## 4 Results
### Improved Performance on the Argoverse Dataset
#### 4.2.3 Findings  
Based on both histogram-based and numerical analysis, we make the following findings:  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**Default Gate (10 m, 45\({}^{\circ}\))**} & \multicolumn{2}{c}{**Strict Gate (5 m, 30\({}^{\circ}\))**} \\ \cline{2-5}
**Method** & **Removed** & **Failure [\%]** & **Removed** & **Failure [\%]** \\ \hline MM-VSM (ours) & 1319 & 8.56 & **1781** & **11.56** \\ Semantic [15] & 2436 & 15.81 & 5527 & 35.87 \\ BAAM [13] & **834** & **5.41** & 2 204 & 14.31 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Frames discarded by each acceptance gate (\(N_{\text{tot}}=15,407\)). Bold numbers indicate the lowest failure rate per gate.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Translation [m]**} & \multicolumn{4}{c}{**Rotation [\({}^{\circ}\)]**} \\ \cline{2-7}
**Method** & \(\mu\pm\sigma\) & **Median** & \(P_{95}\) & \(\mu\pm\sigma\) & **Median** & \(P_{95}\) \\ \hline MM-VSM (ours) & \(\mathbf{0.56\pm 0.94}\) & 0.29 & 1.79 & \(\mathbf{6.35\pm 6.49}\) & 4.47 & 20.61 \\ Semantic [15] & \(3.18\pm 2.39\) & 2.59 & 8.16 & \(7.82\pm 7.20\) & 5.47 & 23.48 \\ BAAM [13] & \(2.79\pm 1.50\) & 2.44 & 5.51 & \(10.99\pm 4.09\) & 9.95 & 18.30 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Absolute pose error on accepted frames (mean \(\mu\), standard deviation \(\sigma\), median, 95-percentile \(P_{95}\)). Boldface marks the best (lowest mean).  
Figure 8: Translational APE histogram. In **green** the APE histogram of MM-VSM, in **blue** Semantic [15], and in **red** BAAM [13].  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Axis [\({}^{\circ}\)]** & **MM-VSM (Ours)** & **Semantic [15]** & **BAAM [13]** \\ \hline Roll & \(\mathbf{2.60\pm 3.23}\) & \(2.78\pm 3.26\) & \(2.88\pm 1.87\) \\ Pitch & \(\mathbf{3.28\pm 4.86}\) & \(3.62\pm 3.67\) & \(9.71\pm 3.41\) \\ Yaw & \(3.09\pm 4.66\) & \(4.78\pm 6.73\) & \(\mathbf{2.97\pm 3.43}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Local-frame roll, pitch, and yaw error on accepted frames (mean \(\mu\pm\sigma\) in degrees). Lower is better; best mean per axis in bold.  
* **Translational accuracy.** MM-VSM significantly improves the robustness and accuracy of Semantic, producing the best translational APE on the evaluated frames, and also failing fewer times than BAAM.
* **Rotational accuracy.** In total rotational APE, MM-VSM outperforms BAAM and significantly improves Semantic.
* **Local-frame RPY alignment.** Using roll/pitch/yaw defined in the _target's own axes_, MM-VSM is best on roll (2.60\({}^{\circ}\)) and pitch (3.28\({}^{\circ}\)), whereas BAAM is best on yaw (2.97\({}^{\circ}\)). Semantic sits consistently in the middle. Thus, BAAM's overall rotation error stems primarily from roll-pitch misalignment, which is indicative of the training bias, due to the shifted camera position and viewpoint.
* **Accuracy vs. robustness.** MM-VSM delivers the best accuracy _and_ passes the strict gate most often (lowest failure 11.56%). BAAM is the most robust under the default gate (5.41% failures) but trades off accuracy; Semantic is weakest on both gates.
* **Histograms.** Looking at the head of the histograms, Semantic offers better peak accuracy compared to BAAM, and MM-VSM produces large improvements over both. This indicates that our LiDAR pipeline succesfully removes failures correcting Semantic's errors.
* **Axis-specific trends.** MM-VSM excels at stabilizing vehicle roll and pitch; BAAM delivers the sharpest yaw on average, which benefits heading-aware downstream tasks.  
In summary, MM-VSM occupies the sweet spot on the accuracy-robustness spectrum, while BAAM favours robustness at the expense of roll-pitch accuracy. Note that BAAM (and its OpenPifpaf feature extractor) were trained on ApolloCar3D, whose slightly different camera viewpoint induces a static bias on the Argoverse validation suite--visible in BAAM's roll-pitch, and slight pose errors.