Convolutional and ℓ21-norm neural network for bone age estimation

Abstract

Bone age (BA) assessment is critical for evaluating children for potential endocrine, genetic and growth disorders. The evaluation of BA reading may vary among the readers. We use an Inception-v3 convolutional neural network to extract features and propose the novel ℓ<inf>21</inf>-norm random vector functional link neural network (LR21-RVFL) for the automatic assessment of bone age. Random vector functional link neural network (RVFL) suffers in the presence of noise and outliers due to the squared loss function. To overcome these challenges, we incorporate an ℓ<inf>21</inf>-norm-based loss function in the RVFL model to improve the robustness of the model. Moreover, we used ℓ<inf>21</inf>-based regularization to suppress the redundant/irrelevant features and hence, generate a less complex model. The proposed LR21-RVFL model achieves better performance compared to baseline models (except R21-RVFL) in bone age prediction. Moreover, we evaluate the models on the classification of UCI and KEEL datasets. © 2025 Elsevier B.V., All rights reserved.