A New Method for Time Normalization Based on the Continuous Phase: Application to Neck Kinematics

There is growing interest in analyzing human movement data for clinical, sport, and ergonomic applications. Functional Data Analysis (FDA) has emerged as an advanced statistical method for overcoming the shortcomings of traditional analytic methods, because the information about continuous signals can be assessed over time. This paper takes the current literature a step further by presenting a new time scale normalization method, based on the Hilbert transform, for the analysis of functional data and the assessment of the effect on the variability of human movement waveforms. Furthermore, a quantitative comparison of well-known methods for normalizing datasets of temporal biomechanical waveforms using functional data is carried out, including the linear normalization method and nonlinear registration methods of functional data. This is done using an exhaustive database of human neck flexion-extension movements, which encompasses 423 complete cycles of 31 healthy subjects measured in two trials of the experiment on different days. The results show the advantages of the novel method compared to existing techniques in terms of computational cost and the effectiveness of time-scale normalization on the phase differences of curves and on the amplitude of means, which are assessed by Root Mean Square (RMS) values of functional means of angles, angular velocities, and angular accelerations. Additionally, the confidence intervals are obtained through a bootstrapping process.