# Supervised Contrastive Learning for 3D Cross-Modal Retrieval
## 4 Experiments
### Ablation Study: Impact of Compositions  
To verify the effectiveness of the proposed method, experiments were conducted on ModelNet40 dataset for evaluation based on the mean average precision (mAP) metric. The results demonstrated that the proposed method achieved better performance than the existing methods. To provide a detailed analysis of the results, ablation studies addressing these aspects are presented in this section. Impact of Batch Size: The proposed method, cross-modal supervised contrastive learning (CSupCon), was evaluated based on positive and negative samples within a batch. Contrastive learning tends to be less sensitive to the influence of batch size. To verify our assumption, we conducted experiments by varying the batch size. The results are illustrated in Table 1. While the center loss-based CLF [3] was heavily influenced by changes in batch size, our proposed contrastive learning-based method was relatively less influenced by batch size. Consequently, the proposed method can be employed regardless of batch size. Impact of Loss Functions: To verify the influence of each objective function in the proposed method, we conducted an ablation study on the impact of these losses to analyze their significance. The results are presented in Table 2. Estimating the overall context using label prediction through the fixed projection head (FPH) strategy and performing contrastive learning for each data through CSupCon displayed performance as expected. In addition, improving the inter-modal variation by adding MSE loss also aided performance. Impact of Fixed Projection Head: The proposed method uses the FPH strategy which fixes the projection head during label prediction. To prove the efficiency of the strategy, we performed an ablation study. Table 3 shows performance differences before and after applying the FPH strategy. The results show that the FPH strategy improved the extraction of distinguishable features. Impact of Softmargin: The proposed method involves applying a margin during similarity comparison, to enhance performance by making the comparison more challenging. As shown in Table 4, the results were improved for retrieval tasks with Softmargin applied. Therefore, raising the difficulty level during similarity comparison using Softmargin improved the overall performance. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Batch sizes**} \\ \cline{3-10}
**Retrieval Tasks** & \multicolumn{3}{c}{**24**} & \multicolumn{3}{c}{**48**} & \multicolumn{3}{c}{**96**} & \multicolumn{3}{c}{**128**} \\ \cline{3-10}  & & **CLF** & **Ours** & **CLF** & **Ours** & **CLF** & **Ours** & **CLF** & **Ours** \\ \hline Image & Image & 63.56 & 90.07 & 85.64 & 90.08 & 90.23 & 90.43 & 90.30 & 90.37 \\ Image & Mesh & 73.22 & 89.72 & 86.94 & 89.45 & 89.59 & 89.73 & 89.80 & 89.81 \\ Image & Point & 72.08 & 90.25 & 85.59 & 89.68 & 89.04 & 90.08 & 88.30 & 90.69 \\ Mesh & Image & 88.44 & 88.35 & 88.91 & 89.13 & 88.51 & 88.95 & 89.10 & 88.15 \\ Mesh & Mesh & 68.81 & 89.10 & 86.50 & 89.46 & 88.11 & 89.04 & 87.30 & 88.78 \\ Mesh & Point & 84.60 & 89.13 & 86.67 & 89.12 & 87.37 & 88.84 & 88.20 & 89.01 \\ Point & Image & 82.44 & 89.47 & 85.44 & 89.19 & 87.04 & 89.86 & 88.70 & 89.92 \\ Point & Mesh & 67.46 & 89.69 & 84.67 & 89.12 & 87.11 & 89.62 & 88.30 & 89.88 \\ Point & Point & 83.56 & 90.18 & 86.62 & 89.33 & 87.58 & 90.12 & 88.10 & 90.88 \\ \hline \multicolumn{2}{c}{Average mAP} & \multicolumn{3}{c}{76.02} & \multicolumn{3}{c}{**89.55**} & \multicolumn{3}{c}{86.33} & \multicolumn{3}{c}{**89.40**} & \multicolumn{3}{c}{88.29} & \multicolumn{3}{c}{**89.63**} & \multicolumn{3}{c}{88.68} & \multicolumn{3}{c}{**89.72**} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ablation study to verify the experimental results according to batch sizes on the ModelNet40 dataset. The numbers in bold represent the highest average mAP in the evaluation.