## 4 Results and Discussion  
The proposed system was tested in the following conditions:  
Measurements were taken by an optometrist with no previous experience with the application. Also, the optometrist was not given any information about the algorithm used to determine the measured parameters so as not to influence the final result. In addition to this, the real measurements were not communicated to the operator prior to finishing the measurement cycle. Initial data is obtained by measuring the distances and angles using basic methods: rulers and protactors. A total of approximately 50 measurements was taken for each point along the x-axis, at 50, 60, 70, 80, 90, and 100 cm. Each measurement consisted of one frontal, one right, and one left image. An average total of 150 images was captured and interpreted at 50 cm before moving on to 60 cm and so on. In total, over 300 measurements were taken, with over 900 images interpreted in total. Actual mannequin measurements are as follows:  
Interpupillary distance (ID): 51.5 mm  
Semi-distance left (IDL): 26.5 mm  
Semi-distance right (IDR): 25 mm  
Pantoscopic angle (PA): 8 degrees  
Vertex distance (VD): 11.5 mm  
In the following part of the paper, the results obtained after the measurements are presented and discussed as needed. As previously mentioned, the results were determined for the interpupillary distance (total (ID) and semi-distances (IDL and IDR)), pantoscopic angle, and vertex distance depending on the distance to the target and compared with the real data. The data obtained was interpreted in graphic form both for individual distances to the target and concatenated in order to compare the dispersion of the results on all the distances to the target approached. In addition, average measured distance, average absolute error (modulus of the difference between the measured data and the real data), and standard deviations for all parameters of interest were calculated and presented in graphic and tabular form. During the measurements, each set of data was uploaded individually to an online private database and later downloaded for processing. The data revealed a clear difference between taking the measurements at different distances from the mannequin, with absolute  
Figure 11: Side image automatic marker recognition. errors increasing for interpupillary distance from an average of 0.5 mm to over 2 mm, as shown in Figures 12 and 13. Figure 12: (**a**) Interuppillary measurement at 50 cm; (**b**) Interupillary measurement at 60 cm; (**c**) Interuppillary measurement at 70 cm; (**d**) Interuppillary measurement at 80 cm; (**e**) Interupillary measurement at 90 cm; (**f**) Interupillary measurement at 100 cm; (**g**) Comparison chart of error distribution obtained for interpupillary distance. A detailed description of the errors at each distance was needed, as shown in Figure 12a-f. Each of these graphs shows the actual average distance measured as line plots, as well as the actual measured distance as points in each of the charts. To further allow a trend to be observed, a general chart of the measurements was plotted, as shown in Figure 12g. There is a clear increase in error over 70 cm, with the error increasing the further the mannequin is from the tablet. In the current case, the absolute errors for each distance could be attributed to the movement of the camera by the optometrist during image acquisition or errors in image recognition (color and pupillary markers). Interrupillary distance measurement has also produced the semi-pupillary distance, the distance between the center of the mannequin's face and pupil. These measurements were also plotted in graphs shown in Figure 14a-f, with a concatenated view in the graph shown in Figure 14g. The same behavior can be observed as the absolute error increases with lower precision in the obtained images. The pantoscopic angle is the tilt of eyeglass lenses towards the cheeks, enhancing vision and comfort. Vertex distance is the space between the back of the lens and the front of the eye.