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Visual Psychophysics and Physiological Optics  |   November 2012
Visual Acuity, Crowding, and Stereo-Vision Are Linked in Children with and without Amblyopia
Author Affiliations & Notes
  • John A. Greenwood
    From the UCL Institute of Ophthalmology, University College London, London, United Kingdom; the
  • Vijay K. Tailor
    National Institute for Health Research Biomedical Research Centre for Ophthalmology at Moorfields Eye Hospital National Health Service Foundation Trust, London, United Kingdom;
    Strabismus and Paediatric Service, Moorfields Eye Hospital, London, United Kingdom;
  • John J. Sloper
    National Institute for Health Research Biomedical Research Centre for Ophthalmology at Moorfields Eye Hospital National Health Service Foundation Trust, London, United Kingdom;
    Strabismus and Paediatric Service, Moorfields Eye Hospital, London, United Kingdom;
  • Anita J. Simmers
    Vision Sciences, Department of Life Sciences, Glasgow Caledonian University, Glasgow, United Kingdom; and the
  • Peter J. Bex
    Schepens Eye Research Institute, Harvard Medical School, Boston, Massachusetts.
  • Steven C. Dakin
    From the UCL Institute of Ophthalmology, University College London, London, United Kingdom; the
    National Institute for Health Research Biomedical Research Centre for Ophthalmology at Moorfields Eye Hospital National Health Service Foundation Trust, London, United Kingdom;
  • Corresponding author: John A. Greenwood, Laboratoire Psychologie de la Perception, Université Paris Descartes, Paris, France; john.greenwood@parisdescartes.fr
Investigative Ophthalmology & Visual Science November 2012, Vol.53, 7655-7665. doi:10.1167/iovs.12-10313
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      John A. Greenwood, Vijay K. Tailor, John J. Sloper, Anita J. Simmers, Peter J. Bex, Steven C. Dakin; Visual Acuity, Crowding, and Stereo-Vision Are Linked in Children with and without Amblyopia. Invest. Ophthalmol. Vis. Sci. 2012;53(12):7655-7665. doi: 10.1167/iovs.12-10313.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: During development, the presence of strabismus and anisometropia frequently leads to amblyopia, a visual disorder characterized by interocular acuity differences. Although additional deficits in contrast sensitivity, crowding (the impaired recognition of closely spaced objects), and stereoacuity are common, the relationship between these abilities is unclear.

Methods.: We measured the covariation between these four abilities in children 4 to 9 years of age (n = 72) with strabismus, anisometropia, or mixed strabismus/anisometropia, and unaffected controls. Children reported the orientation of a target (a modified “Pac-Man,” similar to Landolt-C stimuli) using four “ghosts” as references. Using a modified staircase procedure we measured threshold size (acuity), contrast detection, foveal crowding (the minimum separation between target and ghost-flankers supporting accurate identification), and stereoacuity (with random-dot stereogram ghosts).

Results.: Group averages revealed significant interocular differences (IODs) in acuity for all three clinical groups (0.2–0.3 log minutes), and significant crowding IODs for the strabismic and mixed groups (0.6 and 0.4°, respectively). Nonetheless, crowding IODs were correlated with acuity IODs in all four groups (r values between 0.43 and 0.59 and P < 0.05; P = 0.07 in the mixed group). Similarly, the occurrence of stereo-blindness (most common in strabismic and mixed groups) was associated with a significant increase in IODs for both acuity and crowding (each P < 0.05). No correlations were found with contrast detection.

Conclusions.: Our results demonstrate an association between IODs in acuity and crowding and, furthermore, between these IODs and the presence of stereo-vision. We suggest that the deficits derived from strabismus and anisometropia lay along a continuum with abilities observed during normal development.

Introduction
It is well known that abnormal visual experience can have a profound effect on the development of the visual system. In the case of children with anisometropia (unequal refractive error) and/or strabismus (ocular misalignment), a common outcome is unilateral amblyopia, a developmental visual disorder whose defining feature is reduced acuity in one eye that persists despite optical correction. 1,2 The development of amblyopia is also associated with a range of additional deficits, including anomalies in contrast detection, 26 elevated visual crowding, 79 and reduced stereoacuity or complete stereo-blindness. 2,10 Although each is becoming increasingly well understood in isolation, little is known about the relationship between these deficits, particularly during childhood when strabismus and anisometropia first develop. 
Aside from the definitive acuity deficits, amblyopia is most frequently associated with deficits in stereo-vision. This can range from an elevation in stereoacuity thresholds, the magnitude of which correlates with the interocular difference in acuity, 1012 to complete stereo-blindness, which is particularly common in strabismus 2,13,14 and cases of severe anisometropia. 2,10,12,15 The link between these deficits in acuity and stereo-vision has been attributed to altered neural selectivities within cortical area V1: the abnormal visual experience that causes amblyopia may shift both the selectivity of monocular neurons away from the amblyopic eye and reduce the number of binocular neurons. 1,2,1618 Improvements in visual acuity resulting from binocular therapy 19,20 further suggest that there may be a causal link between acuity and stereo-vision, although a similar training regime focused on stereoacuity did not improve acuity thresholds. 21 The relationship between these impairments in stereo-vision and other amblyopic deficits is unknown. 
A more complex pattern of deficits has been observed for achromatic contrast sensitivity. Although significant impairments in contrast sensitivity have been observed in the amblyopic eye of adults, 46 amblyopic children may show milder deficits. 3 Additionally, although the amblyopic eye of anisometropes typically supports higher contrast-detection thresholds than does the fellow eye, in strabismus there have been reports of improved contrast-detection thresholds when observers use their amblyopic eye. 2,6 It is possible that these changes reflect a redeployment of binocular cells as monocular cells, 2 which may suggest a relationship between these anomalies in contrast detection and the stereo-deficits described above. The variation in contrast-detection thresholds also suggests that the nature of these effects depends on both the progression and the type of amblyopia. 
Finally, a particularly striking functional consequence of amblyopia is an elevation in crowding, the impairment in object recognition that occurs when an otherwise visible target object is flanked by similar elements. 7,9,22 In “normal” adult vision, crowding is widely viewed as a “compulsory pooling” of target and flanker signals 2325 that is strongest in the peripheral field and minimal in the fovea. 9,26 In amblyopia, particularly when accompanied by strabismus, crowding is clearly evident in the fovea and can extend over spatial extents similar to crowding in the typical periphery. 79 Elevated foveal crowding has also been observed in typically developing children, 2729 which may persist as late as 11 years. 29 Indeed, linear (so-called crowded) letter charts are generally considered better detectors of amblyopia in children than isolated letters. 28,30,31 The relationship between these three instances of crowding—in the “normal” periphery, the developing fovea, and the amblyopic fovea—is currently unclear. Many theories have been proposed to account for crowding, 9 with one view describing both peripheral and amblyopic forms as the consequence of a neural undersampling of the visual field. 8 As with the mechanisms underlying stereo-deficits, this suggests a potential link with acuity loss. Accordingly, some relation has been reported between acuity and crowding in adults, 7,8,32 although others report that its magnitude exceeds the scale of acuity losses. 33,34 This relationship is yet to be examined in children, and the relationship between crowding and other amblyopic deficits is unknown. 
These four deficits (acuity, contrast detection, crowding, and stereo-vision) are not the only functional consequences of amblyopia, but the similarities in their proposed mechanisms led us to consider how they might covary across individuals. In particular, if each were indeed linked with alterations in either the balance of monocular cells responding to each eye, or the proportion of binocular cells, then we may expect them to covary in their magnitude. The aim of the present study was thus to examine the relationship between acuity, contrast detection, crowding, and stereoacuity in children with and without strabismus and/or anisometropia. We further sought to equate stimulus and task demands across these tasks and consequently developed a novel paradigm, tailored to children, that involves simple characters in an easy-to-understand and engaging context. 
Methods
Participants
We examined 72 children, between 4 and 9 years of age (54–107 months; mean = 80.7), divided into four groups: those with strabismus (n = 18), anisometropia (n = 16), or mixed strabismus/anisometropia (n = 19), and controls (n = 19). All were tested at the Children's Eye Centre in Moorfields Eye Hospital (London, UK). 
Children in the control group were selected to have acuity better than 0.10 logMAR (logarithm of the minimum angle of resolution), in the absence of any preexisting visual deficits. Inclusion in the strabismic group was on the basis of manifest heterotropia and an interocular refractive difference less than 1 diopter in any meridian. Conversely, the anisometropic group had an interocular refractive difference of 1 diopter or more in any meridian, without significant heterotropia. Children with both a manifest heterotropia and interocular refractive differences greater than 1 diopter were included in the mixed group. There was no requirement for the presence of amblyopia in the three “clinical” groups because we sought to assess a range of visual abilities. We also sought a mix of stereo-vision abilities for each group, and thus the observed frequencies of stereo-blindness for these groups should not be taken as indicative of the overall population. Children with paralytic or restrictive strabismus, as well as those with additional visual deficits (e.g., cataracts or macular dystrophies) or neurologic deficits (e.g., dyslexia or autism), were excluded. The orthoptic details for all children are presented in Supplemental Tables S1 to S4 (see Supplementary Material and Supplementary Tables S1S4). 
Pretesting
All children underwent a full orthoptic assessment, including logMAR acuity (with Thompson v2000 software; Thompson Software Solutions, Herts, UK), TNO stereoacuity testing, ocular motility, binocular function (prism fusion range), and cover tests for near and distance fixation. The angle of any heterotropia or heterophoria was measured by prism cover test. Where required, cycloplegic refraction was performed within the 6 months prior to involvement in our study (but never immediately prior to our experiments). 
Apparatus
Experiments were run using a commercial software program (MATLAB; The MathWorks, Ltd., Cambridge, UK) on a Dell PC (Dell, Round Rock, TX) running PsychToolbox. 35,36 Stimuli were presented on a liquid crystal display monitor (SyncMaster 2233RZ LCD monitor; Samsung Electronics, Seoul, South Korea), with 1680 × 1050 pixel resolution and 120-Hz refresh rate. The monitor was calibrated using a spectrophotometer (Konica Minolta Sensing Americas, Ramsey, NJ) and linearized in software, giving a maximum luminance of 92.8 cd/m2. Because these monitors allow only 6-bit contrast resolution, bit-stealing 37 was used to obtain 442 brightness levels (approximately 8.8 bits). 
Children wore stereo-shutter glasses (nVidia Corp., Santa Clara, CA), which alternated at 120 Hz (delivering images to each eye at 60 Hz) and were custom-mounted in a children's ski-mask frame to give a comfortable fit over spectacles (Fig. 1A). Children viewed the stimuli from 3 m, wearing their full correction (as required), and made verbal responses that were recorded by the experimenter using the computer keyboard. To aid in the psychophysical tasks (e.g., for acuity: “which color ghost was Vac-Man facing?”), large reference pictures of the ghosts were attached to the monitor edges. This allowed children to report either the location of a ghost or, if preferred, its color. 
Figure 1. 
 
Apparatus and stimuli. (A) Stimuli were viewed through stereoscopic shutter glasses mounted in a children's ski mask (inset) and presented on a 3D-compatible monitor viewed at 3 m. An example trial of the acuity/contrast task is depicted. Children reported the color of the ghost that Vac-Man was facing. Colored cards were present on the monitor edges for reference. (B) An example frame from the “reward animation” (see Supplementary Material and Supplementary Movies S2S4). (C) Depiction of the crowding stimuli. Ghosts were rendered achromatically and presented at random orientations at a fixed separation from Vac-Man. The task was as in (A), with the reference cards assisting color memory. (D) An example frame from the stereo task with monocular “shadow” contours, representing input to one of the eyes. Children were required to help Vac-Man find the ghost that “popped out” in depth. (E) An example ghost from the stereo task with a monocular “shadow,” viewable with red–green anaglyphs (red filter to the right eye; actual stimuli were achromatic). (F) An example ghost from the random-check stereo task, with a disparity offset defined purely by the random-check elements.
Figure 1. 
 
Apparatus and stimuli. (A) Stimuli were viewed through stereoscopic shutter glasses mounted in a children's ski mask (inset) and presented on a 3D-compatible monitor viewed at 3 m. An example trial of the acuity/contrast task is depicted. Children reported the color of the ghost that Vac-Man was facing. Colored cards were present on the monitor edges for reference. (B) An example frame from the “reward animation” (see Supplementary Material and Supplementary Movies S2S4). (C) Depiction of the crowding stimuli. Ghosts were rendered achromatically and presented at random orientations at a fixed separation from Vac-Man. The task was as in (A), with the reference cards assisting color memory. (D) An example frame from the stereo task with monocular “shadow” contours, representing input to one of the eyes. Children were required to help Vac-Man find the ghost that “popped out” in depth. (E) An example ghost from the stereo task with a monocular “shadow,” viewable with red–green anaglyphs (red filter to the right eye; actual stimuli were achromatic). (F) An example ghost from the random-check stereo task, with a disparity offset defined purely by the random-check elements.
Stimuli and Procedures
Overall, our tasks involved five video-game characters. The centrally located target stimulus, known as Visual Acuity Man (Vac-Man; see Fig. 1A), was a circle with a horizontal bar missing from one half of the center, similar to a “filled-in” Landolt C. The “mouth” width was equal to one-fifth the stimulus diameter, as in the Sloan alphabet. Four ghost characters were also present, acting either as color aids in the identification of Vac-Man's orientation (“which color ghost was Vac-Man facing?”) or achromatic flanker stimuli in the crowding task. The width of each ghost's “leg” gaps was also one-fifth the stimulus diameter. 
Each child completed four tasks (acuity, contrast, crowding, and stereoacuity) twice. The first three tasks involved monocular presentation (once to each eye), whereas the stereoacuity task was performed once with random-pixel arrays and once with additional monocular contours. Children who did not complete all eight tasks were excluded and are not included in the tallies above (three were excluded in this way). 
All children began with the acuity task. Here, Vac-Man was presented in the center of the display and rendered in black at 50% Weber contrast against a midgray background. Four ghosts moved slowly along the monitor boundaries (approximately 2.2–4.4° from the center), each with distinct colors (red to the right, green above, blue left, and orange below; see Fig. 1A). This combination of target-flanker separation, flanker-color, and flanker-motion minimized the chance of any crowding between target and ghosts. 9,22,38,39  
Children were required to indicate which of the four ghosts Vac-Man was facing (four-alternative forced choice), because this was the ghost “he wished to eat.” These responses (based on the color of clearly individuated characters) were designed to avoid both left–right response confusions 40 and source confusions 41,42 as to which element in the multielement display was the target. Normal color-naming abilities were checked using our stimuli, prior to running the experiment. Feedback was given after each trial via brief animations (Vac-Man smiled or frowned), with every third correct response giving longer animations in which a color-rendered Vac-Man “ate” the correct ghost (Fig. 1B; see also Supplementary Material and Supplementary Movie S1). 
Acuity thresholds were assessed by varying the size of Vac-Man (and thus the visibility of the “mouth”) using a QUEST algorithm staircase procedure 43 that converged on 62.5% correct performance. Incorrect responses resulted in an increase in target size and correct responses in a decrease. Three modifications were made to the QUEST routine to increase its suitability for testing children. First, children were given three practice trials with a target mouth-size of 4 minutes of arc to begin each task (although this increased if these trials were failed). Second, to minimize the frustration arising from adaptive procedures placing many trials near threshold, we presented easier catch trials on every fifth trial with stimuli scaled to double the current threshold estimate. Third, to reduce the time required to estimate thresholds, we added an exit criterion: if the SD of the estimated threshold for the past eight trials was less than 0.03 log units (a value deemed reliable during pilot tests), the experimenter was given the option of exiting the task. Otherwise, the QUEST procedure terminated after 32 trials (plus practice). The average number of trials required to reach threshold on the acuity task was 14.7, not including practice. 
Children completed the acuity task once for each eye, with monocular presentation controlled using the stereo-shutter glasses. For children in the control group, their left or right eye was randomly selected to begin; those in clinical groups always began with their fellow eye to ensure comprehension. Although acuity was always completed first, subsequent tests were administered in random order. For all tasks following the acuity measurement, Vac-Man and the ghost-flankers were presented at sizes equal to 2.5-fold the size-threshold (separately for each eye) to ensure their visibility. 
For the contrast-detection task, Vac-Man was again presented in the center of the display, surrounded by four distinctly colored ghosts, and children indicated the ghost that Vac-Man was facing (see Supplementary Material and Supplementary Movie S2). QUEST procedures were similar to the acuity task, albeit modulating Weber contrast instead of size, beginning at 40% Weber contrast. 
For the crowding task, Vac-Man and ghost elements were achromatic and dark against the midgray background at 50% Weber contrast (see Fig. 1C). The ghost-flankers were rendered without their eyes and presented at random orientations. The target and flanker stimuli were thus sufficiently similar to induce crowding 9,38 ; indeed, these stimuli produced strong crowding in the periphery of unaffected adults during pilot testing. Ghost-flankers were positioned in each cardinal direction at a given separation (determined by QUEST) from the centrally located Vac-Man (see Supplementary Material and Supplementary Movie S3). As before, children indicated which ghost Vac-Man was facing, using the color of the ghosts that was also available on reference cards at the monitor edges. As above, these distinct character “identities” were intended to avoid poor performance arising from source confusions, 41,42 rather than an integrative crowding process. QUEST operated as before, but now altered the center-to-center separation between Vac-Man and ghost-flankers to converge on the minimum/critical spacing leading to accurate identification. Because crowding is largely insensitive to stimulus size, 26,44,45 critical spacing is a more reliable measure of crowding than varying size at a fixed separation. Target-flanker separation began at six times the Vac-Man radius. If identification was successful until target and flanker elements were abutting, QUEST continued for three trials and exited if all were correct, recording a zero value. 
Note that these zero values reflect ceiling performance only for our element sizes (scaled to 2.5× the acuity threshold for each child). It is possible that a reduction in element size would reveal a small degree of crowding in these cases by allowing smaller interelement separations. However, because performance under such conditions is limited largely by contrast masking, 46 which operates at or near the resolution limit, we did not attempt further testing with the very small stimuli required to yield reliable estimates of performance. We also deemed the demands of this task (e.g., very high levels of fixation stability) to be beyond the children being tested. Instead, we interpret these zero values as an indication of the functional absence of foveal crowding. 
Finally, we measured stereoacuity both with and without the presence of a monocular “shadow” contour. Ghost stimuli were rendered as random-check stereograms within a circular region. The target was now one of the four ghosts, presented with binocular disparity, whereas the others lay in the zero-disparity plane. An example screen frame is depicted in Figure 1D (also see Supplementary Material and Supplementary Movie S4). Ghosts (without eyes) were defined by a region of checks that were correlated in both left and right eyes, with some displacement to give binocular disparity (as rendered for red/green anaglyphs in Fig. 1E). Surrounding checks were the same in each eye and random checks were used to fill the region left by interocular displacements. The random checks were light or dark squares with 50% Weber contrast. 
In the “contour-based” stereograms, ghosts were additionally cued by a 25% contrast decrement on top of the existing pixel modulations (as in Fig. 1E), which followed the interocular correlation of the constituent pixels. Prior studies have shown that contour information may provide improvements to stereo-vision over purely random-pixel–based stimuli, 4750 although it is not clear whether this reflects the use of additional monocular “cues” to the task. 51,52 In our task, this monocular “shadow” was present in all four ghosts in the display. However, to avoid this “monocular contour” being a cue to the presence of disparity on its own, distractor ghost images were selected randomly from either the right- or left-eye displacements of the target. Thus, horizontal offsets of the ghosts within the circular random-check array could not be used as a cue to the presence of the target ghost (as in Fig. 1D). In the “random-check only” stereograms, monocular shadows were absent and ghosts were defined solely by interocular pixel correlations (depicted in Fig. 1F). Thus, with sufficient stereopsis, the target ghost would be visible in one of the patches and no ghosts would be visible in the distractor patches. 
In each version of the stereo task, children were instructed to “help Vac-Man find the ghost that pops off the screen.” During trials, Vac-Man was centrally located at zero disparity and randomly faced each of the ghosts for brief periods. As above, practice trials were given to begin, with feedback indicating the target ghost to ensure task comprehension. Initially, each of the random checks corresponded to one monitor pixel (19 arcseconds), but if children failed to identify the target these checks were scaled with square dimensions of 2, 4, 8, or 16 monitor pixels. Failure at one scale meant an increment to the next (which typically required four to five trials), until either a satisfactory check size was found or it was clear that the child had no demonstrable stereo-vision. Once the correct scale had been selected, QUEST began with a disparity of 160 arcseconds and ran as before, varying the binocular disparity of the target ghost. Children completed the monocular-contours task first before the random-checks only version. 
All procedures were approved by local and National Health Service ethics boards and conformed to the Declaration of Helsinki. 
Results
Thresholds for the Spatial Tasks
We first consider performance in the three spatial tasks (acuity, contrast-detection, and crowding). The distributions of acuity and contrast thresholds were both significantly skewed and were consequently log-transformed. Crowding values were not transformed due to the high number of zero values. Thresholds for the acuity, contrast-detection, and crowding tasks are presented in Figure 2. Data from the clinical groups are attributed to either the “amblyopic” or “fellow eye”; control group data are kept as left/right eyes. Colored bars depict group means, whereas gray points show individual data. 
Figure 2. 
 
Thresholds for the three spatial tasks. (A) Acuity thresholds, in log minutes of visual arc (equivalent to logMAR). Data are separated into left- and right-eye thresholds for the controls and amblyopic/fellow eye for the three clinical groups. Colored bars show group means; gray points are individual data. Symbols at the top show the significance of paired-samples t-tests between the eyes of group members (as in the figure legend). (B) Contrast-detection thresholds, in log units of percent Weber contrast, expressed as in (A). (C) Thresholds for the spatial extent of foveal crowding, expressed as the center-to-center separation between target and flankers in degrees of visual arc.
Figure 2. 
 
Thresholds for the three spatial tasks. (A) Acuity thresholds, in log minutes of visual arc (equivalent to logMAR). Data are separated into left- and right-eye thresholds for the controls and amblyopic/fellow eye for the three clinical groups. Colored bars show group means; gray points are individual data. Symbols at the top show the significance of paired-samples t-tests between the eyes of group members (as in the figure legend). (B) Contrast-detection thresholds, in log units of percent Weber contrast, expressed as in (A). (C) Thresholds for the spatial extent of foveal crowding, expressed as the center-to-center separation between target and flankers in degrees of visual arc.
Acuity thresholds (Fig. 2A) for the left and right eyes of the control group averaged 0.03 and 0.01 log minutes of arc, respectively, both equivalent to a Snellen acuity of 6/6. There was no significant difference between these values (paired differences t-test: t[18] = 0.66, P = 0.5). Reduced acuity levels were evident in the amblyopic eyes of all three clinical groups, with averages of 0.32, 0.23, and 0.32 log minutes for the strabismic, anisometropic, and mixed groups, respectively (equivalent to Snellen acuities of 6/12 and 6/10), compared with average fellow-eye acuities of 0.10, −0.01, and 0.02 log minutes. These interocular differences were significant for each group (paired differences for strabismic: t[17] = 4.6, P < 0.001; anisometropic: t[15] = 5.9, P < 0.001; and mixed: t[18] = 9.4, P < 0.001). This is solely due to elevations in the amblyopic eye—acuity in the fellow eyes of these groups was not significantly different from that of controls (pooled unpaired t-test between all fellow eyes and both control eyes: t[89] = −0.6, P = 0.56). These acuity values also correlate highly with logMAR values obtained during orthoptic examination (see Supplementary Material and Supplementary Fig. S1A) and show good agreement in a Bland–Altman analysis (see Supplementary Material and Supplementary Fig. S1B). 
Contrast-detection thresholds (Fig. 2B) averaged 15.9% and 14.8% Weber contrast for the left and right eyes of controls, a nonsignificant difference (t[18] = 0.5, P = 0.5). Group averages in the clinical groups showed slight but nonsignificant elevations in the amblyopic eye: strabismic children averaged 19.2% and 17.7% for the amblyopic and fellow eyes (t[17] = 0.5, P = 0.49), anisometropes were 17.3% and 14.0% (t[15] = 1.5, P = 0.16), and the mixed group difference approached significance with 20.0% and 15.8% (t[18] = 1.97, P = 0.06). 
On average, foveal crowding was evident in both eyes of controls (Fig. 2C), with threshold center-to-center separations of 0.13° and 0.18° required for left and right eyes, respectively (a nonsignificant difference, t[18] = −0.97, P = 0.34). These are large values relative to acuity: control children had an average acuity of 1 arc minute, whereas the average crowding extent is ±9 arc minutes around this. Although the amblyopic eye of anisometropes was slightly elevated, with 0.23° compared with 0.17° in their fellow eyes, this difference was nonsignificant (t[18] = 3.03, P = 0.53). Large significant differences, however, were evident in the strabismic group, with an average separation of 0.66° required in the amblyopic eye and 0.10° in the fellow eye (t[17] = 3.7, P = 0.002), and similarly in the mixed group with 0.51° and 0.11°, respectively (t[18] = 3.03, P = 0.007). 
Note that in the fellow eye of the strabismic and mixed groups, and both eyes of anisometropes, the level of crowding resembles that of the control children rather than a zero mean. Indeed, a one-way t-test shows a significantly nonzero mean for these eyes (pooled one-way analysis for all control and fellow-eye thresholds: t[90] = 5.63, P < 0.001). A pooled unpaired t-test between control eyes and fellow eyes was also nonsignificant (t[89] = 0.63, P = 0.53), demonstrating the similarity in these values between the two groups. It would appear that the fellow eyes of these children follow a similar developmental trajectory to those of controls. There was, however, no influence of age across the approximately 50-month range of our sample (see Supplementary Material and Supplementary Fig. S3). 
Correlations between the Spatial Tasks
To examine the relationship between the interocular differences (IODs) shown above, we first converted monocular thresholds to IOD values by subtracting right-eye from left-eye thresholds in the control group and fellow-eye from amblyopic-eye thresholds in the clinical groups. Intertask comparisons of these IODs are plotted in Figure 3. Negative IOD values indicate better performance in the amblyopic eye (or right eye for controls) than the fellow eye (or left eye), and vice versa for positive values. The clustering of data points in Figure 3A shows that there is no clear relationship between the IODs in acuity and contrast detection for any of the four groups (Control: r[17] = −0.02, P = 0.94; strabismus: r[16] = 0.15, P = 0.55; anisometropia: r[14] = 0.26, P = 0.33; mixed: r[17] = 0.21, P = 0.38). Similarly, Figure 3B demonstrates the lack of significant correlations between IODs for contrast detection and crowding (Control: r[17] = −0.07, P = 0.78; strabismus: r[16] = 0.26, P = 0.29; anisometropia: r[14] = 0.15, P = 0.59; mixed: r[17] = 0.22, P = 0.37). 
Figure 3. 
 
Correlations between interocular differences on each of the three spatial tasks. (A) Correlations between interocular differences in acuity (log minutes difference) and contrast detection (log percent difference). Individual points show each observer and lines for each group display the best-fitting line to the data, with significance indicated on the rightward end. (B) Correlations between IODs in contrast detection and crowding, plotted as in (A). (C) Correlations between IODs for acuity and crowding (degrees difference), plotted as in (A). (D) Acuity and crowding IODs are replotted, with running means (±1 child) for the crowding IODs shown as a function of the acuity IOD. Data points (as in C) are dimmed for clarity.
Figure 3. 
 
Correlations between interocular differences on each of the three spatial tasks. (A) Correlations between interocular differences in acuity (log minutes difference) and contrast detection (log percent difference). Individual points show each observer and lines for each group display the best-fitting line to the data, with significance indicated on the rightward end. (B) Correlations between IODs in contrast detection and crowding, plotted as in (A). (C) Correlations between IODs for acuity and crowding (degrees difference), plotted as in (A). (D) Acuity and crowding IODs are replotted, with running means (±1 child) for the crowding IODs shown as a function of the acuity IOD. Data points (as in C) are dimmed for clarity.
Figure 4. 
 
Performance on the two stereo tasks. (A) The percentage of children from each group who achieved measurable stereoacuity thresholds (less than 1000 arcseconds) on either of the contour-based (light gray bars) or the random-check stereo task (RCS task; dark gray bars). (B) Thresholds on the two stereo tasks, plotted in log seconds of arc. Data are taken only from children with measurable stereo on both tasks, grouped into either “control” or “clinical” categories. The latter includes children from the strabismic (blue triangles), anisometropic (green squares), and mixed (yellow inverted triangles) groups. Gray bars show the mean thresholds for each group on each task. The results of paired differences t-tests are shown for each group at the top of the figure, with significance levels shown in the figure legend.
Figure 4. 
 
Performance on the two stereo tasks. (A) The percentage of children from each group who achieved measurable stereoacuity thresholds (less than 1000 arcseconds) on either of the contour-based (light gray bars) or the random-check stereo task (RCS task; dark gray bars). (B) Thresholds on the two stereo tasks, plotted in log seconds of arc. Data are taken only from children with measurable stereo on both tasks, grouped into either “control” or “clinical” categories. The latter includes children from the strabismic (blue triangles), anisometropic (green squares), and mixed (yellow inverted triangles) groups. Gray bars show the mean thresholds for each group on each task. The results of paired differences t-tests are shown for each group at the top of the figure, with significance levels shown in the figure legend.
Figure 3C shows the much stronger relationship between acuity and crowding. Positive correlations are evident in all groups, with larger interocular differences in acuity associated with larger interocular differences in crowding. This was significant for the control (r[17] = 0.54, P = 0.02), strabismic (r[16] = 0.59, P = 0.01), and anisometropic (r[14] = 0.52, P = 0.04) groups, and approached significance in the mixed group (r[17] = 0.43, P = 0.07). The relationship is such that for strabismic children, for instance, a 1-minute increase in the IOD for acuity (without log conversion) corresponds to a 0.24° increase in the IOD for crowding. So, although the control and anisometropic groups do not show significant IODs in crowding at the group level (Fig. 2), the small IODs that do occur are nonetheless well predicted by their interocular acuity differences. The larger crowding IODs of the strabismic and mixed groups are similarly well predicted by interocular acuity differences, although the nonsignificant correlation for the mixed group appears to arise from those with the largest acuity IODs, whose crowding IODs were disproportionately large. Accordingly, Figure 3D plots the running mean for crowding IOD values for a given child with their nearest neighbors (±1 child) sorted by the size of acuity IODs. For the strabismic and mixed groups there is a sharp rise in crowding IODs once acuity differences rise above 0.25 to 0.35 log minutes. In contrast, control and anisometropic values show a linear relationship throughout their ranges. 
Note that the lack of correlation between contrast sensitivity and either acuity or crowding, reported above, is important since it demonstrates that children performing well on one test did not necessarily mean they would perform well on another. This rules out any explanation of the substantial intertask correlations between acuity and crowding based on general cognitive factors such as attention. 
Stereoacuity Thresholds
We consider performance on the stereo tasks separately here because of the significant number of children who failed to achieve measurable stereoacuity values. Children were considered to have “passed” these tasks if their thresholds were below 1000 arcseconds, a value well above the range of stereoabilities expected for children of this age. 10,14,51,53 For each group, the percentage of children who passed each stereo task is plotted in Figure 4A. In each case, more children achieved measurable stereoacuity thresholds in the monocular-contours–based task than in the random-checks–only version (control: 18/19 vs. 16/19; strabismic: 5/18 vs. 2/18; anisometropic: 13/16 vs. 10/16; and mixed: 5/19 vs. 2/19). 
To examine the precise stereoacuity thresholds obtained, we next consider only the children with measurable stereoacuity on both stereo tasks (i.e., the latter proportions for each group above). Because this reduced the number of children in the clinical groups significantly, we compare our control children with a pooled “clinical” group consisting of children from each of the three categories. As with the acuity and contrast-detection thresholds, stereoacuity thresholds were significantly skewed and were thus log-transformed, as presented in Figure 4B. Control children achieved average stereoacuities of 61 and 104 arcseconds on the contour and random-check tasks, respectively, whereas children in the clinical group achieved thresholds of 98 and 187 arcseconds on the two tasks. A two-way ANOVA gave a significant main effect of group (F[1,56] = 5.92, P = 0.018), reflecting the higher thresholds in the clinical group, and a significant main effect of stereo task (F[1,56] = 7.25, P = 0.009), with a nonsignificant interaction (F[1,56] = 0.06, P = 0.80). That is, both groups performed better on the contours task than the random-check stereo task, although clinical children were worse overall. These values correlate significantly with TNO stereoacuity thresholds obtained during orthoptic examination and show modest agreement in Bland–Altman analyses (see Supplementary Material and Supplementary Fig. S2, ). 
The Presence of Stereo-Vision
To examine the relationship between stereoacuity and the three spatial tasks, we sought to include those without measurable stereo-thresholds in the analysis, but without assigning these children arbitrary stereo-thresholds (which could potentially bias correlation analyses). We therefore divided children into two groups: “stereo,” for those with measurable thresholds (below 1000 arcseconds) on either of our Vac-Man stereo tasks, and “nonstereo” for those who failed both tasks. Children were grouped in this way regardless of their clinical condition. Note that we did not incorporate data from the control group simply to avoid them dominating the “stereo” category. This gave a population of 23 stereo and 30 nonstereo observers, whose thresholds are plotted in Figure 5. Individual points show observers grouped by their clinical condition, whereas gray bars show overall means. 
Figure 5. 
 
Interocular differences on the three spatial tasks for stereo and nonstereo observers in the three clinical groups. (A) IODs in acuity, plotted in log minutes difference. Points show individual observers (colored according to their clinical classification), whereas group averages are shown as gray bars. The result of a two-way t-test between stereo and nonstereo observers is indicated by the central bracket, with significance levels shown in the figure legend. (B) IODs in contrast-detection thresholds, in log percent difference units, plotted as in (A). (C) IODs in crowding, in degrees of difference, plotted as in (A).
Figure 5. 
 
Interocular differences on the three spatial tasks for stereo and nonstereo observers in the three clinical groups. (A) IODs in acuity, plotted in log minutes difference. Points show individual observers (colored according to their clinical classification), whereas group averages are shown as gray bars. The result of a two-way t-test between stereo and nonstereo observers is indicated by the central bracket, with significance levels shown in the figure legend. (B) IODs in contrast-detection thresholds, in log percent difference units, plotted as in (A). (C) IODs in crowding, in degrees of difference, plotted as in (A).
Figure 5A plots the IODs in acuity, which are smaller in the stereo group (an average 0.2 log minute difference) than the nonstereo group (0.3 log minute), a significant difference (unpaired t-test: t[51] = −2.07, P = 0.04). Inspection of the individual points reveals this pattern in each of the three clinical groups. In contrast, interocular differences for contrast detection (Fig. 5B) were similar for stereo and nonstereo individuals, and did not differ significantly (t[51] = −0.87, P = 0.39), although there was a tendency for nonstereo strabismic children to have improved contrast detection in their amblyopic eye. 
Crowding IODs show a large difference between the groups (Fig. 5C), with small IODs for stereo children (0.05° on average) and large IODs for nonstereo children (0.58° on average), a significant difference (t[51] = −3.78, P < 0.001). Although this could be due to the predominance of strabismic and mixed amblyopes in the nonstereo group, the same pattern is clearly evident within each of the three clinical categories. Interestingly, the sole control subject who failed both our stereo tasks also showed elevated crowding with an IOD of −0.86°, much larger than the average control IOD of −0.01°. A similar pattern is evident within the “stereo” category of children when precise stereoacuity thresholds are plotted against these IOD values (see Supplementary Material and Supplementary Fig. S4), although the reduced range of these values and lower subject numbers considerably reduces the clarity of these effects. 
Discussion
We report four key findings. The first two document the threshold abilities of children in the control and clinical groups, and replicate previous results, while the second two present novel insights into the correlation between these thresholds. 
Visual Abilities in Childhood and Amblyopia
First, our Vac-Man paradigm successfully detected the interocular acuity differences of strabismic, anisometropic, and mixed amblyopia, as well as interocular differences in foveal crowding for the strabismic and mixed groups. This pattern of crowding deficits is consistent with previous observations in childhood 28,30,31 and adult 79 amblyopia, and rises above the already significant levels of crowding that we observe in both eyes of all children (as observed previously 2729 ). Here we demonstrate crowding using a task with clearly individuated elements (that are nonetheless sufficiently similar to induce crowding), thus avoiding the possibility of poor performance due to source confusions 41,42 or miscomprehension of the task. 
Our second key finding is that children had higher pass rates and lower stereoacuity thresholds in a stereo task with monocular contours than a random-checks–only version of the same task. This is consistent with prior observations, 4750 although others have argued that these improvements reflect the use of monocular cues. 51,52 That is, the contours could provide either spatial displacement cues (e.g., if the element offset in depth was clearly displaced leftward in one eye) or motion parallax cues during head movement. In our task, the use of horizontal displacement cues was eliminated by randomly sampling the zero-disparity distractors from either of the left- or right-eye stereo-images. Motion parallax cues should also have been minimal given the 3-m viewing distance. 54 We suggest instead that the contours may serve as a vergence cue to guide more efficient fusion of the two images. 47,50 It is also possible that the larger contours aid stereopsis because of their additional low spatial frequency content, whereas random-check stimuli rely exclusively on high spatial frequencies. In anisometropic adults, stereoacuity indeed shows greater impairments in the high spatial frequency range. 55 This finding not only suggests that amblyopic stereoacuities may be systematically underestimated, but also that stereo-training programs may have greater success if the initial stages use contour-rich stimuli. 
Unlike previous studies, we did not observe any differences in contrast-detection sensitivity between our groups. The lack of effect on contrast detection in children differs from adult amblyopia, where the amblyopic eye of anisometropes and mixed strabismic–anisometropes typically shows impaired contrast detection, whereas that of strabismics often improves. 2 We report a trend toward this pattern in our data, with the majority of our strabismic group showing better contrast detection in the amblyopic eye (67%) compared with more even distributions in the anisometropic (50%) and mixed (42%) groups. The changes in the visual system that produce this pattern of improvements and deficits may simply take longer to develop than the effects on acuity and crowding observed herein. Accordingly, although contrast deficits are evident in adults with broadband stimuli 4,5 (albeit at different magnitudes depending on the spatiotemporal frequency and color content6), deficits have been observed in children only with high spatial-frequency stimuli. 3 The use of narrowband stimuli may more closely reveal the development of these effects. 
Crowding and Its Relation to Acuity
Our third key finding is that interocular differences in acuity and crowding correlate for children in all groups (including control and anisometropic children, albeit trending in the mixed group). This suggests that childhood deficits in acuity and crowding are linked, regardless of their magnitude. Importantly, this correlation is not simply a general covariation in psychophysical performance, as contrast-detection thresholds did not correlate with either acuity or crowding. 
The correlation between acuity and crowding in strabismic children is consistent with that shown previously in strabismic adults. 7,8,32 Others, however, have found that the scale of foveal crowding in strabismic adults can greatly exceed that of their acuity losses. 33,34 In fact, our data show both features: although acuity and crowding IODs correlate for all children, crowding IODs in the strabismic and mixed groups increase sharply once acuity IODs exceed some critical value (Fig. 3D). This additional increase in crowding more closely resembles the excessive scale of crowding observed in cases of adult strabismus 33,34 and was greatest in the mixed group, resulting in the nonsignificant trend between acuity and crowding for these children. Further, the few anisometropes in our sample with large acuity IODs do not exhibit this sharp elevation in crowding, suggesting that this additive crowding may require the presence of strabismus. Were the strength of this additive element to increase over time, it could produce the dissociation between acuity and crowding observed in some adult amblyopes. 33,34 This differs from the “normal” adult fovea, where acuity and crowding continue to be correlated, 7 consistent with our observations in unaffected children. Although the magnitude of foveal crowding decreases significantly in adulthood, 29 the correlation with acuity thus appears to remain. It could be the case that acuity and crowding are initially linked, before diverging in strabismic amblyopia (if unsuccessfully treated) as the deficit builds over time. 
A potential complication with the observed link between acuity and crowding arises from our variation in stimulus sizes, which were scaled relative to acuity thresholds. Although crowding is largely size invariant in both the strabismic fovea 34 and the normal periphery, 44,56 in the normal adult fovea it varies with size. 46 Our observed covariations between acuity and the extent of foveal crowding could therefore simply result from the larger stimulus sizes used to measure crowding. Although the size tuning of foveal crowding in children is not known, dividing the spatial extent of crowding by acuity thresholds nonetheless reveals a persistent degree of crowding in all groups (see Supplementary Material and Supplementary Fig. S5A). The increase in crowding IODs for nonstereo children over those with intact stereo-vision is similarly resistant to this correction (see Supplementary Material and Supplementary Fig. S5B). Since stimulus size and acuity were directly proportional in our study, it is not possible to determine whether size-corrected crowding values continue to correlate with acuity, but given the above we suggest that these correlations are unlikely to solely reflect variations in stimulus size. 
Stereo-Vision and Its Relation to Acuity and Crowding
Our fourth key finding is that interocular differences in both acuity and crowding were significantly larger for children without measurable stereoacuity than for those with measurable stereoacuity. Correlations between these abilities were also evident in children with measurable stereoacuity thresholds (see Supplementary Material and Supplementary Fig. S4). Together, these results suggest a link between acuity, crowding, and stereo-vision both in normal development and in cases of strabismus and anisometropia. This link between large IODs in acuity and the loss of stereo-vision has been observed previously in adults, 2,10,12 but to our knowledge, the present study is the first demonstration of a link between stereo-vision and crowding. 
The correlation between these three deficits suggests that they may share a common cause. Accordingly, both interocular acuity differences and the loss of stereoacuity have previously been attributed to a loss of binocular cells and a shift in the selectivity of monocular cells away from the amblyopic eye. 1,2,1618 The loss of binocular cells would obviously impair stereo-vision, while this in conjunction with the shift in monocular cell selectivities could also impair acuity. That is, with monocular viewing, the amblyopic eye of a nonstereo observer would have access only to its own monocular cells, whereas the fellow eye would also have access to the formerly binocular cells. In addition, this redirection of cell selectivities could also lead to elevations in crowding; if crowding were the result of a neural undersampling of the visual field, 8 then the reduced sampling of the amblyopic eye may prompt an increase in this pooling process. In the normally developing visual system, the maturation of these cell selectivities may give similar linkages between these abilities. 
Alternately, both strabismic and anisometropic amblyopia have been linked with an increase in positional noise, 5759 which could certainly reduce the visibility of fine detail and hinder the detection of the interocular correlations in stereo-vision. Positional uncertainty has also been proposed to account for crowding, 60,61 although weighted averaging provides a closer approximation of the systematic errors that arise in crowded conditions. 23,24 It is possible that positional noise may contribute to these processes in the case of amblyopia, however. 62 Age-related improvements are also seen for Vernier acuity in normally developing children, 63,64 suggesting that the maturation of positional encoding processes could similarly underlie the linked impairments in acuity, crowding, and stereo-vision. Of course, these two mechanisms (alterations in cell selectivity and increased positional noise) are not mutually exclusive and some combination of the two is possible. 
The Neural Loci of These Abilities
If acuity, crowding, and stereo-vision do share a common basis, as we suggest above, where could the neural changes that give rise to these covariations occur? An obvious candidate is V1, which changes substantially under amblyopic conditions. 1,18 As above, shifts in the ocular dominance of V1 cells could account for both the acuity losses and the disruption of stereo-vision observed herein. However, it has been noted that the scale of psychophysical deficits in amblyopia does not match the scale of physiologic changes in V1. 65 Changes beyond V1 are therefore likely, although precisely where these changes occur is unclear. 
The neural basis of crowding is even more elusive. It has long been thought to occur at least at the level of V1 binocular cells, 66 although many psychophysical effects have suggested that its primary operation may be at higher levels. 26,6770 Recent work suggests that crowding may in fact operate at multiple levels in the visual hierarchy, 71 increasingly modulating activity throughout cortical regions V1 to V4. 72 The multilevel nature of crowding could mean that some of the elevated crowding we observe results from changes in early visual cortex (e.g., V1). These early-stage deficits could produce the covariation with acuity and stereo-vision, although of course this could also arise if these alterations in V1 selectivity were inherited by higher-level regions. In contrast, the apparent dissociation of crowding from acuity with large IODs (in the presence of strabismus) could reflect distinct processes beyond V1. Similarly, although the developmental forms of crowding we observe in our control group could reflect the maturation of V1 function, the late maturation of connectivity and function in higher cortical regions 73 suggests that later-stage processes could be what drive these elevations. The neural changes that give rise to elevated crowding may thus be widespread throughout the visual system. Regardless of their origins, however, our results suggest that these changes have consistent effects on acuity, crowding, and stereo-vision. 
Supplementary Materials
Acknowledgments
The authors thank Kate Naylor, Emma Jenkinson, Marko Nardini, Eliza Burton, and Jennifer Bales for help with recruitment, and Elaine Anderson and Gary Rubin for helpful discussion. 
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Footnotes
 Supported by the Special Trustees of Moorfields, the UK Department of Health through the award made by the National Institute for Health Research to Moorfields Eye Hospital and UCL Institute of Ophthalmology for a Biomedical Research Centre for Ophthalmology, and a Marie Curie Intra-European Fellowship (JAG).
Footnotes
 Disclosure: J.A. Greenwood, None; V.K. Tailor, None; J.J. Sloper, None; A.J. Simmers, None; P.J. Bex, None; S.C. Dakin, None
Figure 1. 
 
Apparatus and stimuli. (A) Stimuli were viewed through stereoscopic shutter glasses mounted in a children's ski mask (inset) and presented on a 3D-compatible monitor viewed at 3 m. An example trial of the acuity/contrast task is depicted. Children reported the color of the ghost that Vac-Man was facing. Colored cards were present on the monitor edges for reference. (B) An example frame from the “reward animation” (see Supplementary Material and Supplementary Movies S2S4). (C) Depiction of the crowding stimuli. Ghosts were rendered achromatically and presented at random orientations at a fixed separation from Vac-Man. The task was as in (A), with the reference cards assisting color memory. (D) An example frame from the stereo task with monocular “shadow” contours, representing input to one of the eyes. Children were required to help Vac-Man find the ghost that “popped out” in depth. (E) An example ghost from the stereo task with a monocular “shadow,” viewable with red–green anaglyphs (red filter to the right eye; actual stimuli were achromatic). (F) An example ghost from the random-check stereo task, with a disparity offset defined purely by the random-check elements.
Figure 1. 
 
Apparatus and stimuli. (A) Stimuli were viewed through stereoscopic shutter glasses mounted in a children's ski mask (inset) and presented on a 3D-compatible monitor viewed at 3 m. An example trial of the acuity/contrast task is depicted. Children reported the color of the ghost that Vac-Man was facing. Colored cards were present on the monitor edges for reference. (B) An example frame from the “reward animation” (see Supplementary Material and Supplementary Movies S2S4). (C) Depiction of the crowding stimuli. Ghosts were rendered achromatically and presented at random orientations at a fixed separation from Vac-Man. The task was as in (A), with the reference cards assisting color memory. (D) An example frame from the stereo task with monocular “shadow” contours, representing input to one of the eyes. Children were required to help Vac-Man find the ghost that “popped out” in depth. (E) An example ghost from the stereo task with a monocular “shadow,” viewable with red–green anaglyphs (red filter to the right eye; actual stimuli were achromatic). (F) An example ghost from the random-check stereo task, with a disparity offset defined purely by the random-check elements.
Figure 2. 
 
Thresholds for the three spatial tasks. (A) Acuity thresholds, in log minutes of visual arc (equivalent to logMAR). Data are separated into left- and right-eye thresholds for the controls and amblyopic/fellow eye for the three clinical groups. Colored bars show group means; gray points are individual data. Symbols at the top show the significance of paired-samples t-tests between the eyes of group members (as in the figure legend). (B) Contrast-detection thresholds, in log units of percent Weber contrast, expressed as in (A). (C) Thresholds for the spatial extent of foveal crowding, expressed as the center-to-center separation between target and flankers in degrees of visual arc.
Figure 2. 
 
Thresholds for the three spatial tasks. (A) Acuity thresholds, in log minutes of visual arc (equivalent to logMAR). Data are separated into left- and right-eye thresholds for the controls and amblyopic/fellow eye for the three clinical groups. Colored bars show group means; gray points are individual data. Symbols at the top show the significance of paired-samples t-tests between the eyes of group members (as in the figure legend). (B) Contrast-detection thresholds, in log units of percent Weber contrast, expressed as in (A). (C) Thresholds for the spatial extent of foveal crowding, expressed as the center-to-center separation between target and flankers in degrees of visual arc.
Figure 3. 
 
Correlations between interocular differences on each of the three spatial tasks. (A) Correlations between interocular differences in acuity (log minutes difference) and contrast detection (log percent difference). Individual points show each observer and lines for each group display the best-fitting line to the data, with significance indicated on the rightward end. (B) Correlations between IODs in contrast detection and crowding, plotted as in (A). (C) Correlations between IODs for acuity and crowding (degrees difference), plotted as in (A). (D) Acuity and crowding IODs are replotted, with running means (±1 child) for the crowding IODs shown as a function of the acuity IOD. Data points (as in C) are dimmed for clarity.
Figure 3. 
 
Correlations between interocular differences on each of the three spatial tasks. (A) Correlations between interocular differences in acuity (log minutes difference) and contrast detection (log percent difference). Individual points show each observer and lines for each group display the best-fitting line to the data, with significance indicated on the rightward end. (B) Correlations between IODs in contrast detection and crowding, plotted as in (A). (C) Correlations between IODs for acuity and crowding (degrees difference), plotted as in (A). (D) Acuity and crowding IODs are replotted, with running means (±1 child) for the crowding IODs shown as a function of the acuity IOD. Data points (as in C) are dimmed for clarity.
Figure 4. 
 
Performance on the two stereo tasks. (A) The percentage of children from each group who achieved measurable stereoacuity thresholds (less than 1000 arcseconds) on either of the contour-based (light gray bars) or the random-check stereo task (RCS task; dark gray bars). (B) Thresholds on the two stereo tasks, plotted in log seconds of arc. Data are taken only from children with measurable stereo on both tasks, grouped into either “control” or “clinical” categories. The latter includes children from the strabismic (blue triangles), anisometropic (green squares), and mixed (yellow inverted triangles) groups. Gray bars show the mean thresholds for each group on each task. The results of paired differences t-tests are shown for each group at the top of the figure, with significance levels shown in the figure legend.
Figure 4. 
 
Performance on the two stereo tasks. (A) The percentage of children from each group who achieved measurable stereoacuity thresholds (less than 1000 arcseconds) on either of the contour-based (light gray bars) or the random-check stereo task (RCS task; dark gray bars). (B) Thresholds on the two stereo tasks, plotted in log seconds of arc. Data are taken only from children with measurable stereo on both tasks, grouped into either “control” or “clinical” categories. The latter includes children from the strabismic (blue triangles), anisometropic (green squares), and mixed (yellow inverted triangles) groups. Gray bars show the mean thresholds for each group on each task. The results of paired differences t-tests are shown for each group at the top of the figure, with significance levels shown in the figure legend.
Figure 5. 
 
Interocular differences on the three spatial tasks for stereo and nonstereo observers in the three clinical groups. (A) IODs in acuity, plotted in log minutes difference. Points show individual observers (colored according to their clinical classification), whereas group averages are shown as gray bars. The result of a two-way t-test between stereo and nonstereo observers is indicated by the central bracket, with significance levels shown in the figure legend. (B) IODs in contrast-detection thresholds, in log percent difference units, plotted as in (A). (C) IODs in crowding, in degrees of difference, plotted as in (A).
Figure 5. 
 
Interocular differences on the three spatial tasks for stereo and nonstereo observers in the three clinical groups. (A) IODs in acuity, plotted in log minutes difference. Points show individual observers (colored according to their clinical classification), whereas group averages are shown as gray bars. The result of a two-way t-test between stereo and nonstereo observers is indicated by the central bracket, with significance levels shown in the figure legend. (B) IODs in contrast-detection thresholds, in log percent difference units, plotted as in (A). (C) IODs in crowding, in degrees of difference, plotted as in (A).
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