The spine is an articulated, 3D structure with 6 degrees of translational and rotational freedom. Clinical studies have shown spinal deformities are associated with pain and functional disability in both adult and pediatric populations. Clinical decision making relies on accurate characterization of the spinal deformity and monitoring of its progression over time. However, Cobb angle measurements are time-consuming, are limited by interobserver variability, and represent a simplified 2D view of a 3D structure. Instead, spine deformities can be described by 3D shape parameters, addressing the limitations of current measurement methods. To this end, we develop and validate a deep learning algorithm to automatically extract the vertebral midline (from the upper endplate of S1 to the lower endplate of C7) for frontal and lateral radiographs. Our results demonstrate robust performance across datasets and patient populations. Approximations of 3D spines are reconstructed from the unit normalized midline curves of 20,118 pairs of full spine radiographs belonging to 15,378 patients acquired at our institution between 2008 and 2020. The resulting 3D dataset is used to describe global imbalance parameters in the patient population and to build a statistical shape model to describe global spine shape variations in preoperative deformity patients via eight interpretable shape parameters. The developed method can identify patient subgroups with similar shape characteristics without relying on an existing shape classification system.