In this work we propose to use Deep Learning to automatically calculate the coordinates of the vertebral corners in sagittal x-rays images of the thoracolumbar spine and, from those landmarks, to calculate relevant radiological parameters such as L1–L5 and L1–S1 lordosis and sacral slope. For this purpose, we used 10,193 images annotated with the landmarks coordinates as the ground truth. We realized a model that consists of 2 steps. In step 1, we trained 2 Convolutional Neural Networks to identify each vertebra in the image and calculate the landmarks coordinates respectively. In step 2, we refined the localization using cropped images of a single vertebra as input to another convolutional neural network and we used geometrical transformations to map the corners to the original image. For the localization tasks, we used a differentiable spatial to numerical transform (DSNT) as the top layer. We evaluated the model both qualitatively and quantitatively on a set of 195 test images. The median localization errors relative to the vertebrae dimensions were 1.98% and 1.68% for x and y coordinates respectively. All the predicted angles were highly correlated with the ground truth, despite non-negligible absolute median errors of 1.84°, 2.43° and 1.98° for L1–L5, L1–S1 and SS respectively. Our model is able to calculate with good accuracy the coordinates of the vertebral corners and has a large potential for improving the reliability and repeatability of measurements in clinical tasks.