End-to-end deep learning framework for automated angle estimation in hallux valgus from full-field weight-bearing radiographs

A fully automated, end-to-end deep learning framework was developed and validated for accurate and reliable estimation of the hallux valgus angle (HVA) and intermetatarsal angle (IMA) from full-field weight-bearing foot radiographs. The framework combines a YOLOv11m-based foot detection module and a trainable module integrating segmentation and principal component analysis (PCA)-based angle estimation, enabling end-to-end training and inference. A retrospective dataset of 1,753 radiographs from 1,652 patients was used for model development and internal validation, while an external dataset of 121 radiographs was used to assess generalizability. Model performance was evaluated against expert manual annotations using mean absolute error (MAE), root mean squared error (RMSE), and Pearson’s correlation coefficient (r). The YOLOv11m module achieved near-perfect detection on both internal and external datasets. On the internal test dataset, the PCA-based model showed excellent agreement with manual measurements for HVA (r = 0.97, MAE = 1.98°, RMSE = 2.74°) and IMA (r = 0.93, MAE = 1.21°, RMSE = 1.52°). On the external dataset, performance remained robust for both HVA (r = 0.95, MAE = 2.27°, RMSE = 2.82°) and IMA (r = 0.87, MAE = 1.76°, RMSE = 2.13°). On the internal test dataset, 94.89% of HVA and 94.40% of IMA predictions, and on the external test dataset, 93.39% of HVA and 85.95% of IMA predictions fell within predefined clinically acceptable error margins (± 5° for HVA and ± 3° for IMA). The model processed each foot image in 6.3 s, achieving a 24–35 times speed-up over manual measurement. This study demonstrates the feasibility and clinical utility of an end-to-end deep learning framework for fast and accurate angle estimation in hallux valgus using full-field weight-bearing radiographs.