# Crouch Gait Recognition in the Anatomical Space Using Synthetic Gait Data
## 2 Gait Recognition Framework
### Gait Data Acquisition  
The first stage of the gait recognition system is data acquisition, which is used to collect human gait data. Generally, there exist four ways to this purpose: marker-based, non marker-based, floor sensors, and wearable sensors [28]. However, to address the scarcity and availability of crouch gait data, in this work, we propose the generation of synthetic gait data based on reference joint angles of the 2392 OpenSim model [41] and polynomial fitting. Figure 4 shows the eight joint reference angles of the five gaits during a gait cycle [41]. Figure 3: Workflow stages of the crouch gait recognition in the anatomical space. Table 1 summarizes the ROM values of the eight reference joint angles during a gait cycle [41], which is useful for local analysis if each joint is evaluated independently or by each lower limb. As mentioned above, the crouch gait is characterized by excessive knee flexion. As indicated in the table for the right \(q_{4R}\) and the left lower limbs, for \(q_{4L}\) the ROM for the crouch gaits is reduced by up to 50% with respect to the normal gait. However, we can appreciate this effect not only in the knee joints, but also in the hips and ankles, as well as in the rotation and tilt movements of the pelvis. Continuing with data generation, the flowchart of the gait joint angles generator is shown in Figure 5, where GF: gait joint angle, \(n\): number of synthetic joint angles, DAE: desired approximation error, AE: approximation error, K: polynomial degree, i: iteration number, RNA: random noise amplitude, and SNR: signal-to-noise relationship. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Normal**} & \multicolumn{2}{c}{**Crouch 1**} & \multicolumn{2}{c}{**Crouch 2**} & \multicolumn{2}{c}{**Crouch 3**} & \multicolumn{2}{c}{**Crouch 4**} \\
**JA** & **Min** & **Max** & **Min** & **Max** & **Min** & **Max** & **Min** & **Max** & **Min** & **Max** \\ \hline \(q_{1}\) & \(-3.57\) & \(2.56\) & \(0.02\) & \(11.56\) & \(-29.01\) & \(-6.14\) & \(-24.5\) & \(-2.31\) & \(28.86\) & \(45.37\) \\ \(q_{2}\) & \(-4.10\) & \(4.42\) & \(-8.12\) & \(-22.27\) & \(-5.54\) & \(6.05\) & \(-9.52\) & \(-0.84\) & \(-24.92\) & \(-14.8\) \\ \(q_{3R}\) & \(-16.82\) & \(25.26\) & \(18.29\) & \(54.36\) & \(14.23\) & \(42.54\) & \(9.89\) & \(45.91\) & \(17.25\) & \(64.45\) \\ \(q_{4R}\) & \(-58.25\) & \(-2.27\) & \(-68.75\) & \(-57.64\) & \(-73.46\) & \(-54.91\) & \(-47.27\) & \(-26.25\) & \(-72.13\) & \(-37.31\) \\ \(q_{5R}\) & \(-14.07\) & \(10.75\) & \(13.07\) & \(34.16\) & \(-24.15\) & \(-8.2\) & \(-39.07\) & \(-29.96\) & \(13.55\) & \(29.48\) \\ \(q_{3L}\) & \(-16.82\) & \(25.26\) & \(29.90\) & \(58.78\) & \(-6.99\) & \(28.55\) & \(-6.44\) & \(31.28\) & \(33.51\) & \(59.40\) \\ \(q_{4L}\) & \(-58.25\) & \(-2.27\) & \(-81.97\) & \(-55.32\) & \(-55.86\) & \(-39.10\) & \(-39.76\) & \(-12.06\) & \(-67.43\) & \(-31.68\) \\ \(q_{5L}\) & \(-14.07\) & \(10.75\) & \(6.89\) & \(29.31\) & \(-9.56\) & \(17.96\) & \(-3.66\) & \(15.10\) & \(-1.06\) & \(9.30\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum and minimum range of movement (ROM) in degrees of the eight joint angles for the 5 gaits. Figure 4: Gait joint angles for the 8 movements for the 5 gaits. Normal (green), crouch-1 (blue), crouch-2 (red), crouch-3 (black), and crouch-4 (magenta). Limit between the stance phase and swing phase of the gait cycle (cyan). Given a joint angle function \(q_{i}\), until the best fit is obtained to the joint angle function, we fit a polynomial curve to obtain the coefficients of a polynomial \(p(x)\) of degree \(k\). Subsequently, the polynomial \(p(x)\) is evaluated at each point in \(x\), where \(x\) in this case is the array of samples from the gait cycle. Next, we calculate the mean square error (MSE) (AE), between \(q_{i}\) and the evaluation of \(p(x)\). The process continues until the stop criterion is satisfied (\(AEDAE\)). The degree of polynomial \(k\) is inversely proportional to the desired error (\(DAE=0.2\)) for this case.