Recent advances combining outer images and deep-learning algorithms (DLA) show promising results in the detection and the characterization of the Adolescent Idiopathic Scoliosis (AIS). However, these methods are providing a limited 2D characterization while scoliosis is defined in 3D. In this study we propose an inference method that takes as input a depth map of the back of a person and outputs the 3D shape estimation of the thoracolumbar spine. Our DLA method predicts 3D vertebrae positions with an average 3D error of 7.1mm (std: 4.7mm). From the predicted 3D positions, scoliosis can be located and estimated with a mean absolute error (MAE) of 5.5° (std: 6.2°) in the frontal plane. Moreover, sagittal alignments can be estimated with a MAE of 6.4° (std: 5.5°) in kyphosis and 8.3° (std: 6.8°) in lordosis. In addition, our nonionizing approach can detect scoliosis with an accuracy of 89%.