## 5 Ablation Study of the Proposed Pose Estimation Model  
In this section, we perform ablation experiments on the Pascal3D dataset to validate the effectiveness of the proposed model. Unlike the baseline model, the proposed model includes three key modules and is trained using an additional quaternion loss function. Table 9 shows how we have conducted ablation studies for each of these modules. All model variants were trained under the same conditions outlined in the implementation details. Table 10 presents the results for each modified model. In Table 9, VUF refers to the variance uncertainty model in our proposed approach, GCE denotes the Guided Cost Volume Excitation module, CGF refers to Context and Geometry Fusion, and Q loss specifies whether a quaternion loss was employed during training. As shown in Table 10, adding the proposed modules to the baseline progressively improves performance. Specifically, the VUF module alone shows little improvement over the baseline. The VUF module leverages variance uncertainty for each predicted angle to enhance performance; however, it incurs feature loss during the module's internal attention process, so an additional auxiliary module is required to boost performance further. By supplementing VUF with the GCE module (VUF+GCE), the network compensates for this loss and improves performance, as observed in Table 10. Next, to assess the effect of the quaternion loss function, we compare the proposed model to a VUF-full ablation variant \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \begin{tabular}{c} **Aero-** \\ **plane** \\ **(275)** \\ \end{tabular} & \begin{tabular}{c} **Bicycle** \\ **(118)** \\ \end{tabular} & \begin{tabular}{c} **Boot** \\ **(232)** \\ \end{tabular} & \begin{tabular}{c} **Bootle** \\ **(251)** \\ \end{tabular} & \begin{tabular}{c} **Bus** \\ **(154)** \\ \end{tabular} & \begin{tabular}{c} **Car** \\ **(080)** \\ \end{tabular} & \begin{tabular}{c} **Chair** \\ **(244)** \\ \end{tabular} & \begin{tabular}{c} **Dining** \\ **Table** \\ **(213)** \\ \end{tabular} & \begin{tabular}{c} **Motorbike** \\ **(39)** \\ \end{tabular} & \begin{tabular}{c} **Sofa** \\ **(113)** \\ \end{tabular} & \
\begin{tabular}{c} **Train** \\ **Monitor** \\ **(222)** \\ \end{tabular} &
\begin{tabular}{c} **Tv** \\ **(2113)** \\ \end{tabular} \\ \hline \multicolumn{22}{c}{_Aci30_} \\ \hline PoseContrast & 81 & 82 & 59 & 92 & 96 & 93 & 84 & 52 & 88 & 85 & 81 & 85 & 82 \\ VUF- & 82 & 81 & 62 & 92 & 95 & 93 & 82 & **62** & 89 & 87 & 79 & 80 & 82 \\ VUF + GCE & 85 & 81 & 60 & **93** & 97 & 93 & 86 & 57 & 89 & 90 & 81 & 85 & 83 \\ VUF-full & 82 & 84 & 64 & 92 & **99** & 92 & **87** & 57 & 89 & **92** & **82** & 85 & **84** \\ Proposed & **87** & 81 & **65** & 92 & 97 & **94** & 83 & **62** & **90** & 82 & 81 & **86** & 83 \\ \hline \multicolumn{22}{c}{_Median Error_} \\ \hline PoseContrast & 11.25 & 15.63 & 22.39 & 7.68 & **2.68** & **4.67** & 10.7 & 20.88 & **11.48** & 10.76 & 5.64 & 11.19 & 11.25 \\ VUF- & 12.66 & 14.31 & 21.79 & 9.05 & 3.56 & 5.61 & 10.31 & 14.02 & 12.92 & 10.99 & 7.13 & 12.5 & 11.24 \\ VUF + GCE & 10.62 & **14** & 20.18 & 8.17 & 3.01 & 4.85 & 10.41 & 14.27 & 12.13 & 11.64 & 5.58 & 12.29 & 10.6 \\ VUF-full & **10.47** & 15.67 & 18.96 & 7.5 & 3.08 & 4.86 & **9.85** & 13.51 & 11.95 & 13.05 & **5.56** & 11.85 & 10.53 \\ Proposed & 11.7 & 14.71 & **18.47** & 7.84 & 2.84 & 4.83 & 9.98 & **11.71** & 11.98 & **10.75** & 6.18 & **10.88** & **10.16** \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of the quantitative results of the ablation models. The baseline model is PoseContrast. The best performance is highlighted in bold. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Similarity Measure** & **Better** & **SS** & **Worse** \\ \hline SM-AT & 1.138 & 0.271 & \(-\)0.349 \\ SM-NI & 1.075 & 0.261 & \(-\)0.097 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Correlation score per sample between pose performance and similarity measurement. Pose performance comparison is with respect to PosefromShape.