# Computer Vision Measurement of Pointer Meter Readings Based on Inverse Perspective Mapping
## 3 Experiments and Analysis
### Measure One Pointer Meter  
Under the same conditions, the three operators sequentially observed the same location of the pointer and recorded the readings of the pointer meter. Average value of the readings was used as the reference value for assessing the repeatability of the present method. Then, under keeping that the pointer location was the same with the operators observing, images of the pointer meter were taken from three different angles, as shown in Figure 5, and reading of the pointer meter was measured by the present method and the conventional method [25]. In Appendix B, the images of the pointer meter taken from three different angles were given for all the location of the pointer in the measurement. First, the radius \(r_{l}\) and \(r_{s}\) from the rotation center to the midpoint of long scales and short scales on the pointer meter were measured, that is \(r_{l}=602.5\) mm and \(r_{s}=584.6\) mm respectively. And angle between the zero scale and the maximum scale was measured, that was \(\alpha=271.5^{\circ}\). So, the world coordinates of the midpoints of short scales were obtained based on Equation (1). Second, the pixel coordinates of all the midpoints of scales and critical points (including rotation center and ends of pointer) were detected. After calibration the intrinsic parameters, the extrinsic parameters can be calibrated by the pixel coordinates and world coordinates of midpoints of short scales, as shown in Figure 6a. The extrinsic parameters were expressed as \([R,T]=\left[ \begin{array}{ccc}0.7620&0.6469&-7.2419\\ -0.6467&0.7626&-14.4477\\ 0.0326&0.0070&-895.6315\end{array} \right]\). And the world coordinates of midpoints on the short scales were transformed into the camera coordinates by the extrinsic parameters. Figure 4: (**a**) Measured pointer meter with radius of 620 mm; (**b**) measured pointer meters with a radius of 406 mm. Figure 5: Measured pointer meter captured from three different angles; (**a**) the camera at position 1; (**b**) the camera at position 2; (**c**) the camera at position 3. 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, as shown in Figure 7. Therefore, the coordinates of the critical point on the pointer meter can be corrected in this way, identifying the reading of the pointer meter by Equation (4). The coordinates of the endpoint of the pointer and rotation center in each pose were reported during the measurement in Tables 2 and 3. After rotating the meter image, changes of the coordinates of the endpoints and rotation center were shown in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Reference Values \(f_{0}\)** & **Coordinates of Pointer** & **Coordinates of Pointer** \\  & **(MPa)** & **Endpoint \(e_{1}\)(\(x_{e1}\),\(y_{e1}\))** & **Reverse Projection \(e\)(\(x_{e}\),\(y_{e}\))** \\ \hline
1 & 6.2 & (373.7191, 534.5052) & (249.1572, 526.5000) \\
2 & 10.7 & (432.0370, 310.4386) & (298.5000, 301.3333) \\
3 & 12.9 & (510.9333, 203.0400) & (382.0533, 191.0400) \\
4 & 18.6 & (753.3243, 65.5000) & (653.6667, 52.0270) \\
5 & 23.9 & (1010.6000, 115.6711) & (929.1842, 104.5000) \\
6 & 26.9 & (1095.8000, 176.6250) & (1020.5000, 170.4412) \\
7 & 30.2 & (1211.5000, 373.8158) & (1151.5000, 359.5834) \\
8 & 35.1 & (1206.5000, 645.8571) & (1164.5000, 627.8919) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison for the pixel coordinates of pointer endpoint. Figure 6: (**a**) Result of all the midpoints of short scales in the pointer meter with radius of 620 mm; (**b**) result of all the midpoints of short scales of the meter on the left in the image with radius of 406 mm. Figure 7: (**a**) Illustration of pointer meter plane before Reverse Projection; (**b**) illustration of pointer meter plane after Reverse Projection.