Corneal Reflection Research Articles

Eye movement disorders: A new approach to preliminary screening of Parkinson's disease.

To investigate the characteristics and diagnostic values of the eye movement disorders in patients with Parkinson's disease (PD-EMDs), this cross-sectional study enrolled 127 Chinese patients with PD and 80 healthy controls, and divided them into training and validation sets based on enrollment time. Performance in the five oculomotor paradigms was assessed using an infrared pupil and a corneal reflection tracking device. The primary characteristics of PD-EMDs were elucidated as inaccurate fixation with high deviation (frequency and total quantity); inaccurate saccades with delayed reaction and low velocity; saccadic pursuit with high deviation, delayed reaction, and velocity; and decreased visual search ability. Subgroup comparison shows that PD-EMDs can be related with PD stages, motor subtypes, frozen gait, and drowsiness. Finally, we developed and externally validated a model for PD preliminary screening using multivariate stepwise logistic regression analysis, comprising four oculomotor parameters (fixation accuracy, pro-saccade velocity, anti-saccade accuracy, and visual search duration), cognition score and educational years. The model has good feasibility with satisfactory performance on the receiver operating characteristic, calibration, and decision curves, and broad clinical applicability with better discrimination for more advanced PD patients and non-tremor-dominant PD patients. A nomogram was created to make the model more user-friendly in the clinical setting. Overall, we have demonstrated the presence of PD-EMDs and their prospective value for PD preliminary screening.

35‐3: Modeling Eye Movement and Reflection in Virtual Environments for Eye Tracking

Eye movement tracking plays a pivotal role in use interaction within Virtual Reality (VR) environments. Our research focuses on an advanced eye movement simulation using virtual environment for eye tracking training and eye tracking precision evaluating platform. We developed a real‐eye model, enhanced light refraction and corneal reflections under infrared LED light with eye rotation. Our study also customized screen,light source and cameras placement to capture eye images more faithfully. We also presents a noval testing methology and equipments of spatial accuracy testing of the eye‐tracking systems. The proposed proprietary eye‐tracking test system designed to recreate scenarios of human gaze and provide true values for eye gaze directions. Overall, the integration of Pupil Center Corneal Reflection (PCCR) based dataset generation and testing platform mark a significant advancement, enabling huge database, precise groudtruth training and accurate results testing.

P‐44: A Smart Eye Tracking System Based on Linear Array Sensors

Eye tracking as an important human‐machine interface plays avital role in immersive displays such as augmented reality (AR) and virtual reality (VR). Different from near infrared (NIR) camerabased methods, the proposed corneal reflection method based on principle of eyeball co‐vision takes advantage of using eye‐safe 940‐ nm vertical cavity surface emitting laser (VCSEL) and dual‐column linear array sensor (DCLAS) to obtain coordinates of the eyeball's moving positions through detecting its reflected light. The DCLAS not only delivers high sensitivity at eye‐safe NIR wavelength, but also has high spatial resolution for position accuracy and wide dynamic range to suppress ambient light influence. Together with low power consumption, good wearability, low data redundancy and simple computing algorism, a great promise can be made to enable smart eye tracking for AR/VR.

A method for extracting corneal reflection images from multiple eye images

The incident light reflected from the cornea is rich in information about the human surroundings, and these reflected rays are imaged by the camera, which can be used for research on human consciousness and gaze analysis, and produce certain help in the fields of psychology, human computer interaction and disease diagnosis. However, limited by the low corneal reflection ability, when a high-definition camera captures corneal reflecting rays, a large amount of color and texture interference from the iris can seriously contaminate the corneal reflection images, resulting in low usability and ubiquity of corneal reflection images. In this paper, we propose a corneal reflection image extraction method with multiple eye images as input. We align the iris regions of multiple eye images with the help of iris localization method, and by comparing multiple iris regions, we obtain the complementary iris regions, so that the iris interference in the corneal reflection region can be stripped completely. A large number of experiments have demonstrated that our work can effectively mitigate iris interference and effectively improve the quality of corneal reflection images.

Measurement of invivo lens shapes using IOLMaster 700 B-scan images: Comparison with phakometry.

This study compared invivo crystalline lens shape measurements using B-scan images from the IOLMaster 700 with phakometry. Twenty-four young adult participants underwent IOLMaster 700 and phakometry measurements under cycloplegia (1% cyclopentolate). The IOLMaster 700 generated B-scan images along six meridians in 30° increments, which were analysed using custom MATLAB software to determine lens surface radii of curvature. Phakometry measurements were obtained using Purkinje images reflected from the lens surfaces. The IOLMaster 700 image analysis method yielded a lower mean anterior lens surface spherical equivalent power (+6.20 D) than phakometry (+7.55 D); however, the two measurements were strongly correlated (R(21) = 0.97, p < 0.0001). The astigmatic power vectors (J0 and J45) for the anterior lens surface were significantly higher for the IOLMaster 700 measurements, with only J0 showing a significant moderate positive correlation (R(21) = 0.57, p = 0.005). For the posterior lens surface, the IOLMaster 700 measurements had a higher mean spherical power (+14.28 D) compared to phakometry (+13.70 D); however, a strong positive correlation (R(21) = 0.90, p < 0.0001) was observed. No significant correlations were noted for posterior lens surface astigmatic vectors (J0 and J45). The IOLMaster 700 estimates for the equivalent lens mean spherical power were slightly lower than those for phakometry, with a mean difference of -0.72 D, and both methods were positively correlated (R(21) = 0.94, p < 0.0001). The findings demonstrate that IOLMaster 700 B-scan image analysis technique provides similar estimates of lens surface powers to phakometry. These results highlight the potential of the IOLMaster 700 to provide measurements of lens shape, informing future research and clinical use.

Investigation of crystalline lens overshooting: ex vivo experiment and optomechanical simulation results.

Introduction: Crystalline lens overshooting refers to a situation in which the lens momentarily shifts too much from its typical location immediately after stopping the rotational movement of the eye globe. This movement can be observed using an optical technique called Purkinje imaging. Methods: In this work, an experimental setup was designed to reproduce this effect ex vivo using a fresh porcine eye. The sample was rotated 90° around its centroid using a high-velocity rotation stage, and the Purkinje image sequences were recorded, allowing us to quantify the overshooting effect. The numerical part of the study consisted of developing a computational model of the eye, based on the finite element method, that allowed us to understand the biomechanical behavior of the different tissues in this dynamic scenario. A 2D fluid-structure interaction model of the porcine eye globe, considering both the solid parts and humors, was created to reproduce the experimental outcomes. Results: Outputs of the simulation were analyzed using an optical simulation software package to assess whether the mechanical model behaves optically like the real ex vivo eye. The simulation predicted the experimental results by carefully adjusting the mechanical properties of the zonular fibers and the damping factor. Conclusion: This study effectively demonstrates the importance of characterizing the dynamic mechanical properties of the eye tissues to properly comprehend and predict the overshooting effect.

Objective and independent measurement of scattering caused by the cornea and crystalline lens

meritxell.vilaseca@upc.eduThere are several methods that provide information on the intraocular scattering. Procedures based on the observation of the lens through the slit lamp from which a gradation of the state of every cataract is assessed (e.g. lens opacities classification system III ‐ LOCS III) are the most widely used in clinics. Nevertheless, they provide information related to the back‐scattered light and not forward scattering, which is responsible for the degradation of vision. To do so, a procedure that assess retinal straylight using a device based on a psychophysical compensation‐comparison approach was proposed, in which the subject's task is a forced‐choice between two half fields to decide which one flickers more intensely. From these measurements, a psychometric function is fitted and used to determine the straylight compensation level log(s) on the basis of a few stimuli responses.As an alternative approach, some attempts have been made to use the double‐pass as a means of objectively estimating forward scattering. The double‐pass technique is a procedure that is able to capture the complete optical information of the eye, including the effect of higher‐order aberrations and intraocular scattering within a small visual angle. Artal et al. proposed the Objective Scatter Index (OSI) calculated from double‐pass images for estimating scattering with the intention to grade cataracts. This technique was also used successfully to account for scattered light in patients with keratitis and uveitis, and those undergoing refractive surgery. More recently, a new Frequency Scatter Index (FSI3) based on the analysis of double‐pass retinal images in the frequency domain has also been suggested, as a means of minimizing the impact of optical aberrations on the results obtained.Nevertheless, all of the former methods provide information on the total scattered light in the eye, which consists of the combined contributions originating from different ocular structures. In this regards, we recently proposed a technique for the objective and independent assessment of scattering caused by the cornea and the lens based on the analysis of the contrast of the third and fourth Purkinje images. The technique was preliminarily validated first by using artificial eyes with different levels of corneal and lens scattering; second, it was validated in eyes wearing customized contact lenses to simulate corneal scattering and eyes with nuclear cataracts. Finally, it was tested on a larger population of eyes with cataracts and corneal disorders to prove its clinical usefulness.In this work, we review all the above‐mentioned techniques that have been proposed for objective intraocular scattering assessment, putting especial emphasis on the last one based on Purkinje images, and compare their results and clinical performance.

Precise localization of corneal reflections in eye images using deep learning trained on synthetic data

We present a deep learning method for accurately localizing the center of a single corneal reflection (CR) in an eye image. Unlike previous approaches, we use a convolutional neural network (CNN) that was trained solely using synthetic data. Using only synthetic data has the benefit of completely sidestepping the time-consuming process of manual annotation that is required for supervised training on real eye images. To systematically evaluate the accuracy of our method, we first tested it on images with synthetic CRs placed on different backgrounds and embedded in varying levels of noise. Second, we tested the method on two datasets consisting of high-quality videos captured from real eyes. Our method outperformed state-of-the-art algorithmic methods on real eye images with a 3–41.5% reduction in terms of spatial precision across data sets, and performed on par with state-of-the-art on synthetic images in terms of spatial accuracy. We conclude that our method provides a precise method for CR center localization and provides a solution to the data availability problem, which is one of the important common roadblocks in the development of deep learning models for gaze estimation. Due to the superior CR center localization and ease of application, our method has the potential to improve the accuracy and precision of CR-based eye trackers.

Poster Session I: Digital dual-Purkinje-image eye tracking enables precise determination of visual receptive fields in fixating macaques.

Understanding the relationship between visual stimuli and neural activity is a fundamental goal in visual neuroscience. However, the study of visual neurophysiology in awake primates is complicated by the constant occurrence of eye movements, even during periods of nominal fixation. To address this challenge, we adapted a recently developed high-resolution digital dual-Purkinje-image (dDPI) eye tracker (Wu et al., 2023) for use with macaque monkeys. In addition to tracking the Purkinje images, we simultaneously estimate the pupil center and size: a first for video eye tracking. We then sought to evaluate the efficacy of dDPI eye tracking for studying visual processing in fixating macaques by recording single neurons from the lateral geniculate nucleus while a spatially-correlated noise stimulus was displayed. Our analyses show that, as a result of properly accounting for eye movements post-hoc, the predictive performance of generalized linear models improves and the estimates center radii contract to values equal to or smaller than those reported in the literature. Notably, correcting for eye movements using the locations of the pupil center and corneal reflection-the standard method in video eye tracking-yielded worse model fits and larger receptive field sizes. This finding implies that the pupil center is an inaccurate reporter of small eye movements, while the Purkinje images may be veridical during fixations.

Unexpected corneal reflection phenomenon alters smartphone 3D image-based models of the eye

Abstract Reconstruction of a 3D eye model by photogrammetry from a smartphone video could be prospectively used in self-diagnosis, screening and telemedicine monitoring of diseases of the front part of the eye and its surroundings. The main use could be found in the treatment of diseases of the curvature and surface of the cornea and in follow-up after some refractive procedures. In our work, we create 3D image-based models of the eye after scanning the face with a smartphone. An unexpected phenomenon appeared during the reconstruction of the transparent cornea – a crater-like depression was formed at the place where nearby objects reflected on the cornea, which corresponds to the first Purkinje image, the so-called glint. We thus encountered complications that may arise when modelling transparent living structures from a video taken in a normal environment, which will need to be solved if we want to create such 3D models of the eye using this method for medical purposes. Another 3D reconstruction approach or additional algorithms must be considered as a future work.

Poster Session I: Characteristics and coordination of microsaccades in 6 Dimensions.

The study of microsaccades, the small and rapid eye movements that occur during fixation, has focused on horizontal and vertical movements, while their torsional component remains relatively uncharted territory in vision research. We used video eye tracking to investigate microsaccades binocularly with horizontal and vertical movements tracked by pupil and corneal reflection and torsion by iris pattern. Five participants looked at a central dot for 20 trials of 20 seconds while seated, and their heads rested on a chin rest. For each microsaccade (N=2040), we measured the displacement of the eye along each dimension, and defined version as the average and vergence as the difference between the motion of the left and right eye. The average horizontal vertical and torsional components were 0.7, 0.3, and 0.1 deg for version and 0.1, 0.1, and 0.1 deg for vergence, respectively. Next, we measured the correlation between each component pair. We found that when the eyes moved to the left or right together, they also rotated by 0.3 deg (top towards the same side) for each degree of horizontal movement (R = 0.94, p < 0.01). When the eyes moved up (down), for each degree of vertical movement, they diverged (converged) 0.08 deg horizontally (R = -0.53, p < 0.01) and rotated 0.09 deg outward (inward; R = -0.47, p < 0.01). There was no strong correlation between other combinations. These results show that microsaccades follow similar kinematics at a minute scale as larger saccades.

How Do Most Young Moderate Hyperopes Avoid Strabismus?

Uncorrected hyperopic children must overcome an apparent conflict between accommodation and vergence demands to focus and align their retinal images. This study tested hypotheses about simultaneous accommodation and vergence performance of young hyperopes to gain insight into ocular motor strategies used to maintain eye alignment. Simultaneous eccentric photorefraction and Purkinje image tracking were used to assess accommodative and vergence responses of 26 adult emmetropes (AE) and 94 children (0-13 years) viewing cartoons. Children were habitually uncorrected (CU) (spherical equivalent refractive error [SE] -0.5 to +4 D), corrected and aligned (CCA), or corrected with a history of refractive esotropia (CCS). Accommodative and vergence accuracy, dissociated heterophoria, and vergence/accommodation ratios in the absence of retinal disparity cues were measured for 33- and 80-cm viewing distances. In binocular viewing, median accommodative lags for 33 cm were 1.0 D (AE), 1.33 D (CU), 1.25 D (CCA), and 1.0 D (CCS). Median exophorias at 80 and 33 cm were 1.2 and 4.5 pd (AE), 0.8 and 2.5 pd (CU), and 0 and 1.2 pd (CCA), respectively. Without disparity cues, most response vergence/accommodation ratios were between 1 and 2 meter angle/D (∼5-10 pd/D) (69% of AE, 44% of CU, 60% of CCA, and 50% of CCS). Despite apparent conflict in motor coupling, uncorrected hyperopes were typically exophoric and achieved adultlike accuracy of both vergence and accommodation simultaneously, indicating ability to compensate for conflicting demands rather than bias to accurate vergence while tolerating inaccurate accommodation. Large lags and esophoria are therefore atypical. This analysis provides normative guidelines for clinicians and a deeper mechanistic understanding of how hyperopes avoid strabismus.

Autism symptoms, functional impairments, and gaze fixation measured using an eye-tracker in 6-year-old children.

Autism spectrum disorder (ASD) is a neurodevelopmental disorder clinically characterized by abnormalities in eye contact during social exchanges. We aimed to clarify whether the amount of gaze fixation, measured at the age of 6 years using Gazefinder, which is an established eye-tracking device, is associated with ASD symptoms and functioning. The current study included 742 participants from the Hamamatsu Birth Cohort Study. Autistic symptoms were evaluated according to the Autism Diagnostic Observation Schedule, Second Edition (ADOS-2), and the functioning of the participating children in real life was assessed using the Japanese version of the Vineland Adaptive Behavior Scales, Second Edition (VABS-II). The Gazefinder system was used for gaze fixation rates; two areas of interest (eyes and mouth) were defined in a talking movie clip, and eye gaze positions were calculated through corneal reflection techniques. The participants had an average age of 6.06 ± 0.14 years (males: 384; 52%). According to ADOS, 617 (83%) children were assessed as having none/mild ASD and 51 (7%) as severe. The average VABS-II scores were approximately 100 (standard deviation = 12). A higher gaze fixation rate on the eyes was associated with a significantly lower likelihood of the child being assigned to the severe ADOS group after controlling for covariates (odds ratio [OR], 0.02; 95% confidence interval [CI], 0.002-0.38). The gaze fixation rate on the mouth was not associated with ASD symptoms. A higher gaze fixation rate on the mouth was associated with a significantly lower likelihood of the child being assigned to the low score group in VABS-II socialization after controlling for covariates (OR, 0.18; 95% CI, 0.04-0.85). The gaze fixation rate on the eyes was not associated with functioning. We found that children with low gaze fixation rates on the eyes were likely to have more ASD symptoms, and children with low gaze fixation rates on the mouth were likely to demonstrate poorer functioning in socialization. Hence, preschool children could be independently assessed in the general population for clinically relevant endophenotypes predictive of ASD symptoms and functional impairments.

A new method based on deep learning and image processing for detection of strabismus with the Hirschberg test

Strabismus is a condition in which one or both eyes do not work in parallel or in harmony. People with strabismus have one eye looking straight ahead while the other eye looks inwards, outwards, upwards or downwards. This condition can affect both eyes. Strabismus is a common eye condition that affects about 4 % of the world's population. Tests such as Hirschberg, Cover and Krimsky are used to detect strabismus. In the Hirschberg test, a light source is held at a distance of 50 cm so that it falls on the centre of each eye. The horizontal and vertical distance between the centre of gravity of the light reflected from the cornea and the centre of the pupil indicates the degree of strabismus. In this study, deep learning and image processing algorithms are used to detect the eye, corneal reflection, iris and pupil on a patient's facial image. Based on the Hirschberg test, the horizontal and vertical shifts for both eyes were measured to determine the patient's degree of strabismus. In this way, the Hirschberg test used in strabismus screening was performed automatically by software. The correct detection of the pupil and the light reflected from the cornea by the algorithm means that the eye has been measured correctly. The software was tested on the facial images of 88 strabismic patients of different sexes and ages. 91 % of the 88 patients, or 80 patients, had their left eye measured correctly. 90 % of the 88 patients, or 79 patients, had their right eye measured correctly. The results for each eye obtained from the correct measurements were found to have an error of maximum ± 2°. This error is due to the fact that a real eye is in three-dimensional space, while the digital eye image is in two-dimensional space, and was only observed in the test results of some patients. This algorithm can be tested on patients of all ages and is not affected by morphological differences in the patients' faces. Successful results have been observed experimentally that this newly proposed method can be used in strabismus screening.

Investigation of Camera-Free Eye-Tracking Glasses Compared to a Video-Based System.

Technological advances in eye-tracking have resulted in lightweight, portable solutions that are capable of capturing eye movements beyond laboratory settings. Eye-tracking devices have typically relied on heavier, video-based systems to detect pupil and corneal reflections. Advances in mobile eye-tracking technology could facilitate research and its application in ecological settings; more traditional laboratory research methods are able to be modified and transferred to real-world scenarios. One recent technology, the AdHawk MindLink, introduced a novel camera-free system embedded in typical eyeglass frames. This paper evaluates the AdHawk MindLink by comparing the eye-tracking recordings with a research "gold standard", the EyeLink II. By concurrently capturing data from both eyes, we compare the capability of each eye tracker to quantify metrics from fixation, saccade, and smooth pursuit tasks-typical elements in eye movement research-across a sample of 13 adults. The MindLink system was capable of capturing fixation stability within a radius of less than 0.5∘, estimating horizontal saccade amplitudes with an accuracy of 0.04∘± 2.3∘, vertical saccade amplitudes with an accuracy of 0.32∘± 2.3∘, and smooth pursuit speeds with an accuracy of 0.5 to 3∘s, depending on the pursuit speed. While the performance of the MindLink system in measuring fixation stability, saccade amplitude, and smooth pursuit eye movements were slightly inferior to the video-based system, MindLink provides sufficient gaze-tracking capabilities for dynamic settings and experiments.

Eye detection and coarse localization of pupil for video-based eye tracking systems

A video-based eye tracking system generally captures NIR images, each of which contains one or two eyes of a subject. The subject’s point of gaze is then determined using 3D eye model and pupil centre corneal reflection technique. Eye detection and pupil localization play significant roles in video-based eye tracking systems. However, face rotation, wearing glasses, eye-shape variation and illumination variation make it difficult to detect an eye and localize a pupil accurately in the images captured by video-based eye tracking systems. In this paper, we proposed an eye detector that adopts a coarse-to-fine strategy. The eye detector consists of three classifiers: an ATLBP-THACs feature-based cascade classifier, a branch CNN and a multi-task CNN. We also proposed a method for coarse pupil localization. Coarse localization is an important step for pupil localization since it can provide initial pupil coordinates for a fine pupil localization method. Given a downscaled eye image, a shallow CNN is used to estimate the location of seven landmarks. On this basis, pupil center and radius are estimated. A method for small dim target enhancement is used to increase the contrast between pupil and background. The main goal of pupil enhancement is to make it easier to binarize an eye image. At last, component filtering is made by utilizing the estimated pupil center and radius. We collected a dataset named neepuEYE dataset that consists of 5500 NIR eye images from 109 people. The images can be used to generate augmented samples for training an eye detector since they contain eyes with different shape, orientation and pupil localization. Experimental results show that our eye detector is a fast and robust detector. Furthermore, our method for coarse pupil localization can obtain not only high detection rate but also high localization speed.

High-resolution eye-tracking via digital imaging of Purkinje reflections.

Reliably measuring eye movements and determining where the observer looks are fundamental needs in vision science. A classical approach to achieve high-resolution oculomotor measurements is the so-called dual Purkinje image (DPI) method, a technique that relies on the relative motion of the reflections generated by two distinct surfaces in the eye, the cornea and the back of the lens. This technique has been traditionally implemented in fragile and difficult to operate analog devices, which have remained exclusive use of specialized oculomotor laboratories. Here we describe progress on the development of a digital DPI, a system that builds on recent advances in digital imaging to enable fast, highly precise eye-tracking without the complications of previous analog devices. This system integrates an optical setup with no moving components with a digital imaging module and dedicated software on a fast processing unit. Data from both artificial and human eyes demonstrate subarcminute resolution at 1kHz. Furthermore, when coupled with previously developed gaze-contingent calibration methods, this system enables localization of the line of sight within a few arcminutes.

Maximizing valid eye-tracking data in human and macaque infants by optimizing calibration and adjusting areas of interest.

Remote eye tracking with automated corneal reflection provides insights into the emergence and development of cognitive, social, and emotional functions in human infants and non-human primates. However, because most eye-tracking systems were designed for use in human adults, the accuracy of eye-tracking data collected in other populations is unclear, as are potential approaches to minimize measurement error. For instance, data quality may differ across species or ages, which are necessary considerations for comparative and developmental studies. Here we examined how the calibration method and adjustments to areas of interest (AOIs) of the Tobii TX300 changed the mapping of fixations to AOIs in a cross-species longitudinal study. We tested humans (N = 119) at 2, 4, 6, 8, and 14 months of age and macaques (Macaca mulatta; N = 21) at 2 weeks, 3 weeks, and 6 months of age. In all groups, we found improvement in the proportion of AOI hits detected as the number of successful calibration points increased, suggesting calibration approaches with more points may be advantageous. Spatially enlarging and temporally prolonging AOIs increased the number of fixation-AOI mappings, suggesting improvements in capturing infants' gaze behaviors; however, these benefits varied across age groups and species, suggesting different parameters may be ideal, depending on the population studied. In sum, to maximize usable sessions and minimize measurement error, eye-tracking data collection and extraction approaches may need adjustments for the age groups and species studied. Doing so may make it easier to standardize and replicate eye-tracking research findings.

A Corneal Surface Reflections-Based Intelligent System for Lifelogging Applications

Corneal Surface Reflections, or reflections on our eye-surface, have been shown as a valid and more socially acceptable source of information for passive lifelogging applications by prior work. However, automatic analysis of corneal surface reflections from a single RGB camera to support passive lifelogging is not extensively investigated in prior work. To address this, we developed a synthetic and self-supervised learning-based two-stage pipeline of deep learning models to detect objects in these reflections. Our prototype only consists a single RGB camera looking into the eye. We collected data from different users in uncontrolled environments using the prototype and trained our system to detect multiple classes of objects present in a typical office environment. We then evaluated our model in partially-controlled and in-the-wild scenarios. In addition, based on the findings from a follow up user study and prior work, we discuss strengths and weaknesses of our system and using corneal surface reflections for passive lifelogging. Finally, we opensource our source codes and trained checkpoints.

An Improved Cross-Ratio Based Gaze Estimation Method Using Weighted Average and Polynomial Compensation

The cross-ratio (CR)-based method exploits the invariance property of CRs in projective transformation to determine a screen point corresponding to the pupil center. However, this point is essentially the intersection of the eyeball optical axis (OA) and the screen, rather than the actual point-of-regard (POR). In addition, the premise of CR calculation is that the corneal reflection points of four on-screen light sources are coplanar with the 3D pupil center, but they are only assumed to be coplanar. To solve these issues, this paper proposes an improved CR-based gaze estimation method using weighted average and polynomial compensation. Under the configuration of a single camera and two light sources, the 3D corneal center and the normal vector of virtual pupil plane are first estimated using the eyeball imaging model, and then four reference planes parallel to the virtual pupil plane are determined based on the geometric model of pupil and screen corner points. The screen point corresponding to the intersection of each reference plane and the line connecting the camera optical center and the imaging pupil center is calculated using the conventional CR-based method. Thus, the point where the OA intersects the screen is determined by the weighted average of these four points. Finally, a polynomial is learned to compensate it to the POR. The experimental results show that the gaze accuracy can reach 1.33° when the more accurate eye is selected, and it would be improved by 24% by calculating the joint POR, which is competitive with the state-of-the-art methods using more complex systems. On the basis of simplifying the system configuration of CR-based methods, the proposed method avoids the non-coplanarity of 3D pupil center and corneal reflection plane, and improves the gaze estimation performance.