## 4 Results
### Quantitative Evaluation  
#### 4.2.1 Tracking Performance  
Table 1 presents a comparison of RK-SLAM with the NeRF-based and 3 DGS-based SLAM algorithms on the TUM-RGBD dataset. Evidently, RK-SLAM achieved state-of-the-art performance, outperforming the second-best approach by 0.25 cm on average. Notably, in the fr3/Office sequence, our method outperformed the second-best approach by 0.34 cm (approximately a 23% improvement), which is a significant margin. Table 2 shows the performance of RK-SLAM on the ScanNet dataset. Although its performance on ScanNet was not as strong as on the TUM-RGBD dataset, it still achieved good results on  
some sequences, securing a place in the top three in terms of average performance. This demonstrates the potential of RK-SLAM.  
Table 3 compares RK-SLAM with the NeRF-based and 3 DGS-based SLAM algorithms on the Replica dataset. RK-SLAM, again, achieved the best performance. Although the margin over the second-best result was only 0.01 cm, RK-SLAM achieved the best performance in five out of eight sequences, significantly outperforming the second-best method, which ranked first in only two sequences. Moreover, it is noteworthy that the standard deviation of RK-SLAM across all sequences was 0.037, which was significantly better than the second-best at 0.058 and the third-best at 0.212. This indicates that RK-SLAM delivers more stable performance across different sequences.  
In summary, we evaluated the performance of RK-SLAM on two types of datasets, and it consistently achieved competitive results. Notably, compared to CG-SLAM, RK-SLAM demonstrated a comparable performance on the Replica dataset while significantly outperforming it on the TUM-RGBD dataset. The results clearly highlight the robustness of RK-SLAM with depth.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **fr1/desk** & **fr2/xyz** & **fr3/Office** & **Avg.** \\ \hline NICE-SLAM & 2.70 & 1.80 & 3.00 & 2.50 \\ Co-SLAM & 2.40 & 1.70 & 2.40 & 2.17 \\ Point-SLAM & 4.34 & 1.31 & 3.48 & 3.04 \\ GS-SLAM & 3.30 & 1.30 & 6.60 & 3.73 \\ SplaTAM & 3.35 & 1.24 & 5.16 & 3.25 \\ CG-SLAM & 2.43 & 1.20 & 2.45 & 2.03 \\ MonoGS & 1.50 & 1.44 & 1.49 & 1.47 \\ RK-SLAM (Ours) & 1.30 & 1.21 & 1.15 & 1.22 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Camera tracking results on TUM-RGBD dataset (ATE RMSE [cm], the smaller, the better). The table marks the first, second, and third best results.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Methods** & **Sc.0059** & **Sc.0106** & **Sc.0169** & **Sc.0181** & **Sc.0207** & **Avg.** \\ \hline NICE-SLAM & 14.00 & 7.90 & 10.90 & 13.40 & 6.20 & 10.48 \\ Co-SLAM & 12.29 & 10.9 & 6.62 & 13.43 & 7.13 & 10.07 \\ Point-SLAM & 8.29 & 11.86 & 22.16 & 14.77 & 9.54 & 13.32 \\ SplaTAM & 10.10 & 17.72 & 12.08 & 11.10 & 7.46 & 11.69 \\ CG-SLAM & 7.46 & 8.88 & 8.16 & 11.60 & 5.34 & 8.31 \\ RK-SLAM (Ours) & 6.62 & 12.59 & 12.44 & 11.88 & 8.14 & 10.33 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Camera tracking results on ScanNet dataset (ATE RMSE [cm], the smaller, the better). The table marks the first, second, and third best results.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Methods** & **R0** & **R1** & **R2** & **O0** & **O1** & **O2** & **O3** & **O4** & **Avg.** \\ \hline Point-SLAM & 0.61 & 0.41 & 0.37 & 0.38 & 0.48 & 0.54 & 0.69 & 0.75 & 0.52 \\ GS-SLAM & 0.48 & 0.53 & 0.33 & 0.52 & 0.41 & 0.59 & 0.46 & 0.7 & 0.50 \\ SplaTAM & 0.31 & 0.40 & 0.29 & 0.47 & 0.27 & 0.29 & 0.32 & 0.55 & 0.36 \\ MonoGS & 0.33 & 0.22 & 0.29 & 0.36 & 0.19 & 0.25 & 0.12 & 0.81 & 0.32 \\ CG-SLAM & 0.29 & 0.27 & 0.25 & 0.33 & 0.14 & 0.28 & 0.31 & 0.29 & 0.27 \\ RK-SLAM (Ours) & 0.27 & 0.24 & 0.25 & 0.26 & 0.19 & 0.24 & 0.32 & 0.28 & 0.26 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Camera tracking results on Replica dataset (ATE RMSE [cm], the smaller, the better). The table marks the first, second, and third best results.