A COMPARISON OF DIFFERENT AUTOMATIC METHODS FOR SMOOTHING AND DIFFERENTIATION IN BIOMECHANICS

  • V. Baltzopoulos
  • G. Giakas

Abstract

A number of different automatic filtering techniques have recently been developed for data smoothing and differentiation in biomechanics. These techniques use different optimisation criteria for the selection of an optimal filtering parameter without operator intervention, using information in the measurements. The purpose of this study was to compare the most recent automatic filtering methods for data smoothing using benchmark and example biomechanical data. The smoothing methods compared in this study were 1) Generalised cross-validation using quintic splines (GCV) (Woltring H. 1985 Human Movement Science, 4,229-245) 2) Power spectrum based bandwidth and filtering model determination (PS)(D’Amico M and Ferrigno G. 1990, Medical & Biological Engineering & Computing, 28, 407-415) 3) Least squares cubic splines (LS)(Simons, W and Yang K, 1991, Journal of Biomechanical Engineering, 113, 348-351) and 4) Regression model based cut-off frequency selection (RM) (Yu B. 1989, Proceedings of the XU International Congress of Biomechanics, University of California, Los Angeles). These methods were applied to benchmark data by Lanshammar (1982, Journal of Biomechanics, 15, 99-105) and Vaughan (1982, International Journal of Biomedical Computing, 2, 349-362). The evaluation of the smoothing process using the above methods was performed by comparing the error between the second derivatives after smoothing and the criterion derivatives of the benchmark data sets. The frequency domain response. of the different smoothing techniques was also examined. The mean error for the first data set was 2.91,2.82, 2.83 and 3.51 rad.S-2 for the four methods respectively. The corresponding errors for the second data set were 0.39, 2.58, 4.90 and 3.62 m.S-2.These results suggest that GCV and PS are superior to LS and RM. The GCV performed better especially in the constant acceleration conditions (Vaughan, 1982). However application of the GCV in a reduced data set, violating boundary conditions and signal to noise assumptions produced unacceptable results compared to PS. In conclusion, successful application of automatic filtering methods based on statistical or power spectrum depends on whether the data set satisfies the assumptions concerning the time series and noise characteristics. It is recommended that boundary condition, frequency domain and periodicity characteristics of biomechanical data are carefully examined before the application of automatic smoothing techniques.