## 4 Experimentation and Discussion
### Measurement Results of Interupillary Distance and Pupillary Height  
To evaluate the effectiveness of our research, we recruited a total of 30 diverse participants for testing. The selection of participants was done randomly, without any restrictions based on age, gender, or race. Each participant was instructed to capture facial images using the same equipment. During the image capture process, we ensured ample lighting conditions and had participants seated in designated chairs to minimize movement. A tripod was positioned approximately 30 cm in front of each participant at eye level to hold a smartphone. The smartphone's camera was aligned with the participant's eyes. Figure 14: Fifteen pose angles of an object. Participants were instructed to gaze directly at the smartphone's camera on the tripod without closing or tilting their eyes, avoiding any special circumstances. In addition to using our method for testing, we also employed traditional ruler-based measurement of PD and an auto-refractometer (AU) for PD measurements. These additional measurement methods will be used for comparison and analysis along with our research results. The final measured experimental results can be found in Table 3.  
In order to compare the differences among three different measurement methods, we generated a line graph (Figure 15) to plot the data from the three groups. From the graph, it can be observed that there is no significant difference among the data obtained from these three different measurement methods. Additionally, we conducted a repeated measurement variance analysis based on the measured data. Thirty testers used rulers to measure the pupillary distance (\(M=61.53,SD=4.493\)), used AU to measure the pupillary distance (\(M=61.49,SD=4.11\)), and used the model proposed in this paper to measure the pupillary distance (\(M=61.42,SD=4.15\)). The Greenhouse-Geisser correction estimated value for deviation from sphericity is denoted as \(\omega=0.657\). Our results indicate that there is no significant difference between the pupillary distance measured using the model proposed in this paper and that measured using rulers or AU, \(F(1.31,38.12)=0.156,\ p>0.05,\ \text{partial}\ \eta^{2}=0.005\). Therefore, we conclude that the results of using the model proposed in this paper to measure the pupillary distance are accurate. \begin{table}
\begin{tabular}{c c c c} \hline
**Subject** & **Computed (mm)** & **AU Measurement (mm)** & **Ruler Measurement (mm)** \\ \hline
1 & 61.1 & 61.8 & 60 \\
2 & 63.8 & 63.4 & 62 \\
3 & 57.2 & 57.6 & 58 \\
4 & 58.1 & 58.5 & 57 \\
5 & 63.8 & 64. In this experiment, we used the values measured by an auto-refractometer as the standard value and calculated the relative errors between the values calculated by our model and the measurements taken by a ruler as compared to the standard value. In comparison to the values measured by an auto-refractometer, the relative error of the pupil distance calculated by our model was all below 2%, with most being smaller than the relative error of ruler measurements. In contrast, the relative error of some ruler measurements was close to 3%. The specific numerical values are shown in Figure 16. Therefore, using values calculated by our model and those measured by an auto-refractometer is more consistent with a high degree of accuracy compared to the ruler measurements. In experiments conducted in groups 5, 18, 25, and 27, our method exhibited a higher relative error compared to measurements taken with a ruler. After careful analysis, we believe this could be attributed to the following reasons: (1) insufficient lighting resulting in unclear photos with noise, leading to inaccurate pupil localization, while ruler measurements are not affected by image quality issues, and (2) participants may have had tilted heads or averted gazes during photo capture, which introduced errors in our method, although these errors remained within an acceptable range. We have conducted in-depth research into these issues and will address them in our future studies. [PERSON] et al.