## 3 Experiments and Results
### Experiment 4  
This experiment was based on Set 4. Specifically, Set 4 was used to compare the accuracy of uniform and non-uniform models for general horizontal measurements. Both  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Working** & \multicolumn{4}{c}{**Non-Uniform**} & \multicolumn{4}{c}{**Uniform**} \\ \cline{2-9}
**Distance** & \multicolumn{2}{c}{**Error**} & \multicolumn{2}{c}{**Magnitude of Error**} & \multicolumn{2}{c}{**Error**} & \multicolumn{2}{c}{**Magnitude of Error**} \\ \cline{2-9}
**Interval** **(mm)** & **Mean (mm)** & **Std (mm)** & **Mean (mm)** & **Std (mm)** & **Mean (mm)** & **Std (mm)** & **Mean (mm)** & **Std (mm)** \\ \hline (0, 5) & 0.003 & 0.039 & 0.029 & 0.026 & \(-0.192\) & 0.077 & 0.192 & 0.075 \\ \hline \([5,10)\) & \(-0.012\) & 0.049 & 0.04 & 0.031 & \(-0.  
models were trained with all data points from Set 1. Additionally, Set 4 was recorded in the presence of laser points. Therefore, the required working distance was estimated using the improved PCA method (Equations (16) and (17)). To investigate the effect of working distance on general horizontal measurement in the uniform model, measurement errors from a 5 mm line segment recorded at working distances of 5.12, 9.98, 14.98, and 20.18 mm were computed. One-way ANOVA with a trimming level of 0.2 and 1000 bootstrap samples [32] was non-significant (\(p=0.61\)). Figure 12A presents boxplot of errors for different working distances. To investigate the effect of length of the target object on general horizontal measurement in the uniform model, measurement errors from 5, 10, 15, and 20 mm line segments recorded at the working distance of 20.18 mm were computed. One-way ANOVA with a trimming level of 0.2 and 1000 bootstrap samples [32] was non-significant (\(p=0.22\)). Figure 12B presents boxplot of errors for target objects with different lengths. Considering these non-significant results, all measurement errors were combined into a single group. The overall measurement error was \(-0.8\pm 0.69\) mm, and the magnitude of error was 0.86 \(\pm\) 0.6 mm for the uniform method. A similar approach was followed for the non-uniform method. Figure 13 presents boxplot of errors for this analysis. The effects of working distance (\(p=0.64\)) and length of the target object (\(p=0.43\)) were non-significant. Considering these non-significant results, all measurement errors were combined into a single group. The overall measurement error for the non-uniform method was \(-0.2\pm 0.29\) mm, and the magnitude of error was 0.27 \(\pm\) 0.24 mm. Figure 12: Performance of uniform model for general measurements: (**A**) effect of working distance, and (**B**) effect of object length. Figure 13: Performance of non-uniform model for general measurements: (**A**) effect of working distance, (**B**) effect of object length. Comparing boxplots and average errors of both methods indicate that errors from the uniform approach on average is three times higher than the non-uniform method. These results demonstrate the advantage of the proposed non-uniform approach. Investigation of boxplots of Figure 12 may indicate a general trend for errors of the uniform method. Specifically, the measurement error seems to increase with the working distance and length of the target object. In experiment 2, we saw a strong and positive correlation between uniform method error and these two parameters, which confirms this subjective observation. However, the objective analysis of ANOVA failed to detect a significant trend. Experiment 2 relied on the detection of circular shapes. This specific geometry enabled us to achieve sub-pixel resolution on measuring the length of target objects (i.e., radii of circles). However, experiment 4 was based on the detection of lines, which has the resolution of a pixel. Investigation of the performance of the non-uniform method also supports this. Specifically, the non-uniform method showed very week correlations in experiment 2 (Table 3).