## 2 Materials and Methods
### Metrics  
As SLAM, SFM, and VO are ill-posed problems that can be addressed from multiple perspectives and a wide variety of techniques, comparing the final obtained 3D reconstruction is not the best alternative for monocular RGB methods because of the different sparsity, scale, and type of output that each method brings, due to the difficulty of accruing accurate groundtruth maps [81]. At the same time, trajectories can be acquired using INS, GPS, LASER, RADAR, LIDAR, and Kinect systems, among others, with acceptable accuracy. In this way, as discussed in [6], the best way of comparing SLAM and VO algorithms of diverse nature (see Figures 1 and 2) is by comparing the output trajectory in each algorithm, because even if the method is focused on reconstruction only, it has been demonstrated that solving both problems of landing and mapping simultaneously brings the best reconstruction results [3], as the quality of the final reconstruction tightly depends in the quality of the ego-motion estimation. Hence, the metrics we used for this comparison are entirely based on ego-motion estimation, which can be effectively compared for all SLAM and VO algorithms. Among the different metrics for ego-motion available in the literature, we found that the metrics present in most of the methods listed in [9] were: the absolute trajectory RMSE (ATE), the relative pose RMSE (RPE), the cumulated trajectory, rotation, and scale errors, the alignment error, and the alignment RMSE. The ATE and RPE are local pose accuracy metrics proposed by [81], commonly applied along with the EUROC dataset. The relative pose error is a metric for the accuracy of an estimated trajectory over a defined time interval \(\Delta\). In this way, this metric corresponds to the drift of the estimated trajectory. For a sequence of estimated poses \(\mathbf{P}_{1},\ \ldots,\ \mathbf{P}_{n}\ \in SE(3)\)  
Figure 2: Examples of each indoor algorithm sequence execution _seq-01_—TUM-Mono dataset. The implemented methods were: (**a**) ORB-SLAM2, (**b**) DF-ORB-SLAM, (**c**) LSD-SLAM, (**d**) DSO, (**e**) CNN-DSO, (**f**) LDSO, (**g**) DSM, (**h**) DynaSLAM, (**i**) SVO, and (**j**) CNN-SVO. and a ground truth trajectory \(\mathbf{Q}_{1}\),..., \(\mathbf{Q}_{n}\)\(\in\)\(SE(3)\), the relative pose error for each timestamp \(i\) is:  
\[\mathbf{E}_{i}:=\Big{(}\mathbf{Q}_{i}^{-1}\mathbf{Q}_{i+\Delta}\Big{)}^{-1}\Big{(}\mathbf{P}_{i}^ {-1}\mathbf{P}_{i+\Delta}\Big{)} \tag{1}\]  
So, for a sequence of n poses, an \(m=n-\Delta\) number of relative poses is obtained. Then the root mean square error (\(RMSE\)) for such errors over all the timestamps of the sequence can be calculated as:  
\[RMSE(\mathbf{E}_{ixn},\ \Delta):=\sqrt{\frac{1}{m}{\sum_{i=1}^{m}}{\|trans(\mathbf{E}_{i}) \|}^{2}} \tag{2}\]  
where \(trans(\mathbf{E}_{i})\) corresponds to the translational component of the relative pose error \(\mathbf{E}_{i}\). Many VO or SLAM systems can be evaluated for a timestep interval \(\Delta=1\), but some methods work on frames or keyframes windows (like [21; 30; 63]); thus, different \(\Delta\) values might be appropriate for testing. So, for SLAM systems' evaluation, it can also be useful to obtain the \(RMSE\) for all the possible time intervals:  
\[RMSE(\mathbf{E}_{ixn})=\frac{1}{n}{\sum_{\Delta=1}^{m}}\ RMSE(\mathbf{E}_{ixn},\ \Delta) \tag{3}\]  
The ATE was proposed to evaluate the estimated trajectory's global consistency. The ATE estimation was achieved by comparing the absolute distances between the estimated trajectory and the ground truth directly.