# Computer Vision Measurement of Pointer Meter Readings Based on Inverse Perspective Mapping
## 3 Experiments and Analysis
### Measure One Pointer Meter
Then, the readings of the pointer meter were compared with the reference value to calculate absolute errors, as shown in Tables 4 and 5. Here, \(f_{0}\) was the reference value; \(f_{1}{}^{(1)},f_{1}{}^{(2)},f_{1}{}^{(3)}\) respectively represented the results of readings measured by conventional methods in the meter image taken from three angles; \(f_{2}{}^{(1)},f_{2}{}^{(2)},f_{2}{}^{(3)}\) respectively represented the results of readings measured by proposed methods in the meter image taken from the three angles which kept the same angle as conventional measurement. The pointer meter used in the experiment was a 0 to 40 MPa pressure gauge with a precision of \(\delta=\frac{\Delta_{\text{max}}}{40}\times 100\%=\)0.4%, and the pointer meter's maximum allowable absolute error was \(\Delta_{\text{max}}=0.16\) MPa. The range accuracy of the meter reached 2 digits after the decimal point. In order to make the accuracy of the meter recognition algorithm reach the accuracy of the meter range, this paper kept the effective digit to the next digit of the precision. The pixel coordinates of mid-point scales were achieved using the sub-pixel detection method to improve the measurement resolution. In the experiment, the image of the pointer meter was \(1292\times 964\) pixels captured by a camera. We estimated the arc length \(l=8.6\) pixel by calculating the distance between center points of \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Reference Values**} & **Position 1** & **Position 2** & **Position 3** \\  & \(f_{0}\) **(MPa)** & \(f_{1}{}^{(1)}\) **(MPa)** & \(f_{1}{}^{(2)}\) **(MPa)** & \(f_{1}{}^{(3)}\) **(MPa)** \\ \hline
1 & 6.2 & 6.059 & 6.342 & 6.301 \\
2 & 10.7 & 10.542 & 10.796 & 10.859 \\
3 & 12.9 & 12.753 & 12.806 & 13.043 \\
4 & 18.6 & 18.469 & 18.507 & 18.748 \\
5 & 23.9 & 24.039 & 23.771 & 23.752 \\
6 & 26.9 & 27.021 & 27.057 & 26.753 \\
7 & 30.2 & 30.358 & 30.306 & 30.059 \\
8 & 35.1 & 34.966 & 35.002 & 35.254 \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of the results of readings measured by conventional methods in the meter image taken from three angles. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**No. **} & \multicolumn{2}{c}{**Reference Values \(f_{0}\)**} & **Coordinates of Rotation** & **Coordinates of Rotation Center after** \\  & **(MPa)** & **Center \(c_{1}\)(\(\mathbf{x}_{c1}\),\(\mathbf{y}_{c1}\))** & **Reverse Projection \(c\)(\(\mathbf{x}_{c}\),\(\mathbf{y}_{c}\))** \\ \hline
1 & 6.2 & (757.5000, 522.1006) & (757.2410, 522.1089) \\
2 & 10.7 & (758.1498, 525.2314) & (758.3  
two adjacent scales, and the radius of the pointer meter region \(r=363.77\) pixel can also be calculated. Then, the angle \(\delta=\frac{180^{\circ}\times l}{\pi\times r}=1.36^{\circ}\) was converted from the arc length. And the angle \(\delta_{v}\) occupied by each pixel was \(0.15^{\circ}\). Therefore, the camera's hardware resolution was \(0.15^{\circ}\) under this experimental condition which includes strength of illumination and the distance \(d=1.5\) m between camera and measured meter plane. As shown in Tables 6 and 7, the absolute errors \(\Delta f_{2}(^{1}),\Delta f_{2}(^{2}),\Delta f_{2}(^{3})\) of the measurement by proposed method were mostly between 1 kPa and 9 kPa. The maximum absolute error 9 kPa still did not exceed the absolute errors \(\Delta f_{1}(^{1}),\Delta f_{1}(^{2}),\Delta f_{1}(^{3})\) of measurement by the conventional method. In addition, through the proposed method, the readings of the measured pointer meter in the images taken from three angles had almost no change compared with the reference values. It can be seen from the experimental results that the identification accuracy of the pointer meter calibration system was within the allowable range. Compared with the conventional measurement method, the maximum relative error was \(\Delta f_{r}=0.022\%\), which met the measurement requirements.