Binocular Fixation Research Articles

New results in stereopsis and Listing's law.

Human eyes' optical components are misaligned. This study presents comprehensive geometric constructions in the binocular system, with the eye model incorporating the fovea that is displaced from the posterior pole and the lens that is tilted away from the eye's optical axis. It extends their previously considered horizontal misalignment with the vertical components. When the eyes' binocular posture changes, 3D spatial coordinates of the retinal disparity (iso-disparity curves), the subjective vertical horopter, and the eye's torsional orientation transformations are visualized in GeoGebra's simulations. The consequences and functional roles of vertical misalignment of the eye's optical components are explained in the following findings: (1) The classic Helmholtz theory, which states that the subjective vertical retinal meridian inclination to the retinal horizon explains the backward tilt of the perceived vertical horopter, is less relevant when the eye's optical components are misaligned. Instead, the lens vertical tilt provides the retinal vertical criterion that explains the experimentally measured vertical horopter inclination. (2) Listing's law, which originally restricts single-eye torsional positions and has imprecise binocular extensions, is formulated for binocular fixations using Euler's rotation theorem. It, however, replaces Listing's plane, which is defined for eyes looking at infinity, with the eyes muscles' natural tonus resting position corresponding to the abathic distance fixation of empirical straight frontal horopter. This new meaning of Listing's plane provides neurophysiological significance that has remained elusive.

The preferred retinal loci when the eyes converge.

The preferred retinal locus (PRL) is the position on the retina to which humans direct stimuli during fixation. In healthy normal eyes, it has been shown to be very stable across time and between different tasks. Previous measurements of the PRL have been made under monocular viewing conditions. The current study examines where the PRLs in the two eyes' retinas are when subjects fixate binocularly and whether they shift when the demand for the eyes to converge is changed. Our apparatus allows us to see exactly where binocular stimuli fell on the two retinas during binocular fixation. Thus, our technique bypasses some of the issues involved in measuring binocular alignment with subjective techniques and previous objective techniques that use conventional eye trackers. These results show that PRLs shift slightly but systematically as the demand for convergence increases. The shifts cause under-convergence (also called exo fixation disparity) for near targets. They are not large enough to cause a break in binocular fusion. The fixation disparity we observed with increasing vergence demand is similar to fixation disparity observed in previous reports.

Analyses of eye movement parameters in children with anisometropic amblyopia

ObjectiveTo investigate the characteristics of eye movement in children with anisometropic amblyopia, and to compare those characteristics with eye movement in a control group.Methods31 children in the anisometropic amblyopia group (31 amblyopic eyes in group A, 31 contralateral eyes in group B) and 24 children in the control group (48 eyes in group C). Group A was subdivided into groups Aa (severe amblyopia) and Ab (mild-moderate amblyopia). The overall age range was 6–12 years (mean, 7.83 ± 1.79 years). All children underwent ophthalmic examinations; eye movement parameters including saccade latency and amplitude were evaluated using an Eyelink1000 eye tracker. Data Viewer and MATLAB software were used for data analysis.ResultsMean and maximum saccade latencies, as well as mean and maximum saccade amplitudes, were significantly greater in group A than in groups B and C before and after treatment (P < 0.05). Mean and maximum saccade latencies were significantly different among groups Aa, Ab, and C (P < 0.05). Pupil trajectories in two detection modes suggested that binocular fixation was better than monocular fixation.ConclusionsEye movement parameters significantly differed between contralateral normal eyes and control eyes. Clinical evaluation of children with anisometropic amblyopia should not focus only on static visual acuity, but also on the assessment of eye movement.

Riemannian geometries of visual space: Variable curvature and horizon

Two‐dimensional (2D) images of light beams reflected off the objects in space impinge on the retinal photoreceptors of our two laterally separated eyes. Nevertheless, we experience our visual percept as a single 3D entity—our visual world that we tend to identify with the physical world. However, experiments point to different geometries in these two worlds. Using the binocular system with asymmetric eyes (AEs), this article studies the global geometric aspects of visual space in the Riemannian geometry framework. The constant‐depth curves in the horizontal field of binocular fixations consist of families of arcs of ellipses or hyperbolas depending on the AE parameters and the eyes' fixation point. For a single set of AE parameters, there is a unique symmetric fixation at the abathic distance such that the constant‐depth conics are straight frontal lines. Critically, the distribution of these constant‐depth lines is independent of such fixations. In these cases, a two‐parameter family of the Riemann metrics is proposed to account for the retinotopy of the brain's visual pathways and simulated constant‐depth lines. The obtained geodesics for a subset of metric parameters include incomplete geodesics that give finite distances to the horizon. The Gaussian curvature of the phenomenal horizontal field is analyzed for all the metric parameters. The sign of the curvature can be inferred from the global behavior of the constant‐depth ellipses and hyperbolas only when for the metric parameters for which the constant‐depth frontal lines at the abathic distance fixations are geodesics.

Targeting displacement as an indicator of binocular fixation in normal Chinese adults.

The stability of fixation is crucial for the development of visual function. In this study, we quantify the deviation of visual target during fixational and saccadic tasks using eye-tracking technology, reflecting the control ability and characteristics of fixational displacement among healthy adults in a convenient method. One hundred healthy participants aged between 18 and 55 years were recruited in the study. All participants underwent a complete ophthalmic assessment. The eye positions in the fixational and saccadic tasks were documented and analyzed by the Tobii eye-tracking system. Participants were grouped by age and gender. Targeting displacement (TD), defined as the average displacement between visual target and the mean of fixation points corresponding to that stimuli, was used to quantitatively observe fixational displacement in the horizontal and vertical directions. There was a strong reproducibility of TD as an indicator of fixation (ICC 0.812 to 0.891, p < 0.001). The TD in fixational task was significantly smaller than that of the saccadic task (3.884 ± 0.525 vs. 4.484 ± 0.509, p < 0.001) among normal people. Moreover, the difference of TD in the horizontal and vertical meridians was related to the nature of the task: In the fixational task, the TD in horizontal was smaller than that in the vertical (p < 0.001), whereas the TD in horizontal was larger than that in vertical in the saccadic task (p = 0.003). In the different age and gender groups: There was no significant difference between different gender and age groups in fixational task. However, during the saccadic task, males had smaller TD in the vertical direction than females (4.061 ± 0.495 vs. 4.404 ± 0.484, p = 0.002), and the average TD increased with age, mainly in the vertical direction (all p < 0.05). The fixation stability decreased significantly in the group over 50-years-old. By reporting the fixational displacement of different genders and ages in fixational and saccadic tasks, as well as different longitude lines among normal people, our study might provide an objective, quantitative and convenient reference index for the evaluation of fixation stability in visual impairment diseases and aging phenomenon of visual function.

Analysis of Characteristic Eye Movement Behaviors of Young Adults with Different Degrees of Myopia

To measure the parameters of eye movement of young adult patients of myopia, to compare the differences in the parameters of patient groups with varied degrees of myopia, and to analyze the correlation between eye movement parameters and axial length (AL) and spherical equivalent refraction (SER). A total of 91 young adult patients of myopia were recruited. The subjects were divided into three groups of low, moderate, and high myopia according to their SER. Information on the subjects' age and sex was collected and general clinical examination was completed. The subjects' binocular fixation, reflexive saccade, and antisaccade were measured with eye tracker. One-way ANOVA or Kruskal-wallis test was used to compare the general data and eye movement parameters of the three groups of myopic patients. Pearson or Spearman correlation analysis was used to analyze AL and SER's correlation with 95% bivariate contour ellipse area (BCEA) and saccadic parameters. The 95% BCEA for mild, moderate, and high myopia groups were 2.08 (0.54, 14.69) deg 2, 4.99 (0.94, 49.22) deg 2, and 5.79 (2.18, 64.91) deg 2, respectively. There was significant difference between the 95% BCEA of the three groups ( P=0.029). The 95% BCEA of the mild myopia group was significantly smaller than that of the high myopia group ( P=0.01). There were no significant differences in saccadic parameters among the three groups ( P>0.05). There was a significant positive correlation between 95% BCEA and AL ( r=0.342, P=0.001). There was a significant negative correlation between 95% BCEA and SER ( r=-0.322, P=0.002). There was no significant correlation between the parameters of saccadic movement and the AL or SER ( P>0.05). For young adult myopic patients, the longer the AL is, the higher the degree of the myopia and the worse the fixation stability becomes. The fixation stability of patients with high myopia was significantly worse than that of patients with mild myopia. There was no significant difference in saccadic parameters in patients with different degrees of myopia.

Correlation of saccade amplitude during refusion with the fusional convergence amplitude in patients with intermittent exotropia

ABSTRACT In patients with intermittent exotropia (IXT), to investigate the correlation between fusional convergence amplitude and saccade during refusion, as well as the differences in saccade caused by suppression. We measured the fusional convergence amplitude using a synoptophore. Suppression was assessed in 15 patients with IXT (mean age 18.1 ± 11.0 yrs, range 8–54 yrs) having diplopia during exotropia. We performed the cover-uncover test and recorded the saccade during the shift from exotropia to binocular fixation using an eye-tracking system. We analyzed the correlation between the fusional convergence amplitude on the one hand and the saccade peak velocity (PV), the saccade amplitude, and the saccade amplitude of the fusion on the other. We also investigated the difference of those saccade variables between patients with and without suppression. In 15 patients with IXT, the median fusional convergence amplitude was 14 (range 0–60) °, and suppression was confirmed in 11 patients. When the cover was removed from the dominant eye, the fusional convergence amplitude showed a positive correlation with the saccade PV and the amplitude in non-dominant eye (r = 0.570, p = 0.042 and r = 0.669, p = 0.012, respectively). The mean saccade PV, the mean saccade amplitude and the mean saccade amplitude of the fusion were not significantly different with the presence or the absence of the suppression. The fusional convergence amplitude was correlated with saccade in patients with IXT. The saccade during refusion can thus be used to quantitatively evaluate sensory and/or motor fusion.

Is Fixation Preference a Potential Indicator of Macular Function in Children?

Objectives:Fixation preference testing is widely used to detect amblyopia, particularly in preverbal children. Pattern electroretinogram (pERG) is an electrophysiological test which is a sensitive indicator of macular function. The aim of this study was to investigate the relationship between fixation preference and macular function on pERG in children with strabismus.Materials and Methods:The study included 11 children with strabismus. All underwent ophthalmological examination including fixation preference by binocular fixation pattern test, best corrected visual acuity (BCVA) assessment, and pERG.Results:The mean age of the patients was 10.09±1.18 years. All patients had unilateral fixation. The mean BCVA was 0.85±0.17 in preferred and 0.48±0.19 in non-preferred eyes (p=0.003). The mean p50 amplitude was 6.07±2.06 μV in preferred and 5.29±2.20 μV in non-preferred eyes (p=0.203), and the mean N95 amplitude was 8.27±2.86 μV and 8.03±3.24 μV respectively (p=0.594). BCVA was correlated with p50 and N95 amplitudes in the non-preferred eyes (p=0.023 and p=0.014). Interocular BCVA difference was correlated with interocular P50 amplitude difference (r=0.688, p=0.019).Conclusion:Although amblyopia is typically considered a cortical phenomenon, future larger studies are needed to investigate the relationship between fixation preference and macular electrophysiological function.

Measurement of ocular counter-roll using iris images during binocular fixation and head tilt.

ObjectiveTo compare the ocular counter-roll (OCR) measured using iris images during binocular fixation and head tilt with OCR measured via fundus photography.MethodsFifty-three healthy college students participated in this study. The mean OCR was measured by collection of iris images and fundus images under seven head tilt conditions (0 degrees; 10, 20, and 30 degrees right; and 10, 20, and 30 degrees left). Three iris images (crossed pupil center, pupil center, and pupil periphery) were taken using a slit-lamp biomicroscope with an ophthalmic camera and a half-silvered mirror; fundus images were collected via fundus photography. The mean OCR values were compared between images taken with each method.ResultsNo iris images or head tilt conditions revealed any significant differences in mean OCR comparison with fundus images. The mean difference in OCR was smallest, and the correlation was greatest, between the crossed pupil center and fundus images.ConclusionA half-silvered mirror and iris images can replace fundus photography for the measurement of OCR.

Foveal shape, ultrastructure and photoreceptor composition in yellow-legged gull, Larus michahellis (Naumann, 1840)

The anatomical and histological features of the foveae in a gull, Larus michahellis, were investigated combining immunofluorescence and transmission electron microscopy. In an area of higher acuity, which extends in a band across the field of view, a central convexiclivate deep fovea was observed near of the pecten oculi. Moreover, a shallow fovea was present in the dorsonasal region. The central deep fovea was characterized by a remarkably and well-excavated pit containing extremely thin cones and a radial displacement of the cone axons and inner retinal layers. Immunofluorescence demonstrated the absence of rods and the presence of violet and green/red sensitive cone opsins. Ultrastructural analyses confirmed the lack of double cones, and specialized Muller cell processes forming a network that stabilizes the foveal structure. This deep central fovea, which provides the highest resolution and colour discrimination, may be used for monocular sideways vision of distant objects and a binocular fixation. The dorsonasal fovea was shallower and all retinal layers were present at the pit. This fovea showed the same composition of photoreceptors than central fovea and could be implied in magnification of a wide monocular part of the retinal image. The bifoveate condition of yellow-legged gull retina would allow the formation of three separate and distinct visual fields: two wide lateral monocular fields mediated by the dorsonasal and the central foveae, and a small binocular field mediated by the central deep fovea depending on ocular movements.

Deep Binocular Fixation Prediction Using a Hierarchical Multimodal Fusion Network

RGB-D data are increasingly being used for myriad computer vision tasks. For such tasks, most methods simply concatenate or add feature vectors from RGB images and depth maps and allow the two modalities to complement each other mutually. However, such a fusion strategy results in inefficient and inadequate performance. In this study, we propose deep binocular fixation prediction based on a hierarchical multimodal fusion network that suitably combines RGB and depth maps. In the proposed method, a novel convolutional block attention module completely extracts image texture features and retains spatial information. In addition, a pyramid dilated-convolution module refines feature information, further improving the fusion of RGB and depth maps. Experimental results indicate that the proposed network achieves state-of-the-art performance on the NUS and NCTU datasets.

Functional Anatomy of Muscle Mechanisms: Compensating Vertical Heterophoria

Magnetic resonance imaging (MRI) of extraocular muscle function was used to evaluate the role of newly recognized mechanisms underlying compensation of large heterophoria by vertical fusional vergence (VFV). Prospective case series. At one academic center, 8 adults with large hyperphoria and supernormal VFV underwent MRI during monocular and binocular fixation of a centered, near target. Contractility of the rectus and superior oblique (SO) extraocular muscles in hypertropic and hypotropic eyes was determined from changes in posterior partial volume (PPV). Five of 8 patients could sustain binocular fusion in the scanner. In those patients, VFV corrected approximately 5-degree misalignment, approximately 5-fold greater than normal VFV. Vertical strabismus was compensated mainly by significant contractility of the lateral more than the medial compartment of the inferior rectus (IR) in both eyes (P < .005). The superior rectus (SR) and inferior oblique muscles had no significant contractile contribution, although the hypotropic SO relaxed significantly. The IR lateral compartment and SR medial compartment significantly co-relaxed when binocular fusion was attained from monocular target fixation (P < .01). Although VFV protects patients from small muscle imbalances over the lifespan, even enhanced VFV may be inadequate to avert diplopia. Compensation of hyperphoria by VFV is accomplished mainly by IR muscle relaxation in the hypotropic eye, principally in its selectively innervated lateral compartment, whereas the SO contributes little. Fusion involves compartmentally selective co-relaxation in hypotropic eye vertical rectus muscles. Taken together, these overall findings suggest a physiologic basis to prefer therapeutic surgical weakening of the medial IR in the hypotropic eye.

Vergence Eye Movements: From Basic Science to Clinical Application - Foreword to the Special Issue.

The abstract book of the last European Conference on Eye Movements [1] lists abstracts of 373 presentations, but less than five percent investigate vergence eye movements, i.e. the coordination of the right and left eye. Why then a special issue on this neglected issue? Human vision under natural conditions involves both eyes in coordination controlled by interacting processes subsumed under the concept of vergence.. Further, vergence is important for people in their daily lives since disorders of vergence can have serious consequences: ophthalmologists deal with squinting patients on the basis of heterophoria and heterotropia testing, eye strain or visual complaints can be related to impaired vergence dynamic or less accurate static vergence, remediation by optometrist includes vergence training or prism eye glasses, etc.

Predictive Model for Dyslexia from Eye Fixation Events

Dyslexia is a specific learning disorder where the individual often find difficulty in spelling and reading words fluently. Dyslexia is non-curable but with right remedial support, dyslexics can become highly successful in academics and life. Eye movement patterns during reading process can provide an in-depth understanding about reading disorders caused by dyslexia. Eye movements can be captured using eye-tracker, from which the relationship between how eyes move with respect to the words they read can be understood. In this work, a set of binocular fixation and saccade features were extracted from raw eye tracking data based on statistical measures. Machine learning algorithms such as Random Forest Classifier (RF), Support Vector Machine (SVM) for classification and K-Nearest Neighbor (KNN) were analyzed to output classification models for prediction of dyslexia. KNN gave higher levels of accuracy of 95% compared to SVM and RF over a small feature set of features related to fixations and saccades. These eye features can be used as a basis for developing screening means for prediction of dyslexia. Prediction of dyslexia at an early stage can help children to go for remediation which helps them for academic excellence.

Eye movement analysis using a binocular video-ophthalmoscope.

This paper describes an application of binocular video-ophthalmoscope for binocular eye movement analysis during target fixation. We analyze eye movements during monocular and binocular fixation and the changes in eye position for 73 subjects. We show that the standard deviations of differences between eye shifts for vertical and horizontal movements are higher for binocular fixation with respect to monocular fixation. We also present different examples of eye movement visualization.

Implementation of a Virtual Reality rendered in Portable Devices for Strabismus Treatment based on Conventional Visual Therapy.

In order to propose alternative treatments for strabismus, conventional visual therapies implemented in VR, which could be rendered in portable devices for pediatric strabismus treatment is proposed in this paper. In comparison with other virtual environments for visual correction proposes, the proposed system is based on conventional visual therapies for amblyopia and strabismus treatment. Three fundamental visual therapeutic exercises were considered in the present proposal: (1) Brock cord, (2) approach technique, and (3) convergence and divergence. The first exercise, Brock Cord, has the purpose of improving the binocular fixation for exotropia and esotropia. The second exercise pursues to normalize the Cerebral Perfusion Pressure by an approach technique. The third exercise known as fusion of eccentric circles, aims vision training by converging and diverging objects at specific distances. Before a clinical application, it was paramount important to guarantee system simplicity and versatility for both clinicians and infant patients. Therefore, the user experience evaluation of a sample of 45 students between 17 and 28 years old was undertaken. The system proposed in this paper achieved a pragmatic quality above average (1.73), a parameter that reflects simplicity and versatility. In addition, the present VR system displayed attractiveness (2.03) and hedonic (1.90) qualities above average. Then, it is expected that end-users will follow the visual exercise program.

Functional anatomy of extraocular muscles during human vergence compensation of horizontal heterophoria

We employed magnetic resonance imaging to quantify human extraocular muscle (EOM) contractility during intermittent convergent and divergent strabismus with each eye viewing monocularly at 20 cm compared with centered target fusion. Contractility, indicated by posterior partial volume change, was analyzed in transverse rectus and in medial and lateral superior oblique (SO) muscle compartments. In five subjects with intermittent esotropia, abduction of the deviated eye to monocular target fixation was associated with significant whole lateral rectus (LR) contraction, but with medial rectus (MR) relaxation that was significantly greater in the superior than inferior compartment. Esotropic eye abduction to binocular fusion was associated with similar relaxation in the two MR compartments, but with greater contraction in the LR's superior than inferior compartment. The whole diverging eye SO muscle relaxed. In three subjects with intermittent exotropia, converging eye fusional adduction was associated with significant whole LR relaxation and with MR contraction attributable to significantly greater contraction in the superior than inferior compartment. In adduction of the exotropic eye to monocular target fixation but not fusional adduction, the whole SO exhibited significant relaxation. Rectus pulley positions were not significantly altered by fusion of either form of intermittent strabismus. Globe rotational axis was eccentric in intermittent strabismus, rolling the eye so that rectus EOM lever arms facilitated vergence. These results confirm, and extend to fusion of intermittent horizontal strabismus, differential compartmental function in horizontal rectus EOMs and suggest a novel role for the SO in compensation of both intermittent esotropia and exotropia. NEW & NOTEWORTHY Disjunctive eye movements normally permit binocular fixation in near visual space but also compensate for mechanical imbalances in binocular alignment developing over the life span. Magnetic resonance imaging of the extraocular muscles demonstrates important differential function in muscle compartments during compensation of large-angle intermittent convergent and divergent strabismus in humans. Eye translation during rotation also enhances vergence compensation of intermittent strabismus.

An alignment maximization method for the kinematics of the eye and eye-head fixations

The orientation of human eyes is uniquely defined with respect to their gaze direction, known as Donders’ law. Further, the manner in which the eyes follow Donders’ law varies as a function of the situation. When the head is stationary, the Donders’ surfaces are flat planes but they tilt when eye fixation distance changes. These planes also shift and rotate when head orientation changes with respect to the direction of gravito-inertial acceleration. When the head is free to rotate, the Donders’ surfaces are twisted. In this paper, we present a systematic method to analyze the kinematics of the eye under different gaze situations utilizing the measurement of alignment between various coordinate frames. Kinematic equations are presented for various eye movements ranging from simple head-fixed monocular shifts of eye gaze to complex eye-head shifts of gaze. At each stage, we show that simulated eye orientations that derived from our equations are able to capture the variations of Donders’ surfaces and they are comparable with experimental results in the literature. The final equations we propose provide the unified kinematics of head-upright far gaze, head-upright binocular fixation, head static tilted monocular gaze and head-free monocular gaze.

Do pupil-based binocular video eye trackers reliably measure vergence?

A binocular eye tracker needs to be accurate to enable the determination of vergence, distance to the binocular fixation point and fixation disparity. These measures are useful in e.g. the research fields of visual perception, binocular control in reading and attention in 3D. Are binocular pupil-based video eye trackers accurate enough to produce meaningful binocular measures? Recent research revealed potentially large idiosyncratic systematic errors due to pupil-size changes. With a top of the line eye tracker (SR Research EyeLink 1000 plus), we investigated whether the pupil-size artefact in the separate eyes may cause the eye tracker to report apparent vergence when the eyeballs do not rotate. Participants were asked to fixate a target at a distance of 77 cm for 160 s. We evoked pupil-size changes by varying the light intensity. With increasing pupil size, horizontal vergence reported by the eye tracker decreased in most subjects, up to two degrees. However, this was not due to a rotation of the eyeballs, as identified from the absence of systematic movement in the corneal reflection (CR) signals. From this, we conclude that binocular pupil-CR or pupil-only video eye trackers using the dark pupil technique are not accurate enough to be used to determine vergence, distance to the binocular fixation point and fixation disparity.

Variability in monocular and binocular fixation during standard automated perimetry.

The aim of this cross-sectional study was to use standard automated perimetry to compare fixation variability among the dominant eye fixation, non-dominant eye fixation, and binocular fixation conditions. Thirty-five eyes of 35 healthy young participants underwent standard automated perimetry (Humphrey 24–2 SITA-Standard) in dominant eye fixation, non-dominant eye fixation, and binocular fixation conditions. Fixation variability during foveal threshold and visual field measurement, which was recorded using a wearable eye-tracking glass and calculated using the bivariate contour ellipse area (deg2), was compared among the three fixation conditions. Further, the association of bivariate contour ellipse area with ocular position and fusional amplitude during binocular fixation was analysed. There were no significant differences in bivariate contour ellipse area during foveal threshold measurement among the dominant eye fixation (1.75 deg2), non-dominant eye fixation (1.45 deg2), and binocular fixation (1.62 deg2) conditions. In contrast, the bivariate contour ellipse area during visual field measurement in binocular fixation (2.85 deg2) was significantly lower than the bivariate contour ellipse area in dominant eye fixation (4.62 deg2; p = 0.0227) and non-dominant eye fixation (5.24 deg2; p = 0.0006) conditions. There was no significant difference in bivariate contour ellipse area during visual field measurement between dominant eye fixation and non-dominant eye fixation conditions. There was no significant correlation between bivariate contour ellipse area and either ocular position or fusional amplitude during both foveal threshold and visual field measurements. Thus, fixation variability might be improved in binocular fixation conditions during a long-duration test, such as visual field measurement.