# Gaze Estimation via Strip Pooling and Multi-Criss-Cross Attention Networks
## 4 Experiment
### Ablation Studies  
In this paper, we linearly combine cross-entropy loss and smooth L1 loss, and we use different regression coefficients to optimize the network. For a fair comparison with L2 CS-Net, only regression coefficients 1 and 2 are chosen here, and we conducted ablation experiments on the performance of 2 regression losses with the Gaze360 dataset on front 180\({}^{\circ}\). In Figure 9, the regression coefficients \(\beta\) of the regression loss for all experiments were set to 2 to facilitate a fair comparison. We found that using smooth L1 loss as a regression loss function or improving the backbone network can both improve the performance of gaze estimation. Moreover, for both L2 CS-Net and SPMCCA-Net, using smooth L1 loss as a regression loss function significantly improves the stability and convergence speed of the models during training. \begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **RT-Gene** \\ \hline Mnist [8] & 14.9\({}^{\circ}\) \\ FullFace [22] & 10.0\({}^{\circ}\) \\ RT-Gene [32] & 8.6\({}^{\circ}\) \\ FARE-Net [13] & 8.4\({}^{\circ}\) \\ Dilated-Net [10] & 8.38\({}^{\circ}\) \\ CA-Net [15] & 8.27\({}^{\circ}\) \\ AGE-Net [14] & 7.44\({}^{\circ}\) \\ Gaze360 [31] & 7.06\({}^{\circ}\) \\ L2 CS-Net [17] (baseline) & 6.68\({}^{\circ}\) \\ \hline
**SPMCCA-Net (\(\beta\) = 1)(ours)** & **6.63\({}^{\circ}\)** \\
**SPMCCA-Net (\(\beta\) = 2)(ours)** & **6.61\({}^{\circ}\)** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The results of comparison between the proposed model and other methods on RT-Gene. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **MSE (P)** & **MSE (Y)** & **RMSE (P)** & **RMSE (Y)** & **MAPE (P)** & **MAPE (\(\Omega\))** \\ \hline L2 CS-Net & 145.85 & 89.92 & 12.08 & 9.48 & 121.60\% & 394.00\% \\ Ours (Gaze360) & **143.18** & **84.15** & **11.97** & **9.17** & **101.85\%** & **377.01\%** \\ L2 CS-Net (RT-Gene) & 22.53 & 30.82 & 4.75 & 5.55 & 358.62\% & 315.17\% \\ Ours (RT-Gene) & **21.83** & **29.75** & **4.67** & **5.45** & **323.59\%** & **260.98\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The performance measure of MAE, RMSE, and MAPE. As shown in Table 4, we validated the proposed method and the baseline method for gaze estimation using face images with resolutions of 448 \(\times\) 448, 224 \(\times\) 224, and 112 \(\times\) 112, on Gaze360 and RT-Gene, and fixed the regression coefficient \(\beta\) to 2. It can be observed that the proposed SPMCCA-Net in this paper can effectively reduce the mean angular error compared to the baseline model, regardless of the resolution used. Additionally, the mean processing time of our proposed method is about 1.45 s for a 448 \(\times\) 448 image, 0.24 s for a 224 \(\times\) 224 image, and reduced to about 0.08 s for a 112 \(\times\) 112 image, which allows us to make effective practical applications. Figure 8: Visualization of gaze estimation on the Gaze360 dataset. Figure 9: Training convergence graph of L2 CS-Net and SPMCCR-Net on Gaze360. We also validated the two modules on the Gaze360 dataset through ablation experiments to compare their impact on the network (smooth L1 loss is adopted in both regression loss sections). Table 5 shows that, when the backbone network only incorporates the strip pooling module to enhance its ability for capturing long-distance dependencies between the eyes and reduce interference from redundant information, the mean angular error is 10.21\({}^{\circ}\) and 6.63\({}^{\circ}\), which produces a mean angular error reduction of 0.12\({}^{\circ}\) and 0.02\({}^{\circ}\) in comparison with the baseline method on Gaze360 and RT-Gene. When only the multi-criss-cross attention module is engaged, the network captures global context information and can also capture long-distance dependencies between the eyes, resulting in an average angular error of 10.26\({}^{\circ}\) and 6.63\({}^{\circ}\), which produces a mean angular error reduction of 0.07\({}^{\circ}\) and 0.02\({}^{\circ}\) in comparison with the baseline method on Gaze360 and RT-Gene.