From Kellgren-Lawrence to Calcium Pyrophosphate Crystal Deposition: A Soft-Labelling Framework for Knee Osteoarthritis Assessmen

Background and objective. Conventional Deep Learning (DL) approaches for Knee Osteoarthritis (KOA) grading rely on one-hot labels, which fail to capture both the ordinal uncertainty of Kellgren--Lawrence (KL) and Calcium Pyrophosphate Deposition Disease (CPPD) severity scores and the asymmetric relationship between the two scales observed in clinical practice. Methods. We retrospectively collected 2172 knee X-ray images, including 968 radiographs jointly annotated for KL and CPPD severity. An ordinal DL framework based on soft-labelling was developed for both tasks, replacing one-hot targets with unimodal probability distributions centred on the annotated grade. Four formulations were investigated: binomial, beta, triangular, and exponential. Results. All soft-labelling strategies consistently outperformed the nominal baseline. For CPPD grading, the triangular formulation achieved the highest Quadratic Weighted Kappa (QWK) and the lowest Mean Absolute Error (MAE) (QWK = 0.796; MAE = 0.438), while the beta formulation yielded the most balanced class-wise performance considering Average MAE (AMAE) and Maximum MAE (MMAE) across classes (AMAE = 0.458; MMAE = 0.573). For KL grading, the beta-based approach provided the best overall performance, achieving the highest QWK together with the lowest MAE and class-wise errors (QWK = 0.777; MAE = 0.529; AMAE = 0.523; MMAE = 0.775). Statistical analysis demonstrated significant improvements over conventional one-hot supervision (p < 0.001).