## 3 Results
### Comparative Analysis
The first row of Figure 7 presents the sparse-direct methods, DSO, CNN-DSO, LDSO, and DSM, demonstrating an outstanding performance compared to the rest of the evaluated methods belonging to different taxonomy classifications placing the sparse-direct methods as the best alternative for the Visual Odometry, SLAM, and 3D reconstruction tasks. It can be noticed that the CNN-DSO performed worse than the original DSO algorithm in sequences 13 and 22 but outperformed the DSO in sequence 39. The LDSO performance was close to the DSO, but it presented a better trajectory in some forward sequences and overcame the DSO in sequence 21. The DSM performed similarly to the rest of the sparse-direct approaches but occasionally presented trajectory loss issues affecting the overall performance. Furthermore, the DynaSLAM considerably outperformed the ORB-SLAM2, especially in challenging sequences like 18, 19, 21, 22, 23, 27, 28, 38, 39, and 40, among others, where the ORB-SLAM commonly failed. However, it occasionally presented trajectory loss and initialization issues. The ORB-SLAM2 optical flow implementation performed slightly worse on forwards and considerably worse on backward, especially in scenes 21, 22, 38, 39, 40, 46, 48, and 50. In contrast, the CNN SVO version considerably reduced the RMSE in most sequences compared to the SVO but still constantly failed in the outdoor sequences 21 and 22, showing random initialization and trajectory loss issues. As reported in [21], the SVO and LSD-SLAM methods had the worst results over the whole dataset, which was why [PERSON] et al. [21] did not include these methods in their study. However, we think it is vital to report such results and the errors attributed to these algorithms' commonly known initialization and trajectory loss errors over the sequences of the TUM-Mono dataset. The results processed on the TUM-Mono benchmark for the cumulative translation error \(e_{t}\), rotation error \(e_{r}\), scale error \(e^{\prime}_{s}\), start-segment alignment error \(e^{s}_{align}\), end-segment alignment error \(e^{\prime}_{align}\), and the translational RMSE \(e_{RMSE}\) were gathered in a database defining the method as the categoric variable. The statistical results were processed using R programing language. First, we removed the blank observations for the executions, where each algorithm became lost or could not initialize; so, the Mahalanobis distances were [88]  
Figure 7: The color-coded alignment error \(e_{align}\) for each algorithm in the TUM-Mono dataset. as a multivariate data cleaning technique to detect and remove the outlier observations. A 22.4577 cut score based on the \(\chi^{2}\) distribution for a 99.999% interval was set up detecting 344 outlier observations ending with a database of 8860 observations. Then, each dependent variable's normality and homogeneity assumptions were verified to select the appropriate statistical test for comparisons. For example, for the translation error, the \(p\)-values of 2.2 \(\times\) 10\({}^{-16}\) for the DSO, LDSO, CNN-DSO, DSM, DynaSLAM, ORB-SLAM, DF-ORB-SLAM, CNN-SVO, SVO, and LSD-SLAM methods were obtained in the Lilliefors (Kolmogorov-Smirnov) normality test; so, the sample did not reach the normality assumption. We applied [PERSON]'s test obtaining a \(p\)-value of 2.2 \(\times\) 10\({}^{-16}\) for the homogeneity assumption; so, the sample did not meet the homogeneity assumption. The rest of the dependent variables had similar assumptions verification results; thus, it was concluded that the sample was not parametric. Hence, the Kruskal-Wallis test was selected as the general test, with the Wilcoxon signed rank as a pairwise post hoc test. Figure 8 and Table 3 present the results obtained by applying the differences tests. As presented in Figure 8 and Table 3, the sample identified significant differences between the implemented algorithms.