scholarly journals V1 neurons encode the perceptual compensation of false torsion arising from Listing’s law

2020 ◽  
Vol 117 (31) ◽  
pp. 18799-18809
Author(s):  
Mohammad Farhan Khazali ◽  
Hamidreza Ramezanpour ◽  
Peter Thier
Keyword(s):  
Visual System ◽  
Eye Position ◽  
Two Dimensional ◽  
V1 Neurons ◽  
Listing's Law ◽  
Listing’S Law ◽  
Torsional Component ◽  
Eye Torsion

We try to deploy the retinal fovea to optimally scrutinize an object of interest by directing our eyes to it. The horizontal and vertical components of eye positions acquired by goal-directed saccades are determined by the object’s location. However, the eccentric eye positions also involve a torsional component, which according to Donder’s law is fully determined by the two-dimensional (2D) eye position acquired. According to von Helmholtz, knowledge of the amount of torsion provided by Listing’s law, an extension of Donder’s law, alleviates the perceptual interpretation of the image tilt that changes with 2D eye position, a view supported by psychophysical experiments he pioneered. We address the question of where and how Listing’s law is implemented in the visual system and we show that neurons in monkey area V1 use knowledge of eye torsion to compensate the image tilt associated with specific eye positions as set by Listing’s law.

scholarly journals V1 neurons encode the perceptual compensation of “false torsion” arising from Listing’s law

2018 ◽  
Author(s):  
Mohammad Farhan Khazali ◽  
Peter Thier
Keyword(s):  
Eye Movements ◽  
Visual System ◽  
Eye Position ◽  
V1 Neurons ◽  
Listing's Law ◽  
Listing’S Law ◽  
Torsional Component

AbstractWe try to deploy the retinal fovea to optimally scrutinize an object of interest by directing our eyes to it. Horizontal and vertical components of these fixation eye movements are determined by the object’s location. However, fixation eye movements also involve a torsional component, which according to Listing’s law is fully determined by the 2D eye position acquired. According to Von Helmholtz knowledge of the torsion provided by this law alleviates the perceptual interpretation of the image tilt that changes with fixation, a view supported by psychophysical experiments he pioneered. We address the question where and how Listing’s law is implemented in the visual system and we show that neurons in monkey area V1 use knowledge of torsion to compensate the image tilt associated with specific eye positions as set by Listing’s law.

Human Oculomotor System Accounts for 3-D Eye Orientation in the Visual-Motor Transformation for Saccades

1998 ◽  
Vol 80 (5) ◽  
pp. 2274-2294 ◽  
Author(s):  
Eliana M. Klier ◽  
J. Douglas Crawford
Keyword(s):  
Reference Frame ◽  
Oculomotor System ◽  
Gaze Direction ◽  
Eye Position ◽  
Look Up Table ◽  
Listing's Law ◽  
Listing’S Law ◽  
Reference Frame Transformation ◽  
Visual Motor ◽  
Frame Transformation

Klier, Eliana M. and J. Douglas Crawford. Human oculomotor system accounts for 3-D eye orientation in the visual-motor transformation for saccades. J. Neurophysiol. 80: 2274–2294, 1998. A recent theoretical investigation has demonstrated that three-dimensional (3-D) eye position dependencies in the geometry of retinal stimulation must be accounted for neurally (i.e., in a visuomotor reference frame transformation) if saccades are to be both accurate and obey Listing's law from all initial eye positions. Our goal was to determine whether the human saccade generator correctly implements this eye-to-head reference frame transformation (RFT), or if it approximates this function with a visuomotor look-up table (LT). Six head-fixed subjects participated in three experiments in complete darkness. We recorded 60° horizontal saccades between five parallel pairs of lights, over a vertical range of ±40° ( experiment 1), and 30° radial saccades from a central target, with the head upright or tilted 45° clockwise/counterclockwise to induce torsional ocular counterroll, under both binocular and monocular viewing conditions ( experiments 2 and 3). 3-D eye orientation and oculocentric target direction (i.e., retinal error) were computed from search coil signals in the right eye. Experiment 1: as predicted, retinal error was a nontrivial function of both target displacement in space and 3-D eye orientation (e.g., horizontally displaced targets could induce horizontal or oblique retinal errors, depending on eye position). These data were input to a 3-D visuomotor LT model, which implemented Listing's law, but predicted position-dependent errors in final gaze direction of up to 19.8°. Actual saccades obeyed Listing's law but did not show the predicted pattern of inaccuracies in final gaze direction, i.e., the slope of actual error, as a function of predicted error, was only −0.01 ± 0.14 (compared with 0 for RFT model and 1.0 for LT model), suggesting near-perfect compensation for eye position. Experiments 2 and 3: actual directional errors from initial torsional eye positions were only a fraction of those predicted by the LT model (e.g., 32% for clockwise and 33% for counterclockwise counterroll during binocular viewing). Furthermore, any residual errors were immediately reduced when visual feedback was provided during saccades. Thus, other than sporadic miscalibrations for torsion, saccades were accurate from all 3-D eye positions. We conclude that 1) the hypothesis of a visuomotor look-up table for saccades fails to account even for saccades made directly toward visual targets, but rather, 2) the oculomotor system takes 3-D eye orientation into account in a visuomotor reference frame transformation. This transformation is probably implemented physiologically between retinotopically organized saccade centers (in cortex and superior colliculus) and the brain stem burst generator.

Three-dimensional visuo-motor control of saccades

2013 ◽  
Vol 109 (1) ◽  
pp. 183-192 ◽  
Author(s):  
Bernhard J. M. Hess
Keyword(s):  
Motor Control ◽  
Reverse Engineering ◽  
Visual Information ◽  
Three Dimensional ◽  
Engineering Problem ◽  
Line Of Sight ◽  
Eye Position ◽  
Listing's Law ◽  
Saccade Onset ◽  
Listing’S Law

Although the motion of the line of sight is a straightforward consequence of a particular rotation of the eye, it is much trickier to predict the rotation underlying a particular motion of the line of sight in accordance with Listing's law. Helmholtz's notion of the direction-circle together with the notion of primary and secondary reference directions in visual space provide an elegant solution to this reverse engineering problem, which the brain is faced with whenever generating a saccade. To test whether these notions indeed apply for saccades, we analyzed three-dimensional eye movements recorded in four rhesus monkeys. We found that on average saccade trajectories closely matched with the associated direction-circles. Torsional, vertical, and horizontal eye position of saccades scattered around the position predicted by the associated direction-circles with standard deviations of 0.5°, 0.3°, and 0.4°, respectively. Comparison of saccade trajectories with the likewise predicted fixed-axis rotations yielded mean coefficients of determinations (±SD) of 0.72 (±0.26) for torsion, 0.97 (±0.10) for vertical, and 0.96 (±0.11) for horizontal eye position. Reverse engineering of three-dimensional saccadic rotations based on visual information suggests that motor control of saccades, compatible with Listing's law, not only uses information on the fixation directions at saccade onset and offset but also relies on the computation of secondary reference positions that vary from saccade to saccade.

Straight Lines, ‘Uncurved Lines’, and Helmholtz's ‘Great Circles on the Celestial Sphere’

Perception ◽  
10.1068/p5652 ◽  
2007 ◽  
Vol 36 (9) ◽  
pp. 1275-1289 ◽  
Author(s):  
Brian Rogers ◽  
Kenneth Brecher
Keyword(s):  
Visual System ◽  
Visual Space ◽  
Listing's Law ◽  
Lack Of Information ◽  
Listing’S Law ◽  
The World ◽  
Celestial Sphere ◽  
Straight Lines ◽  
Different Parts

Helmholtz's famous pincushioned chessboard figure has been used to make the point that straight lines in the world are not always perceived as straight and, conversely, that curved lines in the world can sometimes be seen as straight. However, there is little agreement as to the cause of these perceptual errors. Some authors have attributed the errors to the shape of the retina, or the amount of cortex devoted to the processing of images falling on different parts of the retina, while others have taken the effects to indicate that visual space itself is curved. Helmholtz himself claimed that the ‘uncurved lines on the visual globe’ corresponded to ‘direction circles’ defined as those arcs described by the line of fixation when the eye moves according to Listing's law. Careful re-reading of Helmholtz together with some additional observations lead us to the conclusion that two other factors are also involved in the effect: (i) a lack of information about the distance of peripherally viewed objects and (ii) the preference of the visual system for seeing the pincushion squares as similar in size.

scholarly journals Chameleon eye position obeys Listing's law

2001 ◽  
Vol 41 (17) ◽  
pp. 2245-2251 ◽  
Author(s):  
Peter S Sándor ◽  
Maarten A Frens ◽  
Volker Henn
Keyword(s):  
Eye Position ◽  
Listing's Law ◽  
Listing’S Law

scholarly journals Visual-Motor Transformations Required for Accurate and Kinematically Correct Saccades

1997 ◽  
Vol 78 (3) ◽  
pp. 1447-1467 ◽  
Author(s):  
J. Douglas Crawford ◽  
Daniel Guitton
Keyword(s):  
Reference Frame ◽  
Eye Position ◽  
Target Displacement ◽  
Listing's Law ◽  
Listing's Plane ◽  
Listing’S Law ◽  
Reference Frame Transformation ◽  
Visual Motor ◽  
Frame Transformation ◽  
Listing’S Plane

Crawford, J. Douglas and Daniel Guitton. Visual-motor transformations required for accurate and kinematically correct saccades. J. Neurophysiol. 78: 1447–1467, 1997. The goal of this study was to identify and model the three-dimensional (3-D) geometric transformations required for accurate saccades to distant visual targets from arbitrary initial eye positions. In abstract 2-D models, target displacement in space, retinal error (RE), and saccade vectors are trivially interchangeable. However, in real 3-D space, RE is a nontrivial function of objective target displacement and 3-D eye position. To determine the physiological implications of this, a visuomotor “lookup table” was modeled by mapping the horizontal/vertical components of RE onto the corresponding vector components of eye displacement in Listing's plane. This provided the motor error (ME) command for a 3-D displacement-feedback loop. The output of this loop controlled an oculomotor plant that mechanically implemented the position-dependent saccade axis tilts required for Listing's law. This model correctly maintained Listing's law but was unable to correct torsional position deviations from Listing's plane. Moreover, the model also generated systematic errors in saccade direction (as a function of eye position components orthogonal to RE), predicting errors in final gaze direction of up to 25° in the oculomotor range. Plant modifications could not solve these problems, because the intrisic oculomotor input-output geometry forced a fixed visuomotor mapping to choose between either accuracy or Listing's law. This was reflected internally by a sensorimotor divergence between input-defined visual displacement signals (inherently 2-D and defined in reference to the eye) and output-defined motor displacement signals (inherently 3-D and defined in reference to the head). These problems were solved by rotating RE by estimated 3-D eye position (i.e., a reference frame transformation), inputting the result into a 2-D–to–3-D “Listing's law operator,” and then finally subtracting initial 3-D eye position to yield the correct ME. This model was accurate and upheld Listing's law from all initial positions. Moreover, it suggested specific experiments to invasively distinguish visual and motor displacement codes, predicting a systematic position dependence in the directional tuning of RE versus a fixed-vector tuning in ME. We conclude that visual and motor displacement spaces are geometrically distinct such that a fixed visual-motor mapping will produce systematic and measurable behavioral errors. To avoid these errors, the brain would need to implement both a 3-D position-dependent reference frame transformation and nontrivial 2-D–to–3-D transformation. Furthermore, our simulations provide new experimental paradigms to invasively identify the physiological progression of these spatial transformations by reexamining the position-dependent geometry of displacement code directions in the superior colliculus, cerebellum, and various cortical visuomotor areas.

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.

Axes of eye rotation and Listing's law during rotations of the head

1991 ◽  
Vol 65 (3) ◽  
pp. 407-423 ◽  
Author(s):  
J. D. Crawford ◽  
T. Vilis
Keyword(s):  
Head Rotation ◽  
Three Dimensions ◽  
Eye Position ◽  
Gaze Stabilization ◽  
Listing's Law ◽  
Listing's Plane ◽  
Listing’S Law ◽  
Eye Rotation ◽  
Indirect Path ◽  
Listing’S Plane

1. The vestibuloocular reflex (VOR) was examined in four alert monkeys during rotations of the head about torsional, vertical, horizontal, and intermediate axes. Eye positions and axes were recorded in three dimensions (3-D). Visual targets were used to optimize gaze stabilization. 2. Axes of eye rotation during slow phases showed small but systematic deviations from collinearity with the axes of head rotation. These noncollinearities apparently resulted from vector summation of torsional, vertical, and horizontal VOR components with different gains. 3. VOR gain was lowest about a head-fixed torsional axis that was correlated with the primary gaze direction, as determined by Listing's law for saccades. As a result, rotation of the head about a partially torsional axis produced noncollinear slow phases, with axes that tilted toward Listing's plane. 4. During slow phases, eye position changed not only in the direction of rotation, but also systematically in other directions. Even axes of eye rotation within Listing's plane caused eye position to move out of the plane to a torsional position that was then held. Thus Listing's law for saccades cannot be a product of plant mechanics. 5. VOR slow phases were simulated with the use of a model that incorporated 3-D rotational kinematics into the indirect path and the oculomotor plant. This demonstrated that the observed pattern of position changes is the expected consequence of rotating the eye about a fixed axis and that to hold these positions the indirect path must employ a 3-D velocity-to-position transformation. 6. Quick phases not only corrected the violations of Listing's law produced by slow phases but anticipated them by directing the eye toward a plane rotated in the direction of head rotation. This was modeled by inputting the vestibular signal to a Listing's law operator that is shared by the quick phase and saccadic systems.

Three-Dimensional Kinematics of Ocular Drift in Humans With Cerebellar Atrophy

2000 ◽  
Vol 83 (3) ◽  
pp. 1125-1140 ◽  
Author(s):  
D. Straumann ◽  
D. S. Zee ◽  
D. Solomon
Keyword(s):  
Vertical Velocity ◽  
Three Dimensional ◽  
Cerebellar Atrophy ◽  
Eye Position ◽  
Downbeat Nystagmus ◽  
Ocular Motor ◽  
Listing's Law ◽  
Listing’S Law ◽  
Horizontal Gaze ◽  
Velocity Bias

One of the signs of the cerebellar ocular motor syndrome is the inability to maintain horizontal and vertical fixation. Typically, in the presence of cerebellar atrophy, the eyes show horizontal gaze-evoked and vertical downbeat nystagmus. We investigated whether or not the cerebellar ocular motor syndrome also includes a torsional drift and, specifically, if it is independent from the drift in the horizontal-vertical plane. The existence of such a torsional drift would suggest that the cerebellum is critically involved in maintaining the eyes in Listing's plane. Eighteen patients with cerebellar atrophy (diagnosis confirmed by magnetic resonance imaging) were tested and compared with a group of normal subjects. Three-dimensional eye movements (horizontal, vertical, and torsional) during attempted fixations of targets at different horizontal and vertical eccentricities were recorded by dual search coils in a three-field magnetic frame. The overall ocular drift was composed of an upward drift that increased during lateral gaze, a horizontal centripetal drift that appeared during lateral gaze, and a torsional drift that depended on horizontal eye position. The vertical drift consisted of two subcomponents: a vertical gaze-evoked drift and a constant vertical velocity bias. The increase of upward drift velocity with eccentric horizontal gaze was caused by an increase of the vertical velocity bias; this component did not comply with Listing's law. The horizontal-eye-position–dependent torsional drift was intorsional in abduction and extorsional in adduction, which led to an additional violation of Listing's law. The existence of torsional drift that is eye-position–dependent suggests that the cerebellum is critically involved in the implementation of Listing's law, perhaps by mapping a tonic torsional signal that depends on the direction of the line of sight. The magnitude of this signal might reflect the difference in torsional eye position between the torsional resting position determined by the mechanics of the eye plant and the torsional position required by Listing's law.

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