# Gaze Estimation via Strip Pooling and Multi-Criss-Cross Attention Networks
## 4 Experiment
### Training & Results  
We use the official training weights of ResNet-50 on the ImageNet dataset provided by PyTorch as the pre-training weights for this model. The proposed network takes a face image of size 448 \(\times\) 448 as input, which keeps the same image resolution size as the baseline model for training and validation, and is trained with the Adam optimizer. We trained the model for 50 epochs with a learning rate of 0.00001 and a batch size of 16. The mean angular error is the most commonly used evaluation metric in gaze estimation, which is similar to the mean absolute error by measuring the angle between the predicted gaze direction and the true gaze direction. We followed the evaluation criteria in [2,4] and chose mean angular error as the performance evaluation index. The mean angular error (\(\circ\)) can be expressed as:  
\[L_{angular}=\frac{g\cdot\hat{g}}{||g||\times||\hat{g}||}, \tag{10}\]  
where the real gaze direction is \(g\in\mathbb{R}^{3}\) and the predicted gaze direction is \(\hat{g}\in\mathbb{R}^{3}\). A lower value of \(L_{angular}\) indicates better model performance (lower gaze estimation error). In order to make a fair comparison with the baseline model, we chose to adopt 1 and 2 as the values of the regression coefficients because the L2 CS-Net baseline model was trained to adopt only these two values as the regression coefficients. Table 1 compares the SPMCCA-Net model with other available gaze estimation models on the Gaze360 dataset. We follow the evaluation criteria adopted by [31], but only in relation to the front 180\({}^{\circ}\) and front-facing (within 20\({}^{\circ}\)) postures to allow for fair comparison with all related methods, which are trained and evaluated on datasets within the 180\({}^{\circ}\) range. SPMCCA-Net clearly outperforms other current mainstream methods on the Gaze360 dataset. Although SPMCCA-Net does not achieve a lower mean angular error on the front 180\({}^{\circ}\) compared to the DAM method [34] under the field of gaze target detection, it achieves a lower mean angular error on the front facing when compared to DAM. More specifically, it produces a mean angular error reduction of 0.28\({}^{\circ}\) in comparison with the baseline method on front 180\({}^{\circ}\) and a mean angular error reduction of 0.64\({}^{\circ}\) in comparison with the baseline method on front 180\({}^{\circ}\) on front facing, which achieves gaze performance with 10.13\({}^{\circ}\) (mean angular error) on front 180\({}^{\circ}\)and 8.40\({}^{\circ}\) (mean angular error) on front facing when \(\beta\) = 2. Table 2 shows the results of the comparison between the proposed model and other methods on the RT-Gene dataset. The proposed SPMCCA-Net achieves better performance with a 6.61\({}^{\circ}\)mean angular error when \(\beta\) = 2, which produces a mean angular error reduction of 0.07\({}^{\circ}\) in comparison with the baseline method within 40\({}^{\circ}\). As an estimation task, gaze estimation has some similarities with other estimation tasks, such as the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) used in [34]. As shown in Table 3, we calculated the MSE, RMSE, and MAPE values for \begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **Front 180\({}^{\circ}\)** & **Front Facing** \\ \hline FullFace [22] & 14.99\({}^{\circ}\) & N/A \\ Dilated-Net [10] & 13.73\({}^{\circ}\) & N/A \\ RT-Gene [32] & 12.26\({}^{\circ}\) & N/A \\ CA-Net [15] & 12.20\({}^{\circ}\) & N/A \\ Gaze360 [31] & 11.4\({}^{\circ}\) & 11.1\({}^{\circ}\) \\ GazeTR [16] & 10.62\({}^{\circ}\) & N/A \\ DAM [35] & 9.6\({}^{\circ}\) & 9.2\({}^{\circ}\) \\ L2 CS-Net (\(\beta\) = 2) [17] & 10.41\({}^{\circ}\) & 9.04\({}^{\circ}\) \\ (baseline) & & \\ \hline
**SPMCCA-Net (\(\beta\) = 1)(ours)** & **10.16\({}^{\circ}\)** & **8.62\({}^{\circ}\)** \\
**SPMCCA-Net (\(\beta\) = 2)(ours)** & **10.13\({}^{\circ}\)** & **8.40\({}^{\circ}\)** \\ \hline \hline \end{tabular}
\end{table}