## 4 Results
### Ablation Study  
We conducted experimental evaluations on the TUM-RGBD dataset to assess the performance improvements brought by RK-SLAM's sub-Gaussian and related keyframe window. Table 6 presents the results of the ablation study, including both tracking and mapping performances. Notably, for the variant without the related keyframe window, we replaced it with the keyframe window proposed in [28] using the same parameter settings. As shown in Table 6, the method without sub-Gaussians performs worse than RK-SLAM in both tracking and rendering. It indicates that the sub-Gaussian approach contributes to improvements in both aspects. Regarding the choice of keyframe windows, compared to the related keyframe window used in RK-SLAM, employing the sliding keyframe window proposed in [28] results in significant performance gaps in both tracking and rendering. This is especially evident in tracking performance, where the related keyframe window brings a notable improvement, achieving an average enhancement of 0.17 cm across the three sequences in the TUM-RGBD dataset. For the mapping results, as shown in Figure 4, we selected a frame from the fr3/Office sequence for comparison. It is evident that RK-SLAM demonstrates superior detail preservation, particularly when compared to the method without sub-Gaussians. To explore the optimal size for the sliding window \(W_{s}\), we conducted the following experiments. The purpose of the sliding window is to enable sub-Gaussians to adjust dynamically with the fine-tuned poses of the keyframes. Thus, we designed a sliding window with a relatively large size (set to 5) to track the pose changes of the keyframes within it. Theoretically, when a keyframe undergoes significant fine-tuning, it is necessary for the sub-Gaussians to adjust accordingly. Conversely, once the keyframe's pose stabilizes, the sub-Gaussians can be united into the refined Gaussians \(\mathbf{G}_{0}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Sub-** \\ **Gaussian** \\ \end{tabular} } & \multicolumn{2}{c}{**Related**} & \multirow{2}{*}{**Metrics**} & \multirow{2}{*}{**fr1/desk**} & \multirow{2}{*}{**fr2/xyz**} & \multirow{2}{*}{**fr3/Office**} & \multirow{2}{*}{**Avg.**} \\  & & & & & & & \\ \hline \multirow{4}{*}{\begin{tabular}{c} **X** \\ \end{tabular} } & \multirow{4}{*}{✓} & PSNR \(\uparrow\) & 21.50 & 21.92 & 20.06 & 21.16 \\  & & SSIM \(\uparrow\) & 0.736 & 0.710 & 0.688 & 0.711 \\  & & LPIPS \(\downarrow\) & 0.255 & 0.229 & 0.266 & 0.250 \\  & & ATE RMSE \(\downarrow\) & 1.41 & 1.292 & 1.22 & 1.28 \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} **Y** \\ \end{tabular} } & \multirow{4}{*}{✗} & PSNR \(\uparrow\) & 20.89 & 21.12 & 20.24 & 20.75 \\  & & SSIM \(\uparrow\) & 0.726 & 0.705 & 0.700 & 0.710 \\  & & LPIPS \(\downarrow\) & 0.266 & 0.245 & 0.268 & 0.260 \\  & & ATE RMSE \(\downarrow\) & 1.44 & 1.36 & 1.38 & 1.39 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} **Y** \\ \end{tabular} } & \multirow{4}{*}{✓} & PSNR \(\uparrow\) & 22.31 & 22.47 & 20.67 & 21.82 \\  & & SSIM \(\uparrow\) & 0.741 & 0.729 & 0.710 & 0.727 \\  & & LPIPS \(\downarrow\) & 0.254 & 0.220 & 0.251 & 0.242 \\  & & ATE RMSE \(\downarrow\) & 1.30 & 1.21 & 1.15 & 1.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Ablation study on TUM-RGBD dataset. The ✓ means with the corresponding method, and ✗ means without the corresponding method. \(\uparrow\) means that the bigger the metric, the better, and \(\downarrow\) means that the smaller the metric, the better. The table marks the first\(\downarrow\) second\(\downarrow\), and third best results. In Figure 5, we illustrate the relationship between the extent of the keyframe pose fine-tuning and the number of iterations. The shaded area represents the range of fine-tuning extents, while the solid line denotes the mean value at each iteration. From the result, we observe that the fine-tuning extent decreases overall with an increasing number of iterations.