# Video-Based Gaze Detection for Oculomotor
## 3 Results  
A total of 469 test sessions of horizontal and vertical pro-saccades were analyzed and validated, for a total of 14,768,320 sample frames. Simple qualitative time-series analyses, as shown in Figure 5, clearly demonstrate the improvement in gaze detection accuracy when the CGM was utilized on top of the NLGEM. While the saccade timing (step function in time) was distinctive in both video-based retrievals, the NLGEM + CGM output was much closer to that of the reference IR eye tracker. Figure 4: A schematic diagram demonstrating the stimuli displayed during a single horizontal saccade (left panel) and vertical saccade (right panel) task over time. The time interval containing the displaced stimulus is constant and set to 1500 ms, while the time interval in which the monitor is empty between the disappearance of the biased stimulus and the reappearance of the centered stimulus is constant and set to 300 ms.  
Further quantitative analyses with reference to the IR eye tracker showed that, while the mean absolute error (MAE) of the estimated gaze with the NLGEM itself was 4.71 degrees, the CGM decreased the MAE to 1.80 degrees. This indicates that adding the CGM improved the accuracy by a factor of 2.5, reducing the MAE by 62%. An interesting and distinctive difference was observed between the accuracy levels for the horizontal and vertical gaze detections. Adding the CGM reduced the MAE in the horizontal axis by 58% and in the vertical axis by 65%, achieving MAE values of 0.93 degrees and 1.31 degrees, respectively (see Table 2). When comparing the MAE distributions of the gaze detection based on the two models, we found a significantly narrower MAE distribution when the CGM was applied after the NLGEM, allowing better confidence when aggregating multiple samples (see Figure 6). A closer look at the error distributions of the vertical and horizontal gaze locations provided by the video-based gaze estimation models (see Figure 7) revealed that the CGM significantly improved the error distribution symmetry, in addition to the MAE values. While the error distribution of the NLGEM estimated gaze locations seemed to be multimodal and to vary with different PoR locations, after the CGM was utilized, the gaze estimation error was characterized by a narrow modal distribution. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **MAE** & **MAE** \\  & **NLGEM [deg]** & **NLGEM + CGM [deg]** \\ \hline Horizontal & 2.20 & 0.93 \\ Vertical & 3.70 & 1.31 \\ Norm & 4.71 & 1.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean average error (MAE) calculations (degrees) for the video-based NLGEM and the NLGEM combined with the CGM gaze estimation location compared with the IR eye tracker. The MAE was calculated separately for the horizontal and vertical axes and the absolute error distance (Norm). Figure 5: The horizontal gaze location as a function of time of a single subject during a horizontal pro-saccadic session, as measured using a specialized IR eye tracker (green line), video-based NLGEM gaze estimation (blue line), and video-based NLGEM + CGM gaze estimation (red line). Figure 6: The mean average error (MAE) distributions of the video-based NLGEM gaze estimation (blue) and the video-based NLGEM + CGM gaze estimation (red) in the vertical axis (right panel), in the horizontal axis (center panel), and when calculated for its norm (i.e., the absolute distance from the target; left axis). Each box represents the range between the upper and lower quartiles, and the median is indicated by the inner line. The green triangles represent the mean values. The bars extend 1.5 IQRs from the lower and upper quartiles. Figure 7: The video-based NLGEM gaze estimation (blue) and the video-based NLGEM + CGM gaze estimation (red) vs. the specialized IR eye tracker gaze estimation (black) during pro-saccade tasks in the horizontal direction (**a**) and vertical direction (**b**). The inner panels show the error distribution of the video-based models, with reference to the IR eye tracker.