Pectus excavatum (PE) is the most common abnormality of the thoracic cage, whose severity is evaluated by extracting three indices (Haller, correction and asymmetry) from computed tomography (CT) images. To date, this analysis is performed manually, which is tedious and prone to variability. In this paper, a fully automatic framework for PE severity quantification from CT images is proposed, comprising three steps: (1) identification of the sternum's greatest depression point; (2) detection of 8 anatomical keypoints relevant for severity assessment; and (3) measurements' geometric regularization and extraction. The first two steps rely on heatmap regression networks based on the Unet++ architecture, including a novel variant adapted to predict 1D confidence maps. The framework was evaluated on a database with 269 CTs. For comparative purposes, intra-observer, inter-observer and intra-patient variability of the estimated indices were analyzed in a subset of patients. The developed system showed a good agreement with the manual approach (a mean relative absolute error of 4.41%, 5.22% and 1.86% for the Haller, correction, and asymmetry indices, respectively), with limits of agreement comparable to the inter-observer variability. In the intra-patient analysis, the proposed framework outperformed the expert, showing a higher reproducibility between indices extracted from distinct CTs of the same patient. Overall, these results support the feasibility of the developed framework for the automatic, accurate and reproducible quantification of PE severity in a clinical context.