ASTEROID: A New Clinical Stereotest on an Autostereo 3D Tablet

Abstract

Purpose: To describe a new stereotest in the form of a game on an autostereoscopic tablet computer designed to be suitable for use in the eye clinic and present data on its reliability and the distribution of stereo thresholds in adults.

Methods: Test stimuli were four dynamic random-dot stereograms, one of which contained a disparate target. Feedback was given after each trial presentation. A Bayesian adaptive staircase adjusted target disparity. Threshold was estimated from the mean of the posterior distribution after 20 responses. Viewing distance was monitored via a forehead sticker viewed by the tablet's front camera, and screen parallax was adjusted dynamically so as to achieve the desired retinal disparity.

Results: The tablet must be viewed at a distance of greater than ∼35 cm to produce a good depth percept. Log thresholds were roughly normally distributed with a mean of 1.75 log10 arcsec = 56 arcsec and SD of 0.34 log10 arcsec = a factor of 2.2. The standard deviation agrees with previous studies, but ASTEROID thresholds are approximately 1.5 times higher than a similar stereotest on stereoscopic 3D TV or on Randot Preschool stereotests. Pearson correlation between successive tests in same observer was 0.80. Bland-Altman 95% limits of reliability were ±0.64 log10 arcsec = a factor of 4.3, corresponding to an SD of 0.32 log10 arcsec on individual threshold estimates. This is similar to other stereotests and close to the statistical limit for 20 responses.

Conclusions: ASTEROID is reliable, easy, and portable and thus well-suited for clinical stereoacuity measurements.

Translational relevance: New 3D digital technology means that research-quality psychophysical measurement of stereoacuity is now feasible in the clinic.

Keywords: binocular vision; depth perception; psychophysics; stereoacuity; stereopsis.

Figures

Figure 1

Top-down view of eyes viewing a parallax-barrier autostereoscopic display. Image reproduced from Figure 1b of Serrano-Pedraza et al.

Figure 2

Parallax on the column-interleaved display. We use the notation of Serrano-Pedraza et al., where DI refers to the parallax in physical pixels and DH to parallax in pixels of the half-images. (A) The minimum possible parallax, where corresponding points are adjacent pixels (DI = 1, DH = 0). (B) One H-pixel of positive parallax (DI = 3, DH = 1). (C) One H-pixel of negative parallax (DI = −1, DH = −1). P is the width of one physical pixel, so the screen parallax P is P = pDI. The distance of the virtual object from the viewer is d = VI/(I − P), where V is the viewing distance and I is the interocular distance. When the parallax is small compared to the interocular distance, rather than exaggerated as shown here for clarity, a parallax change of ΔP causes a change in virtual distance Δd ≈ ΔP V/I.

Figure 3

Screenshot showing the test stimulus, with four patches of random-dot patterns. Three of these have a uniform disparity of +Δ/2, depicting a planar surface behind the screen, whereas the top-right patch contains a “target” region with disparity −Δ/2 (in front of the screen) on a background surface with disparity −Δ/2. The relative disparity between target and background is thus Δ. The yellow symbols, including the dashed square indicating the target, are shown for illustration and were not present in the stimulus.

Figure 4

Binocular occlusion geometry for our stimulus where a target surface (outlined in dashed yellow lines) appears in front of a background. (A) The front surface occludes different regions of the background in the two eyes. The pink (green) shaded regions indicate which parts of the stimulus are visible to the left (right) eye, respectively. To the left of the front surface, there is a narrow strip of the back surface that is visible only to the left eye. Dots in this region are accordingly left-monocular, visible only to the left eye. The same applies for the right eye, for a strip to the right of the front surface. (B) Shows the resulting left- and right-eye half-images. Most dots are binocular, that is, visible in both eyes, so a disparity can be defined. Dots on the back surface have uncrossed disparity (position in the left half-image is to the left of position in the right half-image), whereas dots on the front surface have crossed disparity (position in the left half-image is to the right of position in the right half-image). The monocular dots have no matching dots in the other eye and are said to be uncorrelated. Nothing identifies the uncorrelated dots in either half-image individually; they can be detected only when the two eyes' half-images are compared.

Figure 5

The sticker used as a target for distance tracking. Its dimensions are 37 mm wide by 35 mm high.

Figure 6

Screenshots from the animation showing the four stimuli being shuffled and dealt out again as a cue to the random stimulus location.

Figure 7

How accuracy and precision of threshold estimates depends on the level defined as threshold performance. The horizontal axis shows Θ, the proportion of correct answers defined as “threshold” (see Equation 8) and (above) the corresponding disparity values in log10 units. The vertical axis on each plot shows the bias in estimated threshold, that is, the difference between the threshold estimate returned after 20 trials and the model's true threshold θm, expressed in log10 stereo threshold units. By definition, Ψ(θm) = Θ. Black dots show the mean threshold estimate of 2000 simulated staircase procedures, as described in the Methods. Error bars show the standard deviation. The bias is close to zero, and the standard deviation is roughly constant, over a wide range of Θ (∼50%–80%). The staircase assumes the psychometric function given by Equation 9 with b = 4.885/log10 arcsec, λ = 0.03, g = 0.25, and Θ specified by the horizontal axis. The model observer is assumed to have a psychometric function with the same form and the same values of λ and g, but different slope parameters bM, as specified in each panel.

Figure 8

(A) Threshold estimates obtained on a simulated version of ASTEROID for four different example model observers. (B) Ninety-five percent limits of agreement for pairs of threshold estimates from the same four model observers. Model observers differ in their true stereo threshold, indicated by position on the horizontal axis, and in their lapse rate and the steepness of their psychometric function, as indicated by the different colored curves. Black: λM = 0.03, bM = 4.885/log10 arcsec; red: λ = 0.03, bM = 14.654/log10 arcsec; blue: λM = 0.03, bM = 2.931/log10 arcsec; green: λM = 0.1, bM = 4.885. In every case the simulated ASTEROID assumed λ = 0.03, b = 4.885.

Figure 9

Measured thresholds for two observers as a function of viewing distance. Symbols show measured thresholds (each from at least 20 nonpractice trials), slightly jittered to avoid overlap. Lines show trend obtained by loess smoothing; ribbon shows 95% confidence interval.

Figure 10

Test-retest reliability of ASTEROID assessed from 40 adult observers. (A) Stereo threshold on second test plotted against stereo threshold on first test. Solid line = identity, dashed line = 1.96 times standard deviation of difference in log10 arcsec (95% limits of agreement.) (B) Bland-Altman plot showing test-retest agreement on ASTEROID. Vertical axis shows the difference, in log arcseconds, between the results of two tests. The horizontal axis shows the mean result (the arithmetic mean of the log thresholds, which is the geometric mean of the thresholds in arcseconds). The horizontal dotted line shows the mean of all 35 differences. The horizontal dashed lines show the ±1.96 SD of the differences, which are Bland & Altman's 95% limits of agreement.

Figure 11

Results from 10 adults who completed three tests with ASTEROID (vertical axis) and three tests with an equivalent test presented on a stereoscopic 3D TV (horizontal axis). Data points show the mean of the three values obtained from each test (mean of log arcsecond) and error bars show ±1 SD. The solid line shows the identity, that is, perfect agreement. The dotted line shows the identity offset by the mean difference between the results, while the dashed lines show the Bland-Altman 95% limits of agreement between the two tests, that is, the mean difference ± 1.96 times the standard deviation of the difference. Means are computed on log thresholds, which correspond to the geometric mean of the thresholds in arcseconds.

Figure 12

Distributions of stereo thresholds obtained on ASTEROID (red, 74 participants) and from a similar test presented on a stereoscopic 3D TV in an earlier study (blue, 91 participants, corrected from 2AFC to 4AFC as described in the text). In both cases participants were adults aged from 18 to nearly 80 years. The thin lines show Gaussian distributions with the same mean and standard deviation as the corresponding data-set. Means and standard deviations excluded threshold estimates over 1000 arcsec, reflecting the view that stereoacuity reflects a mixture of two distributions: a roughly log-normal distribution (shown with the curves here) and a smaller proportion of observers who are stereoblind. Threshold estimates over 1000 arcsec were considered stereoblind and are plotted at 1000 arcsec.

Figure 13

Results from 52 adults who completed one test with ASTEROID (vertical axis) and one with the Randot Preschool stereotest (horizontal axis). Points have been jittered slightly horizontally to avoid symbol overlap. The black line marks the identity. Marginal distributions are shown along the sides. The correlation coefficient between log thresholds is r = 0.37 (P = 0.01).

Figure 14

Because disparity psychometric functions are quite shallow, even the steepest part of the curve spans a wide range of disparities. A 4.3-fold change in disparity (e.g., going from 33 to 141 arcsec for a threshold of 100 arcsec) only changes performance from 38% correct to 84% correct. Psychometric function (red curve) is given by Equation 9 with the parameters specified in that section, a threshold of θ = 100 arcsec, and disparity Δ indicated on the horizontal axis.