) and quantitative
computed tomography (QCT) provide high accuracy in diagnosing osteoporosis;
however, these modalities require special equipment and scan protocols.
Measuring BMD from an x-ray image provides an opportunistic screening, which is
potentially useful for early diagnosis. The previous methods that directly
learn the relationship between x-ray images and BMD require a large training
dataset to achieve high accuracy because of large intensity variations in the
x-ray images. Therefore, we propose an approach using the QCT for training a
generative adversarial network (GAN) and decomposing an x-ray image into a
projection of bone-segmented QCT. The proposed hierarchical learning improved
the robustness and accuracy of quantitatively decomposing a small-area target.
The evaluation of 200 patients with osteoarthritis using the proposed method,
which we named BMD-GAN, demonstrated a Pearson correlation coefficient of 0.888
between the predicted and ground truth DXA-measured BMD. Besides not requiring
a large-scale training database, another advantage of our method is its
extensibility to other anatomical areas, such as the vertebrae and rib bones.
