## 4 Results
### Results on Depth Estimation and Its Precision--Experiment A  
We examined how measured depths based on RealSense behave under different lighting conditions, and similarly estimated depths in MiDaS and Alhashim. The Figure 9 shows the depth values of all 3 objects corresponding to the different methods.  
Figure 9a shows the RealSense data with objects situated like in experiment setup 3 in Figure 4. As we can see, the variance of the values for the right object is surprisingly lower than for the others under different illumination conditions. Moreover, the values are in the range of the real values in centimeters. For the MiDaS method (Figure 9b), we can confirm the progressive trend of depth values with increasing distances. Moreover, the estimated depth values in MiDaS are on the order of 100,000 with unknown scale. In the Alhashim method (Figure 9c), the estimated depth increases with increasing distance and the values are in the range of 0 to 10 without unit. Since we will later compare the results of the depth estimation and the depth difference estimation for each method itself, we do not need to use the same unit for all methods, since this would require additional measurements to find the scale and the shift to obtain absolute measurements in centimeters, and this is not our goal.  
In addition, there is a possibility that the figure raises a question regarding the points that can be considered as outliers in the boxplots. However, it is important to consider the fact that these values occur under different illumination conditions and we do not want to ignore the effect of this parameter in our data set. Therefore, we did not remove these points but kept them to consider them in the analysis.  
Figure 10 shows the dispersion of the datasets corresponding to the boxplots in the Figure 9. The estimated depth values of the left object at the distances \"d + 0\" and \"d + 8\" are more scattered with the MiDaS method than with other methods under different lighting conditions (Figure 10). In addition, the depth of the middle object measured by the RealSense cameras at distances \"d + 8\" and \"d + 16\" shows a larger discrepancy in the data than the other methods. It should be noted that the range of the standard deviation is different for the different objects. For example, for the left object there is a high standard deviation (more than 0.8) and for the right object there is a low standard deviation (less  
Figure 9: Depth values of objects provided by the RealSense camera (**a**), by the MiDaS method (**b**) and by the Alhashim method (**c**) under different lighting conditions.  
than 0.14). But if we look at the Figure 10, we can easily see the big difference between Alhashim and the other methods.  
Table 1 reports the quantification of the dispersion of the estimated depth for different methods. As explained in Section 3.6.1, the dispersion is calculated by multiplying the maximum normalized standard deviation by a distance. For example, for the RealSense data, the maximum standard deviation (0.061) is at distance \"d + 24\". Thus, the value for RealSense given in Table 1 shows the two standard deviations measured by multiplying 0.061 by \"d + 24\" twice, which is 2 \(\times\) (0.061 \(\times\) 42 cm) = 5.1. In general, the depth estimation is more consistent when the dispersion is smaller. The results show that 95% of the values provided by RealSense have a standard deviation of less than 5.1 cm at different distances and lighting conditions, while this value is 9.8 cm for MiDaS and 25.3 cm for Alhashim (Table 1).  
Results on Effect of the Light in Depth EstimationFigure 11: The depth estimation under 3 lighting conditions (from left to right);dark, medium and light brightness. (**a**) using the RealSense 3D camera, (**b**) using a 2D image and MiDaS as the algorithm for depth estimation, (**c**) using a 2D image and Alhashim as the algorithm for depth estimation.