# Wind Speed Measurement via Visual Recognition of Wind-Induced Waving Light Stick Target
## 4 Experimental Validation
### Model Validation
#### 4.3.1 Validation of Pure View Cases  
In validation tests of pure imaging views, camera parameters are given in Table 2 including the stick length, object distance, optical deviation, focal length, and camera resolution in bottom, side, and front views. Among them, the camera is placed at a deviation of 70.4 mm and 68.7 mm, respectively, in bottom and side view. In front view, the camera is placed at the same position as in side view case. However, the stick is adjusted by only REV2# in the front plate. In pure deviated bottom view, the stick lines are in its initial vertical direction in the front plate. The plate is rotated by REV1# in the range of \(\pm\)90\({}^{\circ}\) at an interval of 15\({}^{\circ}\). Imaging length \(X_{\rm P}\) is calculated by identifying the pixel coordinates of the fixed and free stick ends, which are then substituted into Equation (6) to acquire the yaw angle \(\alpha\) at each REV1# case. To better compare and validate the test results, two continuous curves are given for the proposed detection model by obtaining the imaging length \(X_{\rm P}\) from the discretized yaw angle \(\alpha\) (0.5\({}^{\circ}\) interval) based on Equation (5) as the dashed red line, and also by acquiring the yaw angle \(\alpha\) from the above discretized imaging length \(X_{\rm P}\) based on Equation (6) as the blue solid line in Figure 19 below. Left and right limit angles are computed according to Equations (10) and (11), and depicted as the two horizontal lines; the top 77.6\({}^{\circ}\) describes the left and the bottom \(-\)83.2\({}^{\circ}\) denotes the right limit angle. The 13 detected yaw angles are illustrated as circular, blue-edge markers which go well with the detection model, while the red markers are the results beyond the limit. From the above, it is seen that when the yaw angle cases vary between the left and right angle limits, the detected yaw angles agree well with the theoretical detection model (Equation (6)). However, when REV1# is \(\pm\)90\({}^{\circ}\) beyond the limit of \(-\)83.2 to 77.6\({}^{\circ}\), there is a big deviation between the detected and the expected, as shown in the red circular markers. Due to the geometrical relationship, the detected and the expected yaw angles are symmetric to the left and right limits, respectively, for 90\({}^{\circ}\) and \(-\)90\({}^{\circ}\) yaw angle cases. In pure deviated side view, the camera is placed in front of the front plate, but the stick stays at the same position while the front plate is rotated in the same way as in the bottom view cases. The identified imaging length \(X_{\rm P}\) is substituted into Equation (18) to acquire the yaw angle \(\alpha\) at each REV1# case. The left and right limits are calculated as 90\({}^{\circ}\) and \(-\)13.0\({}^{\circ}\) according to Equation (22) and Equation (23). The detection model from yaw angle to imaging length, and the inversion model, are respectively denoted as the dashed \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Deviated Bottom View** & **Deviated Side View** & **Deviated Front View** \\ \hline Stick length L (mm/px) & 225/1101 & 225/1238 & 225/1238 \\ Object distance DO (mm/px) & 670/3279 & 600/3301 & 600/3301 \\ Deviation S (mm/px) & 70.4/344 & 68.7/387 & 68.7/387 \\ Focal length f (px) & 3273 & 3273 & 3273 \\ Camera resolution (px) & 3024 \(\times\) 4032 & 3024 \(\times\) 4032 & 3024 \(\times\) 4032 \\ \hline \hline \end{tabular} Note: ‘px’ denotes unit ‘pixel’.  
\end{table} 
Table 2: Camera parameters. red line and solid blue line in Figure 20. Detected yaw angles in 13 REV1# imaging cases are illustrated as circular blue-edge markers, among which the red markers indicate the results that are beyond the limit. It can be observed that when the REV1# imaging cases vary between 90\({}^{\circ}\) and \(-\)13.0\({}^{\circ}\), the detected yaw angles agree well with the theoretical detection model (Equation (18)).