Three-Dimensional Ocular Kinematics During Eccentric Rotations: Evidence for Functional Rather Than Mechanical Constraints

2003 ◽  
Vol 89 (5) ◽  
pp. 2685-2696 ◽  
Author(s):  
Dora E. Angelaki
Keyword(s):  
Extraocular Muscle ◽  
Three Dimensional ◽  
Peripheral Retina ◽  
Eye Position ◽  
Image Stabilization ◽  
3D Kinematics ◽  
Mechanical Constraints ◽  
Rotation Axes ◽  
A Site ◽  
Eye Velocity

Previous studies have reported that the translational vestibuloocular reflex (TVOR) follows a three-dimensional (3D) kinematic behavior that is more similar to visually guided eye movements, like pursuit, rather than the rotational VOR (RVOR). Accordingly, TVOR rotation axes tilted with eye position toward an eye-fixed reference frame rather than staying relatively fixed in the head like in the RVOR. This difference arises because, contrary to the RVOR where peripheral image stability is functionally important, the TVOR like pursuit and saccades cares to stabilize images on the fovea. During most natural head and body movements, both VORs are simultaneously activated. In the present study, we have investigated in rhesus monkeys the 3D kinematics of the combined VOR during yaw rotation about eccentric axes. The experiments were motivated by and quantitatively compared with the predictions of two distinct hypotheses. According to the first (fixed-rule) hypothesis, an eye-position-dependent torsion is computed downstream of a site for RVOR/TVOR convergence, and the combined VOR axis would tilt through an angle that is proportional to gaze angle and independent of the relative RVOR/TVOR contributions to the total eye movement. This hypothesis would be consistent with the recently postulated mechanical constraints imposed by extraocular muscle pulleys. According to the second (image-stabilization) hypothesis, an eye-position-dependent torsion is computed separately for the RVOR and the TVOR components, implying a processing that takes place upstream of a site for RVOR/TVOR convergence. The latter hypothesis is based on the functional requirement that the 3D kinematics of the combined VOR should be governed by the need to keep images stable on the fovea with slip on the peripheral retina being dependent on the different functional goals of the two VORs. In contrast to the fixed-rule hypothesis, the data demonstrated a variable eye-position-dependent torsion for the combined VOR that was different for synergistic versus antagonistic RVOR/TVOR interactions. Furthermore, not only were the eye-velocity tilt slopes of the combined VOR as much as 10 times larger than what would be expected based on extraocular muscle pulley location, but also eye velocity during antagonistic RVOR/TVOR combinations often tilted opposite to gaze. These results are qualitatively and quantitatively consistent with the image-stabilization hypothesis, suggesting that the eye-position-dependent torsion is computed separately for the RVOR and the TVOR and that the 3D kinematics of the combined VOR are dependent on functional rather than mechanical constraints.

Implications of rotational kinematics for the oculomotor system in three dimensions

1987 ◽  
Vol 58 (4) ◽  
pp. 832-849 ◽  
Author(s):  
D. Tweed ◽  
T. Vilis
Keyword(s):  
Three Dimensional ◽  
Oculomotor System ◽  
Three Dimensions ◽  
Eye Position ◽  
Head Velocity ◽  
Listing’S Law ◽  
Indirect Path ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
Eye Velocity

1. This paper develops three-dimensional models for the vestibuloocular reflex (VOR) and the internal feedback loop of the saccadic system. The models differ qualitatively from previous, one-dimensional versions, because the commutative algebra used in previous models does not apply to the three-dimensional rotations of the eye. 2. The hypothesis that eye position signals are generated by an eye velocity integrator in the indirect path of the VOR must be rejected because in three dimensions the integral of angular velocity does not specify angular position. Computer simulations using eye velocity integrators show large, cumulative gaze errors and post-VOR drift. We describe a simple velocity to position transformation that works in three dimensions. 3. In the feedback control of saccades, eye position error is not the vector difference between actual and desired eye positions. Subtractive feedback models must continuously adjust the axis of rotation throughout a saccade, and they generate meandering, dysmetric gaze saccades. We describe a multiplicative feedback system that solves these problems and generates fixed-axis saccades that accord with Listing's law. 4. We show that Listing's law requires that most saccades have their axes out of Listing's plane. A corollary is that if three pools of short-lead burst neurons code the eye velocity command during saccades, the three pools are not yoked, but function independently during visually triggered saccades. 5. In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions. This is not the only algebraic system for describing rotations, but it is the one that best fits the needs of the oculomotor system, and it yields much simpler models than do rotation matrix or other representations. 6. Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion. 7. Many testable predictions made by quaternion models also turn up in models based on other mathematics. These predictions are therefore more fundamental than the specific models that generate them. Among these predictions are 1) to compute eye position in the indirect path of the VOR, eye or head velocity signals are multiplied by eye position feedback and then integrated; consequently 2) eye position signals and eye or head velocity signals converge on vestibular neurons, and their interaction is multiplicative.(ABSTRACT TRUNCATED AT 400 WORDS)

Computing three-dimensional eye position quaternions and eye velocity from search coil signals

1990 ◽  
Vol 30 (1) ◽  
pp. 97-110 ◽  
Author(s):  
Douglas Tweed ◽  
Werner Cadera ◽  
Tutis Vilis
Keyword(s):  
Three Dimensional ◽  
Eye Position ◽  
Search Coil ◽  
Eye Velocity

Primate Translational Vestibuloocular Reflexes. I. High-Frequency Dynamics and Three-Dimensional Properties During Lateral Motion

2000 ◽  
Vol 83 (3) ◽  
pp. 1637-1647 ◽  
Author(s):  
Dora E. Angelaki ◽  
M. Quinn McHenry ◽  
Bernhard J. M. Hess
Keyword(s):  
Eye Movements ◽  
High Frequency ◽  
Three Dimensional ◽  
Eye Position ◽  
Lateral Motion ◽  
Visually Guided ◽  
Torsional Response ◽  
Target Eccentricity ◽  
Eye Velocity ◽  
Tilt Response

The dynamics and three-dimensional (3-D) properties of the primate translational vestibuloocular reflex (trVOR) for high-frequency (4–12 Hz, ±0.3–0.4 g) lateral motion were investigated during near-target viewing at center and eccentric targets. Horizontal response gains increased with frequency and depended on target eccentricity. The larger the horizontal and vertical target eccentricity, the steeper the dependence of horizontal response gain on frequency. In addition to horizontal eye movements, robust torsional response components also were present at all frequencies. During center-target fixation, torsional response phase was opposite (anticompensatory) to that expected for an “apparent” tilt response. Instead torsional response components depended systematically on vertical-target eccentricity, increasing in amplitude when looking down and reversing phase when looking up. As a result the trVOR eye velocity vector systematically tilted away from a purely horizontal direction, through an angle that increased with vertical eccentricity with a slope of ∼0.7. This systematic dependence of torsional eye velocity tilt on vertical eye position suggests that the trVOR might follow the 3-D kinematic requirements that have been shown to govern visually guided eye movements and near-target fixation.

Three-Dimensional Vestibuloocular Reflex of the Monkey: Optimal Retinal Image Stabilization Versus Listing's Law

2000 ◽  
Vol 83 (6) ◽  
pp. 3264-3276 ◽  
Author(s):  
Hubert Misslisch ◽  
Bernhard J. M. Hess
Keyword(s):  
Retinal Image ◽  
Three Dimensional ◽  
Oculomotor Control ◽  
Slow Phase ◽  
Eye Position ◽  
Vestibuloocular Reflex ◽  
Image Stabilization ◽  
Listing's Law ◽  
Listing’S Law ◽  
Visual Background

If the rotational vestibuloocular reflex (VOR) were to achieve optimal retinal image stabilization during head rotations in three-dimensional space, it must turn the eye around the same axis as the head, with equal velocity but in the opposite direction. This optimal VOR strategy implies that the position of the eye in the orbit must not affect the VOR. However, if the VOR were to follow Listing's law, then the slow-phase eye rotation axis should tilt as a function of current eye position. We trained animals to fixate visual targets placed straight ahead or 20° up, down, left or right while being oscillated in yaw, pitch, and roll at 0.5–4 Hz, either with or without a full-field visual background. Our main result was that the visually assisted VOR of normal monkeys invariantly rotated the eye around the same axis as the head during yaw, pitch, and roll (optimal VOR). In the absence of a visual background, eccentric eye positions evoked small axis tilts of slow phases in normal animals. Under the same visual condition, a prominent effect of eye position was found during roll but not during pitch or yaw in animals with low torsional and vertical gains following plugging of the vertical semicircular canals. This result was in accordance with a model incorporating a specific compromise between an optimal VOR and a VOR that perfectly obeys Listing's law. We conclude that the visually assisted VOR of the normal monkey optimally stabilizes foveal as well as peripheral retinal images. The finding of optimal VOR performance challenges a dominant role of plant mechanics and supports the notion of noncommutative operations in the oculomotor control system.

Combined Influence of Vergence and Eye Position on Three-Dimensional Vestibulo-Ocular Reflex in the Monkey

2002 ◽  
Vol 88 (5) ◽  
pp. 2368-2376 ◽  
Author(s):  
H. Misslisch ◽  
B.J.M. Hess
Keyword(s):  
Three Dimensional ◽  
Head Rotation ◽  
Eye Position ◽  
Near Vision ◽  
Ocular Reflex ◽  
Rotation Axes ◽  
Eye Rotation ◽  
Visual Background ◽  
Vestibulo Ocular Reflex ◽  
Head Rotations

This study examined two kinematical features of the rotational vestibulo-ocular reflex (VOR) of the monkey in near vision. First, is there an effect of eye position on the axes of eye rotation during yaw, pitch and roll head rotations when the eyes are converged to fixate near targets? Second, do the three-dimensional positions of the left and right eye during yaw and roll head rotations obey the binocular extension of Listing's law (L2), showing eye position planes that rotate temporally by a quarter as far as the angle of horizontal vergence? Animals fixated near visual targets requiring 17 or 8.5° vergence and placed at straight ahead, 20° up, down, left, or right during yaw, pitch, and roll head rotations at 1 Hz. The 17° vergence experiments were performed both with and without a structured visual background, the 8.5° vergence experiments with a visual background only. A 40° horizontal change in eye position never influenced the axis of eye rotation produced by the VOR during pitch head rotation. Eye position did not affect the VOR eye rotation axes, which stayed aligned with the yaw and roll head rotation axes, when torsional gain was high. If torsional gain was low, eccentric eye positions produced yaw and roll VOR eye rotation axes that tilted somewhat in the directions predicted by Listing's law, i.e., with or opposite to gaze during yaw or roll. These findings were seen in both visual conditions and in both vergence experiments. During yaw and roll head rotations with a 40° vertical change in gaze, torsional eye position followed on average the prediction of L2: the left eye showed counterclockwise (ex-) torsion in down gaze and clockwise (in-) torsion in up gaze and vice versa for the right eye. In other words, the left and right eye's position plane rotated temporally by about a quarter of the horizontal vergence angle. Our results indicate that torsional gain is the central mechanism by which the brain adjusts the retinal image stabilizing function of the VOR both in far and near vision and the three dimensional eye positions during yaw and roll head rotations in near vision follow on average the predictions of L2, a kinematic pattern that is maintained by the saccadic/quick phase system.

Vertical Eye Position–Dependence of the Human Vestibuloocular Reflex During Passive and Active Yaw Head Rotations

1999 ◽  
Vol 81 (5) ◽  
pp. 2415-2428 ◽  
Author(s):  
Matthew J. Thurtell ◽  
Ross A. Black ◽  
G. Michael Halmagyi ◽  
Ian S. Curthoys ◽  
Swee T. Aw
Keyword(s):  
Three Dimensional ◽  
Head Position ◽  
Eye Position ◽  
Vestibuloocular Reflex ◽  
Head Velocity ◽  
High Acceleration ◽  
Position Dependence ◽  
Head Impulses ◽  
Eye Velocity ◽  
Head Rotations

Vertical eye position–dependence of the human vestibuloocular reflex during passive and active yaw head rotations. The effect of vertical eye-in-head position on the compensatory eye rotation response to passive and active high acceleration yaw head rotations was examined in eight normal human subjects. The stimuli consisted of brief, low amplitude (15–25°), high acceleration (4,000–6,000°/s2) yaw head rotations with respect to the trunk (peak velocity was 150–350°/s). Eye and head rotations were recorded in three-dimensional space using the magnetic search coil technique. The input-output kinematics of the three-dimensional vestibuloocular reflex (VOR) were assessed by finding the difference between the inverted eye velocity vector and the head velocity vector (both referenced to a head-fixed coordinate system) as a time series. During passive head impulses, the head and eye velocity axes aligned well with each other for the first 47 ms after the onset of the stimulus, regardless of vertical eye-in-head position. After the initial 47-ms period, the degree of alignment of the eye and head velocity axes was modulated by vertical eye-in-head position. When fixation was on a target 20° up, the eye and head velocity axes remained well aligned with each other. However, when fixation was on targets at 0 and 20° down, the eye velocity axis tilted forward relative to the head velocity axis. During active head impulses, the axis tilt became apparent within 5 ms of the onset of the stimulus. When fixation was on a target at 0°, the velocity axes remained well aligned with each other. When fixation was on a target 20° up, the eye velocity axis tilted backward, when fixation was on a target 20° down, the eye velocity axis tilted forward. The findings show that the VOR compensates very well for head motion in the early part of the response to unpredictable high acceleration stimuli—the eye position– dependence of the VOR does not become apparent until 47 ms after the onset of the stimulus. In contrast, the response to active high acceleration stimuli shows eye position–dependence from within 5 ms of the onset of the stimulus. A model using a VOR-Listing’s law compromise strategy did not accurately predict the patterns observed in the data, raising questions about how the eye position–dependence of the VOR is generated. We suggest, in view of recent findings, that the phenomenon could arise due to the effects of fibromuscular pulleys on the functional pulling directions of the rectus muscles.

Crosstalk Minimization Method for Eye-tracking-based 3D Display

2020 ◽  
Author(s):  
Seok Lee ◽  
Juyong Park ◽  
Dongkyung Nam
Keyword(s):  
Image Processing ◽  
Eye Tracking ◽  
Three Dimensional ◽  
Processing Method ◽  
Eye Position ◽  
Relative Location ◽  
3D Display ◽  
Minimization Method ◽  
3D Crosstalk ◽  
Pixel Value

In this article, the authors present an image processing method to reduce three-dimensional (3D) crosstalk for eye-tracking-based 3D display. Specifically, they considered 3D pixel crosstalk and offset crosstalk and applied different approaches based on its characteristics. For 3D pixel crosstalk which depends on the viewer’s relative location, they proposed output pixel value weighting scheme based on viewer’s eye position, and for offset crosstalk they subtracted luminance of crosstalk components according to the measured display crosstalk level in advance. By simulations and experiments using the 3D display prototypes, the authors evaluated the effectiveness of proposed method.

scholarly journals Three-Dimensional Site Characterization Model of Bangalore Using Support Vector Machine

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Pijush Samui
Keyword(s):  
Support Vector Machine ◽  
Three Dimensional ◽  
Site Characterization ◽  
Standard Penetration Test ◽  
Support Vector ◽  
Characterization Model ◽  
Svm Model ◽  
Input Variables ◽  
Learning Machine ◽  
A Site

The main objective of site characterization is the prediction of in situ soil properties at any half-space point at a site based on limited tests. In this study, the Support Vector Machine (SVM) has been used to develop a three dimensional site characterization model for Bangalore, India based on large amount of Standard Penetration Test. SVM is a novel type of learning machine based on statistical learning theory, uses regression technique by introducing ε-insensitive loss function. The database consists of 766 boreholes, with more than 2700 field SPT values () spread over 220 sq km area of Bangalore. The model is applied for corrected () values. The three input variables (, , and , where , , and are the coordinates of the Bangalore) were used for the SVM model. The output of SVM was the data. The results presented in this paper clearly highlight that the SVM is a robust tool for site characterization. In this study, a sensitivity analysis of SVM parameters (σ, , and ε) has been also presented.

Chloridobis(1,10-phenanthroline-κ2 N,N′)copper(I) hexahydrate

2007 ◽  
Vol 63 (3) ◽  
pp. m826-m828 ◽  
Author(s):  
H. Zhong ◽  
X.-R. Zeng ◽  
X.-M. Yang ◽  
Q.-Y. Luo ◽  
S.-Z. Xiao
Keyword(s):  
Three Dimensional ◽  
Water Molecules ◽  
Stacking Interactions ◽  
Coordination Geometry ◽  
Rotation Axes ◽  
Trigonal Bipyramidal ◽  
Distorted Trigonal Bipyramidal Coordination ◽  
Cl Atom ◽  
Phenanthroline Ligands ◽  
Distorted Trigonal Bipyramidal

The CuI atom in the title complex, [CuCl(C12H8N2)2]·6H2O, exists in a distorted trigonal-bipyramidal coordination geometry defined by one Cl atom and four N atoms of two 1,10-phenanthroline ligands. In the crystal structure, molecules are linked into a three-dimensional framework by O—H...O hydrogen bonds and π–π stacking interactions. Four water molecules lie on crystallographic twofold rotation axes.

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