Postural Symmetry Evaluation Using Wavelet Correlation Coefficients Calculated for the Follow-Up Posturographic Trajectories
Keywords:Correlation, discrete wavelet transform, follow-up posturography, postural symmetry evaluation
The paper presents an original method enabling postural symmetry evaluation using weighted averages of the wavelet correlation coefficients obtained individually for the corresponding x and y components of the cantered follow-up posturographic trajectories registered during the clockwise and counterclockwise visual stimulations. In the process the x and y components of both trajectories undergo 7-stage db2 discrete wavelet decomposition. The correlations of the detail coefficients are evaluated at all levels of the decomposition structure whereas the correlations of the approximation coefficients are calculated only at its last level. Applied weighting factors constitute the sums of energies of the reconstructed details or approximations corresponding to a particular level of decomposition. The ultimate measure of postural symmetry in the herein presented method is the quantity based on the vector distance of the point whose coordinates constitute the values of the obtained weighted correlation coefficients (individually for the x and y components), from the point representing the state of ideal symmetry. This quantity assumes the values within the range of [0,1], where 1 is identified with the maximum postural symmetry dynamics whereas the value of 0 represents the state of maximum anti-symmetry dynamics (analysed trajectories are out of phase by π [rad]). The applicability of the herein presented method was verified in the process of postural symmetry evaluation carried out in the group of 30 patients rehabilitated after total hip arthroplasty.
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