Corneal Reflection Research Articles

Reconstructing ocular surfaces by Purkinje images using an exact ray approach: estimating IOL decenter and tilt

Recently, an alternate method for recovering the shape of the anterior surface of an intraocular lens (IOL) (by Purkinje images), and capable of returning a Zernike polynomial representation of that surface, was proposed (Ophthal. Physiol Opt., 29, 2009, 80-91). However, in moving toward a clinically applicable method, it is important to estimate parameters such as surface radius, lens tilt and decenter. Previously, radius of curvature (for the anterior surface of an IOL) was estimated by finding the best-fit sphere. A methodology is presented here to recover lens tilt and decenter using this alternate method. The theory is developed and then tested in simulation. An IOL is added to the Navarro eye, and then recovered by assuming: (i) the same 'full eye', and (ii) a reduced two surface version (the 'simplified' eye). A number of decenter and tilt settings are tested, from which root mean squared (RMS) surface errors, best-fit spheres, tilt and decenter values are estimated. Mis-measurement of the axial position of the posterior surface of the IOL is also simulated. The full eye model produces low RMS surface and radii of curvature errors, that increase linearly with axial shift. The error behaviour is not greatly affected by changes in IOL decenter and/or tilt. The simplified eye (n = 1.32 for aqueous) with n = 1.4760 (at lambda = 880 nm) for the IOL, fits the 'full eye' results most consistently. Lens decenter is consistently estimated to within 0.015 mm (for a 1 mm decenter), and tilt <0.15 degrees (for a 5 degree tilt).

A novel method for gaze tracking by local pattern model and support vector regressor

This paper presents a novel eye gaze tracking method with allowable head movement based on a local pattern model (LPM) and support vector regressor (SVR). The LPM, a combination of improved pixel-pattern-based texture feature (PPBTF) and local-binary-pattern texture feature (LBP), is employed to calculate texture features from the characteristics of the eyes and a new binocular vision scheme is adopted to detect the spatial coordinates of the eyes. The texture features from LPM and the spatial coordinates together are fed into support vector regressor (SVR) to match a gaze mapping function, and subsequently to track gaze direction under allowable head movement. The experimental results show that the proposed approach results in better accuracy in estimating the gaze direction than the state-of-the-art pupil center corneal reflection (PCCR) method.

New Methods for the Assessment of Accommodative Convergence

The authors introduced a new objective method for measuring horizontal eye movements based on the first Purkinje image with the use of infrared charge-coupled device (CCD) cameras and compared stimulus accommodative convergence to accommodation (AC/A) ratios as determined by a standard gradient method. The study included 20 patients, 5 to 9 years old, who had intermittent exotropia (10 eyes) and accommodative esotropia (10 eyes). Measurement of horizontal eye movements in millimeters (mm), based on the first Purkinje image, was obtained with a TriIRIS C9000 instrument (Hamamatsu Photonics K.K., Hamamatsu, Japan). The stimulus AC/A ratio was determined with the far gradient method. The average values of horizontal eye movements (mm) and eye deviation (Delta) (a) before and (b) after an accommodative stimulus of 3.00 diopters (D) were calculated with the following formula: horizontal eye movements (mm/D) and stimulus AC/A ratio (Delta/D) = (b - a)/3. The average values of the horizontal eye movements and the stimulus AC/A ratio were 0.5 mm/D and 3.8 Delta/D, respectively. Correlation analysis showed a strong positive correlation between these two parameters (r = 0.92). Moreover, horizontal eye movements are directly proportional to the AC/A ratio measured with the gradient method. The methods used in this study allow objective recordings of accommodative convergence to be obtained in many clinical situations.

Improving the Accuracy and Reliability of Remote System-Calibration-Free Eye-Gaze Tracking

Remote eye-gaze tracking provides a means for nonintrusive tracking of the point-of-gaze (POG) of a user. For application as a user interface for the disabled, a remote system that is noncontact, reliable, and permits head motion is very desirable. The system-calibration-free pupil-corneal reflection (P-CR) vector technique for POG estimation is a popular method due to its simplicity, however, accuracy has been shown to be degraded with head displacement. Model-based POG-estimation methods were developed, which improve system accuracy during head displacement, however, these methods require complex system calibration in addition to user calibration. In this paper, the use of multiple corneal reflections and point-pattern matching allows for a scaling correction of the P-CR vector for head displacements as well as an improvement in system robustness to corneal reflection distortion, leading to improved POG-estimation accuracy. To demonstrate the improvement in performance, the enhanced multiple corneal reflection P-CR method is compared to the monocular and binocular accuracy of the traditional single corneal reflection P-CR method, and a model-based method of POG estimation for various head displacements.

Reconstructing ocular surfaces by Purkinje images: an exact ray approach

A method originally developed for corneal topography (using discrete sources and Zernike polynomials) was extended to estimate the geometry of ocular surfaces internal to the eye. The approach was tested in simulation as a candidate method for phakometry. Purkinje images from the anterior surface of an intra-ocular lens (IOL) (aligned and decentered) were simulated using the Navarro eye. The 'full' Navarro eye and a simplified eye were assumed for recovery purposes. Root mean square (RMS) errors and (anterior) IOL radii of curvatures (best-fit spheres) were estimated. The robustness of the method to axial shifts in lens position (both eye models) along with assumed refractive index (simplified eye only) was tested. When axial shifts were ignored, RMS errors for the full eye were sub-micron (<0.8 microm), and radii of curvature errors were approximately 1 microm. Axial shifting increased these errors linearly. The n = 1.32 error curve (simplified eye) matched the full eye error curves closely (for both RMS error and IOL lens radius), although the RMS error curve exhibited some asymmetry for a decentered IOL. The nominal refractive index (n = 1.3305) was sub-optimal in all cases. The resulting method is a potentially useful way to estimate the geometry of the internal ocular surfaces.

Determining the zone of reflection for posterior corneal surface comparison phakometry

Although comparison phakometry has been used by a number of studies to measure posterior corneal shape, these studies have not calculated the size of the posterior corneal zones of reflection they assessed. This paper develops paraxial equations for calculating posterior corneal zones of reflection, based on standard keratometry equations and equivalent mirror theory. For targets used in previous studies, posterior corneal reflection zone sizes were calculated using paraxial equations and using exact ray tracing, assuming spherical and aspheric corneal surfaces. Paraxial methods and exact ray tracing methods give similar estimates for reflection zone sizes less than 2 mm, but for larger zone sizes ray tracing methods should be used.

Applicability of Infrared Photorefraction for Measurement of Accommodation in Awake-Behaving Normal and Strabismic Monkeys

This study was designed to use infrared photorefraction to measure accommodation in awake-behaving normal and strabismic monkeys and describe properties of photorefraction calibrations in these monkeys. Ophthalmic trial lenses were used to calibrate the slope of pupil vertical pixel intensity profile measurements that were made with a custom-built infrared photorefractor. Day to day variability in photorefraction calibration curves, variability in calibration coefficients due to misalignment of the photorefractor Purkinje image and the center of the pupil, and variability in refractive error due to off-axis measurements were evaluated. The linear range of calibration of the photorefractor was found for ophthalmic lenses ranging from -1 D to +4 D. Calibration coefficients were different across monkeys tested (two strabismic, one normal) but were similar for each monkey over different experimental days. In both normal and strabismic monkeys, small misalignment of the photorefractor Purkinje image with the center of pupil resulted in only small changes in calibration coefficients, that were not statistically significant (P>0.05). Off-axis measurement of refractive error was also small in the normal and strabismic monkeys (approximately 1 D to 2 D) as long as the magnitude of misalignment was <10 degrees. Remote infrared photorefraction is suitable for measuring accommodation in awake, behaving normal, and strabismic monkeys. Specific challenges posed by the strabismic monkeys, such as possible misalignment of the photorefractor Purkinje image and the center of the pupil during either calibration or measurement of accommodation, that may arise due to unsteady fixation or small eye movements including nystagmus, results in small changes in measured refractive error.

Optical effects of anti-TGFbeta treatment after photorefractive keratectomy in a cat model.

To assess the contribution of corneal myofibroblasts to optical changes induced by photorefractive keratectomy (PRK) in a cat model. The transforming growth factor (TGF)-beta-dependence of feline corneal keratocyte differentiation into alpha-smooth muscle actin (alphaSMA)-positive myofibroblasts was first tested in vitro. Twenty-nine eyes of 16 cats were then treated with -10 D PRK in vivo and divided into two postoperative treatment groups that received either 100 microg anti-TGFbeta antibody for 7 days, followed by 50 microg dexamethasone for another 7 days to inhibit myofibroblast differentiation, or vehicle solution for 14 days (control eyes). Corneal thickness and reflectivity were measured by optical coherence tomography. Wavefront sensing was performed in the awake-behaving state before surgery and 2, 4, 8, and 12 weeks after surgery. Wound healing was monitored using in vivo confocal imaging and postmortem alphaSMA immunohistochemistry. In culture, TGFbeta caused cat corneal keratocytes to differentiate into alphaSMA-positive myofibroblasts, an effect that was blocked by coincubation with anti-TGFbeta antibody. In vivo, anti-TGFbeta treatment after PRK resulted in less alphaSMA immunoreactivity in the subablation stroma, lower corneal reflectivity, less stromal regrowth, and lower nonspherical higher order aberration induction than in control eyes. However, there were no intergroup differences in epithelial regeneration or lower order aberration changes. Anti-TGFbeta treatment reduced feline corneal myofibroblast differentiation in vitro and after PRK. It also decreased corneal haze and fine-grained irregularities in ocular wavefront after PRK, suggesting that attenuation of the differentiation of keratocytes into myofibroblast can significantly enhance optical quality after refractive surface ablations.

Optical aberration measurements in dog and cat eyes: interest &amp; limit

Abstract Purpose To measure the ocular optical aberrations in dog and cat using a wavefront aberrometer based on Hartmann‐Shack technology. Methods Two dogs and one cat were sedated (Medetomidine, 0.1 mg/kg) and their right eye (RE) pupils were artificially dilated (tropicamide). Wavefront aberrations were measured using an irx3 aberrometer (Imagine Eyes, Orsay, France). Prior to each measurement, the eye was aligned with the instrument optical axis by centering both the eye pupil and Purkinje images. The Hartmann‐Shack spot images were produced by an array of 1024 microlenses that defined a 7.2x7.2 mm square area in the pupil plane. In preliminary tests, spot image histograms were optimized by adjusting the sensor acquisition time. Wavefront aberrations were then repeatedly measured 10 times in each animal’s RE. Spherical defocus, astigmatism and Zernike coefficients up to the 8th order were finally analyzed. Results The optimal acquisition time was 10 ms for all animals, instead of 33 ms when measuring human eyes. Refractive errors could be analyzed in a 6 mm pupil diameter in all cases. The dilated pupil often exceed the sensor area. The average refractive errors in dog #1, dog #2 and the cat were +2.9D(‐2.0D)111°;‐0.8D(‐0.8D)126° and +3.3D(‐2.1D)98°, respectively while their Root Mean Square (RMS) higher‐order aberrations amounted to 1.9, 1.1, and 2.1 µm RMS respectively. Standard deviation in sphere and cylinder was 1.0D in the cat and less than 0.5D in both dogs. Standard deviation in the higher‐order RMS was 0.8 µm in the cat and less than 0.5 µm in both dogs. The observation of individual data revealed that a significant part of this variability was due to blink‐related changes in aberrations. Conclusion Ocular optical aberrations can be easily measured in dog and cat using a Hartmann‐Shack aberrometer with reduced image acquisition time. The tested animals had relatively large higher‐order wavefront aberrations when compared to date measured in healthy human eyes. Measurement reproducibility was notably affected by tear layer effects. This variability could probably be reduced using a larger sensor area, specific head contention device and artificial tears. This new diagnostic technique is easily feasible without any use of anaesthesia and provides less variability and more detailed information than skiascopy. Wavefront aberrometry could be useful in both research and clinical applications.

Investigation of the Cross-Ratios Method for Point-of-Gaze Estimation

The cross-ratios method for point-of-gaze (PoG) estimation uses the invariance property of cross-ratios in projective transformations. The inherent causes of the subject-dependent PoG estimation bias exhibited by this method have not been well characterized in the literature. Using a model of the eye and the components of a system (camera, light sources) that estimates PoG, a theoretical framework for the cross-ratios method is developed. The analysis of the cross-ratios method within this framework shows that the subject-dependent estimation bias is caused mainly by: 1) the angular deviation of the visual axis from the optic axis and 2) the fact that the virtual image of the pupil center is not coplanar with the virtual images of the light sources that illuminate the eye (corneal reflections). The theoretical framework provides a closed-form analytical expression that predicts the estimation bias as a function of subject-specific eye parameters. The theoretical framework also provides a clear physical interpretation for an existing empirically derived two-step procedure that compensates for the estimation bias and shows that the first step of this procedure is equivalent to moving the corneal reflections to a new plane that minimizes the distance from this plane to the virtual image of the pupil center.

Minimization of influence by the drooping eyelid in extracting pupil center for eye tracking systems

Precise pupil center detection is an important factor for gaze tracking in video-oculography (VOG) systems. Existing methods perform well to extract the features when the area of pupil in eye image is clear, whereas, interferences, such as eyelashes, corneal reflection etc., will lead to a low success rate. One main reason is the closure of eyelids. In this paper, a systemic 3D transformation algorithm is proposed to accurately ascertain the pupil center, in spite of the complicating factors mentioned above. Experiments show the good performance of our method. And the pupil center could be extracted accurately, even though only 25% of the pupil is visible.

Fake iris detection method using Purkinje images based on gaze position

Until now, most research on iris recognition has been focused on recognition algorithms and iris camera systems. There has been little research into fake iris detection, although recently its importance has been greatly emphasized. Fake iris detection refers to the process of detecting and defeating fake iris images. In this work, we propose a new method of defeating fake iris attacks using Purkinje images based on gaze position. Our research presents the following four improvements over previous works. First, we calculate the theoretical positions and distances between the Purkinje images based on the 3-D human eye model. Second, by using these positions and distances (which changed according to gaze positions), we design a more robust way of detecting fake irises. Third, since it is not necessary to align the center of the user's eyeball with the optical axis of the camera, the proposed method can be used in practical iris systems. Fourth, by activating the illumination infrared-light-emitting diode (IR-LED), the distance-measuring IR-LED and the Purkinje IR-LED alternatively, we obtain accurate positions for the Purkinje images according to the user's gaze position. Experimental results show that the false rejection rate (FRR) is 0.2% and the false acceptance rate (FAR) is 0.2%.

Binocular Lens Tilt and Decentration Measurements in Healthy Subjects with Phakic Eyes

Tilt and decentration of the natural crystalline lens affect optical quality of the foveal image. However, little is known about the distributions of these variables in healthy subjects with phakic eyes and about their correlations in both eyes. A simple, portable, easy-to-use, and partially automated device was developed to study lens tilt and decentration in both eyes of 11 healthy subjects with phakic eyes. The first, third, and fourth Purkinje images (P1, P3, P4) were visualized using a single infrared (IR) light-emitting diode (LED), a planar lens (F = 85 mm; f/number of 1.4), and an infrared sensitive analog video camera. Software was developed to mark pupil edges and positions of P1, P4, and P3 with the cursor of the computer mouse, for three different gaze positions, and an automated regression analysis determined the gaze position that superimposed the third and fourth Purkinje images, the gaze direction for which the lens was oriented perpendicularly to the axis of the IR LED. In this position, lens decentration was determined as the linear distance of the superimposed P3/P4 positions from the pupil center. Contrary to previous approaches, a short initial fixation of a green LED with known angular position calibrated the device as a gaze tracker, and no further positional information was necessary on fixation targets. Horizontal and vertical kappa, horizontal and vertical lens tilt, and vertical lens decentration were highly correlated in both eyes of the subjects, whereas horizontal decentration of the lens was not. There was a large variability of kappa (average horizontal kappa -1.63 degrees +/- 1.77 degrees [left eyes] and +2.07 degrees +/- 2.68 degrees [right eyes]; average vertical kappa +2.52 degrees +/- 1.30 degrees [left eyes] and +2.77 degrees +/- 1.65 degrees [right eyes]). Standard deviation from three repeated measurements ranged from 0.28 degrees to 0.51 degrees for kappa, 0.36 degrees to 0.91 degrees for horizontal lens tilt, and 0.36 degrees to 0.48 degrees for vertical lens tilt. Decentration was measured with standard deviations ranging from 0.02 mm to 0.05 mm. All lenses were found tilted to the temporal side with respect to the fixation axis (on average by 4.6 degrees ). They were also decentered downward with respect to the pupil center by approximately 0.3 mm. Lens tilts and positions could be conveniently measured with the described portable device, a video camera with a large lens. That the lenses were tilted to the temporal side in both eyes, even if corrected for kappa, was unexpected. That they were displaced downward with respect to the pupil center could be related to gravity.

Effects of fixation instability on multifocal VEP (mfVEP) responses in amblyopes

The cortical activity of subjects with compromised central vision (e.g., amblyopes) is thought to be much weaker for stimulation of the affected eye than in the fellow eye. Because these subjects are known to exhibit considerable difficulties in keeping steady fixation, we investigated the effects of anomalous fixation on their multifocal visual-evoked potential (mfVEP) responses using a dual Purkinje image (dPi) eye tracker. Our results show that mfVEP responses to stimulation of the central 5 degrees were depressed in the affected eye compared to those in the normal eye and the magnitude of response reductions was proportional to the degree of visual acuity loss in amblyopic subjects. Fixation was far less stable while viewing with the affected eye than with the fellow eye, some exhibiting jerk nystagmus and/or saccadic oscillations. Normal subjects with artificially imposed nystagmus showed similar reductions of VEP responses. The relative magnitudes of the deficits in mfVEP responses were tightly correlated with the degree of fixation instability. These results suggest that the interpretation of anomalous neural or perceptual processing in amblyopic subjects must take the effects of unsteady fixation during measurements into consideration in order to reveal the true nature and extent of sensory neural deficits.

Separating corneal reflections for illumination estimation

Eyes exhibit a significant amount of specular reflection and could be used to derive a detailed estimate of frontal illumination. To determine a more accurate estimate of illumination from the environment, iris color and texture should be separated from the specularly reflected light, since they may substantially obscure reflections of the scene. In this paper, a method is presented for separating corneal reflections in an image of human irises. We consider the iris texture to be diffuse, and the observed image color is produced as the sum of the diffuse component and the specular component. A number of methods have been proposed to separate or decompose these two components. To our knowledge, all methods that use a single input image demonstrated success in only limited cases, such as for uniform colored lighting and simple object textures. They are not applicable to irises, which exhibit intricate textures and complicated reflections of the environment. To make this problem feasible, our method capitalizes on physical characteristics of human irises to obtain an illumination estimate that encompasses the prominent light contributors in the scene. Results of the algorithm are presented for eyes of different colors, including light colored eyes for which reflection separation is necessary to determine a valid illumination estimate.

Scan Path Differences and Similarities During Emotion Perception in those With and Without Autism Spectrum Disorders

Typical adults use predictable scan patterns while observing faces. Some research suggests that people with autism spectrum disorders (ASD) instead attend to eyes less, and perhaps to the mouth more. The current experiment was designed as a direct measure of scan paths that people with and without ASD use when identifying simple and complex emotions. Participants saw photos of emotions and chose emotion labels. Scan paths were measured via infrared corneal reflectance. Both groups looked significantly longer at eyes than mouth, and neither overall looking time at eyes nor first fixations distinguished the groups. These results are contrary to suggestions that those with ASD attend preferentially to the mouth and avoid the eyes. Furthermore, there was no interaction between group and area of the face: the ratio of attention between eyes and mouth did not differ between the ASD and control groups. However, those with ASD looked at the eyes less than the control group when viewing complex emotions.

A model-based approach to video-based eye tracking

Video-based eye tracking typically relies on tracking the pupil and a first-surface corneal reflection (CR) of an illumination source. The positional difference between these two features is used to determine the observer's eye-in-head orientation. With the use of head-mounted eye trackers, this positional difference is unavoidably affected by relative movements between the eye tracking camera and the subject's eye. Video-based trackers also suffer from problems resulting in poor CR detection, such as spurious reflections being mistaken as the desired CR. We approach these problems by modelling how these features—pupil and CR—are affected by different relative movements of the eye. Optical relationships between the offset of the apparent pupil centre and that of the CR are derived. An experiment was conducted with five observers to support these derivations. Solutions to the aforementioned problems using these offset relationships are provided. The first application compensates for movements of an eye tracking camera with respect to the eye and reduces noise in the final eye orientation data. The second application is prediction of CR locations for artefact removal in the new eye tracking system prototype.

Computerized mouse pupil size measurement for pupillary light reflex analysis

Accurate measurement of pupil size is essential for pupillary light reflex (PLR) analysis in clinical diagnosis and vision research. Low pupil–iris contrast, corneal reflection, artifacts and noises in infrared eye imaging pose challenges for automated pupil detection and measurement. This paper describes a computerized method for pupil detection or identification. After segmentation by a region-growing algorithm, pupils are detected by an iterative randomized Hough transform (IRHT) with an elliptical model. The IRHT iteratively suppresses the effects of extraneous structures and noise, yielding reliable measurements. Experimental results with 72 images showed a mean absolute difference of 3.84% between computerized and manual measurements. The inter-run variation for the computerized method (1.24%) was much smaller than the inter-observer variation for the manual method (7.45%), suggesting a higher level of consistency of the former. The computerized method could facilitate PLR analysis and other non-invasive functional tests that require pupil size measurements.

Changes in crystalline lens radii of curvature and lens tilt and decentration during dynamic accommodation in rhesus monkeys

Dynamic changes in crystalline lens radii of curvature and lens tilt and decentration were measured during centrally stimulated accommodation in four iridectomized eyes of two adolescent rhesus monkeys. Phakometry measurements were performed dynamically using a custom-built, video-based, Purkinje-image instrument. Lens anterior and posterior radii were calculated from reflections of paired light sources from the ocular surfaces (Purkinje images PI, PIII, and PIV). Lens tilt and decentration were calculated assuming linearity between Purkinje image positions, eye rotation, lens tilt, and decentration. Because the monkey eyes were iridectomized, Purkinje images were referred to the mid-point of the double first Purkinje image (PI). Mean unaccommodated values of anterior and posterior lens radii of curvature were 11.11 +/- 1.58 mm and -6.64 +/- 0.62 mm, respectively, and these decreased relatively linearly with accommodation in all eyes, at a rate of 0.48 +/- 0.14 mm/D and 0.17 +/- 0.03 mm/D for anterior and posterior lens surfaces, respectively. Tilt and decentration did not change significantly with accommodation except for tilt around the horizontal axis, which changed at a rate of 0.147 +/- 0.25 deg/D. These results are important to fully characterize accommodation in rhesus monkeys.

角膜反射を利用した瞳孔位置検出の高精度化

In general, the relative position between the centers of the pupil and corneal reflection are used for precise eye-gaze detection. Recently, for stable pupil detection under various ambient light conditions, the pupil has been detected by the difference between the bright and dark pupil images. However, due to the difference in acquisition timing between the bright and dark images, the precision of the pupil position easily decreases when the head moves. We propose a compensation method which differentiates those pupil images after shifting one of the images so that the positions of corneal reflections in both images should match, and show its effectiveness.