# Presenting a Human Pupil Orbit Model (HPOM) for Eye-Gaze Tracking
## 4 Discussion
This is because a cost increase leads to an increasing number of straight lines being used in the ORCP inference section. Therefore, the cost and the processing time are subordinate to the AAE. On the other hand, the effect of the AAE on the accuracy of the HPOM cannot be confirmed owing to the characteristics of RANSAC in that the estimation process is repeated until an optimal model is found. The MDG affects the accuracy of the HPOM and processing time. A processing time of over 60 s is seen when the MDG is set to 0. On the other hand, when the MDG is greater than 0, the processing time is greatly reduced to under 1 s. This result means MDG accurately satisfied our goal of decreasing the processing time. The accuracy of the HPOM is almost constant when the MDG is set to 0, regardless of the AAE used. However, the accuracy of the HPOM is irregular when the MDG is not 0. Setting the MDG to greater than 0 seems to reduce the accuracy of the HPOM estimation. This result is thought to be the result of a lack of discernment in the method that uses the MDG. The MDG only compares the angle of straight lines without considering the intersection point in the ORCP inference section. Thus, lines passing through the ORCP with the same slope are disregarded if lines that do not pass through the ORCP are first classified as inliers. Therefore, the accuracy of the HPOM becomes irregular regardless of the MDG when the MDG is greater than 0. In conclusion, the MDG effectively reduces the processing time, but brings the penalty of reduced HPOM accuracy. The accuracy of the proposed method is reliant on the RANSAC method. As such, our approach relies on the quality and amount of data used for HPOM estimation. In particular, the amount of data from repeatedly photographing the face may produce satisfactory estimates, while camera performance affects the quality of data that can be collected. This is because when the shape of the pupil cannot be accurately identified, pupil shape analysis to estimate HPOM becomes impossible. In addition, the proposed method needs at least three images with different eye-gaze directions. This condition is caused by the characteristic of the RANSAC method. The RANSAC method is a technique for approximating the expected model that can explain the entire data using a small amount of data. This means that the RANSAC method has an advantage because the model can be approximated even though the data contains errors. However, in the hypothesis step of the RANSAC method, model approximation is not possible if the data consist only of errors or if all data are identical. This means that the data have not linearity or does not match to the expect model. Therefore, the proposed method has a same weakness of the RANSAC method. On the other hand, the proposed method can estimate the HPOM regardless of the camera's distance from the face as long as it can acquire the pupil shape. In addition, the consumption time is very short at 0.4 s. In other words, our method can respond in real time even when the subject being monitored moves. Incidentally, in this paper, we limited HPOM to a sphere, but later research is planned where this will be expanded to ellipsoids. Moreover, we plan to conduct further research with the aim of improving accuracy.