*5.3. Localization Using the Compact Maps*

This section evaluates the performance of the compact maps to solve the localization problem. The objective is to achieve a compactness that presents a balance between computing time and accuracy of localization. To carry out the evaluation, among the mapping results, the spectral clustering algorithm is selected with the *gist* descriptor (*k*<sup>3</sup> = 32 and *nmasks* = 16). With this configuration, a map per environment is built, using the training images. After that, the test images are used to solve the localization problem. The previous subsection proved that the best option to build the compressed map was through the use of the *gist* descriptor. Nevertheless, the three proposed global appearance descriptors are proposed again to solve the localization task (because mapping and localization are two independent processes, and the performance of the descriptors could be different in a localization framework). For each test image, its descriptor is calculated (either by FS, HOG, or *gist*), and then, it is compared with the cluster representatives of the compact map. Afterwards, the most similar cluster is retained. Three distance measures are considered for this comparison: (1) the correlation distance, (2) the cosine distance, and (3) the Euclidean distance. In order to carry out a realistic comparison, despite the real position of the robot being provided by the database, only visual information will be used to estimate the position of the robot. The metric information will be used only as ground truth, for comparison purposes.

**Figure 15.** Clusters obtained in the COLD environments through the use of Spectral clustering and *gist* description. (**a**) Freiburg and (**b**) Saarbrücken environment.

(b)

## 5.3.1. Localization in the Quorum V Environment

Figure 16 shows the average localization error (cm) obtained when FS (first row), HOG (second row), and *gist* (third row) are used, respectively, as the descriptor. Figure 17 presents the computational time (s). In the case of HOG, the effect of homomorphic filtering adds a constant time of 0.02 s per test image. Regarding the number of clusters, *nc* = 872 is considered since this value provides the case in which the localization is solved without compacting the map. This value is used as a reference to know the relative utility of the compacted map.

**Figure 16.** Results of the localization process with FS, HOG, and *gist* used to describe the representatives of the clusters and the test images: average localization error (cm) vs. number of clusters. Quorum V environment.

The FS descriptor is not good for localization since the best choice (correlation distance) presents errors between 650 cm and 800 cm depending on the number of clusters and the size of the descriptor. HOG clearly improves the localization task. Except for the case *k*<sup>2</sup> = 2, the average localization error decreases as the number of clusters increases, and these values go from 500 cm when *nc* is low and achieve values under 100 cm (when *nc* is high). As for the *gist* descriptor, it also produces relatively good results, but they are not as good as those obtained through the use of HOG. The localization task achieves the best results when the correlation distance is used.

Regarding the computation time, with the FS descriptor, as the number of clusters increases, the computational time required for the localization task increases substantially. With HOG, the time is much lower than FS, and it keeps constant independently of the number of clusters. This means that the time to calculate the descriptor is higher than the time to compare it with the map. The computation time required for *gist* is also worse than HOG. The time required by *gist* is around twice the time with HOG.

**Figure 17.** Results of the localization process with FS, HOG, and *gist* used to describe the representatives of the clusters and the test images: average computing time vs. number of clusters. Quorum V environment.

In general, as the number of clusters increases, the computation time required for the localization task also increases, and the average localization error decreases. This is an expected behaviour due to the fact that a high number of clusters means that the map is less compact and the information stays in representatives of the clusters whose distance to the test image is lower. Hence, the more clusters, the more comparisons with representatives must be carried out. This leads to a higher computation time and lower average localization error distance. Thus, a balance between these behaviours must be achieved. Therefore, in order to solve the localization in an environment whose properties are similar to the Quorum V environment (grid-distributed data), the optimal values are reached through the use of a HOG descriptor with *k*<sup>2</sup> = [32, 64] and correlation distance.
