# Computer Vision Measurement of Pointer Meter Readings Based on Inverse Perspective Mapping
## 3 Experiments and Analysis
### Measure Two Pointer Meters  
As with measuring one pointer meter, the three operators sequentially observed the same location of the pointer of the meter on the left in the image and recorded the readings under the same conditions. Average value of the readings of the meter on the left in the image was used as the reference value \(g_{0}(^{1})\). And the three operators sequentially observed again the same location of the pointer of the meter on the right in the image and recorded the readings. Average value of the readings of the meter on the right in the image was used as the reference value \(g_{0}(^{2})\). The reference values \(g_{0}(^{1})\) and \(g_{0}(^{2})\) were used for assessing the repeatability of the present method. In order to verify that multiple pointer meters can be measured based on the proposed method, two pointer meters which had the same size and the same range were measured. The actual radius on the pointer meter from the rotation center to the midpoint of long scales and short scales was measured, that was 469 mm and 455 mm respectively. The angle between the zero scale line and the maximum scale line was measured, that was \(\alpha=271.8^{\circ}\). Then, the world coordinates of the one of pointer meters' short scales midpoints in were obtained based on Equation (1). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Absolute Error of Position 1** & **Absolute Error of Position 2** & **Absolute Error of Position 3** \\  & **\(\Delta f_{1}(^{1})\)=\(\big{|}f_{1}(^{1})\)–\(f_{0}\big{|}\) (kPa)** & \(\Delta f_{1}(^{2})\)=\(\big{|}f_{1}(^{2})\)–\(f_{0}\big{|}\) (kPa)** & \(\Delta f_{1}(^{3})\)=\(\big{|}f_{1}(^{3})\)–\(f_{0}\big{|}\) (kPa) \\ \hline
1 & 141 & 142 & 101 \\
2 & 158 & 96 & 159 \\
3 & 147 & 94 & 143 \\
4 & 131 & 93 & 148 \\
5 & 139 & 129 & 148 \\
6 & 121 & 157 & 147 \\
7 & 158 & 106 & 141 \\
8 & 140 & 98 & 154 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Measurement absolute errors by the conventional method. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Absolute Error of Position 1** & **Absolute Error of Position 2** & **Absolute Error of Position 3** \\  & \(\Delta f_{2}(^{1})\)=\(\big{|}f_{2}(^{1})\)–\(f_{0}\big{|}\) (kPa)** & \(\Delta f_{2}(^{2})\)=\(\big{|}f_{2}(^{2})\)–\(f_{0}\big{|}\) (kPa) & \(\Delta f_{2}(^{3})\)=\(\big{|}f_{2}(^{3})\)–\(f_{0}\big{|}\) (kPa) \\ \hline
1 & 2 & 1 & 6 \\
3 & 3 & 2 & 2 \\
4 & 1 & 4 & 5 \\
5 & 3 & 9 & 2 \\
6 & 1 & 1 & 1 \\
7 & 2 & 1 & 2 \\
8 & 1 & 1 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Measurement absolute errors by the proposed method. First, the pixel coordinates of all the midpoints of scales and critical points (including rotation center and ends of pointer) of the two pointer meters were detected. The translation distance D between the two pointer meters can be calculated using the distance between rotation centers of the two pointer meters, as shown in Figure 8a. After calibration the intrinsic parameters, the extrinsic parameters can be calibrated by the pixel coordinates and world coordinates of midpoints of short scales of the meter on the left in the image, as shown in Figure 6b. The extrinsic parameters were expressed as \([R,T]=\left[ \begin{array}{ccc}0.2261&0.9732&-0.0416\\ 0.0039&0.0418&0.9991\\ 0.9741&-0.2261&0.0056\\ \end{array} \right]\). And the world coordinates of midpoints on the short scales of the meter on the left in the image were transformed into the camera coordinates by the extrinsic parameters. Second, normal vector \(\overset{\rightarrow}{k}\) of the meter surface was calculated by the camera coordinates of three midpoints to obtain the rotation transformation matrix \(M\) of the meter image based on Equation (2). The meter image was rotated by the matrix \(M\) to make the meter image parallel to the surface of the meter.