Distance Measurement Between a Camera and a Human Subject Using Statistically Determined Interpupillary Distance

Abstract

This paper presents a non-intrusive method for estimating the distance between a camera and a human subject using a monocular vision system and statistically derived interpupillary distance (IPD) values. The proposed approach eliminates the need for individual calibration by utilizing average IPD values based on biological sex, enabling accurate, scalable distance estimation for diverse users. The algorithm, implemented in Python 3.12.11 using the MediaPipe Face Mesh framework, extracts pupil coordinates from facial images and calculates IPD in pixels. A sixth-degree polynomial calibration function, derived from controlled experiments using a uniaxial displacement system, maps pixel-based IPD to real-world distances across three intervals (20–80 cm, 80–160 cm, and 160–240 cm). Additionally, a geometric correction is applied to compensate for in-plane facial rotation. Experimental validation with 26 participants (15 males, 11 females) demonstrates the method’s robustness and accuracy, as confirmed by relative error analysis against ground truth measurements obtained with a Bosch GLM120C laser distance meter. Males exhibited lower relative errors across the intervals (3.87%, 4.75%, and 5.53%), while females recorded higher mean relative errors (6.0%, 6.7%, and 7.27%). The results confirm the feasibility of the proposed method for real-time applications in human–computer interaction, augmented reality, and camera-based proximity sensing.

1. Introduction

A particularly significant application area is human-to-camera distance estimation, which underpins the development of responsive graphical user interfaces (GUIs). For instance, intelligent document viewers and adaptive content delivery systems rely heavily on accurate proximity measurements to tailor user experience in real time [1]. Furthermore, distance estimation is integral to autofocus algorithms in imaging devices, allowing for the automatic optimization of image quality without requiring manual adjustments [2]. Beyond user-centric applications, this capability extends its influence into safety-critical and autonomous domains, such as autonomous driving (ADAS), where vehicles must continuously and precisely gauge the distance to surrounding objects to ensure safe navigation [3]. Similarly, in robotics, effective spatial perception is essential for tasks ranging from navigation to manipulation within complex environments [4]. Moreover, emerging technologies in Augmented Reality (AR) and Virtual Reality (VR) demand real-time and precise distance measurements to create immersive, responsive virtual environments that closely mimic real-world spatial interactions [5,6].

Traditionally, binocular vision systems, which rely on stereo image pairs to triangulate distances, have been widely employed for such purposes due to their ability to resolve depth directly. Furthermore, effective stereo vision requires dual-camera setups with precise extrinsic and intrinsic calibration, as well as additional computational resources for stereo correspondence and rectification. These constraints limit their practicality in embedded or resource-constrained scenarios. Consequently, monocular methods—based on single-camera inputs—have garnered increasing attention due to their hardware simplicity and ease of integration into existing imaging platforms [7]. In sensitive applications, where velocity of the visual task and the placement is critical, binocular measures are relatively robust [8,9].

Despite the growing importance of distance estimation, the development of methods that are both non-intrusive and calibration-free remains a significant technical challenge [10]. This paper introduces a novel approach leveraging average anatomical features—specifically, interpupillary distance (IPD)—as a dimensional reference for estimating subject distance using a monocular camera, without requiring personalized calibration.

Monocular distance estimation typically necessitates prior knowledge of a dimensional reference to resolve scale ambiguity inherent to single-camera systems [11]. Depending on the application domain, various types of reference features have been employed. For example, smartphone applications designed for video-based distance measurement, such as Smart Distance and Distance Measure, use either known physical landmarks or complementary smartphone sensors, including accelerometers, to facilitate accurate measurement [12,13]. In automotive contexts, distance estimation methods often assume a priori knowledge of object dimensions, such as the average width of vehicles [14]; however, this assumption introduces considerable variability, as both vehicle and lane dimensions can differ significantly across geographic regions, limiting the generalizability and robustness of such approaches. Other methods employ identifiable features like license plate dimensions or artificial markers as scale references. Nonetheless, small physical markers pose challenges in the case of long-range detection, as beyond 30 m it becomes increasingly difficult. Furthermore, marker dimensions vary globally, limiting their applicability across regions [15]. Additional techniques for monocular distance estimation include leveraging camera motion across a known displacement to infer scale through pixel variation [16,17], placing physical reference markers at predetermined distances [18], exploiting defocus blur characteristics of target objects [19], or using lens focus adjustments to estimate subject distance [20].

When estimating the distance between a camera and a human subject, anatomical features such as interpupillary distance or iris diameter are frequently employed as intrinsic dimensional references. Prior work has demonstrated the feasibility of using IPD for distance estimation [21]; however, such methods generally require individual calibration for each subject and depend on real-time facial recognition [22], limiting their practical applicability. Alternative methods based on iris diameter as a reference have also been proposed [23], but they often suffer from higher inter-subject variability and measurement challenges.

In contrast, the method presented in this paper exploits the average interpupillary distance, which exhibits relatively low variability across the general population, to enable accurate and generalizable distance estimation without the need for individualized calibration. By leveraging this stable anatomical reference, the proposed approach enhances estimation accuracy and broadens applicability, particularly in scenarios where subject-specific calibration is impractical or impossible [24,25].

2. Methods

This paper presents a novel monocular distance estimation method that eliminates the need for individual user calibration by leveraging a statistically established average interpupillary distance (IPD), which varies according to biological sex [26]. Conventional approaches for estimating the distance between a camera and a user typically rely on either physical reference markers within the scene or personalized biometric calibration for each individual, which limits scalability and practical deployment in real-world applications. The method proposed herein aims to achieve a balance between simplicity, generalizability, and robustness, making it particularly suitable for human–computer interaction scenarios.

The proposed approach exploits the relatively stable and measurable nature of the IPD across adult populations. The IPD, defined as the distance between the centers of the pupils, constitutes a consistent anatomical feature observable in frontal facial images. Biometric data reported in [27] indicate the following mean IPD values derived from a statistically significant sample:

• 61.53 mm for adult females, with a standard deviation (SD) of ±2.66 mm;
• 65.32 mm for adult males, with a standard deviation (SD) of ±1.50 mm.

These population-based averages serve as biometric references for inferring real-world scale from image pixel measurements. By detecting the pixel distance between the pupil centers in a captured image—using computer vision frameworks such as MediaPipe FaceMesh—and associating this measurement with the known average IPD, the method estimates the physical distance between the subject and the camera based on the principles of pinhole camera geometry.

A key innovation of this approach is the removal of the dependency on per-user calibration, which is traditionally required to accommodate individual facial dimension variability. Instead, the method assumes that subjects conform to a normal distribution centered on the population mean.

Although this assumption introduces some approximation, the relatively low standard deviation of IPD—especially among male subjects—ensures that the resultant error remains within acceptable limits for many practical applications, including interface adaptation and gaze correction.

To enhance accuracy, the system optionally incorporates a sex classification module—based on facial features or external inputs—to select the appropriate average IPD for the subject. In the present implementation, the user’s biological sex is manually selectable via keyboard input. For real-world deployment, this manual selection could be replaced with automated classification modules based on facial features or integration with user profile data in authenticated systems. Such automation could improve usability, particularly in consumer or industrial applications, but must be balanced against considerations of algorithmic bias, user privacy and informed consent.

This distance estimation approach offers several advantages:

• It is non-intrusive, requiring no physical markers or auxiliary devices;
• It is scalable and suitable for real-time deployment across diverse populations;
• It is hardware-agnostic, adaptable to different camera models through a one-time calibration procedure specific to the camera’s optics;
• It is computationally efficient, enabling integration with mobile and embedded platforms.

Calibration Procedure

The calibration process utilizes a printed frontal facial image with known IPD values as a reference standard (Figure 1), specifically 61.53 mm assigned for female calibration and 65.32 mm assigned for male calibration. These values are incorporated as reference inputs within the distance measurement algorithm.

During calibration, the printed image is positioned in front of the camera, which is mounted on a uniaxial displacement system to precisely control its distance from the image (Figure 2). At multiple predetermined distances (d), images are captured, and the pixel coordinates of the pupil centers are extracted through graphical analysis. The interpupillary distance in pixels is calculated for each frame as the Euclidean distance between the detected pupil centers. This technique is performed at multiple established distances to generate a dataset that correlates pixel-based inter-pupillary distance measurements with actual distances. From this dataset, a calibration function d = f(IPD) is derived, characterizing the relationship between the real-world distance and the interpupillary pixel distance. This calibration curve encapsulates the optical parameters of the camera and its imaging characteristics.

The calibration is performed once per camera model, assuming fixed resolution and focal length. Subsequently, real-time distance estimation is accomplished by detecting the interpupillary pixel distance of the subject’s face in video frames and applying the calibrated function to estimate the physical distance from the camera.

Pupil detection and IPD estimation were implemented in Python, utilizing the MediaPipe Face Mesh framework. Image data was acquired using the camera integrated into the calibration stand. The imaging device is a consumer-grade webcam with a native resolution of 1280 × 720 pixels.

The uniaxial displacement system was electrodynamically actuated and servo-controlled using a closed-loop PID control architecture. The system was designed for precise and repeatable displacement, and its main components are described as follows:

• Structural frame: a fixed steel frame served as the support base. The frame was equipped with mounting holes to facilitate modular attachment of system components and external fixtures.
• The cart, actuated via a rack-and-pinion mechanism (Ø6.35 mm, 24 teeth), moved along a stainless-steel shaft supported by linear bearings. The cart had a mass of 500 g and was designed to carry an additional 370 g of load. The increased total mass provided enhanced inertia, contributing to effective vibration damping of the structure during motion.
• Actuation system: the system was powered by a high-performance DC servomotor, capable of achieving a nominal speed of 4160 rpm and an angular acceleration of 40 × 10³ rad/s². Key motor parameters included a back electromotive force (EMF) constant of 0.804 mV/rpm, a torque constant of 7.67 × 10⁻³ Nm/A, and a mechanical time constant of 17 ms, enabling robust and accurate actuation performance.
• Gearbox: a single-stage gearbox (23/1 series) with a 3.71:1 reduction ratio and 100% efficiency was coupled to the motor. The gearbox reduced the load on the motor and enhanced torque transmission to the cart.
• Power amplifier brush DC servomotor: the amplifier was powered by a 230 V AC input and provided a continuous output of ±24 V, controlled via a ±10 V input signal.
• Position feedback: a high-resolution optical encoder was integrated into the system for accurate position sensing. The encoder featured a resolution of 0.0235 mm (4096 counts/rev in quadrature mode, equivalent to 1024 lines/rev) and could track rotational speeds up to 10,000 rpm. It operated as a rotary-to-digital converter based on phased array detector technology. The encoder was attached to a 148 mm diameter, 56-tooth pinion gear.
• Data Acquisition and Control Interface (DAQ): a board with eight configurable digital input/output channels interfaced with the encoder. It provided real-time conversion of shaft angle, speed, and direction into TTL-compatible quadrature signals. The board was equipped with two 5-pin DIN encoder input connectors and supported 16-bit count values. It allowed initialization of the encoder count and optional reloading on index pulses. The entire system was controlled via a LabVIEW 2024 Q3-based PID control loop.

The control system was implemented using a closed-loop PID controller, continuously adjusting the cart’s position based on encoder feedback. The PID parameters—proportional gain (Kp), integral time (Ti), and derivative time (Td)—were determined using the Ziegler–Nichols tuning method. Initially, the integral and derivative terms were set to zero, and the proportional gain was incrementally increased until sustained oscillations were observed at the ultimate gain (Ku = 0.116) and ultimate period (Tu = 0.01 min).

The final controller parameters were computed as:

• Kp = 0.6 × Ku = 0.07
• Ti = 0.5 × Tu = 0.005 min
• Td = 0.125 × Tu = 0.0013 min

The control algorithm was implemented in LabVIEW using the Control Design and Simulation Toolkit. The control loop consisted of four main functional blocks:

• HIL Initialize—initializes the hardware-in-the-loop (HIL) interface;
• HIL Read—acquires position feedback from the encoder in real-time;
• HIL Write—transmits control signals to the power amplifier and DC motor;
• PID Controller—calculates the control signal based on error input and feedback.

This configuration enabled real-time, closed-loop control of the cart’s displacement with high precision and stability.

To investigate the dependency between the IPD in pixels and the distance of the image from the camera, three measurement intervals were established: 20–80 cm, 80–160 cm, and 160–240 cm. The positioning of the calibration stand was carried out with high precision using a Bosch GLM 120C laser (Iași, România) distance meter to measure the offset from the camera. Within each interval, the cart holding the web camera was moved in 1 cm increments. At each position, an image was captured and the corresponding IPD in pixels was computed.

The function that provides the best approximation of the calibration data was a sixth-degree polynomial, applicable to both male and female printed face targets.

Figure 3 shows the activity diagram summarizing the sequence of phases in the proposed method.

3. Results

Accurate estimation of IPD from 2D facial images is often compromised by the subject’s head orientation relative to the camera. Specifically, in-plane facial rotation (i.e., rotation around the camera’s Z-axis) can cause an apparent reduction in the measured IPD due to perspective distortion. To mitigate this effect, a geometric correction method based on facial landmark analysis was proposed.

Using the MediaPipe Face Mesh model, the 2D coordinates of the pupils were extracted along with three additional facial landmarks: the nose tip, and landmarks on the left and right cheeks. These three points define a local facial triangle within the image coordinate space. Two vectors were computed from the nose tip to each cheek point ($\overrightarrow{v_L}$, $\overrightarrow{v_R}$) and their average direction ($\overrightarrow{v_m}$) was used to estimate the in-plane orientation of the face (Figure 4).

A 2D normal vector $\overrightarrow{n}$ is perpendicular to the average direction of the facial plane ($\overrightarrow{v_m}$). The direction of this normal vector gives the frontal orientation of the face in the image.

The raw IPD was calculated as the Euclidean distance between the detected positions of the left and right pupils.

$${IPD}_{raw}=‖P_R-P_L‖,$$

where P_R and P_L are defined by 2D coordinates of the right and left pupils, as detected in the image. IPD_raw is a straight-line distance between the pupils in the 2D image, which is affected by in-plane head rotation.

To correct for in-plane rotation, the angle between the unit pupil vector ($\overrightarrow{v_{eyes}}$) and the unit normal to the estimated facial direction ($\overrightarrow{n}$) was computed.

$$cos\propto ={\displaystyle \frac{\widehat{n}}{\widehat{v_{eyes}}}},$$

where $\widehat{n}={\displaystyle \frac{n}{‖n‖}}$is the unit normal vector pointing in the estimated frontal direction of the face in the 2D image and $\widehat{v_{eyes}}={\displaystyle \frac{v_{eyes}}{‖v_{eyes}‖}}$ is the unit pupil vector. $‖v_{eyes}‖$ and $‖n‖$ are the Euclidean norms of the corresponding vectors, calculated from the coordinates of the pupils, respectively from the coordinates of $\overrightarrow{v_m}$. As $\overrightarrow{n}$ is perpendicular to $\overrightarrow{v_m}$ (90° counterclockwise) its coordinates are inversed and negative for y.

The corrected IPD was obtained by projecting the pupil vector onto the estimated normal direction, which involves multiplying the raw IPD by the cosine of the angle between the two vectors.

$${IPD}_{corrected}={IPD}_{raw}·cos\alpha$$

This method effectively compensates for distortions introduced by in-plane rotation and yields an IPD measurement that more closely approximates the value observed under frontal facial alignment.

As illustrated in Figure 5, in the first case the subject was oriented directly towards the camera, resulting in the same IPD value for both the uncorrected and corrected versions. In the other two cases, the subject’s face was rotated away from the camera’s frontal axis; however, the proposed correction method successfully adjusts the raw IPD value to compensate for this deviation.

The application was tested with the participation of 26 volunteers, all of whom provided informed consent. The test group consisted of 15 male participants aged between 20 and 68 years, and 11 female participants aged between 22 and 67 years. For each individual, the distance to the camera was measured within each of the three calibration intervals. Ten measurements were performed per interval.

Each measurement was carried out using both the proposed method and a Bosch GLM 120C laser distance meter, which served as the ground truth. Relative errors were computed based on the difference between the estimated and reference distances. For each subject and each interval, the minimum, maximum and mean relative errors were calculated from the set of ten individual measurements. The results are presented in

Table 1. Relative error statistics for male participants.

Males
Intervals	20–80 cm			80–160 cm			160–240 cm
Errors	Maximum Relative Errors [%]	Minimum Relative Errors [%]	Mean Relative Errors [%]	Maximum Relative Errors [%]	Minimum Relative Errors [%]	Mean Relative Errors [%]	Maximum Relative Errors [%]	Minimum Relative Errors [%]	Mean Relative Errors [%]
1	4.9	4.4	4.6	5.1	4.2	4.8	6.2	5.4	5.8
2	4.1	3.6	3.9	5.2	4.6	5.0	5.5	5.1	5.4
3	3.6	3.1	3.5	4.9	4.2	4.7	5.7	4.8	5.3
4	4.2	3.5	3.8	4.8	4.5	4.6	6.1	5.3	5.9
5	3.8	3.2	3.7	5.1	4.3	4.8	5.4	4.6	4.9
6	3.9	3.3	3.8	5.2	4.7	5.1	5.3	4.8	5.1
7	4.1	3.6	3.9	4.9	4.4	4.7	6.1	5.4	5.8
8	4.1	3.4	3.7	4.8	4.3	4.4	5.8	5.1	5.5
9	4.6	3.9	4.3	4.8	4.6	4.7	5.5	4.9	5.3
10	4.2	3.5	4.1	5.1	4.1	4.5	6.3	5.2	5.9
11	4.1	3.6	3.9	5.0	4.2	4.9	5.4	5.1	5.3
12	3.8	3.1	3.7	4.9	4.5	4.8	5.7	5.0	5.6
13	3.9	3.3	3.5	5.1	4.1	4.4	5.9	5.1	5.5
14	4.8	3.9	4.0	5.3	4.6	4.9	6.1	5.5	5.9
15	4.1	3.6	3.8	5.2	4.4	4.9	5.8	5.3	5.7
Mean	4.15	3.53	3.87	5.03	4.38	4.75	5.79	5.11	5.53
Std dev	0.38	0.36	0.34	0.16	0.14	0.27	0.33	0.29	0.31
95% CI	-	-	±0.19	-	-	±0.19	-	-	±0.14

and

Table 2. Relative error statistics for female participants.

Females
Intervals	20–80 cm			80–160 cm			160–240 cm
Errors	Maximum Relative Errors [%]	Minimum Relative Errors [%]	Mean Relative Errors [%]	Maximum Relative Errors [%]	Minimum Relative Errors [%]	Mean Relative Errors [%]	Maximum Relative Errors [%]	Minimum Relative Errors [%]	Mean Relative Errors [%]
1	6.5	5.9	6.3	6.9	6.3	6.7	7.5	6.8	7.1
2	6.6	5.8	6.4	6.8	6.1	6.5	7.8	7.1	7.5
3	6.3	5.5	5.9	6.8	6.0	6.6	7.6	7.0	7.3
4	6.4	5.4	5.7	7.0	6.4	6.8	7.2	6.7	7.0
5	6.9	5.8	6.2	7.1	6.2	6.9	7.1	6.4	6.9
6	5.9	5.6	5.8	6.6	6.0	6.4	7.8	6.3	7.5
7	6.3	5.4	5.7	6.9	6.3	6.6	7.5	6.3	7.2
8	5.4	5.9	5.8	6.4	6.1	6.3	7.6	7.1	7.5
9	6.7	6.4	6.6	7.3	6.6	7.1	7.8	7.3	7.5
10	6.1	5.7	5.9	7.2	6.7	7.0	7.7	7.1	7.3
11	6.2	5.3	5.7	7.0	6.5	6.8	7.4	7.0	7.2
Mean	6.3	5.7	6.0	76	6.9	6.7	7.55	6.82	7.27
Std dev	0.47	0.38	0.29	0.26	0.26	0.29	0.25	0.3	0.21
95% CI	-	-	±0.20	-	-	±0.20	-	-	±0.14

.

Confidence intervals were calculated for mean errors to assess precision, but not for maximum and minimum errors, as these extreme values do not support straightforward interval estimation. They were computed as:

$$CI=t_{\alpha /2,df}·{\displaystyle \frac{s}{\sqrt{n}}}$$

With t_α/2,df the t-value for 95% confidence and degrees of freedom df = n − 1, s is the sample standard deviation (Std dev), n is the sample size (15 males and 11 females).

The results obtained from the experimental evaluation highlight the effectiveness and practical viability of using interpupillary distance (IPD) as a printed reference for monocular distance estimation. Across all measurement intervals, the proposed method demonstrated consistent performance, with relative errors remaining within acceptable bounds, particularly for male subjects, whose biological IPD variability is statistically lower.

The error distributions presented in Table 1 and Table 2 indicate that inter-subject variability in interpupillary distance (IPD) contributes significantly to estimation accuracy. Female participants exhibited higher relative errors across all distance ranges, which aligns with biometric data reporting a larger standard deviation of IPD in adult females (61.53 mm ± 2.66 mm) compared to males (65.32 mm ± 1.50 mm) [27]. The current implementation, based on fixed sex-specific mean values, does not account for such deviations; consequently, individuals with atypical or outlier IPDs introduce additional estimation errors. A more general formulation would treat IPD as a random variable following a normal distribution with population-derived parameters and incorporate this variability directly into the inference process. Within a Bayesian framework, the observed pixel-based IPD can be interpreted as the likelihood, while the prior distribution encodes anatomical variability. The resulting posterior distribution would provide both point estimates and credible intervals, thereby quantifying uncertainty and reducing sensitivity to extreme values.

In line with the methodological aim of validating estimation accuracy rather than testing group-level hypotheses, no inferential statistics (e.g., ANOVA, t-test) were applied. Instead, descriptive metrics together with 95% confidence intervals were reported as the most appropriate indicators of accuracy for this proof-of-concept study.

4. Discussion

The present study focused exclusively on adult participants. The choice to use sex-based average IPD rather than age- or ethnicity-adjusted values was motivated by two factors: (1) statistical stability of IPD within adult populations, where variability is relatively low (±2.66 mm for females, ±1.50 mm for males), and (2) the practical aim of minimizing required user data, avoiding the complexity and privacy concerns associated with collecting or inferring additional demographic details. While demographic variation can influence IPD, its impact is smaller than the gain in simplicity and scalability for non-intrusive applications. This limitation has been acknowledged as a potential area for future work involving adaptive demographic scaling.

The correction mechanism applied to account for in-plane facial rotation significantly contributed to improving measurement accuracy, especially in scenarios where the subject’s head was not perfectly aligned with the camera’s optical axis. As observed in the experimental figures, in the absence of such correction, the raw IPD tends to be underestimated due to geometric distortion. By projecting the raw pupil vector onto the estimated facial normal direction, the algorithm successfully compensates for orientation-induced errors, thereby stabilizing IPD-based distance estimation.

The calibration procedure, grounded in a statistically determined average IPD (61.53 mm for females and 64.32 mm for males), proved to be both scalable and repeatable. The use of a printed facial reference in conjunction with a precision-controlled uniaxial displacement system enabled the derivation of a high-fidelity sixth-degree polynomial model mapping pixel-based IPD measurements to physical distance. This function encapsulates the camera’s optical behavior under fixed resolution and focal length, enabling robust real-time distance estimation once calibration is complete. Camera resolution plays a critical role in preserving accuracy, particularly at longer ranges where facial features occupy fewer pixels. In our tests, a 1280 × 720 resolution webcam provided acceptable performance for distances up to 2.4 m. For optimal results, cameras should provide at least 720p resolution, maintain >30 fps and have adequate low-light performance to ensure robust facial landmark detection. The proposed method achieved ~40 ms per frame processing time on a mid-range CPU without GPU acceleration, corresponding to ~25 fps in real time. This suggests that implementation of embedded vision hardware, such as ARM-based processors (e.g., Google Coral, NVIDIA Jetson Nano) with dedicated AI accelerators, is feasible.

In a fixed optical configuration, the pixel-IPD-distance relationship is smooth but nonlinear due to projection geometry, landmark rounding, head-pose correction, and lens distortion remnants. A sixth-degree polynomial provides sufficient flexibility to capture this curvature across the calibrated ranges without oscillatory artifacts. The choice is supported by cross-validated error comparisons against lower/higher degrees and by residual diagnostics. Additionally, the polynomial mapping is computationally lightweight and fully deterministic, which favors embedded real-time implementations. We note that for heterogeneous, multi-camera deployments, machine-learning regressors (e.g., SVR, Random Forest) may improve cross-device generalization and constitute a natural extension of this work.

An analysis of the error distributions presented in the two tables—corresponding to male and female participants—reveals consistent trends with respect to both distance intervals and biological sex. Male participants exhibited lower relative errors across all three distance ranges, with average mean relative errors of approximately 3.87%, 4.75%, and 5.53% for the 20–80 cm, 80–160 cm, and 160–240 cm intervals, respectively. In contrast, female participants recorded higher mean relative errors of 6.0%, 6.7%, and 7.27% across the same intervals. This discrepancy can be attributed in part to the higher standard deviation of interpupillary distance within the female population (±2.66 mm) compared to males (±1.50 mm), as reported in the biometric reference data. Since the method relies on fixed average IPD values, increased inter-subject variability introduces greater estimation error, particularly when individual IPDs deviate from the population mean. Moreover, the relatively smaller average IPD in female subjects results in a lower number of pixels per millimeter in the image space, compounding the sensitivity of measurements to pixel-level inaccuracies. These findings underscore the importance of accounting for biological variation in the design of generalized distance estimation models and suggest that error bounds may be further reduced through dynamic sex estimation or adaptive reference scaling.

However, one critical observation from the results is the degradation in measurement precision at larger distances. As the subject moves farther from the camera, the apparent size of facial features in the image diminishes, resulting in a lower pixel resolution for the IPD measurement. This reduction in pixel density limits the sensitivity of the method, as even small variations in pixel measurement translate to larger absolute errors in real-world distance estimation. This effect is particularly evident in the 160–240 cm interval, where both male and female groups exhibited slightly higher mean relative errors compared to shorter ranges. Despite this limitation, the method maintains its reliability due to the stability of the printed reference and the geometric correction process. For practical applications, the observed resolution loss suggests the importance of selecting appropriate camera resolution and positioning for the target measurement range. Future implementations may benefit from higher-resolution sensors or multi-frame averaging techniques to enhance pixel-level accuracy at greater distances.

Beyond human–camera interactions, the proposed approach could be adapted to other contexts where stable anatomical or morphological features are known. Potential examples include monitoring animals in veterinary or agricultural environments by exploiting average interocular distances or applying similar geometric principles to structured objects in security and traffic monitoring. These extensions illustrate the broader applicability of the method as a non-intrusive monocular distance estimation tool.

5. Conclusions

This study proposed and validated a monocular distance estimation method based on the statistically averaged interpupillary distance (IPD), eliminating the need for subject-specific calibration. Through a structured calibration process using printed face templates and a precisely controlled displacement system, a sixth-degree polynomial function was derived to map pixel-based IPD measurements to real-world distances. The implementation of a geometric correction algorithm for in-plane facial rotation further improved the robustness and accuracy of the method.

Experimental validation involving 26 participants demonstrated that the method achieves consistent and reliable performance across a broad range of distances. The lowest relative errors were observed at shorter distances, with a moderate increase in error at longer ranges due to reduced pixel resolution of facial features. This highlights a key trade-off between camera resolution, subject distance, and measurement precision, suggesting that optimal performance is achieved within the mid-range calibration interval (80–160 cm).

While the method demonstrated consistent performance within the tested range, certain limitations should be noted. The current implementation was validated only up to 2.4 m, beyond this distance, the reduced pixel resolution of facial landmarks may increase estimation error. In addition, the approach relies on sex-based average IPD values, which do not fully capture demographic variability across age groups, ethnicities or individuals with atypical facial proportions. These factors may affect generalization and should be addressed in larger studies through extended calibration datasets and adaptive modeling strategies. Future large-scale studies with balanced cohorts could incorporate formal hypothesis testing to further characterize subgroup effects, complementing the descriptive statistics and confidence intervals reported here.

Future work will explore integrating this method into application OptoGuard [28], where continuous monitoring of user-screen distance can provide alerts to maintain the recommended 40–63 cm range, helping prevent digital eye strain and other computer-related visual disorders.