## 6 Experiments
### Results  
#### 6.4.1 Influence of the Parameters on the Performance of the Algorithm  
Figure 9 shows the results obtained with the HOG descriptor, and Figure 10 with gist for (a) INNOVA, (b) Saarbrucken and (c) Freiburg datasets. In both figures, the first row shows the number of clusters obtained once all the images of each trajectory were processed by the proposed algorithm. The second row presents the average silhouette of the descriptors. These figures show the influence of the parameters \(y\) and \(\Omega\), which are introduced in Table S4. First, considering parameter \(y\), as expected, the higher \(y\) is the fewer clusters will be in the final map. The effect of this parameter is less significant when gist is used, as shown Figure 10. Second, \(\Omega\) limits \(x\), the parameter used in Equation (4). If this value is low, more nodes can be selected on the Node Level Loop closure so it can be more difficult to obtain a high number of consecutive images without being in a cluster so the effect of creating new nodes decreases. However, if this value is too high it may lead to some images in a row not being assigned to any node when no new cluster should be created in the Node Level Loop Closure process. As Figures 9 and 10 show, when HOG is used, the parameter \(y\) has more influence on the number of clusters than \(\Omega\) does, yet with the gist descriptor, the latter has greater influence. The second row of each subfigure in Figures 9 and 10 shows the average silhouette after the mapping process. In general, medium values of \(\Omega\) offer a higher silhouette but the effect of \(y\) is more variable. To better study the results, Table 2 shows the maximum values of silhouette and the number of clusters obtained with the different datasets. It also shows the values of the parameters that lead to that maximum silhouette. It shows how values of \(\Omega\) around 1.85 offer the best results although when using gist descriptor good silhouettes can be also obtained with higher \(\Omega\) values. Meanwhile, the results are not substantially dependent on \(y\). As it is possible to observe, better results are obtained using the HOG descriptorThis behaviour was observed among different experiments and situations, which makes us conclude that HOG is a more suitable option to describe the images with the objective of creating a map incrementally. In addition, the silhouette obtained with the Freiburg dataset is substantially lower than the silhouette obtained with the two other datasets. The reason can be twofold. On the one hand, the route contains a large number of images, and it has some spaces which are visually similar, which challenges the mapping algorithm. On the other hand, the Freiburg environment contains several glass walls, and large and numerous windows, which produce saturations in the images and mixing between the information of adjacent rooms. These phenomena also have a negative impact upon the performance of the method. Figure 9: Results obtained with the HOG descriptor for different values of \(y\) and \(\Omega\) for the datasets (**a**) INNOVA, (**b**) Saarbrücken and (**c**) Freiburg. The first row of each subfigure shows the final number of clusters (colour mapped) and the second one the average silhouette (colour mapped) after the proposed incremental hierarchical mapping process. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**HOG** & & \\ \hline
**Dataset** & **Silhouette** & **Number of Clusters** & **Parameters Values** \\ \hline Route 1 INNOVA & 0.3973 & 6 & \(y=2.25\), \(\Omega=1.7\) \\ Route 2 Saarbrücken & 0.2756 & 16 & \(y=1.25\), \(\Omega=1.85\) \\ Route 3 Freiburg & \(-0.1526\) & 30 & \(y=0.75\), \(\Omega=1.7\) \\ \hline
**Gist** & & \\ \hline
**Dataset** & **Silhouette** & **Number of Clusters** & **Parameters Values** \\ \hline Route 1 INNOVA & 0.2556 & 6 & \(y=1.5\), \(\Omega=2.15\) \\ Route 2 Saarbrücken & 0.1262 & 19 & \(y=1.5\), \(\Omega=1.85\) \\ Route 3 Freiburg & \(-0.1449\) & 34 & \(y=1.5\), \(\Omega=2.3\) \\ \hline \hline \end{tabular}
\end{table}