Visually evoked cyclovergence and extended listing's law

Eye tracking: empirical foundations for a minimal reporting guideline

In this paper, we present a review of how the various aspects of any study using an eye tracker (such as the instrument, methodology, environment, participant, etc.) affect the quality of the recorded eye-tracking data and the obtained eye-movement and gaze measures. We take this review to represent the empirical foundation for reporting guidelines of any study involving an eye tracker. We compare this empirical foundation to five existing reporting guidelines and to a database of 207 published eye-tracking studies. We find that reporting guidelines vary substantially and do not match with actual reporting practices. We end by deriving a minimal, flexible reporting guideline based on empirical research (Section "An empirically based minimal reporting guideline").

Spatial-temporal contrast sensitivity of the eye alignment reflex

The binocular alignment of the eyes involves both voluntary and reflexive mechanisms, but little is known about the visual input and neurological pathway of the reflex component. Our studies examined the role of spatiotemporal frequency and contrast in the control of reflex eye alignment, and compared the contrast sensitivity of the alignment reflex with psychophysical contrast sensitivity. We measured the contrast sensitivity of vertical disparity-driven vergence eye movements in response to bandwidth filtered static or 6 Hz counterphase flickering noise and measured psychophysical detection sensitivity for the same stimuli. Contrast thresholds for producing a detectable vertical alignment change (measured with nonius lines) were determined using a staircase method for 7 spatial frequencies [0.25-16 cycles per degree] and 3 vertical disparities [5, 10, and 30 arcmin] in 7 adults with normal or corrected to normal vision. The main findings of this study are, (1) the vertical alignment reflex had overall relatively high contrast sensitivity, comparable to but somewhat less than visual detection thresholds, (2) the most effective stimulus spatial frequency scaled in inverse proportion to the disparity being stimulated, and (3) unlike psychophysical contrast sensitivity, the eye alignment reflex contrast sensitivity was not improved by flickering low spatial frequencies.

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.

Gaze tracking accuracy in humans: One eye is sometimes better than two

Most modern video eye trackers deliver binocular data. Many researchers take the average of the left and right eye signals (the version signal) to decrease the variable error (precision) up to a factor of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt {2}$\end{document}2. What happens to the systematic error (accuracy) if the left and right eye signals are averaged? To determine the systematic error, we conducted a calibration validation in two experiments (n= 79 and n = 64). The systematic error was computed for the left eye, right eye, and version signals separately. In respectively 29.5 and 25.8% of the participants, the systematic error of a single eye signal was lower than that of the version signal at the cost of a higher variable error. If a small variable error is desirable, and the difference between the left and the right eye is not the topic of study, one should average position data from the left and the right eye (in other words, use the version signal). If a small systematic error is desirable, one should use the signal (from left eye, right eye or version) that delivers the best accuracy. In the latter case, this may cause worse precision than that of the version signal.

Cyclorotation models for eyes and cameras

The human visual system obeys Listing's law, which means that the cyclorotation of the eye (around the line of sight) can be predicted from the direction of the fixation point. It is shown here that Listing's law can conveniently be formulated in terms of rotation matrices. The function that defines the observed cyclorotation is derived in this representation. Two polynomial approximations of the function are developed, and the accuracy of each model is evaluated by numerical integration over a range of gaze directions. The error of the simplest approximation for typical eye movements is less than half a degree. It is shown that, given a set of calibrated images, the effect of Listing's law can be simulated in a way that is physically consistent with the original camera. This condition is important for robotic models of human vision, which typically do not reproduce the mechanics of the oculomotor system.

Vergence effects on the perception of motion-in-depth

When the eyes follow a target that is moving directly towards the head they make a vergence eye movement. Accurate perception of the target's motion requires adequate compensation for the movements of the eyes. The experiments in this paper address the issue of how well the visual system compensates for vergence eye movements when viewing moving targets. We show that there are small but consistent biases across observers: When the eyes follow a target that is moving in depth, it is typically perceived as slower than when the eyes are kept stationary. We also analysed the eye movements that were made by observers. We found that there are considerable differences between observers and between trials, but we did not find evidence that the gains and phase lags of the eye movements were related to psychophysical performance.

Illusory depth induced by binocular torsional misalignment

This study reports a new depth illusion in which a static flat pattern appears stratified stereoscopically when viewed binocularly with an elevated gaze. Three psychophysical experiments measured perceived relative depth and fixational cyclodisparity (a rotation of one eye's view relative to the other eye's view about the line of sight) when flat patterns drawn with solid or dashed curved lines were fixated at various levels of gaze elevation. Experiments 1 and 2 showed that the patterns drawn with solid lines produced illusory depth only at large gaze elevations (downward and upward). Experiment 3 showed that the magnitude of the illusory depth was correlated with that of fixational cyclodisparity. These results suggest that the illusory depth originates in the binocular torsional misalignment generated by gaze elevation.

Vertical ocular responses to constant linear acceleration generated by fore–aft head translation in monkeys

We examined the vertical linear vestibuloocular reflexes (LVORs) elicited by constant linear acceleration (0-0.5 g for >95 ms) during transient fore-aft translation in three monkeys. In the dark condition, small but consistent downward ocular responses to forward translation were observed (latencies >41 ms) when the initial vertical eye positions were at 0 degrees , although eye movements following backward translation were inconsistent among animals. These downward ocular responses showed the following three characteristics: they were independent of vertical gaze eccentricities, their magnitudes were almost proportional to the forward acceleration, and they were reduced by the large-field (not the spot) visual information. These characteristics revealed that the downward ocular responses to forward translation were the tilt LVORs. In addition, we recognized that the translational LVOR, which depended on vertical gaze eccentricities, was working at the same time. Our data suggest that constant linear acceleration during forward translation evokes the tilt LVOR, as well as the illusory tilting perception.

Perceptual compensation for eye torsion

To correctly perceive visual directions relative to the head, one needs to compensate for the eye's orientation in the head. In this study we focus on compensation for the eye's torsion regarding objects that contain the line of sight and objects that do not pass through the fixation point. Subjects judged the location of flashed probe points relative to their binocular plane of regard, the mid-sagittal or the transverse plane of the head, while fixating straight ahead, right upward, or right downward at 30 cm distance, to evoke eye torsion according to Listing's law. In addition, we investigated the effects of head-tilt and monocular versus binocular viewing. Flashed probe points were correctly localized in the plane of regard irrespective of eccentric viewing, head-tilt, and monocular or binocular vision in nearly all subjects and conditions. Thus, eye torsion that varied by +/-9 degrees across these different conditions was in general compensated for. However, the position of probes relative to the midsagittal or the transverse plane, both true head-fixed planes, was misjudged. We conclude that judgment of the orientation of the plane of regard, a plane that contains the line of sight, is veridical, indicating accurate compensation for actual eye torsion. However, when judgment has to be made of a head-fixed plane that is offset with respect to the line of sight, eye torsion that accompanies that eye orientation appears not to be taken into account correctly.

Nature of variability in saccades

We studied the variability in saccades by comparing the peak velocities of saccades with the same target amplitude made with different actual amplitudes. We tested three hypotheses: the pulse-height noise hypothesis (peak velocity and amplitude vary proportionally), the localization noise hypothesis (variability in amplitude and peak velocity lie along the main sequence), and the independent noise hypothesis (variability in amplitude and peak velocity are independent). We measured eye orientation in two experiments by a scleral coil and a video system. Surprisingly, the main source of variability of saccades depended on the measurement system used. A combination of localization noise and independent noise best describes the data obtained by the video system. The independent noise (e.g., measurement inaccuracy) was the main source of variability. For the scleral coils, the variability was considerably larger than for the less accurate video system. The pulse-height noise hypothesis best describes this additional variability. Therefore we conclude that pulse-height noise is the main source of variability in saccades measured with scleral coils. We discuss the influence of scleral coils on saccade generation and suggest that a change in motor strategy due to the discomfort of wearing the coils might be the cause of the increased variability.

Plasticity of convergence-dependent variations of cyclovergence with vertical gaze

Binocular alignment of foveal images is facilitated by cross-couplings of vergence eye movements with distance and direction of gaze. These couplings reduce horizontal, vertical and cyclodisparities at the fovea without using feedback from retinal image disparity. Horizontal vergence is coupled with accommodation. Vertical vergence that aligns tertiary targets in asymmetric convergence is thought to be coupled with convergence and horizontal gaze. Cyclovergence aligns the horizontal retinal meridians during gaze elevation in symmetrical convergence and is coupled with convergence and vertical gaze. The latter vergence-dependent changes of cyclovergence have been described in terms of the orientation of Listing's plane and have been referred to as the binocular extension of Listing's law. Can these couplings be modified? Plasticity has been demonstrated previously for two of the three dimensions of vergence (horizontal and vertical). The current study demonstrates that convergence-dependent changes of the orientation of Listing's plane can be adapted to either exaggerate or to reduce the cyclovergence that normally facilitates alignment of the horizontal meridians of the retinas with one another during gaze elevation in symmetrical convergence. The adaptability of cyclovergence demonstrates a neural mechanism that, in conjunction with the passive forces determined by biomechanical properties of the orbit, could play an active role in implementing Listing's extended law and provide a means for calibrating binocular eye alignment in three dimensions.

The motor side of depth vision

To achieve stereoscopic vision, the brain must search for corresponding image features on the two retinas. As long as the eyes stay still, corresponding features are confined to narrow bands called epipolar lines. But when the eyes change position, the epipolar lines migrate on the retinas. To find the matching features, the brain must either search different retinal bands depending on current eye position, or search retina-fixed zones that are large enough to cover all usual locations of the epipolar lines. Here we show, using a new type of stereogram in which the depth image vanishes at certain gaze elevations, that the search zones are retina-fixed. This being the case, motor control acquires a crucial function in depth vision: we show that the eyes twist about their lines of sight in a way that reduces the motion of the epipolar lines, allowing stereopsis to get by with smaller search zones and thereby lightening its computational load.