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

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)

Oculomotor Reactions in the Cuttlefish, Sepia Officinalis

1970 ◽  
Vol 52 (2) ◽  
pp. 369-384 ◽  
Author(s):  
H. COLLEWIJN
Keyword(s):  
Eye Movements ◽  
Optokinetic Nystagmus ◽  
Eye Position ◽  
Sepia Officinalis ◽  
Search Coil ◽  
Passive Rotation ◽  
Eye Velocity ◽  
Search Coil Technique ◽  
Better Than

1. Eye position in Sepia was measured in restrained animals, using a scleral search coil technique. 2. Optokinetic nystagmus was elicited by drum rotations from 0.035 up to 35°/sec. 3. Passive rotation of Sepia in darkness evoked a transient nystagmus, followed by after-nystagmus at arrest. 4. Combination of these two stimuli yielded the best results, but the ratio eye velocity/surroundings velocity was usually not better than 0.5. 5. Eye movements were conjugate and a closed eye could be driven by a seeing eye. Monocular reactions were smaller than binocular ones, but equal in both directions. 6. Fixation movements could not be demonstrated in the present conditions.

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.

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.

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.

Calibration of three-dimensional eye position using search coil signals in the rhesus monkey

1992 ◽  
Vol 32 (9) ◽  
pp. 1647-1654 ◽  
Author(s):  
B.J.M. Hess ◽  
A.J. Van Opstal ◽  
D. Straumann ◽  
K. Hepp
Keyword(s):  
Rhesus Monkey ◽  
Three Dimensional ◽  
Eye Position ◽  
Search Coil

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.

Anatomy and Physiology of the Primate Interstitial Nucleus of Cajal. II. Discharge Pattern of Single Efferent Fibers

1998 ◽  
Vol 80 (6) ◽  
pp. 3100-3111 ◽  
Author(s):  
Y. Dalezios ◽  
C. A. Scudder ◽  
S. M. Highstein ◽  
A. K. Moschovakis
Keyword(s):  
Smooth Pursuit ◽  
Discharge Pattern ◽  
Eye Position ◽  
Interstitial Nucleus Of Cajal ◽  
Anatomy And Physiology ◽  
Saccade Size ◽  
Saccade Velocity ◽  
Behaving Monkeys ◽  
Eye Velocity ◽  
Vertical Up

Dalezios, Y., C. A. Scudder, S. M. Highstein, and A. K. Moschovakis. Anatomy and physiology of the primate interstitial nucleus of Cajal. II. Discharge pattern of single efferent fibers. J. Neurophysiol. 80: 3100–3111, 1998. Single efferent fibers of the interstitial nucleus of Cajal (NIC) were characterized physiologically and injected with biocytin in alert behaving monkeys. Quantitative analysis demonstrated that their discharge encodes a constellation of oculomotor variables. Tonic and phasic signals were related to vertical (up or down) eye position and saccades, respectively. Depending on how they encoded eye position, saccade velocity, saccade size, saccade duration, and smooth-pursuit eye velocity, fibers were characterized as regular or irregular, bi- or unidirectionally modulated, more or less sensitive, and reliable or unreliable. Further, fibers that did not burst for saccades (tonic) and fibers the eye-position and saccade-related signals of which increased in the same (in-phase) or in the opposite (anti-phase) directions were encountered. A continuum of discharge properties was the rule. We conclude that NIC efferent fibers send a combination of eye-position, saccade-, and smooth-pursuit-related signals, mixed in proportions that differ for different fibers, to targets of the vertical neural integrator such as extraocular motoneurons.

Monkey superior colliculus represents rapid eye movements in a two-dimensional motor map

1993 ◽  
Vol 69 (3) ◽  
pp. 965-979 ◽  
Author(s):  
K. Hepp ◽  
A. J. Van Opstal ◽  
D. Straumann ◽  
B. J. Hess ◽  
V. Henn
Keyword(s):  
Eye Movements ◽  
Superior Colliculus ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Eye Position ◽  
Two Dimensional ◽  
Vestibular Nystagmus ◽  
Rapid Eye Movements ◽  
Q Model

1. Although the eye has three rotational degrees of freedom, eye positions, during fixations, saccades, and smooth pursuit, with the head stationary and upright, are constrained to a plane by ListingR's law. We investigated whether Listing's law for rapid eye movements is implemented at the level of the deeper layers of the superior colliculus (SC). 2. In three alert rhesus monkeys we tested whether the saccadic motor map of the SC is two dimensional, representing oculocentric target vectors (the vector or V-model), or three dimensional, representing the coordinates of the rotation of the eye from initial to final position (the quaternion or Q-model). 3. Monkeys made spontaneous saccadic eye movements both in the light and in the dark. They were also rotated about various axes to evoke quick phases of vestibular nystagmus, which have three degrees of freedom. Eye positions were measured in three dimensions with the magnetic search coil technique. 4. While the monkey made spontaneous eye movements, we electrically stimulated the deeper layers of the SC and elicited saccades from a wide range of initial positions. According to the Q-model, the torsional component of eye position after stimulation should be uniquely related to saccade onset position. However, stimulation at 110 sites induced no eye torsion, in line with the prediction of the V-model. 5. Activity of saccade-related burst neurons in the deeper layers of the SC was analyzed during rapid eye movements in three dimensions. No systematic eye-position dependence of the movement fields, as predicted by the Q-model, could be detected for these cells. Instead, the data fitted closely the predictions made by the V-model. 6. In two monkeys, both SC were reversibly inactivated by symmetrical bilateral injections of muscimol. The frequency of spontaneous saccades in the light decreased dramatically. Although the remaining spontaneous saccades were slow, Listing's law was still obeyed, both during fixations and saccadic gaze shifts. In the dark, vestibularly elicited fast phases of nystagmus could still be generated in three dimensions. Although the fastest quick phases of horizontal and vertical nystagmus were slower by about a factor of 1.5, those of torsional quick phases were unaffected. 7. On the basis of the electrical stimulation data and the properties revealed by the movement field analysis, we conclude that the collicular motor map is two dimensional. The reversible inactivation results suggest that the SC is not the site where three-dimensional fast phases of vestibular nystagmus are generated.(ABSTRACT TRUNCATED AT 400 WORDS)

Neuronal Responses Related to Smooth Pursuit Eye Movements in the Periarcuate Cortical Area of Monkeys

1998 ◽  
Vol 80 (1) ◽  
pp. 28-47 ◽  
Author(s):  
Masaki Tanaka ◽  
Kikuro Fukushima
Keyword(s):  
Eye Movements ◽  
Smooth Pursuit ◽  
Cortical Area ◽  
Eye Position ◽  
Smooth Pursuit Eye Movements ◽  
Neuronal Responses ◽  
Stationary Target ◽  
Pursuit Eye Movements ◽  
Preferred Direction ◽  
Eye Velocity

Tanaka, Masaki and Kikuro Fukushima. Neuronal responses related to smooth pursuit eye movements in the periarcuate cortical area of monkeys. J. Neurophysiol. 80: 28–47, 1998. To examine how the periarcuate area is involved in the control of smooth pursuit eye movements, we recorded 177 single neurons while monkeys pursued a moving target in the dark. The majority (52%, 92/177) of task-related neurons responded to pursuit but had little or no response to saccades. Histological reconstructions showed that these neurons were located mainly in the posterior bank of the arcuate sulcus near the sulcal spur. Twenty-seven percent (48/177) changed their activity at the onset of saccades. Of these, 36 (75%) showed presaccadic burst activity with strong preference for contraversive saccades. Eighteen (10%, 18/177) were classified as eye-position–related neurons, and 11% (19/177) were related to other aspects of the stimuli or response. Among the 92 neurons that responded to pursuit, 85 (92%) were strongly directional with uniformly distributed preferred directions. Further analyses were performed in these directionally sensitive pursuit-related neurons. For 59 neurons that showed distinct changes in activity around the initiation of pursuit, the median latency from target motion was 96 ms and that preceding pursuit was −12 ms, indicating that these neuron can influence the initiation of pursuit. We tested some neurons by briefly extinguishing the tracking target ( n = 39) or controlling its movement with the eye position signal ( n = 24). The distribution of the change in pursuit-related activity was similar to previous data for the dorsomedial part of the medial superior temporal neurons ( Newsome et al. 1988) , indicating that pursuit-related neurons in the periarcuate area also carry extraretinal signals. For 22 neurons, we examined the responses when the animals reversed pursuit direction to distinguish the effects of eye acceleration in the preferred direction from oppositely directed eye velocity. Almost all neurons discharged before eye velocity reached zero, however, only nine neurons discharged before the eyes were accelerated in the preferred direction. The delay in neuronal responses relative to the onset of eye acceleration in these trials might be caused by suppression from oppositely directed pursuit velocity. The results suggest that the periarcuate neurons do not participate in the earliest stage of eye acceleration during the change in pursuit direction, although most of them may participate in the early stages of pursuit initiation in the ordinary step-ramp pursuit trials. Some neurons changed their activity when the animals fixated a stationary target, and this activity could be distinguished easily from the strong pursuit-related responses. Our results suggest that the periarcuate pursuit area carries extraretinal signals and affects the premotor circuitry for smooth pursuit.

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