Quaternion statistics applied to the classification of motion capture data

Unit quaternions give quite new possibilities in an analysis of motion capture data. They provide a compact, holistic axis-angle representation of 3D rotations. An application of descriptive statistics – measures of location and dispersion – is common in numerous problems related to an assessment of joint movements. For those reasons, the paper proposes new approaches to the extraction of motion descriptors on the basis of descriptive statistics of 3D rotations represented by unit quaternions as well as the appropriate classification schemes operating on motion descriptors. Mean and median values and standard deviations are calculated for time series with raw rotational data as well as angular velocities and accelerations. The problem of human gait identification is addressed in the numerical validation of the introduced methods and highly precise marker-based motion capture data are utilized. The results obtained – the accuracy of gait recognition – are compared to the ones achieved by descriptive statistics calculated for time series of Euler angles. The general conclusion is that unit quaternions are effective in the calculation of descriptive statistics. They preserve robust discriminative features of joint movements and they can be applied in numerous challenges of expert and intelligent systems.