# Advancements in Gaze Coordinate Prediction Using Deep Learning: A Novel Ensemble Loss Approach
## 4 Results  
We compared the results before and after implementing the loss function for the three models we applied. The training data remained the same, and we averaged the results over 15 trials using the leave-one-out method [24]. Additionally, no preliminary performance data were available for the ResNet-based model [21], so our reimplementation was based on the paper. Notably, the results of model [21], which is based on ResNet, are of particular interest. \[FOV=2 tan^{-1}(HFOV[\text{mm}]/WD[\text{mm}]/2) \tag{2}\]  
In Table 2, the error of the gaze coordinate predicted by the fully-connected layer of the existing deep learning model (cm) and the error of the gaze coordinate predicted by applying the ensemble loss proposed in this study (cm) were used in the experiment. It was expressed in each of the three models used and converted to 3D error using Equation (2). The picture in Figure 2 provides an additional explanation of the formulas and conversion. Equation (2) is a field of view (FOV) formula that calculates 3D error. In the formula, working distance (WD) refers to the working distance from the lens, which means the millimeter distance between the camera and the subject's eyes, and horizontal FOV (HFOV) represents the millimeter distance when the line of sight is expressed in 2D. In this study, WD was set according to the MPIIFaceGaze dataset construction environment used in the experiment. Lastly, the prediction within two centimeters based on Euclidean distance is expressed as a percent. As a result, there is a clear performance difference between the results of eye tracking in Equation (2), with and without the proposed loss function. In particular, AFF-Net, which currently has the highest level of performance, has implemented a new level of performance by strengthening the loss function. We also retrieved the results for each individual ID and displayed individual error measures in Table 3 below. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model** & **2D (cm)** & **3D (\({}^{\circ}\))** & **L2 within 2 cm (\%)** \\ \hline iTracker (original) & 7.67 & 7.25 & 41.3912 \\ iTracker (with loss function) & 1.31 & 1.51 & 86.7912 \\ AFF-Net (original) & 4.21 & 3.69 & 90.96 \\ AFF-Net (with loss function) & 0.81 & 0.93 & 95.3423 \\ ResNet (original) & 7.50 & 8.58 & 5.9245 \\ ResNet (with loss function) & 1.28 & 1.47 & 88.3912 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average results of each model. Figure 2: Illustration to explain how conversion to 3D degree is applied. We output the scatter plot of ground truth and predicted values for each model. Figures 3-5 illustrate the gaze coordinates predicted by the model using the proposed ensemble loss function, displayed in pixel units at a resolution of 1680 \(\times\) 1050. The results show that all models align more closely with the x = y axis. Specifically, the ResNet model [21] exhibited a low correlation between predicted and actual values when trained solely on the original model. However, the graph demonstrates that there is a significant correlation when the loss function is implemented. This indicates that the loss function enhances the performance of both state-of-the-art and under performing models. We additionally imported some example images of the predictions in Figure 6. The four correct coordinates are shown in red, and each prediction is shown in green, with the name of the model used next to it. Looking first at Figure 6a, we can see that AFF-Net tends to make some predictions for each coordinate. However, in the case of ResNet18, it tends to deviate a lot from the actual coordinates. In the case of iTracker, the top-right and bottom-left coordinates are predicted in a somewhat valid range, but the top-left and bottom-right coordinates are incorrect, just like ResNet18. On the other hand, we can see  
Figure 3: Scatter plot of the predicted and actual values on the x-axis and y-axis for AFF-Net.