Are corresponding points fixed?

Topical Review: Methodological Variables in Clinical and Laboratory Measurements of Fixation Disparity

SIGNIFICANCE

Fixation disparity is a small vergence error that does not disrupt fusion. Fixation disparity measures correlate with binocular symptoms. This article covers methodological differences between clinical fixation disparity measurement devices, findings when objective and subjective fixation disparities are compared, and the potential impact of binocular capture on fixation disparity measurements. Fixation disparity is a small vergence error that occurs in nonstrabismic individuals and does not disrupt fusion. This article reviews clinical fixation disparity variables and their clinical diagnostic value. Clinical devices that are used to measure these variables are described, as are studies in which the output from these devices has been compared. Methodological differences between the devices such as the location of the fusional stimulus, the rate at which judgments of dichoptic alignment are made, and the strength of the accommodative stimulus are all considered. In addition, the article covers theories of the neural origins of fixation disparity and control system models incorporating fixation disparity. Studies in which objective fixation disparities (oculomotor portion of fixation disparity assessed with an eye tracker) and subjective fixation disparities (sensory portion of fixation disparity assessed psychophysically with dichoptic Nonius lines) have been compared are also examined, and consideration is given to why some investigators find differences in these measures, whereas other investigators do not. The conclusion thus far is that there are likely complex interactions between vergence adaptation, accommodation, and the location of the fusional stimulus that lead to differences in objective and subjective fixation disparity measures. Finally, capture of the visual direction of monocular stimuli by adjacent fusional stimuli and the implications for fixation disparity measures are considered.

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.

Radial and Tangential Retinal Magnifications as Functions of Visual Field Angle Across Spherical, Oblate, and Prolate Retinal Profiles

Purpose

To provide a tool for calculating radial and tangential retinal magnifications as functions of field angle and retinal shape and to articulate patterns of magnification across the retina for monocular and binocular combinations of prolate-, oblate-, and spherical-shaped retinas.

Methods

Formulae were derived to calculate radial and tangential retinal magnifications (mm/deg) from field angle (degrees), retinal asphericity (unitless conic constant), retinal vertex radius of curvature (mm), and nodal point position (mm). Monocular retinal magnifications were determined for eyes with prolate, spherical, and oblate retinas as functions of field angle. Bilateral differences in magnifications were examined for combinations of those eyes.

Results

Retinal shape substantially affects magnification profiles even for eyes with the same axial length. Greatest magnification changes across a retina and between eyes, as well as greatest increase in radial-tangential differences (distortion), occur with prolate retinas. Binocular magnification differences were smallest for oblate retinas. Nodal points anterior to the vertex center of curvature and oblate asphericity both cause field-dependent reductions in magnification relative to the fovea (barrel distortion), whereas nodal points posterior to vertex center of curvature and prolate asphericity cause the opposite (pincushion distortion). Retinal magnification differences due to eye shape are much greater than aniseikonia thresholds and chromatic differences in magnification. A spreadsheet tool implements the magnification calculations.

Conclusions

Local retinal magnifications as functions of field angle have substantial effects on objective applications (imaging retinal anatomy) and subjective experiences (aniseikonia) and quantify an ocular property that differs across eye shapes and refractive errors.

Translational Relevance

Methods are provided to customize the calculation of radial and tangential magnifications across the retina for individual eyes, which will bolster the multifactorial study of the effects of foveal and peripheral optics across eye shapes and refractive errors.

Recent understanding of binocular vision in the natural environment with clinical implications

Technological advances in recent decades have allowed us to measure both the information available to the visual system in the natural environment and the rich array of behaviors that the visual system supports. This review highlights the tasks undertaken by the binocular visual system in particular and how, for much of human activity, these tasks differ from those considered when an observer fixates a static target on the midline. The everyday motor and perceptual challenges involved in generating a stable, useful binocular percept of the environment are discussed, together with how these challenges are but minimally addressed by much of current clinical interpretation of binocular function. The implications for new technology, such as virtual reality, are also highlighted in terms of clinical and basic research application.

Human gaze is systematically offset from the center of cone topography

The small physical depression of the human retina, the fovea, is the retinal locus of prime visual resolution, achieved by a peaking topography of the light-sensitive cone photoreceptor outer segments^1-3 and a post-receptor wiring scheme preserving high-density sampling.^4,5 Humans dynamically direct their gaze such that the retinal images of objects of interest fall onto the foveola, the central one-degree diameter of the fovea,^6-8 but it is yet unclear whether a relationship between the individual photoreceptor topography at this location and visual fixation behavior exists.^9,10 By employing adaptive optics in vivo imaging and micro-stimulation,^11-13 we created topographical maps of the complete foveolar cone mosaics in both eyes of 20 healthy participants while simultaneously recording the retinal location of a fixated visual object in a psychophysical experiment with cellular resolution. We found that the locus of fixation was systematically shifted away from the topographical center toward a naso-superior quadrant on the retina, about 5 min of arc of visual angle on average, with a mirror symmetrical trend between fellow eyes. In cyclopean view, the topographical centers were superior to the fixated target, corresponding to areas in the visual field usually more distant^14,15 and thus containing higher spatial frequencies. Given the large variability in foveal topography between individuals, and the surprising precision with which fixation is repeatedly directed to just a small bouquet of cones in the foveola, these findings demonstrate a finely tuned, functionally relevant link between the development of the cellular mosaic of photoreceptors and visual behavior.

The blur horopter: Retinal conjugate surface in binocular viewing

From measurements of wavefront aberrations in 16 emmetropic eyes, we calculated where objects in the world create best-focused images across the central 27∘ (diameter) of the retina. This is the retinal conjugate surface. We calculated how the surface changes as the eye accommodates from near to far and found that it mostly maintains its shape. The conjugate surface is pitched top-back, meaning that the upper visual field is relatively hyperopic compared to the lower field. We extended the measurements of best image quality into the binocular domain by considering how the retinal conjugate surfaces for the two eyes overlap in binocular viewing. We call this binocular extension the blur horopter. We show that in combining the two images with possibly different sharpness, the visual system creates a larger depth of field of apparently sharp images than occurs with monocular viewing. We examined similarities between the blur horopter and its analog in binocular vision: the binocular horopter. We compared these horopters to the statistics of the natural visual environment. The binocular horopter and scene statistics are strikingly similar. The blur horopter and natural statistics are qualitatively, but not quantitatively, similar. Finally, we used the measurements to refine what is commonly referred to as the zone of clear single binocular vision.

The saccade main sequence revised: A fast and repeatable tool for oculomotor analysis

Saccades are rapid ballistic eye movements that humans make to direct the fovea to an object of interest. Their kinematics is well defined, showing regular relationships between amplitude, duration, and velocity: the saccadic 'main sequence'. Deviations of eye movements from the main sequence can be used as markers of specific neurological disorders. Despite its significance, there is no general methodological consensus for reliable and repeatable measurements of the main sequence. In this work, we propose a novel approach for standard indicators of oculomotor performance. The obtained measurements are characterized by high repeatability, allowing for fine assessments of inter- and intra-subject variability, and inter-ocular differences. The designed experimental procedure is natural and non-fatiguing, thus it is well suited for fragile or non-collaborative subjects like neurological patients and infants. The method has been released as a software toolbox for public use. This framework lays the foundation for a normative dataset of healthy oculomotor performance for the assessment of oculomotor dysfunctions.

A Geometric Theory Integrating Human Binocular Vision With Eye Movement

A theory of the binocular system with asymmetric eyes (AEs) is developed in the framework of bicentric perspective projections. The AE accounts for the eyeball's global asymmetry produced by the foveal displacement from the posterior pole, the main source of the eye's optical aberrations, and the crystalline lens' tilt countering some of these aberrations. In this theory, the horopter curves, which specify retinal correspondence of binocular single vision, are conic sections resembling empirical horopters. This advances the classic model of empirical horopters as conic sections introduced in an ad hoc way by Ogle in 1932. In contrast to Ogle's theory, here, anatomically supported horopteric conics vary with the AEs' position in the visual plane of bifoveal fixations and their transformations are visualized in a computer simulation. Integrating horopteric conics with eye movements can help design algorithms for maintaining a stable perceptual world from visual information captured by a mobile robot's camera head. Further, this paper proposes a neurophysiologically meaningful definition for the eyes' primary position, a concept which has remained elusive despite its theoretical importance to oculomotor research. Finally, because the horopteric conic's shape is dependent on the AE's parameters, this theory allows for changes in retinal correspondence, which is usually considered preformed and stable.

The Effect of Age on Binocular Vision Normative Values

PURPOSE

To establish a relationship between age and horizontal heterophoria, horizontal fusional vergence amplitudes, and vergence facility testing.

METHODS

The sample consisted of 112 patients with a mean age of 39.8 ± 14.97 years (range: 18 to 65 years) and was composed of 61 women (54.5%) and 51 men (45.5%). The non-presbyopic group included patients 18 to 39 years old (n = 49) and the presbyopic group included patients 41 to 65 years old (n = 63). Binocular vision was studied by heterophoria horizontal magnitude (prism diopters [PD]), horizontal fusional vergences amplitudes (PD), and vergence facility testing (cycles per minute [cpm]) and quantified with a combination of 3 PD base-in and 12 PD base-out prisms.

RESULTS

Significant differences were obtained in near heterophoria with compensation (exophoria increased by 3.74 PD, t = 2.12, P < .05), distance positive fusional vergence (PFV) recovery (decreased by 2.86 PD, t = 3.03, P < .01), near PFV blur (decreased by 3.13 PD, t = 1.98, P = .05), near PFV break (decreased by 4.45 PD, t = 2.75, P < .01), near PFV recovery (decreased by 4.69 PD, t = 3.30, P < .01), and vergence facility testing (decreased by 2.63 PD, t = 2.77, P < .01).

CONCLUSIONS

The results indicated an increase of exophoria, a decrease in near positive horizontal fusional vergences, and vergence facility was dependent on age; thus, the authors suggest that changes in the normal values should be considered for each age range. [J Pediatr Ophthalmol Strabismus. 2020;57(6):363-371.].

Binocular Eye Movements Are Adapted to the Natural Environment

Humans and many animals make frequent saccades requiring coordinated movements of the eyes. When landing on the new fixation point, the eyes must converge accurately or double images will be perceived. We asked whether the visual system uses statistical regularities in the natural environment to aid eye alignment at the end of saccades. We measured the distribution of naturally occurring disparities in different parts of the visual field. The central tendency of the distributions was crossed (nearer than fixation) in the lower field and uncrossed (farther) in the upper field in male and female participants. It was uncrossed in the left and right fields. We also measured horizontal vergence after completion of vertical, horizontal, and oblique saccades. When the eyes first landed near the eccentric target, vergence was quite consistent with the natural-disparity distribution. For example, when making an upward saccade, the eyes diverged to be aligned with the most probable uncrossed disparity in that part of the visual field. Likewise, when making a downward saccade, the eyes converged to enable alignment with crossed disparity in that part of the field. Our results show that rapid binocular eye movements are adapted to the statistics of the 3D environment, minimizing the need for large corrective vergence movements at the end of saccades. The results are relevant to the debate about whether eye movements are derived from separate saccadic and vergence neural commands that control both eyes or from separate monocular commands that control the eyes independently.SIGNIFICANCE STATEMENT We show that the human visual system incorporates statistical regularities in the visual environment to enable efficient binocular eye movements. We define the oculomotor horopter: the surface of 3D positions to which the eyes initially move when stimulated by eccentric targets. The observed movements maximize the probability of accurate fixation as the eyes move from one position to another. This is the first study to show quantitatively that binocular eye movements conform to 3D scene statistics, thereby enabling efficient processing. The results provide greater insight into the neural mechanisms underlying the planning and execution of saccadic eye movements.

The Active Side of Stereopsis: Fixation Strategy and Adaptation to Natural Environments

Depth perception in near viewing strongly relies on the interpretation of binocular retinal disparity to obtain stereopsis. Statistical regularities of retinal disparities have been claimed to greatly impact on the neural mechanisms that underlie binocular vision, both to facilitate perceptual decisions and to reduce computational load. In this paper, we designed a novel and unconventional approach in order to assess the role of fixation strategy in conditioning the statistics of retinal disparity. We integrated accurate realistic three-dimensional models of natural scenes with binocular eye movement recording, to obtain accurate ground-truth statistics of retinal disparity experienced by a subject in near viewing. Our results evidence how the organization of human binocular visual system is finely adapted to the disparity statistics characterizing actual fixations, thus revealing a novel role of the active fixation strategy over the binocular visual functionality. This suggests an ecological explanation for the intrinsic preference of stereopsis for a close central object surrounded by a far background, as an early binocular aspect of the figure-ground segregation process.

On binocular vision: The geometric horopter and Cyclopean eye

We study geometric properties of horopters defined by the criterion of equality of angle. Our primary goal is to derive the precise geometry for anatomically correct horopters. When eyes fixate on points along a curve in the horizontal visual plane for which the vergence remains constant, this curve is the larger arc of a circle connecting the eyes' rotation centers. This isovergence circle is known as the Vieth-Müller circle. We show that, along the isovergence circular arc, there is an infinite family of horizontal horopters formed by circular arcs connecting the nodal points. These horopters intersect at the point of symmetric convergence. We prove that the family of 3D geometric horopters consists of two perpendicular components. The first component consists of the horizontal horopters parametrized by vergence, the point of the isovergence circle, and the choice of the nodal point location. The second component is formed by straight lines parametrized by vergence. Each of these straight lines is perpendicular to the visual plane and passes through the point of symmetric convergence. Finally, we evaluate the difference between the geometric horopter and the Vieth-Müller circle for typical near fixation distances and discuss its possible significance for depth discrimination and other related functions of vision that make use of disparity processing.

Stereopsis is adaptive for the natural environment

Humans and many animals have forward-facing eyes providing different views of the environment. Precise depth estimates can be derived from the resulting binocular disparities, but determining which parts of the two retinal images correspond to one another is computationally challenging. To aid the computation, the visual system focuses the search on a small range of disparities. We asked whether the disparities encountered in the natural environment match that range. We did this by simultaneously measuring binocular eye position and three-dimensional scene geometry during natural tasks. The natural distribution of disparities is indeed matched to the smaller range of correspondence search. Furthermore, the distribution explains the perception of some ambiguous stereograms. Finally, disparity preferences of macaque cortical neurons are consistent with the natural distribution.

The rate of change of vergence-accommodation conflict affects visual discomfort

Stereoscopic (S3D) displays create conflicts between the distance to which the eyes must converge and the distance to which the eyes must accommodate. Such conflicts require the viewer to overcome the normal coupling between vergence and accommodation, and this effort appears to cause viewer discomfort. Vergence-accommodation coupling is driven by the phasic components of the underlying control systems, and those components respond to relatively fast changes in vergence and accommodative stimuli. Given the relationship between phasic changes and vergence-accommodation coupling, we examined how the rate of change in the vergence-accommodation conflict affects viewer discomfort. We used a stereoscopic display that allows independent manipulation of the stimuli to vergence and accommodation. We presented stimuli that simulate natural viewing (i.e., vergence and accommodative stimuli changed together) and stimuli that simulate S3D viewing (i.e., vergence stimulus changes but accommodative stimulus remains fixed). The changes occurred at 0.01, 0.05, or 0.25 Hz. The lowest rate is too slow to stimulate the phasic components while the highest rate is well within the phasic range. The results were consistent with our expectation: somewhat greater discomfort was experienced when stimulus distance changed rapidly, particularly in S3D viewing when the vergence stimulus changed but the accommodative stimulus did not. These results may help in the generation of guidelines for the creation and viewing of stereo content with acceptable viewer comfort.

Perception via the deviated eye in strabismus

Misalignment of the eyes can lead to double vision and visual confusion. However, these sensations are rare when strabismus is acquired early in life, because the extra image is suppressed. To explore the mechanism of perceptual suppression in strabismus, the visual fields were mapped binocularly in 14 human subjects with exotropia. Subjects wore red/blue filter glasses to permit dichoptic stimulation while fixating a central target on a tangent screen. A purple stimulus was flashed at a peripheral location; its reported color ("red" or "blue") revealed which eye's image was perceived at that locus. The maps showed a vertical border between the center of gaze for each eye, splitting the visual field into two separate regions. In each region, perception was mediated by only one eye, with suppression of the other eye. Unexpectedly, stimuli falling on the fovea of the deviated eye were seen in all subjects. However, they were perceived in a location shifted by the angle of ocular deviation. This plasticity in the coding of visual direction allows accurate localization of objects everywhere in the visual scene, despite the presence of strabismus.

Visual depth from motion parallax and eye pursuit

A translating observer viewing a rigid environment experiences "motion parallax", the relative movement upon the observer's retina of variously positioned objects in the scene. This retinal movement of images provides a cue to the relative depth of objects in the environment, however retinal motion alone cannot mathematically determine relative depth of the objects. Visual perception of depth from lateral observer translation uses both retinal image motion and eye movement. In Nawrot and Stroyan (Vision Res 49:1969-1978, 2009) we showed mathematically that the ratio of the rate of retinal motion over the rate of smooth eye pursuit mathematically determines depth relative to the fixation point in central vision. We also reported on psychophysical experiments indicating that this ratio is the important quantity for perception. Here we analyze the motion/pursuit cue for the more general, and more complicated, case when objects are distributed across the horizontal viewing plane beyond central vision. We show how the mathematical motion/pursuit cue varies with different points across the plane and with time as an observer translates. If the time varying retinal motion and smooth eye pursuit are the only signals used for this visual process, it is important to know what is mathematically possible to derive about depth and structure. Our analysis shows that the motion/pursuit ratio determines an excellent description of depth and structure in these broader stimulus conditions, provides a detailed quantitative hypothesis of these visual processes for the perception of depth and structure from motion parallax, and provides a computational foundation to analyze the dynamic geometry of future experiments.

The zone of comfort: Predicting visual discomfort with stereo displays

Recent increased usage of stereo displays has been accompanied by public concern about potential adverse effects associated with prolonged viewing of stereo imagery. There are numerous potential sources of adverse effects, but we focused on how vergence-accommodation conflicts in stereo displays affect visual discomfort and fatigue. In one experiment, we examined the effect of viewing distance on discomfort and fatigue. We found that conflicts of a given dioptric value were slightly less comfortable at far than at near distance. In a second experiment, we examined the effect of the sign of the vergence-accommodation conflict on discomfort and fatigue. We found that negative conflicts (stereo content behind the screen) are less comfortable at far distances and that positive conflicts (content in front of screen) are less comfortable at near distances. In a third experiment, we measured phoria and the zone of clear single binocular vision, which are clinical measurements commonly associated with correcting refractive error. Those measurements predicted susceptibility to discomfort in the first two experiments. We discuss the relevance of these findings for a wide variety of situations including the viewing of mobile devices, desktop displays, television, and cinema.

Pascal's ring, cardinal points, and refractive compensation

Pascal's ring is a hexagon each of whose corners represents one of the six cardinal points of an optical system and whose sides represent relationships of relative axial position of the cardinal points. Changes to the ring represent the axial displacements of the cardinal points of the visual optical system of an eye that are caused when a spectacle lens compensates for the ametropia. Pascal's schema was described some 70 years ago with little theoretical justification. The purpose of this paper is to derive expressions for the axial locations of the cardinal points of a compound system consisting of an optical instrument and a visual optical system and for the shift caused by the instrument, and to provide theoretical justification for Pascal's schema. The cardinal points are treated not as separate entities but in a unified manner as special cases of an infinite class of special points. Expressions are derived using Gaussian optics. The results are specialized for the case of the eye's ametropia compensated by optical instruments in general and by spectacle lenses in particular. Pascal's schema is shown to be broadly correct although some modification is necessary for the effects on the incident cardinal points especially for the myopic eye.

Depth-cue integration in grasp programming: no evidence for a binocular specialism

When we grasp with one eye covered, the finger and thumb are typically opened wider than for binocularly guided grasps, as if to build a margin-for-error into the movement. Also, patients with visual form agnosia can have profound deficits in their (otherwise relatively normal) grasping when binocular information is removed. One interpretation of these findings is that there is a functional specialism for binocular vision in the control of grasping. Alternatively, cue-integration theory suggests that binocular and monocular depth cues are combined in the control of grasping, and so impaired performance reflects not the loss of 'critical' binocular cues, but increased uncertainty per se. Unfortunately, removing binocular information confounds removing particular (binocular) depth cues with an overall reduction in the available information, and so such experiments cannot distinguish between these alternatives. We measured the effects on visually open-loop grasping of selectively removing monocular (texture) or binocular depth cues. To allow meaningful comparisons, we made psychophysical measurements of the uncertainty in size estimates in each case, so that the informativeness of binocular and monocular cues was known in each condition. Consistent with cue-integration theory, removing either binocular or monocular cues resulted in similar increases in grip apertures. In a separate experiment, we also confirmed that changes in uncertainty per se (keeping the same depth cues available) resulted in larger grip apertures. Overall, changes in the margin-for-error in grasping movements were determined by the uncertainty in size estimates and not by the presence or absence of particular depth cues. Our data therefore argue against a binocular specialism for grasp programming. Instead, grip apertures were smaller when binocular and monocular cues were available than with either cue alone, providing strong evidence that the visuo-motor system exploits the redundancy available in multiple sources of information, and integrates binocular and monocular cues to improve grasping performance.

Nodes and nodal points and lines in eyes and other optical systems

The typical stigmatic optical system has two nodal points: an incident nodal point and an emergent nodal point. A ray through the incident nodal point emerges from the system through the emergent nodal point with its direction unchanged. In the presence of astigmatism nodal points are not possible in most cases. Instead there are structures, called nodes in this paper, of which nodal points are special cases. Because of astigmatism most eyes do not have nodal points a fact with obvious implications for concepts, such as the visual axis, which are based on nodal points. In order to gain insight into the issues this paper develops a general theory of nodes which holds for optical systems in general, including eyes, and makes particular allowance for astigmatism and relative decentration of refracting elements in the system. Key concepts are the incident and emergent nodal characteristics of the optical system. They are represented by 2 x 2 matrices whose eigenstructures define the nature and longitudinal position of the nodes. If a system's nodal characteristic is a scalar matrix then the node is a nodal point. Otherwise there are several possibilities: Firstly, a node may take the form of a single nodal line. Second, a node may consist of two separated nodal lines reminiscent of the familiar interval of Sturm although the nodal lines are not necessarily orthogonal. Third, a node may have no obvious nodal line or point. In the second and third of these classes one can define mid-nodal ellipses. Astigmatic systems exist with nodal points and stigmatic systems exist with no nodal points. The nodal centre may serve as an approximation for a nodal point if the node is not a point. Examples in the Appendix, including a model eye, illustrate the several possibilities.

Probabilistic combination of slant information: weighted averaging and robustness as optimal percepts

Depth perception involves combining multiple, possibly conflicting, sensory measurements to estimate the 3D structure of the viewed scene. Previous work has shown that the perceptual system combines measurements using a statistically optimal weighted average. However, the system should only combine measurements when they come from the same source. We asked whether the brain avoids combining measurements when they differ from one another: that is, whether the system is robust to outliers. To do this, we investigated how two slant cues-binocular disparity and texture gradients-influence perceived slant as a function of the size of the conflict between the cues. When the conflict was small, we observed weighted averaging. When the conflict was large, we observed robust behavior: perceived slant was dictated solely by one cue, the other being rejected. Interestingly, the rejected cue was either disparity or texture, and was not necessarily the more variable cue. We modeled the data in a probabilistic framework, and showed that weighted averaging and robustness are predicted if the underlying likelihoods have heavier tails than Gaussians. We also asked whether observers had conscious access to the single-cue estimates when they exhibited robustness and found they did not, i.e. they completely fused despite the robust percepts.

Image-size differences worsen stereopsis independent of eye position

With the eyes in forward gaze, stereo performance worsens when one eye's image is larger than the other's. Near, eccentric objects naturally create retinal images of different sizes. Does this mean that stereopsis exhibits deficits for such stimuli? Or does the visual system compensate for the predictable image-size differences? To answer this, we measured discrimination of a disparity-defined shape for different relative image sizes. We did so for different gaze directions, some compatible with the image-size difference and some not. Magnifications of 10-15% caused a clear worsening of stereo performance. The worsening was determined only by relative image size and not by eye position. This shows that no neural compensation for image-size differences accompanies eye-position changes, at least prior to disparity estimation. We also found that a local cross-correlation model for disparity estimation performs like humans in the same task, suggesting that the decrease in stereo performance due to image-size differences is a byproduct of the disparity-estimation method. Finally, we looked for compensation in an observer who has constantly different image sizes due to differing eye lengths. She performed best when the presented images were roughly the same size, indicating that she has compensated for the persistent image-size difference.

Limits of stereopsis explained by local cross-correlation

Human stereopsis has two well-known constraints: the disparity-gradient limit, which is the inability to perceive depth when the change in disparity within a region is too large, and the limit of stereoresolution, which is the inability to perceive spatial variations in disparity that occur at too fine a spatial scale. We propose that both limitations can be understood as byproducts of estimating disparity by cross-correlating the two eyes' images, the fundamental computation underlying the disparity-energy model. To test this proposal, we constructed a local cross-correlation model with biologically motivated properties. We then compared model and human behaviors in the same psychophysical tasks. The model and humans behaved quite similarly: they both exhibited a disparity-gradient limit and had similar stereoresolution thresholds. Performance was affected similarly by changes in a variety of stimulus parameters. By modeling the effects of stimulus blur and of using different sizes of image patches, we found evidence that the smallest neural mechanism humans use to estimate disparity is 3-6 arcmin in diameter. We conclude that the disparity-gradient limit and stereoresolution are indeed byproducts of using local cross-correlation to estimate disparity.

Vergence-accommodation conflicts hinder visual performance and cause visual fatigue

Three-dimensional (3D) displays have become important for many applications including vision research, operation of remote devices, medical imaging, surgical training, scientific visualization, virtual prototyping, and more. In many of these applications, it is important for the graphic image to create a faithful impression of the 3D structure of the portrayed object or scene. Unfortunately, 3D displays often yield distortions in perceived 3D structure compared with the percepts of the real scenes the displays depict. A likely cause of such distortions is the fact that computer displays present images on one surface. Thus, focus cues-accommodation and blur in the retinal image-specify the depth of the display rather than the depths in the depicted scene. Additionally, the uncoupling of vergence and accommodation required by 3D displays frequently reduces one's ability to fuse the binocular stimulus and causes discomfort and fatigue for the viewer. We have developed a novel 3D display that presents focus cues that are correct or nearly correct for the depicted scene. We used this display to evaluate the influence of focus cues on perceptual distortions, fusion failures, and fatigue. We show that when focus cues are correct or nearly correct, (1) the time required to identify a stereoscopic stimulus is reduced, (2) stereoacuity in a time-limited task is increased, (3) distortions in perceived depth are reduced, and (4) viewer fatigue and discomfort are reduced. We discuss the implications of this work for vision research and the design and use of displays.

Focus cues affect perceived depth

Depth information from focus cues--accommodation and the gradient of retinal blur--is typically incorrect in three-dimensional (3-D) displays because the light comes from a planar display surface. If the visual system incorporates information from focus cues into its calculation of 3-D scene parameters, this could cause distortions in perceived depth even when the 2-D retinal images are geometrically correct. In Experiment 1 we measured the direct contribution of focus cues to perceived slant by varying independently the physical slant of the display surface and the slant of a simulated surface specified by binocular disparity (binocular viewing) or perspective/texture (monocular viewing). In the binocular condition, slant estimates were unaffected by display slant. In the monocular condition, display slant had a systematic effect on slant estimates. Estimates were consistent with a weighted average of slant from focus cues and slant from disparity/texture, where the cue weights are determined by the reliability of each cue. In Experiment 2, we examined whether focus cues also have an indirect effect on perceived slant via the distance estimate used in disparity scaling. We varied independently the simulated distance and the focal distance to a disparity-defined 3-D stimulus. Perceived slant was systematically affected by changes in focal distance. Accordingly, depth constancy (with respect to simulated distance) was significantly reduced when focal distance was held constant compared to when it varied appropriately with the simulated distance to the stimulus. The results of both experiments show that focus cues can contribute to estimates of 3-D scene parameters. Inappropriate focus cues in typical 3-D displays may therefore contribute to distortions in perceived space.

Why pictures look right when viewed from the wrong place

A picture viewed from its center of projection generates the same retinal image as the original scene, so the viewer perceives the scene correctly. When a picture is viewed from other locations, the retinal image specifies a different scene, but we normally do not notice the changes. We investigated the mechanism underlying this perceptual invariance by studying the perceived shapes of pictured objects viewed from various locations. We also manipulated information about the orientation of the picture surface. When binocular information for surface orientation was available, perceived shape was nearly invariant across a wide range of viewing angles. By varying the projection angle and the position of a stimulus in the picture, we found that invariance is achieved through an estimate of local surface orientation, not from geometric information in the picture. We present a model that explains invariance and other phenomena (such as perceived distortions in wide-angle pictures).

Relative image size, not eye position, determines eye dominance switches

A recent paper examined eye dominance with the eyes in forward and eccentric gaze [Vision Res. 41 (2001) 1743]. When observers were looking to the left, the left eye tended to dominate and when they were looking to the right, the right eye tended to dominate. The authors attributed the switch in eye dominance to extra-retinal signals associated with horizontal eye position. However, when one looks at a near object on the left, the image in the left eye is larger than the one in the right eye, and when one looks to the right, the opposite occurs. Thus, relative image size could also trigger switches in eye dominance. We used a cue-conflict paradigm to determine whether eye position or relative image size is the determinant of eye-dominance switches with changes in gaze angle. When eye position and relative image size were varied independently, there was no consistent effect of eye position. Relative image size appears to be the sole determinant of the switch.

The influence of cyclovergence on unconstrained stereoscopic matching

In order to perceive depth from binocular disparities the visual system has to identify matching features of the two retinal images. Normally, the assigned disparity is unambiguously determined by monocularly visible matching constraints. The assigned disparity is ambiguous when matching is unconstrained, such as when we view an isolated long oblique disparate line. Recently we found that in order to perceive a depth probe at the same depth as the oblique line, the probe needs to have the same horizontal disparity as the line (i.e. matching occurs along horizontal "search-zones" [Vis. Res. 40 (2000) 151]). Here we examined whether the depth probe disparity in unconstrained matching of long lines is influenced by cyclovergence, by cyclorotation between stereogram half-images, or by combinations of the two. We measured retinal rotation (>6 deg in cyclovergence conditions). We found that in those conditions in which the retinal images were the same (a condition with, say, both zero cyclovergence and zero cyclorotation between the half-images, creates the same retinal images as a condition with both 6 deg cyclovergence and 6 deg cyclorotation) assigned depth was the same too, i.e. independent of cyclovergence. Thus, the assigned depth of the test-line seems to be determined solely by the retinal test-line orientation, implying that the binocular matching algorithm does not seem to incorporate the eyes' cyclovergence when matching is unconstrained.