## 4 Experimental Phase and Analysis  
In order to evaluate the performance of the change of domain, a quantitative analysis was used. The following metrics were used to measure the depth estimation on generated images defined in the state-of-the-art [59]. Therefore, six indicators allow describing the performance:  
1. Average relative error (rel): \(\frac{1}{n}\sum_{p}^{n}\frac{\left|Y_{p}-\hat{Y}_{p}\right|}{\hat{Y}_{p}}\);
2. Root mean-squared error (rms): \(\frac{1}{n}\sum_{p}^{n}(Y_{p}-\hat{Y}_{p})^{2}\);
3. Average (\(log_{10}\)) error: \(\frac{1}{n}\sum_{p}^{n}\left|log_{10}(Y_{p})-log_{10}(\hat{Y}_{p})\right|\);
4. Threshold accuracy (\(\delta_{i}\)): % of \(Y_{p}\) s.t. \(\max\{\frac{Y_{p}}{Y_{p}},\frac{\hat{Y}_{p}}{Y_{p}}\}=\delta<thr\) for \(thr=1.25,1.25^{2},1.25^{3}\);  
where \(Y_{p}\) is a pixel in depth image \(Y\), \(\hat{Y}_{p}\) is a pixel in estimated depth image \(\hat{Y}\), and \(n\) is the total number of pixels for each depth image. Table 3 shows the performance of the domain change because an image taken in an authentic environment suggests the virtual representation of the respective authentic image. It is not necessary to obtain a value of zero in the result. Therefore, the metrics help describe the performance of the generated path with the different approaches. The performance of the Deep Convolutional Neural Network's (DNCNN) training is shown in Figure 21, which shows the behavior on 1000 epochs with a normalized output, which had a precision of 90% with 20 test samples. The experiment consisted of describing the evaluation of two different experiments. The first contained all nodes generated by \(A^{*}\) and the behavior throughout the navigation mesh (NavM), where the number of nodes was fewer than that of the full-path \(A^{*}\). Figure 22 represents the behavior of the auto-encoder (AED) training, where 5000 epochs had a precision of 95% with 20 test samples. This experiment, similar to the evaluation before, showed two behaviors with all nodes created by \(A^{*}\) and with the navigation mesh reducing the number of nodes in the path. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **rel-std \(\downarrow\)** & **rms-std \(\downarrow\)** & \(log_{10}\)-std \(\downarrow\) & \(\delta_{1}\)-std \(\uparrow\) & \(\delta_{2}\)-std \(\uparrow\) & \(\delta_{3}\)-std \(\uparrow\) \\ \hline GAN & 0.9481–0.5614 & 0.9418–0.2469 & 0.3479–0.0722 & 0.6767–0.0235 & 0.7925–0.0278 & 0.8491–0.0282 \\ \hline GAN-Noise & 0.1693–0.2068 & 0.3862–0.1420 & 0.2392–0.0832 & 0.8538–0.0592 & 0.9334–0.0463 & 0.9624–0.0367 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of the quantitative metrics in our approach and the standard deviation of 50 samples. \(\downarrow\), lower is better; \(\uparrow\), higher is better. Figure 21: Deep convolutional neural network behavior with navigation meshes and the full path. In this case, hierarchical clustering was not used because this approach did not require training. According to the results, the behaviors of the deep convolutional neural network and auto-encoder with navigation mesh converged before as the output contained fewer nodes than the full path. On the other hand, Table 4 describes the behavior of the evaluation of the vectors based on the Euclidean distance (Equation (12)), the Manhattan distance (Equation (13)), and the similarity by the cosine (Equation (14)) used to analyze the difference between the expected vector \(x\) and the generated vector \(y\). The free collision coefficient of Equation (15) determines if at least one node generates an inadequate path quantitatively. \[euclidean=\sqrt{\sum_{i=0}^{k}(\vec{x_{i}}-\vec{y_{i}})^{2}} \tag{12}\]  
\[manhattan=\sum_{i=0}^{k}|(\vec{x_{i}}-\vec{y_{i}})| \tag{13}\]  
\[cosine\ similarity=\frac{\vec{x}\cdot\vec{y}}{\|\vec{x}\|\|\vec{y}\|} \tag{14}\]  
\[C_{free\ collision}=1-\frac{\sum_{i=1}^{N_{samples}}\left\{ \begin{array}{c} if\ exists\ collision\ c=1\\ else\ c=0\end{array} \right.