A Deep Learning Framework with Spherical Harmonic Encoding for 3D Joint Angle Analysis and Injury Prediction

Abstract

This study focuses on the three-dimensional dynamic analysis of joint angles and the prediction of sports injuries in long-distance runners, addressing the significant limitations of traditional approaches in this field. The research is grounded in the fact that millions of athletes participate in long-distance running events worldwide each year, with nearly 30% experiencing joint-related injuries. Traditional joint angle analysis methods exhibit error rates as high as 15%, and injury prediction accuracy remains limited to around 30%. To overcome these challenges, a novel deep learning-based model was developed, utilizing the public Human3.6M dataset (comprising 500 samples of long-distance running motion) and 300 additional samples collected from 30 professional club athletes. The model integrates a customized feature extraction module, a joint angle encoding component based on spherical harmonics, a temporal dynamics module, and a probabilistic injury prediction mechanism. Experimental results demonstrate that the average joint angle analysis error was reduced to 5.2%, while injury prediction accuracy improved to 75%. Our model adopts a modular deep learning architecture consisting of a feature extraction module with custom kernel functions, a joint angle encoding component based on spherical harmonics, a temporal dynamics modeling component leveraging non-stationary temporal kernels, and a final injury prediction component using a Gaussian Mixture Model integrated with Bayesian inference. Evaluation metrics include joint angle analysis error rate, injury prediction accuracy, precision, recall, and F1 score. On joint angle analysis, the model achieved an average error rate of 5.2%, significantly outperforming the 14.8% of the 3D-Traditional baseline and the 12.3% of the CNN-2D baseline. For injury prediction, the model reached an accuracy of 75%, compared to 35% for the ML-Injury model and 50% for the Simple-DL model. Precision and recall reached 78% and 72% respectively, indicating the model’s superior predictive performance across multiple evaluation dimensions.