# Presenting a Human Pupil Orbit Model (HPOM) for Eye-Gaze Tracking
## 2 Materials and Methods
### Experiments  
The purpose of the experiment we conducted was to verify the validity of the theory proposed in this paper, and was also to analyse the influence of variables in the fitting  
Figure 9: Process of RANSAC to estimate HPOM.  
process. Distance units are expressed in pixels because the pupil is acquired using the camera where distance is measured by pixels. We retained the unit of pixels in order to avoid the complication of a separate conversion process.  
The experiments build on the procedure in Section 2.7 and are simulated by generating virtual data on the assumption that data is obtained based on the suggested environment in Section 2.2. The number of ES refers to the number of samples used to estimate the initial model in the hypothesis stage of the RANSAC method. This number of samples determines processing time, accuracy, and flexibility. In the experiment, space was formed so the x, y, and z-axes were all 500 pixels in size. The simulation data used was acquired using 3D rotation of the pupil disc. The rotating centre point of a pupil disc was set to be the centre of coordinate space, while the distance from the disc centre to the space centre was set to 250 pixels. The pupil disc radius was set to 50 pixels. A total of 100 samples were obtained for HPOM estimation, this was done by converting random position coordinates to positions of the x- and y-axes while RAE was recorded using 3D rotations of the pupil disc. In addition, a dataset of 200 TSs with an inlier to outlier ratio of 1:1 was constructed by randomly generating 100 pieces of noise data, as shown in Figure 10a. Figure 10b shows the distances on the xy-plane from the dataset along with the distribution of the RAE.  
In order to analyse the performance of our method according to independent variables, such as the number of ESs, the values of the AAEs and MDGs, the experiment was performed by setting the processing time, location and distribution of the average ORCP, the radius of the HPOM, and the max cost as the dependent variables. The experiment was carried out over two sessions. In the first session the experiment was verified the validity of the proposed method and repeated 200 times while gradually increasing the ES as the independent variable from 3 to 14 in order to check the accuracy of the HPOM estimated as ES changed. AAE is the tolerance range of RAE, which does not provide flexible estimation of the model if set to an excessively small range. On the other hand, if AAE is set to a wide range, the accuracy of the model may decrease. MDG is a variable for the purpose of reducing the excessive load applied to the system when estimating the HPOM. In order not to affect the first experiment control variables, AAE was fixed at \(\pm\)5 degrees and MDG was fixed at \(\pm\)0 degree. The results were analysed after performing a total of five sets of these experiments.  
In the second session, the ES was fixed, reflecting results of the first experiment, to confirm the model's performance according to changes in the AAE and MDG. Afterwards, the experiment was repeated 200 times while varying the AAE from 1 degree to 5 degrees in 1-degree increments and varying the MDG from 0 to 5 degrees, also by 1 degree increments.  
Figure 10: (**a**) 3D dataset distribution diagram. (**b**) Data set distribution diagram expressed in RAE and the distance between ORCP and each data on the xy-plane.