## 1 Introduction  
The human eye plays a crucial role not only in daily life but also as one of the key features of humans. Eye tracking has a wide range of applications in various fields, such as medical research (psychology, cognition) [1; 2; 3], electronic games [4], and human-computer interaction [5]. Among these, one of the most significant areas of research is ophthalmology. In recent years, the problem of myopia has become increasingly severe, with a growing number of individuals needing to wear corrective glasses. Spectacles are optical devices that operate based on the principle of light refraction [6]. They are used to correct refractive errors by placing a lens of a specific size in front of the eyes. Refractive errors occur when an object does not properly focus on the retina. One of the measurements taken during the spectacle dispensing process is the alignment measurement of the pupillary distance (PD), pupillary height (PH), and optical center (OC) [6] of the lens. Therefore, research on accurate measurements of pupillary distance and height is of great significance. Pupillary distance (PD), defined as the distance between the centers of the two pupils [7], and pupillary height (PH), which refers to the distance from the center of the pupil to the lowest point on the lower rim of the frame measured along the visual axis of the eye passing through the lens, are essential measurement parameters in the fields of ophthalmology and optometry, commonly expressed in millimeters. In Figure 1a, the variables \"\(\mathrm{d}_{\mathrm{lc}}\)\" and \"\(\mathrm{d}_{\mathrm{rc}}\)\" represent the left and right interpupillary distances, respectively. The sum of these distances is referred to as the total PD. Similarly, \"\(\mathrm{h}_{1}\)\" and \"\(\mathrm{h}_{\mathrm{r}}\)\" represent the left and right pupil heights, respectively. These parameters can be utilized in various aspects, such as optometric fitting, customization of eyeglasses, and vision correction. However, inaccurate measurement of PD or PH, or a mismatch between the optical center of the lens and the PD, can cause distorted, blurred, and ambiguous visual images, leading to visual fatigue and damage to the eyes. There have been numerous studies on the importance of PD, including potential applications in biological characteristics. Traditionally, pupillary distance and height measurements have been obtained through manual measurement using rulers by optometrists in the design and manufacturing of eyeglasses, as shown in Figure 1. While this method is convenient and simple, it is prone to significant errors and can be easily influenced by human factors. Modern glasses accommodate far, intermediate, and near vision corrections in the same pair, making the precision requirements even more demanding. To achieve high precision levels, lens manufacturers have developed systems to measure pupil distance to one millimeter or below in error tolerance. This method is called photographic measurement [8], which involves using a camera to capture images of the eye and calculating the pupillary distance based on the size and position of the pupils in the images. The method is more precise but requires manual measurement as well as consideration of factors such as camera distance and angle. With the advancement of technology, a virtual measurement method [9] can also be used by constructing a 3D model of the eye using virtual reality technology, which is not limited by equipment or environmental constraints and can measure multiple parameters. However, this method requires professional software and technical support, and it can be expensive and infeasible for many individuals, while visual impairment affects a large number of people worldwide. Existing methods to measure pupillary distance often have limitations and cannot measure pupillary height. A practical solution would be to use portable devices such as cellphones and tablets since heavy equipment is not portable and sophisticated technologies remain inaccessible to many.