## 4 Results
### Calibration of Camera  
When a new camera is applied in the experiment, calibration is necessary for acquiring the camera's FOV or focal length, which targets for the position-based estimation or size-based estimation. There are various methods to acquire the FOV. The calibration procedure in this experiment was as follows: (1) set up a camera on a tripod with the camera axis parallel to the ground; (2) place reference markings at particular locations according to the live view of the camera; (3) measure the location of reference markings in real-worldcoordinates; and (4) calculate the FOV of the camera from Equations (1)-(3). To acquire the vertical FOV of the camera, a tape measure was laid on the ground and extended from the bottom of the tripod along with the centerline of the camera. A distinguishable object was placed close to the edge in pixel coordinates (Figure 5a-e). Read from the tape measure to record the length of the blind area in real-world coordinates. Repeat the measurement at different heights to find the average.  
Once the height of camera h and the length of bind area b were measured, \(\beta\) and \(\alpha\) could be calculated by Equation (1). Hence, the average of vertical FOV of the camera used in the experiment is shown in Table 2.  
For the horizontal FOV, similar steps were performed, but two objects were placed at the left and right edge in the pixel coordinate (Figure 5f-j). The camera was set up at a certain pitch angle, otherwise the width w would be too far away and close to the vanishing point if we set up the camera horizontally. The height of camera h was measured for calculating the actual distance \(d^{{}^{\prime}}=\sqrt{(d^{2}+h^{2})}\) from the camera to the plane of w when the camera was hoisted at h. The horizontal FOV could be calculated by Equation (3). The average horizontal FOV of the camera in the experiment is shown in Table 3, where the height is fixed to 1.183 m.  
To acquire the focal length of the camera, take several pictures that contain the target objects at different distances (Figure 6). As long as the size of the objects and the distances are known, the focal length can be calculated by the following Equation (13).  
\[f=\ \frac{hD}{H} \tag{13}\]  
where the height of the object in pixel \(h\) can be measured by photo editing software. Tables 4 and 5 show a mean camera's focal length of 424.52 by experiment.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **h (m)** & **b (m)** & \(\beta\) & \(\alpha\) & **Vertical FOV** \\ \hline (a) & 0.794 & 1.56 & 63.03\({}^{\circ}\) & 26.97\({}^{\circ}\) & 53.95\({}^{\circ}\) \\ (b) & 0.959 & 1.88 & 62.97\({}^{\circ}\) & 27.03\({}^{\circ}\) & 54.05\({}^{\circ}\) \\ (c) & 1.079 & 2.15 & 63.35\({}^{\circ}\) & 26.65\({}^{\circ}\) & 53.30\({}^{\circ}\) \\ (d) & 1.167 & 2.39 & 63.97\({}^{\circ}\) & 26.03\({}^{\circ}\) & 52.05\({}^{\circ}\) \\ (e) & 1.254 & 2.57 & 63.99\({}^{\circ}\) & 26.01\({}^{\circ}\) & 52.02\({}^{\circ}\) \\ \hline \multicolumn{6}{c}{Average:} & 63.46\({}^{\circ}\) & 26.54\({}^{\circ}\) & 53.07\({}^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 2: Readings of vertical FOV experiments.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **d (m)** & **w (m)** & \(\gamma\) & **Horizontal FOV** \\ \hline (f) & 1.040 & 1.375 & 23.58\({}^{\circ}\) & 47.16\({}^{\circ}\) \\ (g) & 1.270 & 1.596 & 24.69\({}^{\circ}\) & 49.38\({}^{\circ}\) \\ (h) & 1.500 & 1.782 & 25.00\({}^{\circ}\) & 50.01\({}^{\circ}\) \\ (i) & 1.735 & 1.982 & 25.26\({}^{\circ}\) & 50.53\({}^{\circ}\) \\ (j) & 1.965 & 2.187 & 25.49\({}^{\circ}\) & 50.98\({}^{\circ}\) \\ \hline \multicolumn{6}{c}{Average:} & 24.81\({}^{\circ}\) & 49.61\({}^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 3: Readings of horizontal FOV experiments.