Averaging Three-Dimensional Time-Varying Sequences of Rotations: Application to Preprocessing of Motion Capture Data

The aim of this paper is to propose and initially evaluate our novel algorithm which enables averaging of time-varying sequences of rotations with three degrees of freedom described by quaternions. The methodology is based on Dynamic Time Warping barycenter averaging (DBA) with one minus dot product distance function, Markley’s quaternions averaging method and Gaussian quaternion signal smoothing. The proposed algorithm was successfully applied to generate single, averaged motion capture recording (MoCap) from ten MoCap of mawashi-geri karate kick of black belt Shorin-Ryu karate master. We have used inverse kinematic model. In our experiment mean DTW normalized distance between averaged signal and original signals varied from \(0.713 \cdot 10^{-3}\) for Hips sensor to \(6.153 \cdot 10^{-3}\) for LeftForearm sensor, which were very good results. Also the visualization of the averaged MoCap data showed that the proposed method did not introduce unwanted disturbances and may be usable for that task. That type of averaging has many important applications. For example it can be used to calculate and visualize an average performance of an athlete who performs some activity that he wants to optimize during training. The numerical and visual data may be a very important feedback for coach that supervises the training. Also our method is not limited to MoCap data averaging; it can be applied to average any type of quaternion-based time-varying sequences.