## 3 Results
### Comparative Analysis
By observing the translation error, it can be noticed that the DSO, LDSO, and CNN-DSO methods achieved the most significant performance of the ten evaluated algorithms; despite the DSO performing at 2.18% and 1.05% worse than the DSO and CNN-DSO in this metric, the difference was not significant among them. The DSO, LDSO, and CNN-DSO achieved significantly lower errors than the dense-direct method DSM. The feature-based methods performed significantly worse than the sparse-direct methods, where the DynaSLAM achieved a significantly better performance than the ORB-SLAM2 and DF-ORB-SLAM, reaching a 39.19% and 52.02% translation error reduction, respectively. The CNN-SVO performed slightly worse than the DynaSLAM, but the difference was not significant, while it significantly outperformed its classic version achieving a 47.57% translation error reduction. The LSD-SLAM performed substantially worse in terms of the translation error metric among the ten algorithms. Regarding the rotation error, the DSO and LDSO achieved significantly better results than the rest of the algorithms. Although the DSO showed an average rotation error reduction close to 3.66%, the difference was not significant. The DSO performed significantly better than its neuronal version in the accumulated rotation error metric. The LDSO performed around 5.02% better than the CNN-DSO, but the difference was not significant. The DSM performed significantly worse than the rest of the sparse-direct methods. The feature-based methods performed worse than the sparse-direct methods in the rotation error metric, where the DynaSLAM achieved a better performance than the ORB-SLAM2 and DF-ORB-SLAM, showing an average error reduction close to 33.30% and 54.97%, respectively. The CNN-SVO performed better than the DF-ORB-SLAM, SVO, and LSD-SLAM in terms of the rotation error metric, significantly outperforming its classic SVO version showing a 58.07% average reduction in the rotation error. The LSD-SLAM performed significantly worse than the other methods in the rotation error metric. For the scale error metric, the sparse-direct methods, DSO, LDSO, and CNN-DSO, performed significantly better, where the CNN-DSO showed the best performance by an average 0.49% and 0.23% reduction compared to the DSO and LDSO, but the difference was not significant. The DSM performed significantly worse than the CNN-DSO. The feature-based methods performed significantly worse than the sparse-direct methods on the scale error metric, where the DynaSLAM achieved the significantly best performance and an average reduction of 10.60% and 9.02% compared to the ORB-SLAM2 and DF-ORB-SLAM. The CNN-SVO performed significantly better than the feature-based methods, SVO and LSD-SLAM, exhibiting a 19.14% average error reduction compared to its classic version, SVO. Again, the LSD-SLAM performed worst in the scale error metric. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Translation Error** & **Rotation Error** & **Scale Error** \\ \hline Kruskal–Wallis & \(\chi^{2}=3582.9\) & \(\chi^{2}=2278.4\) & \(\chi^{2}=2419.1\) \\ general test & \(p_{value}=2.2\times 10^{-16}\) & \(p_{value}=2.2\times 10^{-16}\) & \(p_{value}=2.2\times 10^{-16}\) \\ \hline DSO & 0.8064585  & 0.8800369  & 1.064086  \\ LDSO & 0.7892125  & 0.9135608  & 1.061302  \\ CNN-DSO & 0.7980411  & 0.9618528  & 1.058849  \\ DSM & 0.8519143  & 1.1117710  & 1.1064615  \\ DynaSLAM & 1.7473504  & 1.126499  \\ ORB-SLAM2 & 2.873813  & 2.858643  & 1.260155  \\ CNN-SVO & 1.6248001  & 1.415955  & 1.086399  \\ DF-ORB-SLAM & 3.6423921  & 3.494040  \\ SVO & 5.4819407  & 3.3772024  & 1.343603  \\ LSD-SLAM & 9.1403348  & 14.9621188  & 2.044298  \\ \hline \hline \end{tabular}  
Means with different letters in the same column differ significantly according to the Kruskal–Wallis test and pairwise [PERSON] signed rank test for \(p_{value}\leq 0.05\).  
\end{table} 
Table 3: Medians and Kruskal–Wallis comparisons for each algorithm’s translation, rotation, and scale errors.