## 5 Results
### Dependency on Sampling and Routing  
Within a single-stage survey, a parameter directly affecting the resulting survey design is the number of points used to generate the sampling set. A test has been conducted in order to assess how the size of the sampling set is related to the extent and coverage of the resulting survey. This can be used to tune the survey length independently on the focus map driving the spatial prioritization.  
Four different surveys have been generated for four different sampling sets, respectively containing 50, 100, 200, and 400 points (referred to as the sample size, _sd_). Each sampling set has been generated after the same focus map and following the same PPS sampling design (see Figure 14).  
Figure 14: Comparison among different single stage surveys based on different sample sets. From the left, results are shown for 50-, 200-, and 400-point sample sets.  
Figure 13: Upper section: example of omnidirectional image. Lower section: (**A**) Partial rectilinear re-projection of the omnidirectional image. Only a portion of the original image is visible, but the operator can dynamically change the angle of view, direction, and apparent zoom in the re-projected image. (**B**) Rectilinear projection of an omnidirectional image taken in the sample place at a different time, and with rainy weather.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample Set _sd_** & **Survey Length** & **\% of Street** & **Covered Buildings** & **\% of Building** \\
**(No. of pts)** & \(L\) **(km)** & **Network** & **(30 m Buffer)** & **Stock** \\ \hline
50 & 38.5 & 10 & 3629 & 19 \\
100 & 53.7 & 14 & 5279 & 28 \\
200 & 70 & 18.3 & 6414 & 33.5 \\
400 & 104 & 27 & 8567 & 44.8 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Empirical correlation between dimension of the sample sets, length of the resulting survey (in km), and number of covered buildings (_i.e._, lying within a 30-m buffer from the driven route).  
Figure 15: Comparison between the length of the resulting route in the optimized case (blue plot) and in the random case (black plot with red points) (**top**). As the plot shows, the route length is proportional to the square root of the dimension of the sample set, and the random route is systematically longer. Comparison of the expected number of covered policies with respect to route length (in km) for random sampling (black line, red dots) and focused sampling (blue line, blue dots) (**bottom**). The relationship is apparently linear for the focused sampling, while it appears to not be linear for the random sampling, which is much less efficient in any case.  
In Table 6 the empirical correlation between the dimension of the sample set and the length in km of the resulting survey is reported. As displayed by the graph in Figure 15 (top), the length \(L\) of the resulting route is proportional to the square root of the sample size \(sd\):  
\[L=\alpha_{o}+\alpha_{s}\sqrt{sd} \tag{3}\]  
where the fitted coefficients \(\alpha_{0}=-0.7561\) and \(\alpha_{1}=5.1925\), and the r-squared value is 0.9972.  
Since, depending on the selected location, the average speed of the mobile mapping system can be estimated, knowledge of the relationships between sampling set and survey length allows for more efficient preparation of field activities.