# Presenting a Human Pupil Orbit Model (HPOM) for Eye-Gaze Tracking
## 3 Results  
The experiment was carried out using Visual studio 2017 supplied by Microsoft (Washington, DC, USA) and Open Source Computer Vision (OpenCV) supplied by Intel (Los Angeles, CA, USA), an image processing library, on a PC equipped with an Intel Core i7-7700k CPU manufactured in California of United States and SAMSUNG 64G RAM manufactured in Suwon-si of Korea on which the programs were configured and the experiments conducted. The OpenCV library includes various image processing functions and also provides specialized matrix operation functions. Table 1 shows the results from the first experiment. The HPOM could not be calculated successfully when the ES was 3 during these experiments. Therefore, the results were analysed after excluding results when the ES was set to 3. On average the processing time for each experiment was about 80 s when the ES was less than 10. The standard deviation was about \(\pm\)5 s. When the ES was 14, about 470 s were required, with a standard deviation of \(\pm\) 15 s. As the ES increased, the processing time gradually increased. However, this did not affect the average cost. The estimated ORCP remained constant regardless of the ES. In Table 1, the distribution of the ORCP, displayed as a distance, shows a tendency to decrease as ES increases, but when the ES exceeds a certain number, the processing time and distribution both increase. The second experiment was carried out with the ES set to 7, reflecting the average performance from the first experiment. Table 2 shows the results from the second experiment. The processing time was over 1 min when the MDG was set to 0 degrees, while it was less than 1 s when the MDG was above 1 degree. Furthermore, the average of the ORCP and the radius of the HPOM remained constant within a 1-pixel range. The distribution of the ORCP was most concentrated when the MDG was set to 0, independent of the AAE. However, the distribution of the ORCP was irregular when MDG was over 0. The average cost was found to be directly proportional to the AAE without being affected by changes to the MDG. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**ES**} & \multirow{2}{*}{**Processing Time**} & \multicolumn{4}{c}{**ORCP**} & \multirow{2}{*}{**Radius**} & \multirow{2}{*}{**Cost**} \\ \cline{3-3} \cline{5-6}  & & **X** & & & & \\ \cline{3-6}  & **AVG \({}^{1}\) (\(\pm\)SD \({}^{2}\))** & **AVG (\(\pm\)SD)** & **AVG (\(\pm\)SD)** & \(\pm\)SD** & **AVG (\(\pm\)SD)** & **AVG \\ \hline
4 & 82,737.40 (4977.1) & 250.04 (0.0052) & 250.12 (0.0130) & 0.0145 & 249.76 (0.0385) & 105.58 \\
5 & 81,188.50 (2952.3) & 250.04 (0.0016) & 250.12 (0.0049) & 0.0052 & 249.76 (0.0223) & 105.81 \\
7 & 82,808.70 (2450.4) & 250.04 (0.0008) & 250.12 (0.0025) & 0.0032 & 249.77 (0.0137) & 105.95 \\
10 & 85,940.50 (2993.2) & 250.04 (0.0001) & 250.12 (0.0004) & 0.0010 & 249.77 (0.0112) & 106.01 \\
14 & 473,015.30 (15,934.7) & 250.04 (0.0004) & 250.12 (0.0013) & 0.0033 & 249.75 (0.0354) & 106.11 \\ \hline \hline \end{tabular}  
* Average. \({}^{2}\) Standard deviation. \({}^{3}\) Pieces. \({}^{4}\) Millisecond.  
\end{table} 
Table 1: Performance of HPOM estimation according to ES.