# Identification of Location and Camera Parameters for Public Live Streaming Web Cameras
## 5 Examples
### Example 2. More Radial Distortion and Vegetation, More Calibration Points  
Figure 9 illustrates a frame image from another public camera of the same operator. This camera has zero horizon tilt and more substantial radial distortion. We have calibrated the camera and calculated the maps in the season of rich vegetation. Tree foliage complicates the selection and estimation of coordinates of points. The two-way road is visible to the camera. This is a FullHD camera (\(N=1920,M=1080,c_{u}=N/2,c_{v}=M/2\)). The zero horizon tilt is visible on the line \(u=c_{u}\) near \(P_{5}^{v}\) (see Table 4). We select the point \(P^{0}\) as the origin of \(F_{euu}\) (see Table 4). We assess global coordinates of the point \(O\) (the camera position), point \(G\) (the source of the principal point \(C\), Figure 1, Figure 9), and points \(P_{1}^{u},P_{2}^{v},P_{3}^{u},P_{4}^{v}\), and \(P_{5}^{v}\) on the lines \(v=c_{v}\) (index \(u\)) or \(u=c_{u}\) (index \(v\)). Next, we convert the global coordinates to \(F_{euu}\) and append them to Table 4.  
We obtained estimations \(f_{u}^{1}=1161.93,f_{v}^{2}=1382.45,f_{u}^{3}=1168.78,f_{v}^{4}=1354.82\), and \(f_{v}^{5}=1349.67\) using Formulas (15) and (16) and Table 4 data. There are a few points, but one can assume a pattern \(f_{v}>f_{u}\). Perhaps the camera's sensor pixel has a rectangular shape (see (4)). Consider the two hypotheses:  
\[f_{u}=(f_{u}^{1}+f_{u}^{3})/2=1165.355,f_{v}=(f_{v}^{2}+f_{v}^{4}+f_{v}^{5})/3 =1362.313; \tag{50}\]  
\[f_{u}=f_{v}=(f_{u}^{1}+f_{u}^{3}+f_{v}^{2}+f_{v}^{4}+f_{v}^{5})/5=1283.53. \tag{51}\]  
The second variant means the square pixel. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Name** & **Lat** & **Long** & **Height** & \(u\) & \(v\) & \(x_{euu}\) & \(y_{euu}\) & \(z_{euu}\) \\ \hline \(P^{0}\) & 43.168143\({}^{\circ}\) & 131.916257\({}^{\circ}\) & 14 & & & 0 & 0 & 0 \\ \(G\) & 43.168356\({}^{\circ}\) & 131.916733\({}^{\circ}\) & 25 & 960 & 540 & 38.7 & 23.66 & 11 \\ \(O\) & 43.167616\({}^{\circ}\) & 131.916245\({}^{\circ}\) & 56 & & & \(-0.97\) & \(-58.54\) & 42 \\ \(P_{1}^{u}\) & 43.168775\({}^{\circ}\) & 131.916107\({}^{\circ}\) & 18 & 306 & 540 & \(-12.2\) & 70.2 & 4 \\ \(P_{2}^{v}\) & 43.168361\({}^{\circ}\) & 131.916740\({}^{\circ}\) & 15 & 960 & 671 & 39.27 & 24.22 & 0.7 \\ \(P_{3}^{u}\) & 43.168330\({}^{\circ}\) & 131.917431\({}^{\circ}\) & 14 & 1559 & 540 & 116.61 & 25.89 & 0 \\ \(P_{4}^{v}\) & 43.168200\({}^{\circ}\) & 131.916631\({}^{\circ}\) & 13.5 & 960 & 815 & 30.41 & 6.33 & 0 \\ \(P_{5}^{u}\) & 43.169134\({}^{\circ}\) & 131.917249\({}^{\circ}\) & 43 & 960 & 199 & 80.67 & 110.1 & 27 \\ \hline \end{tabular}
\end{table} 
Table 4: The points used for the calibration. Latitude and longitude are in degrees, altitudes and ENU coordinates are in meters, and coordinates of pixels are in \(F_{im}\) units (\(u\) is the column index, \(v\) is the row). Figure 9: Field of view of the public street camera in Vladivostok. Example 2, image \(\Phi\). Let us try variant (50). With \(f_{u}\) and \(f_{v}\) we obtained the intrinsic parameters matrix \(A\) (1). We estimate radial distortion coefficients \(k_{1}\) and \(k_{2}\), put \(k_{1}=-0.17\) and \(k_{2}=0.01\) to compute the mapping \(\Theta\) (17), and apply it to eliminate radial distortion from the (\(\Phi\)). We obtained the undistorted image \(\dot{\Phi}\) (see Figure 10). We showed a cropped and interpolated version of \(\Phi\) in Example 1 (Figure 4). Let us demonstrate the result of mapping \(\Theta\) without postprocessing. The image's resolution \(\dot{\Phi}\) is \(2935\times 1651\), but it contains only \(1920\times 1080\) pixels colored by the camera. So, the black grid is the unfilled pixels of the large rectangular. Let us return to the illustration that is more pleasing to the eye by cutting off part of \(\dot{\Phi}\) and filling the void with interpolation (see Figure 11). We noted that in the field of view of the camera, there is a section of the wall of the building (near \(P_{5}^{n}\)), allowing you to put \(\gamma=0\) (see Figure 9).