Methods for comparing three-dimensional motion trajectories

Analysis of three-dimensional motion trajectories plays an important role in medicine, sports, robotics, and the entertainment industry. This research aims to compare the performance of the following six trajectory analysis algorithms: Euclidean Distance, Mean Squared Error, Dynamic Time Warping, Fréchet Distance, Fuzzy C-Means, and Fuzzy Similarity in terms of scalability, accuracy, computational efficiency, and robustness to speed variations. The research was conducted on the 3DTennisDS dataset containing tennis stroke trajectories recorded with the Vicon motion capture system. Results showed that fuzzy methods offer the best combination of accuracy (Fuzzy Similarity: 0.92, FCM: 0.89) and computational efficiency while maintaining high resistance to dynamic movements. In conclusion, fuzzy algorithms provide the most balanced solution for trajectory comparison in practical applications.