Automated measurement of calcaneal inclination angle via partial semantic segmentation using U-Net

To develop and validate an interpretable deep learning pipeline for the automated measurement of the calcaneal inclination angle (CIA) on lateral weight-bearing foot radiographs using partial semantic segmentation.

This retrospective single-center study included 884 radiographs after the removal of duplicates, partitioned into a development cohort of 779 radiographs and a held-out internal test cohort of 105 radiographs, with no patient contributing to both. Three landmark-relevant anatomical regions were manually annotated: the inferior calcaneal contour (CAL), inferior contour of the fifth metatarsal head (M5), and calcaneal aspect of the inferior calcaneocuboid joint (CC). Each region was segmented by its own single-class U-Net model, trained from scratch with an unweighted Dice + Binary Cross-Entropy loss and early stopping on the validation Dice score, and deterministic post-processing was used to derive four anatomical landmarks and to calculate the CIA. A second observer, a fifth-year radiology resident, independently re-annotated a random subset of 50 development radiographs from a blank canvas. The train/validation split was performed at the patient level, and each network was trained with five predefined seeds. Segmentation performance was evaluated on the validation set, and clinical measurement accuracy was assessed on the held-out test set against three readers who measured independently and blinded. The frozen primary model was then applied without modification to an independent external cohort of 50 radiographs from a second institution, measured by the same three readers under the identical blinded protocol.

Validation Dice scores across the five seeded training runs were 0.935 ± 0.010 for CAL, 0.871 ± 0.005 for M5, and 0.805 ± 0.009 for CC (mean ± standard deviation), with the pre-specified primary run reaching 0.936, 0.865, and 0.807, respectively. In the held-out test cohort, the model showed a mean absolute error (MAE) of 0.690° (95% confidence interval [CI] 0.525-0.855) against the mean of the three readers, with 92.4% of measurements within 2° and 98.1% within 3°. Bland-Altman analysis demonstrated a small negative bias of -0.425° (95% confidence interval -0.620° to -0.230°), with 95% limits of agreement from -2.427° to +1.577°. The intraclass correlation coefficient (ICC) formula ICC(A,1) achieved 0.986 across the model and the three readers and 0.994 among the three readers alone. In the external cohort, the model achieved an MAE of 0.85° against the three-reader mean, with 92.0% of measurements within 2° and an ICC of 0.969.

Partial semantic segmentation combined with deterministic landmark extraction enables rapid and clinically accurate automated CIA measurement on lateral weight-bearing foot radiographs, with an agreement approaching, though not yet equaling, that observed among human readers.

The proposed pipeline enabled fast, reproducible CIA measurement with high expert agreement and may support standardized foot alignment assessment after prospective validation.