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PubMed1994

Toward a general theory of stereopsis: binocular matching, occluding contours, and fusion.

Models of stereopsis have focused on developing strategies for identifying common features in the 2 half-images so that disparity may be computed. This emphasis ignores the unpairable features that arise at occluding contours (half-occlusions). Most models treat half-occlusions as noise or outliers that are interpreted after disparity processing is completed. A series of experiments reveal that occlusion relationships are sensed during the earliest stages of binocular processing. The authors hypothesize the existence of receptive field structures that sense the local structure of stereoscopic occlusion relationships to account for these findings. Finally, a simple theoretical framework is presented in which fusion, stereopsis, and occlusion are unified. This theory explains the co-occurrence of stereopsis and diplopia and how half-occlusions escape the suppression characteristic of binocular rivalry.

Contrast Sensitivity↗
PubMed2004

Stereomotion speed perception: contributions from both changing disparity and interocular velocity difference over a range of relative disparities.

The role of two binocular cues to motion in depth-changing disparity (CD) and interocular velocity difference (IOVD)- was investigated by measuring stereomotion speed discrimination and static disparity discrimination performance (stereoacuity). Speed discrimination thresholds were assessed both for random dot stereograms (RDS), and for their temporally uncorrelated equivalents, dynamic random dot stereograms (DRDS), at relative disparity pedestals of -19, 0, and +19 arcmin. While RDS stimuli contain both CD and IOVD cues, DRDS stimuli carry only CD information. On average, thresholds were a factor of 1.7 higher for DRDS than for RDS stimuli with no clear effect of relative disparity pedestal. Results were similar for approaching and receding targets. Variations in stimulus duration had no significant effect on thresholds, and there was no observed correlation between stimulus displacement and perceived speed, confirming that subjects responded to stimulus speed in each condition. Stereoacuity was equally good for our RDS and DRDS stimuli, showing that the difference in stereomotion speed discrimination performance for these stimuli was not due to any difference in the precision of the disparity cue. In addition, when we altered stereomotion stimulus trajectory by independently manipulating the speeds and directions of its monocular half-images, perceived stereomotion speed remained accurate. This finding is inconsistent with response strategies based on properties of either monocular half-image motion, or any ad hoc combination of the monocular speeds. We conclude that although subjects are able to discriminate stereomotion speed reliably on the basis of CD information alone, IOVD provides a precise additional cue to stereomotion speed perception.

Depth Perception↗
PubMed2002

[Do prisms according to Hans-Joachim Haase improve stereoacuity?].

BACKGROUND: The "Measuring and Correcting Methodology" after H.-J. Haase (MKH) aims at converting "fixation disparity" into bicentral fixation, using prismatic spectacles. In the context of the MKH, fixation disparity is diagnosed by a series of subjective tests. According to H.-J. Haase, a long-standing fixation disparity can lead to "disparate correspondence" between the central areas of both retinae, which consolidates the fixation disparity and gradually converts a "young" into an "old fixation disparity". In "old fixation disparity" it is thought that bicentral fixation does not occur anymore, so that stereoacuity is impaired. However, prismatic spectacles can, according to H.-J. Haase, restitute bicentral fixation and consequently improve stereoacuity, even in some cases of "old fixation disparity". METHODS: Ten non-strabismic subjects with a visual acuity of >/= 1.0 in both eyes were examined. It turned out that all ten had, according to MKH, a "disparate correspondence", 5 subjects with a "young" and 5 with an "old fixation disparity". According to the MKH, a correcting prism was determined. All 10 subjects underwent the automatic Freiburg Stereoacuity Test, without and with the MKH-prism. RESULTS: Without the MKH-prism, the stereoscopic threshold ranged between 1.5 and 14.5 arcsec. With the MKH-prism, the values were not significantly different. CONCLUSION: Stereoacuity ranged between good and excellent in the 5 subjects with "young" as well as in the 5 subjects with "old fixation disparity". The MKH-prism did not improve the stereoacuity in any of the subjects. These results cast doubt on Haase's assertion that an "old fixation disparity" implies a reduced stereoacuity. Hence, the premise for a benefit of the MKH-prism with respect of stereoacuity is not substantiated. In the 5 subjects with a "young fixation disparity", the good stereoacuity is consistent with Haase's theory, so that a benefit of the MKH-prism for stereoacuity was not expected. In previous studies, stereoacuity was found to be better with the MKH-prism than without it. These studies are questionable since learning with repeated testing was not taken into account. We conclude that there is no sound evidence for the assumption that the MKH-prism can improve stereoacuity.

Adult↗
PubMed2004

Relation between static and dynamic aspects of vergence, estimated with a subjective test using flashed dichoptic nonius lines.

The psychophysical technique for measuring vergence with dichoptic nonius lines was used to investigate dynamic responses to step vergence stimuli. Liquid crystal shutter glasses were operated with a cathode ray tube monitor to present convergent or divergent step stimuli of 32 min arc at t = 0. The resulting initial vergence response was estimated with nonius lines that appeared for 80 ms at a fixed delay of 400 ms after the vergence step stimulus. The vergence state reached 400 ms after the step depended on the vergence accuracy assumed before the step, i.e. baseline fixation disparity (FD). The following physiologically plausible results were found: (i) the amount of dynamic vergence changes within 400 ms tended to be negatively correlated between the convergent and divergent direction; (ii) subjects with a smaller convergent dynamic change had a steeper proximity-FD curve measured with static fusion targets as a function of viewing distance; (iii) FD was more eso or more exo depending on whether the vergence change was larger in the convergent or divergent direction respectively.

Convergence, Ocular↗
PubMed1991

Sensory interactions during human fusional response.

The nature of sensory interactions during human fusional response was investigated using band-limited, 10th-derivative-of-Gaussian patterns. Experiments were performed to investigate the effects of spatial separation, disparity magnitude, and stimulus spatial frequency on horizontal sensory fusional amplitudes (SFA). When the disparities in the inducing and probe regions were in the same direction the SFA for the probe increased; when the disparities were in opposite directions the SFA was reduced. Increases and decreases in the SFA for the probe caused by the inducing stimulus were designated enhancement and inhibition respectively. Both enhancement and inhibition increased with increasing inducing disparity. They were evident over a range of spatial frequencies from 0.75 to 3.0 c/deg and among retinal regions separated by as much as 1.5 deg arc. The SFA for the probe was not inhibited when the peak spatial frequency of the inducing stimulus was 2 octaves higher than that of the probe. The observed changes in SFA were found to be due to shifts in location rather than changes in the extent of the fusional range for the probe.

Convergence, Ocular↗
PubMed2001

Short-latency disparity vergence in humans.

Eye movement recordings from humans indicated that brief exposures (200 ms) to horizontal disparity steps applied to large random-dot patterns elicit horizontal vergence at short latencies (80.9 +/- 3.9 ms, mean +/- SD; n = 7). Disparity tuning curves, describing the dependence of the initial vergence responses (measured over the period 90-157 ms after the step) on the magnitude of the steps, resembled the derivative of a Gaussian, with nonzero asymptotes and a roughly linear servo region that extended only a degree or two on either side of zero disparity. Responses showed transient postsaccadic enhancement: disparity steps applied in the immediate wake of saccadic eye movements yielded higher vergence accelerations than did the same steps applied some time later (mean time constant of the decay, 200 ms). This enhancement seemed to be dependent, at least in part, on the visual reafference associated with the prior saccade because similar enhancement was observed when the disparity steps were applied in the wake of saccadelike shifts of the textured pattern. Vertical vergence responses to vertical disparity steps were qualitatively similar: latencies were longer (on average, by 3 ms), disparity tuning curves had the same general form but were narrower (by approximately 20%), and their peak-to-peak amplitudes were smaller (by approximately 70%). Initial vergence responses usually had directional errors (orthogonal components) with a very systematic dependence on step size that often approximated an exponential decay to a nonzero asymptote (mean space constant +/- SD, 1.18 +/- 0.66 degrees ). Based on the asymptotes of these orthogonal responses, horizontal errors (with vertical steps) were on average more than three times greater than vertical errors (with horizontal steps). Disparity steps >7 degrees generated "default" responses that were independent of the direction of the step, idiosyncratic, and generally had both horizontal and vertical components. We suggest that the responses depend on detectors that sense local disparity matches, and that orthogonal and "default" responses result from globally "false" matches. Recordings from three monkeys, using identical disparity stimuli, confirmed that monkeys also show short-latency disparity vergence responses (latency approximately 25 ms shorter than that of humans), and further indicated that these responses show all of the major features seen in humans, the differences between the two species being solely quantitative. Based on these data and those of others implying that foveal images normally take precedence, we suggest that the mechanisms under study here ordinarily serve to correct small vergence errors, automatically, especially after saccades.

Adult↗
PubMed2004

Interaction between luminance gratings and disparity gratings.

It was shown from geometry and photographic measurement that the shading pattern for a sinusoidal corrugated surface of frequency f approximates to a luminance-defined grating of frequency f, 2f or f + 2f in specific relative phase. It was confirmed that a luminance grating modifies the appearance of a suprathreshold stereoscopic corrugated surface, suggesting an interaction between shading and binocular disparity. Disparity thresholds for detecting random-dot, disparity-defined gratings of spatial frequency 0.2 or 0.4 c/deg were measured in the presence of luminance gratings of spatial frequency 0.4 c/deg with the same orientation. Phase-specific facilitation of disparity thresholds was greatest for a phase relationship inconsistent with shading of a corrugated surface, and was disrupted by positional uncertainty. The presence of texture-defined lines (which served to mark explicitly the successive spatial locations of salient depth features in the image) produced a similar pattern of facilitation, in the absence of shape-from-shading cues. The pattern of results indicates direct local interactions, including spatial cueing, rather than interaction of depth cues.

Adult↗
PubMed2005

Short-latency disparity vergence in humans: evidence for early spatial filtering.

Our study was concerned with the disparity detectors underlying the initial disparity vergence responses (DVRs) that are elicited at ultrashort latencies by binocular disparities applied to large images. DVRs were elicited in humans by applying horizontal disparity to vertical square-wave gratings lacking the fundamental (termed here, the "missing fundamental"). In the frequency domain, a pure square wave is composed of odd harmonics--first, third, fifth, seventh, etc.--such that the third, fifth, seventh, etc., have amplitudes that are one-third, one-fifth, one-seventh, etc., that of the first, and the missing fundamental lacks the first harmonic. The patterns seen by the two eyes have a phase difference of one-quarter wavelength, so the disparity of the features and 4n + 1 harmonics (where n = integer) has one sign (crossed or uncrossed), whereas the 4n - 1 harmonics--including the strongest Fourier component (the third harmonic)--has the opposite sign (uncrossed or crossed): spatial aliasing. The earliest DVRs, recorded with the search-coil technique, had minimum latencies of 70 to 80 ms and were generally in the direction of the third harmonic, that is, uncrossed disparities resulted in convergent eye movements. In other experiments on the DVRs, one eye saw a missing fundamental and the other saw a pure sine wave with the contrast and wavelength of the third harmonic but differing in phase by one-quarter wavelength. This resulted in short-latency vergence in accordance with matching of the third harmonic. These data all indicate the importance of the Fourier components, consistent with early spatial filtering prior to binocular matching.

Fourier Analysis↗
PubMed2003

Peak localization of sparsely sampled luminance patterns is based on interpolated 3D surface representation.

Objects in the world are typically defined by contours and local features separated by extended featureless regions. Sparsely sampled profiles were therefore used to evaluate the cues involved in localizing objects defined by such separated features (as opposed to typical Vernier acuity or other line-based localization tasks). Objects, in the form of Gaussian blobs, were defined at the sample positions by luminance cues, binocular disparity cues or both together. Remarkably, the luminance information in the sampled profiles was unable to support localization for objects requiring interpolation when the perceived depth from the luminance cue was cancelled by a disparity cue. Disparity cues, on the other hand, improved localization substantially over that for luminance cues alone. These data indicate that it is only through the interpolated depth representation that the position of the sampled object can be recognized. The dominance of a depth representation in the performance of such tasks shows that the depth information is not just an overlay to the 2D sketch of the positional information, but a core process that must be completed before the position of the object can be recognized.

Cues↗
PubMed1998

Cortical computation of stereo disparity.

Our ability to see the world in depth is a major accomplishment of the brain. Previous models of how positionally disparate cues to the two eyes are binocularly matched limit possible matches by invoking uniqueness and continuity constraints. These approaches cannot explain data wherein uniqueness fails and changes in contrast alter depth percepts, or where surface discontinuities cause surfaces to be seen in depth, although they are registered by only one eye (da Vinci stereopsis). A new stereopsis model explains these depth percepts by proposing how cortical complex cells binocularly filter their inputs and how monocular and binocular complex cells compete to determine the winning depth signals.

Contrast Sensitivity↗
PubMed2000

Effect of onset age of strabismus on the binocular responses of neurons in the monkey visual cortex.

PURPOSE: By 6 weeks of age, neurons in the monkey's primary visual cortex acquire qualitatively adult-like binocular response properties and behaviorally stereopsis emerges. In this study, it was determined whether the onset of strabismus has a more severe impact on cortical binocularity before or after this critical developmental age. METHODS: Infant monkeys were fit with a light-weight helmet which held a total of 27 diopters of base-in prisms in front of their two eyes for a fixed period of two weeks. For one group of infant monkeys, prism-rearing began at 2 weeks of age and for a second group, the onset was at 6 weeks of age. Immediately after the rearing period, i.e., at 4 weeks and 8 weeks of age, respectively, extracellular single-unit recording methods were used to determine the nature and severity of alterations in the binocular response properties of V1 neurons. Dichoptic sinewave gratings were used as visual stimuli. RESULTS: In comparison to normal age-matched infants, V1 neurons in both strabismic groups exhibited reductions in sensitivity to interocular spatial phase disparities (disparity sensitivity) and a higher prevalence of binocular inhibitory interactions (binocular suppression). However, the reduction in disparity sensitivity and the magnitude of binocular suppression were much greater in the late (6-8 weeks) than the early (2- 4 weeks) onset group. CONCLUSIONS: Discordant binocular signals due to brief periods of early strabismus have more serious effects on the development of binocular properties of V1 neurons if they occur shortly after rather than before the emergence of stereopsis (i.e., when the binocular connections are relatively more mature but the visual cortex still shows a high degree of plasticity).

Age of Onset↗
PubMed2006

[Feasibility of prismatic correction of microesotropia using the measuring and correcting methodology by H.-J. Haase].

BACKGROUND: The "Measuring and Correcting Methodology after H.-J. Haase" is based on the assumption that a minute deviation from the orthovergence position (fixation disparity) indicates a difficulty to overcome a larger "vergence angle of rest". Objective recordings have, however, revealed that the subjective tests applied in the "Measuring and Correcting Methodology after H.-J. Haase" can mislead to the assumption of a fixation disparity, although both eyes are aligned exactly to the fixation point. QUESTION: How do patients with an inconspicuously small, yet objectively verified strabismus react to the "Measuring and Correcting Methodology by H.-J. Haase"? METHODS: Eight patients with a microesotropia between 0.5 and 3 degrees were subjected to the "Measuring and Correcting Methodology after H.-J. Haase. RESULTS: In all 8 patients, the prisms determined with the Cross-, Pointer- and Rectangle Tests increased the angle of squint, without reaching a full correction: the original angle prevailed. In the Stereobalance Test, prisms did not reduce the 100 % preponderance of the non-squinting eye. The stereoscopic threshold was between 36 and 1170 arcsec in 7 out of the 8 subjects, and above 4000 arcsec in 1 subject. CONCLUSIONS: (1) In all 8 patients, prisms determined with the "Measuring and Correcting Methodology by H.-J. Haase" increased the angle of strabismus, without reaching bifoveal vision. This uniform result suggests that primary microesotropia cannot be corrected with the "Measuring and Correcting Methodology after H.-J. Haase" (2) A lacking contribution of the strabismic eye to the recognition of a lateral offset between stereo objects, as determined with the Stereobalance Test, does not imply a lack of binocular stereopsis.

Adolescent↗
PubMed2004

Symmetrical horizontal vergence contributes to the asymmetrical pursuit of targets in depth.

When a target travels slowly and smoothly along the line of sight of one eye, the eye that is aligned with the target remains stationary while the other eye adducts. The mechanism that is commonly invoked is that commands signaling conjugate pursuit and symmetrical vergence are combined. The two signals are in the same direction in the adducting eye but are in the opposite direction in the stationary eye and, so, cancel. Recent data have challenged this view and the idea that the two eyes are controlled independently has been resurrected. Pursuit and vergence movements are difficult to separate when they occur together because they have similar latencies and dynamics. We have developed a method where horizontal vergence is "tagged" by training it to have a vertical vergence component that can then be identified in combined pursuit-vergence movements. Four subjects trained eye movements to have a vertical vergence component by fusing vertical disparities that varied in association with horizontal convergence. Following training, the vertical vergence aftereffect was found whenever horizontal vergence was stimulated regardless of whether the horizontal vergence resulted from movement of the target in the midsagittal plane (symmetrical vergence) or from movement of the target along the line of sight of one eye (asymmetrical vergence). The vertical vergence aftereffect was never observed in association with conjugate movements indicating that asymmetrical slow eye movements are not controlled monocularly but contain a vergence component along with symmetrical smooth pursuit.

Adaptation, Physiological↗
PubMed1993

Comparison of fixation disparity measurements obtained with the Wesson Fixation Disparity Card and the Sheedy Disparometer.

We compared the fixation disparity measurements obtained with the Disparometer to those of the Wesson Card. Previous studies suggest that the measurements obtained by these two instruments gave different results. The results of previous studies were based on the analysis of pooled data, which may have led to spurious results. Analysis of our data done in this manner (pooled data) revealed the same findings. However, after analysis of the data based on the separation of subjects according to phoria (exophoria/esophoria), no statistically significant difference was found between the measurements obtained with the Wesson Card and those with the Disparometer.

Adult↗
PubMed1993

Temporal aspects of depth contrast.

Depth contrast is a contrasting change in the depth of a feature that results from changes in the disparities of other objects in the field of view, even though the disparity of the original feature remains unchanged. Depth contrast effects decrease during continuous viewing of the stimuli and may disappear altogether after several minutes unless the disparities of the inducing features change with time. This fading occurs whenever the inducing features have constant disparity, whether they are stationary or oscillating laterally. Depth contrast effects occur whenever the inducing features are visible within half a second before or after presentation of the test features. When test features are enclosed by a rectangle which is just inside of a circumscribing outer trapezoid, the inner rectangle "shields" the test features from the depth-inducing effects of the outer trapezoid. Surprisingly, this shielding effect persists if the inner rectangle and outer trapezoid have the same slant direction, but fades with time if the slants are opposite in direction.

Contrast Sensitivity↗
PubMed1999

Stereoscopic surface perception.

Physiological, computational, and psychophysical studies of stereopsis have assumed that the perceived surface structure of binocularly viewed images is primarily specified by the pattern of binocular disparities in the two eyes' views. A novel set of stereoscopic phenomena are reported that demonstrate the insufficiency of this view. It is shown that the visual system computes the contrast relationships along depth discontinuities to infer the depth, lightness, and opacity of stereoscopically viewed surfaces. A novel theoretical framework is introduced to explain these results. It is argued that the visual system contains mechanisms that enforce two principles of scene interpretation: a generic view principle that determines qualitative scene geometry, and anchoring principles that determine how image data are quantitatively partitioned between different surface attributes.

Algorithms↗
PubMed1995

An adaptable association between vertical and horizontal vergence.

Vertical phoria (vergence error under monocular viewing conditions) can be trained to vary with conjugate eye position. The adaptive response controls the vertical alignment of the two eyes in the absence of binocular disparity and is used to compensate for binocular changes of the oculomotor system induced by developmental and environmental factors. Vertical phoria was associated with horizontal disparity vergence by adapting vertical vergence to two vertically disparate targets separated along the depth axis. This association was primarily dependent on the horizontal vergence as opposed to monocular eye position or binocular conjugate eye position. Following this adapted association with horizontal disparity vergence, vertical phoria aftereffects were also evoked by accommodative vergence. Previous reports have demonstrated an adapted association between vertical phoria and conjugate eye position. The current report examines the difference in the vertical phoria resulting from adaptation to vertically disparate targets separated along either the vertical axis or depth axis. The amplitude of the vertical vergence aftereffect was approximately 4 times greater for targets separated along the depth axis than in the vertical meridian. The association between vertical phoria with conjugate eye position and horizontal vergence is proposed to result from a cross-coupling of vertical vergence with supranuclear regions that control conjugate and horizontal vergence eye movements. A selective interaction would enable the oculomotor system to correct disturbances in specific supranuclear regions as they interface with vertical vergence.

Accommodation, Ocular↗
PubMed1994

Effect of fixation disparity on distance binocular visual acuity.

Subjects with appreciable values (2 delta and greater) of associated 'phoria, as measured by a Mallett unit, had their distance monocular and binocular visual acuities measured. In the latter case measurements were taken both with the associated 'phoria corrected by prisms and without such a correction. The improvement in binocular acuity compared to monocular acuity was less than would occur in normal subjects with minimal associated 'phorias although the improvement differed accordingly as to whether the readings were eso- or exo-in mature. When the associated 'phorias were corrected with prisms the improvement in binocular over monocular visual acuity was similar to that found in normal subjects.

Adult↗