## 4 Experiment and Evaluation
### Evaluation of Pose Estimation  
We evaluated the pose estimation performance through two quantitative metrics, _Acc30_ and _Median Error_, as described in [32,33]. _Acc30_ evaluates the proportion of instances where the angular difference between the predicted and GT angles is within 30\({}^{\circ}\). It is measured in percentage (%). Equations (26)-(31) show the conversion process of Euler angles into rotation transformation matrices, where \(a,e\), and \(i\) denote _Azimuth_, _Elevation_, and _Inplane rotation_, respectively. _Median Error_ quantifies the median of the differences in rotational angles between the predicted and ground truth values, measured in degrees (\({}^{\circ}\)). \[R_{x,y,z}= \begin{bmatrix}r_{11}&r_{12}&\sin(e^{\prime})\sin(a^{\prime})\\ r_{21}&r_{22}&\sin(e^{\prime})\cos(a^{\prime})\\ \sin(i^{\prime})\sin(e^{\prime})&-\cos(i^{\prime})\sin(e^{\prime})&\cos(e^{ \prime})\end{bmatrix}  \tag{26}\]  
\[r_{11}=\cos(i^{\prime})\cos(a^{\prime})-\sin(i^{\prime})\cos(e^{\prime})\sin(a ^{\prime}) \tag{27}\]  
\[r_{12}=\sin(i^{\prime})\cos(a^{\prime})+\cos(i^{\prime})\cos(e^{\prime})\sin(a ^{\prime}) \tag{28}\]  
\[r_{21}=-\cos(i^{\prime})\sin(a^{\prime})-\sin(i^{\prime})\cos(e^{\prime})\cos (a^{\prime}) \tag{29}\]  
\[r_{22}=-\sin(i^{\prime})\sin(a^{\prime})+\cos(i^{\prime})\cos(e^{\prime})\cos(a ^{\prime}) \tag{30}\]  
\[(a^{\prime},e^{\prime},i^{\prime})=(a,e,i)\times\frac{\pi}{180} \tag{31}\]  
The performance was compared with PoseContrast using three test datasets, Pix3D, Pascal3D+, and ObjectNet3D, as shown in Tables 1-3. We trained our proposed model using the Pascal3D+ dataset. We tested the model on the Pix3D and ObjectNet3D datasets to evaluate generalization performance. Table 1 presents the quantitative results on Pascal3D+, showing that the proposed method outperforms the baseline, PoseContrast. Moreover, as shown in Tables 2 and 3, our model performs better than the PoseContrast in generalization evaluations. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \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} **Bottle** \\ **(251)** \\ \end{tabular} & \begin{tabular}{c} **Bus** \\ **(154)** \\ \end{tabular} & \begin{tabular}{c} **Car** \\ **(308)** \\ \end{tabular} & \begin{tabular}{c} **Chair** \\ **(244)** \\ \end{tabular} & \begin{tabular}{c} **Thing** \\ **(21)** \\ \end{tabular} & \begin{tabular}{c} **Mototbike** \\ **(36)** \\ \end{tabular} & \begin{tabular}{c} **Sofa** \\ **(399)** \\ \end{tabular} & \begin{tabular}{c} **Train** \\ **(113)** \\ \end{tabular} & \
\begin{tabular}{c} **Tv Monitor** \\ **(222)** \\ \end{tabular} &
\begin{tabular}{c} **Average** \\ **(2113)** \\ \end{tabular} \\ \hline \multicolumn{12}{c}{_Acc30_} \\ \hline [PERSON] et al. & 80 & 82 & 57 & 90 & **97** & **94** & 72 & **67** & **90** & 80 & **82** & 85 & 81 \\ StarMap [17] & 82 & **86** & 50 & 92 & **97** & 92 & 79 & 62 & 88 & **92** & 77 & 83 & 82 \\ SPPoseLight & 80 & 82 & 58 & **93** & 96 & 92 & 77 & 57 & 88 & 82 & 80 & 79 & 80 \\ PoseContrast & 81 & 82 & 59 & **92** & 96 & 93 & **84** & 52 & 88 & 85 & 81 & 85 & 82 \\ Proposed & **87** & 81 & **65** & **92** & **97** & **94** & 83 & 62 & **90** & 82 & 81 & **86** & **83** \\ \hline \multicolumn{12}{c}{_Median Error_} \\ \hline [PERSON] et al. & 10.9 & **12.2** & 23.4 & 9.3 & 3.4 & 5.2 & 15.9 & 16.2 & 12.2 & 11.6 & 6.3 & 11.2 & 11.5 \\ StarMap [17] & **10.1** & 14.5 & 30.3 & 9.1 & 3.1 & 6.5 & 11.0 & 23.7 & 14.1 & 11.1 & 7.4 & 13.0 & 12.8 \\ PoseContrast & 11.25 & 15.63 & 22.39 & **7.68** & **2.65** & **4.67** & 10.7 & 20.88 & **11.48** & 10.76 & **5.64** & 11.19 & 11.25 \\ 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 \end{tabular}
\end{table}