A Convolution-Based Gait Asymmetry Metric for Inter-Limb Synergistic Coordination

TL;DR

This work tackles gait symmetry assessment by modeling intersegmental coordination as left-right time-series pairs derived from standard video. It introduces two symmetry metrics: a 1/4 cycle shift method that realigns velocity patterns to reveal waveform similarity, and a transfer-function-based method that treats paired body parts as an input–output LTI system with a dissimilarity measure $Dis((a,b),(x,y)) = \frac{\|\mathbf{u}-\mathbf{v}\|^2}{\|\mathbf{u}\| \|\mathbf{v}\|}$ where $\mathbf{u}=a*y$ and $\mathbf{v}=x*b$, and $G(z)=\frac{Y(z)}{X(z)}$. The approach was validated on five subjects performing symmetric and asymmetric gait, showing low dissimilarity and high correlation for symmetric movement, with higher dissimilarity for asymmetry (notably excluding the HH case, which remained relatively symmetric). Importantly, the method relies on smartphone video and OpenPose, enabling accessible gait analysis without specialized equipment, and it points to extensions into 2D vector processing and quaternion-based metrics for richer representations.

Abstract

This study focuses on the velocity patterns of various body parts during walking and proposes a method for evaluating gait symmetry. Traditional motion analysis studies have assessed gait symmetry based on differences in electromyographic (EMG) signals or acceleration between the left and right sides. In contrast, this paper models intersegmental coordination using an LTI system and proposes a dissimilarity metric to evaluate symmetry. The method was tested on five subjects with both symmetric and asymmetric gait.

Figures (13)

• Figure 1: Illustration of dissimilarity metric between LTI systems
• Figure 2: Illustration of dissimilarity metric between LTI systems
• Figure 3: Illustration of dissimilarity metric between LTI systems
• Figure 4: Illustration of symmetry evaluation using
• Figure 5: Left and right ankle speed in motion S after 1/4 period shift transformation