Vision Research 113 (2015) 97–103
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A normative dataset on human global stereopsis using the quick Disparity Sensitivity Function (qDSF) Alexandre Reynaud ⇑, Yi Gao, Robert F. Hess McGill Vision Research, Dept. Ophthalmology, McGill University, Montreal, PQ, Canada
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Article history: Received 6 December 2014 Received in revised form 23 February 2015 Available online 28 May 2015 Keywords: qDSF qCSF Disparity sensitivity Binocular vision Stereopsis Normative data
a b s t r a c t Global stereopsis results from the lateral displacement of distributed textured elements between the eyes. In this study, we investigate how the key parameters of the disparity sensitivity function such as its peak sensitivity and spatial bandwidth are distributed across a pool of normal observers and how large the individual differences are. For this purpose, we adapted the quick Contrast Sensitivity Function (qCSF, Lesmes et al., 2010) to the quick Disparity Sensitivity Function (qDSF). We show that this new method is accurate and allows a rapid measurement of disparity sensitivity for a range of different disparity spatial frequencies. Our results confirm that there is a greater variability in human disparity sensitivity tuning compared to other common visual features, for example, 1st or 2nd order contrast sensitivity. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Stereopsis involves the use of retinal disparity information, as a result of the lateral displacement of the images from the two eyes, to derive object depth. A variant of this that has proved useful in the laboratory is termed global stereopsis and involves the use of random pixel displays. Although this has a long history in cryptography (see Howard & Rogers, 2002), its experimental utility is attributed to Julesz (1960) who used it to show that monocular form information was not a prerequisite for stereopsis. Later, Tyler (1973, 1975) developed a version of the stimulus that allowed an investigation of the dependence of disparity sensitivity on the spatial scale of the stimulus. Since then there have been a host of studies on different aspects of global stereopsis including the effects of eccentricity (Witz & Hess, 2013), field size (Bradshaw & Rogers, 1999), temporal frequency (Lankheet & Lennie, 1996), orientation (Bradshaw & Rogers, 1999; Serrano-Pedraza & Read, 2010; Witz, Zhou, & Hess, 2013) and carrier properties (Hess, Kingdom, & Ziegler, 1999; Lee & Rogers, 1997; Witz & Hess, 2013). The vast majority of these studies have been conducted on a few experienced observers and there is a lack of data concerning the general population. Some studies have specifically used large
⇑ Corresponding author. E-mail address: [email protected] (A. Reynaud). http://dx.doi.org/10.1016/j.visres.2015.04.021 0042-6989/Ó 2015 Elsevier Ltd. All rights reserved.
samples to measure standard stereo-acuity (Bosten et al., 2015) or to estimate the percentage of individuals who have defective stereo vision in the general population. However, using various stimuli, estimations differ. Richards (1970) used a single bar in depth to determine that about 30% of the populations lacks at least one category of disparity detectors (crossed, uncrossed or zero-disparity detectors). On the other hand, Stelmach and Tam (1996), using random dots stereograms, estimated that about 5% of the population was unable to utilize stereo disparity information to perceive depth. To investigate the innate individual differences in stereo ability and in particular the role of spatial scale, we measured the disparity sensitivity (inverse of disparity threshold) as a function of modulation spatial frequency in a large sample of normal observers. We wanted to know how the key parameters of the disparity sensitivity function such as its peak stereo sensitivity and spatial bandwidth were distributed across the normal population, and how large the individual differences were? In order to establish a normative dataset, we used a spatially bandpass fractal noise carrier and set its peak spatial frequency to be 4 times that of the disparity modulation. This ratio has been shown to be in the optimal range for global stereopsis (Lee & Rogers, 1997; Witz & Hess, 2013). Furthermore, to make comparable measurements on the disparity sensitivity of over 60 normal individuals, we adapted the quick Contrast Sensitivity Function (qCSF, Hou et al., 2010; Lesmes et al., 2010), which was originally designed for the rapid measurement of the contrast sensitivity
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function (CSF) across a full range of spatial frequencies and has been subsequently successfully applied to measure second-order sensitivity (Gao et al., 2014; Reynaud et al., 2014), as the quick Disparity Sensitivity Function (qDSF). As the disparity sensitivity function (DSF) presents approximately the same unimodal bell-shape as the first- and second-order sensitivity functions (Bradshaw & Rogers, 1999; Tyler, 1973; van der Willigen et al., 2010), we show that the truncated log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005) used by the qCSF method faithfully describe the disparity sensitivity too and that the qDSF method is accurate and allows the measurement of disparity sensitivity for a range of different disparity spatial frequencies within a ten-minute period.
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b 2. Methods 2.1. Observers Sixty-three subjects (25 males and 38 females, average age = 26.3 ± 5.7 years, range: 18–41 years) participated in the main experiment. Two of them were not able to perform the task although they mentioned clearly seeing the stimulus sometimes. They were classified as stereoblinds and were discarded from the study. This proportion corresponds to the one that has been previously reported in the normal population (Richards, 1970; Stelmach & Tam, 1996). Four subjects of the pool, including two authors, participated in the control experiment. All subjects had normal or corrected-to-normal visual acuity and were free from ocular diseases. Informed consent was obtained from all subjects. This research has been approved by the Ethics Review Board of the McGill University Health Center. It was performed in accordance with the ethical standards laid down in the Code of Ethics of the World Medical Association (Declaration of Helsinki).
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2.2. Apparatus Experiments were run on an Apple iMac11.1 (MacOSX) computer. Stimuli and experimental procedures were programmed with Matlab R2010a (Ó the MathWorks) using the Psychophysics (Brainard, 1997; Kleiner, Brainard, & Pelli, 2007; Pelli, 1997) and qCSF (Lesmes et al., 2010) toolboxes. Data was analyzed off-line using Matlab R2013a (Ó the MathWorks) with the qCSF (Lesmes et al., 2010) and Palamedes (Prins & Kingdom, 2009) toolboxes. Stimuli were displayed on a wide 2300 3D-Ready LED monitor ViewSonic V3D231, gamma corrected with a mean luminance of 100 cd m2. The stereo image input was in top-down VGA format and was displayed in interleaved line stereo mode at a resolution of 19201080p and a refresh rate of 60 Hz: the left eye image was displayed in even scanlines and the right eye image was displayed in odd scanlines. The subject viewed the stimuli at a viewing distance of 70 cm, in a dim-lit room, with passive polarized 3D glasses so that the left image was only seen by the left eye and the right image by the right eye. The polarized filters had the effect of reducing the luminance to about 40%, measured with a photometer. 2.3. Stimuli Stimuli were stereograms composed with spatially filtered 2-D fractal noise carriers. They presented oblique (45° or 135° degrees) sinusoidal corrugations at different frequencies (Fig. 1a). To build the carrier, two-dimensional fractal noise was generated by weighting the amplitude spectrum of an uniformly distributed noise by one over spatial frequency (1/f) and subsequently filtered with a discrete step-edge bandpass filter at a frequency of 4 times
Fig. 1. Methods. (a) Stimuli consisted of 2-D fractal noise stereograms filtered in different frequency bands, viewed with passive polarized glasses on a 3D monitor. Disparity between the two eyes was modulated by an oblique sinusoidal corrugation (here at 135°) at different frequencies. (b) The subject task was to identify the orientation of the disparity-modulation of the stimulus which could be oblique at 45° (left) or 135° (right). (c) The disparity sensitivity function is described by the truncated log-parabola model as a function of the spatial frequency. Two parameters are studied: the peak gain (cmax) and the peak frequency (fmax).
the spatial frequency of the corrugation and a one octave bandwidth. Stimuli visibility was equated by scaling the carrier contrasts to 10 times the contrast thresholds measured for each carrier spatial frequency in a normative dataset (Reynaud et al., 2014). They were respectively set to 32, 27, 25, 27, 33, 47, 75 and 100% (clipped) for carrier frequencies of 0.94, 1.31, 1.83, 2.54, 3.54, 4.93, 6.87, and 9.57 c/d. Sinusoidal corrugation was introduced by shifting the carrier following a vertical sinusoïd of opposite phase for each eye image. Non-integer pixel positions were linearly interpolated between neighboring pixels. Then each pixel line was subsequently shifted one pixel to the right to obtain the 45° corrugation or to the left to obtain the 135° corrugation in each stereogram. Stimuli were presented in a Gaussian aperture of 15° diameter. We checked that
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it was not possible to perform the experiment monocularly in order to ensure that the oblique sinusoidal corrugation did not generate visible compression and expansion artifacts in the carrier noise patterns. 2.4. Procedures and analysis The subjects’ task was to identify the orientation of the disparity corrugation (45° or 135°, Fig. 1b) in a single-interval identification task. A trial time course was as follows: (1) a green fixation dot appeared on the screen, (2) the dot disappeared and the stimulus was presented for 1 s, (3) a red dot appeared until the subject responded by pressing a keypad, (4) after the subject answered, the dot disappeared and audio feed-back about the correctness of the response was provided. Dot luminance was matched to that of the background. 2.4.1. Control experiment – the Method of Constant Stimuli In a control experiment, the disparity thresholds were measured individually with the Method of Constant Stimuli (MCS) for each spatial frequency: 0.24, 0.33, 0.46, 0.64, 0.89, 1.23, 1.72 and 2.39 c/d. The order in which participants performed the different spatial frequency conditions was randomized. The levels of disparity used were 0.13, 0.18, 0.25, 0.36, 0.50, 0.71, 1.00, 1.41, 2.00, 2.83, 4.00 and 5.66 arc min. There were 20 repetitions per condition for each subject. Each measurement took approximately 15 min. The detection thresholds were then determined by fitting a Weibull function of the log-disparity to the psychometric datasets (Eq. (1), maximum likelihood estimation method):
b F W ðx; a; bÞ ¼ 0:5 þ 0:5 1 eðx=aÞ
ð1Þ
where x is the log-disparity, a the log-threshold and b the slope of the psychometric function. The standard deviation of the fitted parameters was estimated by a bootstrapping procedure. 2.4.2. Main experiment – the quick Disparity Sensitivity Function The sensitivity functions were determined using the quick Contrast Sensitivity Function (qCSF) method (Hou et al., 2010; Lesmes et al., 2010). This method is a Bayesian adaptive procedure that was designed for concurrently estimating contrast thresholds across the full spatial-frequency range. Here we adapted it and used it to estimate the quick disparity sensitivity function (qDSF). Before each trial, the method finds the optimal stimulus in order to maximize the expected information gain about the parameters of the disparity sensitivity function (Lesmes et al., 2010). The operative range for the disparity was set from 0.0125 to 12.5 arc min and the frequency range was truncated from 0.24 to 2.39 c/d. An initial prior represents foreknowledge of the subject’s disparity sensitivity function parameters. The initial gain prior was set to 0.8 arc min, the peak frequency prior was set to 0.5 cpd and the bandwidth prior was set to 3 octaves. In this range, the qDSF method will be effective because this range is below the Dmax threshold, where the psychometric functions are monotonically increasing (Filippini & Banks, 2009; Kane, Guan, & Banks, 2014; Tyler, 1975; Wilcox & Hess, 1995; Ziegler, Hess, & Kingdom, 2000). The qDSF measurement took approximately 8 min, was repeated twice, and averaged. The method estimates the sensitivity function with a truncated log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005), which is described by four parameters: the peak gain cmax, the peak frequency, fmax, the bandwidth b and the truncation d:
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2 10 ðf max Þ S0 ðf Þ ¼ log10 ðcmax Þ j log10 ðf Þlog b0 =2 Sðf Þ ¼ log10 ðcmax Þ d if f < f max and S0 ðf Þ < log10 ðcmax Þ d Sðf Þ ¼ S0 ðf Þ else
ð2Þ
with j = log10(2) and b0 = log10(2b). However, we discarded the bandwidth and truncation parameter from our analysis as they were often out of the range of our measurements (Fig. 1c). 3. Results 3.1. Suitability of the truncated log-parabola model As a first step we show that the qCSF method can be adapted to disparity sensitivity measurement. It is known that the disparity sensitivity function has a bell-shape (Bradshaw & Rogers, 1999; Tyler, 1973; van der Willigen et al., 2010). However, the accuracy of the truncated log-parabola model to describe the disparity sensitivity function still needs to be assessed. Thus, we tested this model on the disparity sensitivity measured using the Method of Constant Stimuli. The Fig. 2 presents the measured psychometric functions for one observer at each spatial frequency. The minimum disparity thresholds are estimated by fitting a Weibull function on the log-disparity. We can see that the psychometric functions are monotonic and smooth without showing a drop at high disparities which confirms that, for the fractal noise stimulus and the sinusoidal corrugation used here, the range of disparities tested are within the maximum disparity limit (Dmax; Filippini & Banks, 2009; Tyler, 1975; Wilcox & Hess, 1995; Ziegler, Hess, & Kingdom, 2000). The measured sensitivity with the MCS from four subjects is reported as a function of spatial frequency in Fig. 3. These four subjects’ disparity sensitivities exhibit very different gain and tuning. The first subject’s disparity sensitivity displays a high-pass profile (Fig. 3a). The disparity sensitivity of the second and third subjects displays a band-pass one (Fig. 3b and c). And the last subject’s disparity sensitivity displays a low-pass with very low gain profile (Fig. 3d). The data points are fitted a posteriori with the truncated log-parabola model (Eq. (2), least-squares estimation method). The function faithfully fits the data for all subjects (solid lines in Fig. 3, mean coefficient of determination r2 = 0.80 for the four subjects), therefore we can affirm that the truncated log-parabola is an accurate model to describe disparity sensitivity functions. The qDSF estimates are very consistent with the datapoints too (Fig. 3 dashed lines, mean coefficient of determination r2 = 0.51 for the four subjects). The two studied parameters of the model: the peak gain cmax and the peak frequency fmax are not significantly different between the truncated log-parabola a posteriori estimates and the qDSF estimates (paired Wilcoxon signed rank test, a = 0.05). Hence, we can say that the sensitivity functions estimated with the two methods are consistent and accurate and therefore the qDSF method is an appropriate tool to measure the sensitivity to disparity and so for very different function tunings. 3.2. Normative dataset The average and standard deviation of the disparity sensitivity functions over the 61 subjects are shown in Fig. 4a. We can see that the disparity sensitivity approximately increases from 0.3 arc min1 at low frequencies and peaks at a frequency of 1.2 c/d with a maximum gain of 1.2 arc min1. This tuning for disparity is consistent with previous studies using the same kind of filtered noise stimulus, (Lee & Rogers, 1997; Witz & Hess, 2013). The dashed line shows the disparity-sensitivity function reconstructed from the log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005) with the median parameters
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Fig. 2. Psychometric functions obtained with the MCS at each spatial frequency, respectively in each panel, for the subject AR. The datapoints (crosses) represent the performance of the subject as a function of the disparity, Thresholds (squares) are estimated by fitting a Weibull function on the log-disparity (continuous line, Eq. (1)).
estimated by the qDSF. It accurately represents the data and thereby illustrates the model-derived peak frequency and gain. The thin dark gray line represents the standard deviation of the disparity-sensitivity functions of all the subjects. This variability is
quite large and increases at high spatial frequencies (Legge & Yuanchao, 1989), peaking around 1.7 c/d. We can also observe this increment in variability by the fact that the 5% and 95% percentile boundaries diverge at high-spatial frequencies. In detail, we plot in
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a
b
c
d
Fig. 3. Accuracy of the truncated log-parabola model. Sensitivity measurements and model fits for four subjects. Their disparity sensitivities are reported in function of the spatial frequency. The square symbols represent sensitivity measures with the MCS, error bars indicate standard deviation, solid lines represent a posteriori fits of the MCS data with the truncated log-parabola model (Eq. (2), least-square estimation method), dotted lines represent qDSF measurements. (a) Subject AR presents a high-pass profile. (b) Subject YG presents a band-pass profile. (c) Subject MS presents a band-pass profile. (d) Subject GS presents a low-pass profile.
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b
c
Fig. 4. Normative dataset; (a) averaged sensitivity function from the data (thick black line) with standard deviation (shaded gray area) and sensitivity function reconstructed with the median qDSF parameters using the log-parabola model (dashed line). The gray thin line represents the standard deviation as a function of the spatial frequency and the dotted lines represent the 5% and 95% percentile boundaries. (b) individual sensitivity functions for the 61 subjects. (c) Distribution of the sensitivities at 1.72 c/d.
Fig. 4b the individual disparity-sensitivity functions for all the 61 subjects. These sensitivities are normally distributed at low spatial frequencies below 0.7 c/d and then skewed at high spatial frequencies (Shapiro–Wilk test, a = 0.05). Specifically, the distribution of the sensitivities at 1.72 c/d, high spatial frequency for which the standard deviation is maximal is reported on a log-scale in Fig. 4c. This distribution has a skewness of 0.86. These observations confirm that the tuning for disparity can be very different from subject to subject, some display a low-pass
profile whereas some others display a more band-pass or high-pass one, resulting in the greater variability observed. Such individual differences in disparity spatial frequency sensitivity have already been reported (Legge & Yuanchao, 1989) but their extent within a larger population is only confirmed by the present data. We investigated the consistency between the different sensitivity patterns observed by plotting the maximum gain as a function of the peak frequency for all subjects, as shown in Fig. 5. The distributions of the peak frequency and the log-gain are represented at the
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top and the right-side of the scatter-plot respectively. They are normal (Shapiro–Wilk test, a = 0.05) and look much wider than what has been reported for contrast detection or second-order sensitivities. Although the modulations in luminance and contrast are processed by different neural mechanisms than those involved in disparity, the relative variability in these different functions is worthy of comparison. To compare this relative variability, we compute the coefficients of variation of the peak frequency and the maximum gain for the disparity sensitivity (Table 1). We compare these standardized measures to the ones calculated for first-order (contrast) and second-order (contrast-modulation, orientation-modulation and motion-modulation) sensitivities from our previous study, using the same approach (from Table 1 in Reynaud et al., 2014). The coefficient of variation of the gain distribution is 2 times larger for the disparity sensitivity than for the first- and second-order sensitivities. Furthermore, the coefficient of variation of the frequency is almost 2 times larger for the disparity sensitivity than for the first-order sensitivity. This higher relative variability is significant (one-tailed F-test on the log-values of the gain and peak frequencies, a = 0.05, Lewontin, 1966), however the relative variability of the peak frequency for disparity sensitivity is not different from that of second-order sensitivity. Second, we can see a correlation between the peak frequency and the log-gain (r2 = 0.12, p < 0.01): the higher the peak-frequency, the higher the gain. This indicates that people with poor stereo vision are selectively deficient at high spatial frequencies and not equally poor for all spatial frequencies. 4. Discussion 4.1. Validity of the qDSF Our results are in line with previous studies that have investigated stereo-sensitivity using bandpass filtered noise carriers (Tyler, 1973; Witz, Zhou, & Hess, 2013; Yang & Blake, 1991; Witz, Zhou, & Hess, 2014). However the average disparity
Table 1 Mean (l), standard-deviation (r) and coefficient of variation (cv) of the distributions of the estimates of the maximum gain cmax, and the peak frequency fmax, for the firstand second-order sensitivity functions measured on a normative dataset from Reynaud et al. (2014) and for disparity. Frequencies are expressed in c/d. Disparity gain in arc min1.
cmax 1st order 2nd order Disparity
fmax
l
r
cv
l
r
cv
43.11 5.43 1.17
11.30 1.01 0.56
0.26 0.23 0.48
1.92 1.02 1.24
0.44 0.32 0.41
0.19 0.31 0.33
sensitivity reported here occurs at a higher peak frequency and has a lower maximum gain than what has been observed using spatially broadband random dots carriers (Bradshaw & Rogers, 1999; Schumer & Julesz, 1984; van der Willigen et al., 2010; Westheimer & McKee, 1980), including measurements of depth from motion parallax (Rogers & Graham, 1982). In this study, we used a line-interleaved dichoptic presentation of the stimuli on the screen instead of the previous method of frame interleaving. Line interleaving is superior temporally because there is a much shorter temporal asymmetry although the spatial resolution is reduced. The use of the qCSF method to measure contrast sensitivity and second-order sensitivity has already been validated (Lesmes et al., 2010; Reynaud et al., 2014). In the first section, we demonstrated that the truncated log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005) accurately describes the disparity sensitivity as well. We confirmed that the qDSF and the MCS lead to slightly but not significantly different results. Indeed, it is not surprising that different psychophysical estimation procedures lead to different results (Kingdom & Prins, 2010; Leek, 2001). The constrained shape of the qDSF reduces the risk of outliers, whereas with the MCS, subjects might have attentional benefits due to its prior knowledge of the appearance of the stimulus (Davis & Graham, 1981; Woods, 1996). The standard procedures are time consuming, however the qDSF method requires approximately 10 times less trials and is optimally suitable for large sample sizes and clinical studies (Gao et al., 2014; Hou et al., 2010; Kalia et al., 2012). 4.2. Large variability of the disparity sensitivity between subjects
Fig. 5. Relationship between the peak frequency and the maximum gain of the disparity sensitivity for each subject. Each point represents the peak frequency and maximum gain for each sensitivity function in Fig. 4b with the same color. The black dotted line represents the best-fit linear regression. The histograms of the distribution of the peak frequencies and maximum gains for all subject are respectively represented above and aside of the graph. Note that the gain is represented on a log-scale. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
To study variability and achieve high statistical significance, we built our normative dataset on a large pool of subjects. We decided to focus on a group of younger adults (see Section 2), with not much variability in the age range in order to avoid any age-induced and acuity-induced artifacts. In this normative dataset, we observed a large variability among the observers associated with a significant correlation between the peak frequency and maximum gain of the disparity sensitivity. Such a correlation has already been observed for contrast sensitivity as a function of luminance (Cox, Norman, & Norman, 1999; Rovamo, Mustonen, & Näsänen, 1994) and eccentricity (Pointer & Hess, 1989), or for aging population (Owsley, Sekuler, & Siemsen, 1983) and also for second-order stimuli (Tang & Zhou, 2009). This correlation is not surprising given the unimodal shape of the disparity sensitivity function which increases to a peak and then decreases as a function of spatial frequency (Barten, 1999). This peak occurs at different spatial frequencies for each subjects and leads to either low, medium, or high spatial frequency tuning profiles (Fig. 3). This implies that for the general population, the disparity sensitivity is similar at low disparity spatial frequency, but variable at high disparity spatial frequencies. (Fig. 4b, see also Legge & Yuanchao, 1989).
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In first-order contrast and second-order modulation sensitivities, high spatial frequencies have been shown to be especially vulnerable to disruptions to visual development such as amblyopia (Hess & Howell, 1977; Levi & Harwerth, 1977; Gao et al. 2014) and normal aging (Owsley, Sekuler, & Siemsen, 1983; Tang & Zhou, 2009). Our results show that a significant proportion of young normal binocular subjects have reduced global disparity sensitivity for high disparity spatial frequencies. This is unlikely to be linked to reports of a significant crossed/uncrossed local stereo-anomaly within the normal population (Richards, 1970, 1971; van Ee & Richards, 2002) because our experiment did not depend on explicit ‘‘in front’’/‘‘behind’’ decisions. 5. Conclusions We show that the qDSF method is accurate and allows the measurement of disparity sensitivity for a range of different disparity spatial frequencies within a ten minutes period. With this method, we provide a normative dataset for disparity sensitivity that will be of particular interest for large sample sizes and clinical studies. From this large pool of subjects, our results confirm a greater variability in human disparity sensitivity tuning compared to other common visual features. This variability is particularly pronounced at high spatial frequency disparities. Acknowledgment This work was supported by a Natural Sciences and Engineering Research Council of Canada Grant (NSERC #46528) to RFH. References Ahumada, A. J., Jr., & Peterson, H. A. (1992). Luminance-model-based DCT quantization for color image compression. In B. E. Rogowitz (Ed.). Human vision, visual processing, and digital display III (Vol. 1666, p. 365Y374). Proceedings of the SPIE. Barten, P. G. J. (1999). Contrast sensitivity of the human eye and its effects on image quality SPIE. Bosten, J. M., Goodbourn, P. T., Lawrance-Owen, A. J., Bargary, G., Hogg, R. E., & Mollon, J. D. (2015). A population study of binocular function. Vision Research, 110(Pt A), 34–50. Bradshaw, M. F., & Rogers, B. J. (1999). Sensitivity to horizontal and vertical corrugations defined by binocular disparity. Vision Research, 39, 3049–3056. Brainard, D. H. (1997). The psychophysics toolbox. Spatial Vision, 10, 433–436. Cox, M. J., Norman, J. H., & Norman, P. (1999). The effect of surround luminance on measurements of contrast sensitivity. Ophthalmic and Physiological Optics, 19, 401–414. Davis, E. T., & Graham, N. (1981). Spatial frequency uncertainty effects in the detection of sinusoidal gratings. Vision Research, 21, 705–712. Filippini, H. R., & Banks, M. S. (2009). Limits of stereopsis explained by local crosscorrelation. Journal of Vision, 9(1), 8.1–818. Gao, Y., Reynaud, A., Tang, Y., Feng, L., Zhou, Y., & Hess, R. F. (2014). The amblyopic deficit for 2nd order processing: Generality and laterality. Vision Research. Hess, R. F., & Howell, E. R. (1977). The threshold contrast sensitivity function in strabismic amblyopia: Evidence for a two type classification. Vision Research, 17(9), 1049–1055. Hess, R. F., Kingdom, F. A., & Ziegler, L. R. (1999). On the relationship between the spatial channels for luminance and disparity processing. Vision Research, 39, 559–568. Hou, F., Huang, C.-B., Lesmes, L., Feng, L.-X., Tao, L., Zhou, Y.-F., et al. (2010). QCSF in clinical application: Efficient characterization and classification of contrast sensitivity functions in amblyopia. Investigative Ophthalmology & Visual Science, 51, 5365–5377. Howard, I. P., Rogers, B. J. (2002). Seeing in Depth. Toronto. Julesz, B. (1960). Binocular depth perception of computer generated patterns. Bell System Technical Journal, 39, 1125–1162. Kalia, A., Lesmes, L., Dorr, M., Bex, P., Gandhi, T., Swami, P., et al. (2012). Measurements of contrast sensitivity functions show recovery from extended blindness. Perception, 41. ECVP Abstract Supplement, 154. Kane, D., Guan, P., & Banks, M. S. (2014). The limits of human stereopsis in space and time. Journal of Neuroscience, 34(4), 1397–1408.
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A normative dataset on human global stereopsis using the quick Disparity Sensitivity Function (qDSF) Alexandre Reynaud ⇑, Yi Gao, Robert F. Hess McGill Vision Research, Dept. Ophthalmology, McGill University, Montreal, PQ, Canada
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Article history: Received 6 December 2014 Received in revised form 23 February 2015 Available online 28 May 2015 Keywords: qDSF qCSF Disparity sensitivity Binocular vision Stereopsis Normative data
a b s t r a c t Global stereopsis results from the lateral displacement of distributed textured elements between the eyes. In this study, we investigate how the key parameters of the disparity sensitivity function such as its peak sensitivity and spatial bandwidth are distributed across a pool of normal observers and how large the individual differences are. For this purpose, we adapted the quick Contrast Sensitivity Function (qCSF, Lesmes et al., 2010) to the quick Disparity Sensitivity Function (qDSF). We show that this new method is accurate and allows a rapid measurement of disparity sensitivity for a range of different disparity spatial frequencies. Our results confirm that there is a greater variability in human disparity sensitivity tuning compared to other common visual features, for example, 1st or 2nd order contrast sensitivity. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Stereopsis involves the use of retinal disparity information, as a result of the lateral displacement of the images from the two eyes, to derive object depth. A variant of this that has proved useful in the laboratory is termed global stereopsis and involves the use of random pixel displays. Although this has a long history in cryptography (see Howard & Rogers, 2002), its experimental utility is attributed to Julesz (1960) who used it to show that monocular form information was not a prerequisite for stereopsis. Later, Tyler (1973, 1975) developed a version of the stimulus that allowed an investigation of the dependence of disparity sensitivity on the spatial scale of the stimulus. Since then there have been a host of studies on different aspects of global stereopsis including the effects of eccentricity (Witz & Hess, 2013), field size (Bradshaw & Rogers, 1999), temporal frequency (Lankheet & Lennie, 1996), orientation (Bradshaw & Rogers, 1999; Serrano-Pedraza & Read, 2010; Witz, Zhou, & Hess, 2013) and carrier properties (Hess, Kingdom, & Ziegler, 1999; Lee & Rogers, 1997; Witz & Hess, 2013). The vast majority of these studies have been conducted on a few experienced observers and there is a lack of data concerning the general population. Some studies have specifically used large
⇑ Corresponding author. E-mail address: [email protected] (A. Reynaud). http://dx.doi.org/10.1016/j.visres.2015.04.021 0042-6989/Ó 2015 Elsevier Ltd. All rights reserved.
samples to measure standard stereo-acuity (Bosten et al., 2015) or to estimate the percentage of individuals who have defective stereo vision in the general population. However, using various stimuli, estimations differ. Richards (1970) used a single bar in depth to determine that about 30% of the populations lacks at least one category of disparity detectors (crossed, uncrossed or zero-disparity detectors). On the other hand, Stelmach and Tam (1996), using random dots stereograms, estimated that about 5% of the population was unable to utilize stereo disparity information to perceive depth. To investigate the innate individual differences in stereo ability and in particular the role of spatial scale, we measured the disparity sensitivity (inverse of disparity threshold) as a function of modulation spatial frequency in a large sample of normal observers. We wanted to know how the key parameters of the disparity sensitivity function such as its peak stereo sensitivity and spatial bandwidth were distributed across the normal population, and how large the individual differences were? In order to establish a normative dataset, we used a spatially bandpass fractal noise carrier and set its peak spatial frequency to be 4 times that of the disparity modulation. This ratio has been shown to be in the optimal range for global stereopsis (Lee & Rogers, 1997; Witz & Hess, 2013). Furthermore, to make comparable measurements on the disparity sensitivity of over 60 normal individuals, we adapted the quick Contrast Sensitivity Function (qCSF, Hou et al., 2010; Lesmes et al., 2010), which was originally designed for the rapid measurement of the contrast sensitivity
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function (CSF) across a full range of spatial frequencies and has been subsequently successfully applied to measure second-order sensitivity (Gao et al., 2014; Reynaud et al., 2014), as the quick Disparity Sensitivity Function (qDSF). As the disparity sensitivity function (DSF) presents approximately the same unimodal bell-shape as the first- and second-order sensitivity functions (Bradshaw & Rogers, 1999; Tyler, 1973; van der Willigen et al., 2010), we show that the truncated log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005) used by the qCSF method faithfully describe the disparity sensitivity too and that the qDSF method is accurate and allows the measurement of disparity sensitivity for a range of different disparity spatial frequencies within a ten-minute period.
a
b 2. Methods 2.1. Observers Sixty-three subjects (25 males and 38 females, average age = 26.3 ± 5.7 years, range: 18–41 years) participated in the main experiment. Two of them were not able to perform the task although they mentioned clearly seeing the stimulus sometimes. They were classified as stereoblinds and were discarded from the study. This proportion corresponds to the one that has been previously reported in the normal population (Richards, 1970; Stelmach & Tam, 1996). Four subjects of the pool, including two authors, participated in the control experiment. All subjects had normal or corrected-to-normal visual acuity and were free from ocular diseases. Informed consent was obtained from all subjects. This research has been approved by the Ethics Review Board of the McGill University Health Center. It was performed in accordance with the ethical standards laid down in the Code of Ethics of the World Medical Association (Declaration of Helsinki).
c
2.2. Apparatus Experiments were run on an Apple iMac11.1 (MacOSX) computer. Stimuli and experimental procedures were programmed with Matlab R2010a (Ó the MathWorks) using the Psychophysics (Brainard, 1997; Kleiner, Brainard, & Pelli, 2007; Pelli, 1997) and qCSF (Lesmes et al., 2010) toolboxes. Data was analyzed off-line using Matlab R2013a (Ó the MathWorks) with the qCSF (Lesmes et al., 2010) and Palamedes (Prins & Kingdom, 2009) toolboxes. Stimuli were displayed on a wide 2300 3D-Ready LED monitor ViewSonic V3D231, gamma corrected with a mean luminance of 100 cd m2. The stereo image input was in top-down VGA format and was displayed in interleaved line stereo mode at a resolution of 19201080p and a refresh rate of 60 Hz: the left eye image was displayed in even scanlines and the right eye image was displayed in odd scanlines. The subject viewed the stimuli at a viewing distance of 70 cm, in a dim-lit room, with passive polarized 3D glasses so that the left image was only seen by the left eye and the right image by the right eye. The polarized filters had the effect of reducing the luminance to about 40%, measured with a photometer. 2.3. Stimuli Stimuli were stereograms composed with spatially filtered 2-D fractal noise carriers. They presented oblique (45° or 135° degrees) sinusoidal corrugations at different frequencies (Fig. 1a). To build the carrier, two-dimensional fractal noise was generated by weighting the amplitude spectrum of an uniformly distributed noise by one over spatial frequency (1/f) and subsequently filtered with a discrete step-edge bandpass filter at a frequency of 4 times
Fig. 1. Methods. (a) Stimuli consisted of 2-D fractal noise stereograms filtered in different frequency bands, viewed with passive polarized glasses on a 3D monitor. Disparity between the two eyes was modulated by an oblique sinusoidal corrugation (here at 135°) at different frequencies. (b) The subject task was to identify the orientation of the disparity-modulation of the stimulus which could be oblique at 45° (left) or 135° (right). (c) The disparity sensitivity function is described by the truncated log-parabola model as a function of the spatial frequency. Two parameters are studied: the peak gain (cmax) and the peak frequency (fmax).
the spatial frequency of the corrugation and a one octave bandwidth. Stimuli visibility was equated by scaling the carrier contrasts to 10 times the contrast thresholds measured for each carrier spatial frequency in a normative dataset (Reynaud et al., 2014). They were respectively set to 32, 27, 25, 27, 33, 47, 75 and 100% (clipped) for carrier frequencies of 0.94, 1.31, 1.83, 2.54, 3.54, 4.93, 6.87, and 9.57 c/d. Sinusoidal corrugation was introduced by shifting the carrier following a vertical sinusoïd of opposite phase for each eye image. Non-integer pixel positions were linearly interpolated between neighboring pixels. Then each pixel line was subsequently shifted one pixel to the right to obtain the 45° corrugation or to the left to obtain the 135° corrugation in each stereogram. Stimuli were presented in a Gaussian aperture of 15° diameter. We checked that
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it was not possible to perform the experiment monocularly in order to ensure that the oblique sinusoidal corrugation did not generate visible compression and expansion artifacts in the carrier noise patterns. 2.4. Procedures and analysis The subjects’ task was to identify the orientation of the disparity corrugation (45° or 135°, Fig. 1b) in a single-interval identification task. A trial time course was as follows: (1) a green fixation dot appeared on the screen, (2) the dot disappeared and the stimulus was presented for 1 s, (3) a red dot appeared until the subject responded by pressing a keypad, (4) after the subject answered, the dot disappeared and audio feed-back about the correctness of the response was provided. Dot luminance was matched to that of the background. 2.4.1. Control experiment – the Method of Constant Stimuli In a control experiment, the disparity thresholds were measured individually with the Method of Constant Stimuli (MCS) for each spatial frequency: 0.24, 0.33, 0.46, 0.64, 0.89, 1.23, 1.72 and 2.39 c/d. The order in which participants performed the different spatial frequency conditions was randomized. The levels of disparity used were 0.13, 0.18, 0.25, 0.36, 0.50, 0.71, 1.00, 1.41, 2.00, 2.83, 4.00 and 5.66 arc min. There were 20 repetitions per condition for each subject. Each measurement took approximately 15 min. The detection thresholds were then determined by fitting a Weibull function of the log-disparity to the psychometric datasets (Eq. (1), maximum likelihood estimation method):
b F W ðx; a; bÞ ¼ 0:5 þ 0:5 1 eðx=aÞ
ð1Þ
where x is the log-disparity, a the log-threshold and b the slope of the psychometric function. The standard deviation of the fitted parameters was estimated by a bootstrapping procedure. 2.4.2. Main experiment – the quick Disparity Sensitivity Function The sensitivity functions were determined using the quick Contrast Sensitivity Function (qCSF) method (Hou et al., 2010; Lesmes et al., 2010). This method is a Bayesian adaptive procedure that was designed for concurrently estimating contrast thresholds across the full spatial-frequency range. Here we adapted it and used it to estimate the quick disparity sensitivity function (qDSF). Before each trial, the method finds the optimal stimulus in order to maximize the expected information gain about the parameters of the disparity sensitivity function (Lesmes et al., 2010). The operative range for the disparity was set from 0.0125 to 12.5 arc min and the frequency range was truncated from 0.24 to 2.39 c/d. An initial prior represents foreknowledge of the subject’s disparity sensitivity function parameters. The initial gain prior was set to 0.8 arc min, the peak frequency prior was set to 0.5 cpd and the bandwidth prior was set to 3 octaves. In this range, the qDSF method will be effective because this range is below the Dmax threshold, where the psychometric functions are monotonically increasing (Filippini & Banks, 2009; Kane, Guan, & Banks, 2014; Tyler, 1975; Wilcox & Hess, 1995; Ziegler, Hess, & Kingdom, 2000). The qDSF measurement took approximately 8 min, was repeated twice, and averaged. The method estimates the sensitivity function with a truncated log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005), which is described by four parameters: the peak gain cmax, the peak frequency, fmax, the bandwidth b and the truncation d:
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2 10 ðf max Þ S0 ðf Þ ¼ log10 ðcmax Þ j log10 ðf Þlog b0 =2 Sðf Þ ¼ log10 ðcmax Þ d if f < f max and S0 ðf Þ < log10 ðcmax Þ d Sðf Þ ¼ S0 ðf Þ else
ð2Þ
with j = log10(2) and b0 = log10(2b). However, we discarded the bandwidth and truncation parameter from our analysis as they were often out of the range of our measurements (Fig. 1c). 3. Results 3.1. Suitability of the truncated log-parabola model As a first step we show that the qCSF method can be adapted to disparity sensitivity measurement. It is known that the disparity sensitivity function has a bell-shape (Bradshaw & Rogers, 1999; Tyler, 1973; van der Willigen et al., 2010). However, the accuracy of the truncated log-parabola model to describe the disparity sensitivity function still needs to be assessed. Thus, we tested this model on the disparity sensitivity measured using the Method of Constant Stimuli. The Fig. 2 presents the measured psychometric functions for one observer at each spatial frequency. The minimum disparity thresholds are estimated by fitting a Weibull function on the log-disparity. We can see that the psychometric functions are monotonic and smooth without showing a drop at high disparities which confirms that, for the fractal noise stimulus and the sinusoidal corrugation used here, the range of disparities tested are within the maximum disparity limit (Dmax; Filippini & Banks, 2009; Tyler, 1975; Wilcox & Hess, 1995; Ziegler, Hess, & Kingdom, 2000). The measured sensitivity with the MCS from four subjects is reported as a function of spatial frequency in Fig. 3. These four subjects’ disparity sensitivities exhibit very different gain and tuning. The first subject’s disparity sensitivity displays a high-pass profile (Fig. 3a). The disparity sensitivity of the second and third subjects displays a band-pass one (Fig. 3b and c). And the last subject’s disparity sensitivity displays a low-pass with very low gain profile (Fig. 3d). The data points are fitted a posteriori with the truncated log-parabola model (Eq. (2), least-squares estimation method). The function faithfully fits the data for all subjects (solid lines in Fig. 3, mean coefficient of determination r2 = 0.80 for the four subjects), therefore we can affirm that the truncated log-parabola is an accurate model to describe disparity sensitivity functions. The qDSF estimates are very consistent with the datapoints too (Fig. 3 dashed lines, mean coefficient of determination r2 = 0.51 for the four subjects). The two studied parameters of the model: the peak gain cmax and the peak frequency fmax are not significantly different between the truncated log-parabola a posteriori estimates and the qDSF estimates (paired Wilcoxon signed rank test, a = 0.05). Hence, we can say that the sensitivity functions estimated with the two methods are consistent and accurate and therefore the qDSF method is an appropriate tool to measure the sensitivity to disparity and so for very different function tunings. 3.2. Normative dataset The average and standard deviation of the disparity sensitivity functions over the 61 subjects are shown in Fig. 4a. We can see that the disparity sensitivity approximately increases from 0.3 arc min1 at low frequencies and peaks at a frequency of 1.2 c/d with a maximum gain of 1.2 arc min1. This tuning for disparity is consistent with previous studies using the same kind of filtered noise stimulus, (Lee & Rogers, 1997; Witz & Hess, 2013). The dashed line shows the disparity-sensitivity function reconstructed from the log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005) with the median parameters
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Fig. 2. Psychometric functions obtained with the MCS at each spatial frequency, respectively in each panel, for the subject AR. The datapoints (crosses) represent the performance of the subject as a function of the disparity, Thresholds (squares) are estimated by fitting a Weibull function on the log-disparity (continuous line, Eq. (1)).
estimated by the qDSF. It accurately represents the data and thereby illustrates the model-derived peak frequency and gain. The thin dark gray line represents the standard deviation of the disparity-sensitivity functions of all the subjects. This variability is
quite large and increases at high spatial frequencies (Legge & Yuanchao, 1989), peaking around 1.7 c/d. We can also observe this increment in variability by the fact that the 5% and 95% percentile boundaries diverge at high-spatial frequencies. In detail, we plot in
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a
b
c
d
Fig. 3. Accuracy of the truncated log-parabola model. Sensitivity measurements and model fits for four subjects. Their disparity sensitivities are reported in function of the spatial frequency. The square symbols represent sensitivity measures with the MCS, error bars indicate standard deviation, solid lines represent a posteriori fits of the MCS data with the truncated log-parabola model (Eq. (2), least-square estimation method), dotted lines represent qDSF measurements. (a) Subject AR presents a high-pass profile. (b) Subject YG presents a band-pass profile. (c) Subject MS presents a band-pass profile. (d) Subject GS presents a low-pass profile.
a
b
c
Fig. 4. Normative dataset; (a) averaged sensitivity function from the data (thick black line) with standard deviation (shaded gray area) and sensitivity function reconstructed with the median qDSF parameters using the log-parabola model (dashed line). The gray thin line represents the standard deviation as a function of the spatial frequency and the dotted lines represent the 5% and 95% percentile boundaries. (b) individual sensitivity functions for the 61 subjects. (c) Distribution of the sensitivities at 1.72 c/d.
Fig. 4b the individual disparity-sensitivity functions for all the 61 subjects. These sensitivities are normally distributed at low spatial frequencies below 0.7 c/d and then skewed at high spatial frequencies (Shapiro–Wilk test, a = 0.05). Specifically, the distribution of the sensitivities at 1.72 c/d, high spatial frequency for which the standard deviation is maximal is reported on a log-scale in Fig. 4c. This distribution has a skewness of 0.86. These observations confirm that the tuning for disparity can be very different from subject to subject, some display a low-pass
profile whereas some others display a more band-pass or high-pass one, resulting in the greater variability observed. Such individual differences in disparity spatial frequency sensitivity have already been reported (Legge & Yuanchao, 1989) but their extent within a larger population is only confirmed by the present data. We investigated the consistency between the different sensitivity patterns observed by plotting the maximum gain as a function of the peak frequency for all subjects, as shown in Fig. 5. The distributions of the peak frequency and the log-gain are represented at the
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top and the right-side of the scatter-plot respectively. They are normal (Shapiro–Wilk test, a = 0.05) and look much wider than what has been reported for contrast detection or second-order sensitivities. Although the modulations in luminance and contrast are processed by different neural mechanisms than those involved in disparity, the relative variability in these different functions is worthy of comparison. To compare this relative variability, we compute the coefficients of variation of the peak frequency and the maximum gain for the disparity sensitivity (Table 1). We compare these standardized measures to the ones calculated for first-order (contrast) and second-order (contrast-modulation, orientation-modulation and motion-modulation) sensitivities from our previous study, using the same approach (from Table 1 in Reynaud et al., 2014). The coefficient of variation of the gain distribution is 2 times larger for the disparity sensitivity than for the first- and second-order sensitivities. Furthermore, the coefficient of variation of the frequency is almost 2 times larger for the disparity sensitivity than for the first-order sensitivity. This higher relative variability is significant (one-tailed F-test on the log-values of the gain and peak frequencies, a = 0.05, Lewontin, 1966), however the relative variability of the peak frequency for disparity sensitivity is not different from that of second-order sensitivity. Second, we can see a correlation between the peak frequency and the log-gain (r2 = 0.12, p < 0.01): the higher the peak-frequency, the higher the gain. This indicates that people with poor stereo vision are selectively deficient at high spatial frequencies and not equally poor for all spatial frequencies. 4. Discussion 4.1. Validity of the qDSF Our results are in line with previous studies that have investigated stereo-sensitivity using bandpass filtered noise carriers (Tyler, 1973; Witz, Zhou, & Hess, 2013; Yang & Blake, 1991; Witz, Zhou, & Hess, 2014). However the average disparity
Table 1 Mean (l), standard-deviation (r) and coefficient of variation (cv) of the distributions of the estimates of the maximum gain cmax, and the peak frequency fmax, for the firstand second-order sensitivity functions measured on a normative dataset from Reynaud et al. (2014) and for disparity. Frequencies are expressed in c/d. Disparity gain in arc min1.
cmax 1st order 2nd order Disparity
fmax
l
r
cv
l
r
cv
43.11 5.43 1.17
11.30 1.01 0.56
0.26 0.23 0.48
1.92 1.02 1.24
0.44 0.32 0.41
0.19 0.31 0.33
sensitivity reported here occurs at a higher peak frequency and has a lower maximum gain than what has been observed using spatially broadband random dots carriers (Bradshaw & Rogers, 1999; Schumer & Julesz, 1984; van der Willigen et al., 2010; Westheimer & McKee, 1980), including measurements of depth from motion parallax (Rogers & Graham, 1982). In this study, we used a line-interleaved dichoptic presentation of the stimuli on the screen instead of the previous method of frame interleaving. Line interleaving is superior temporally because there is a much shorter temporal asymmetry although the spatial resolution is reduced. The use of the qCSF method to measure contrast sensitivity and second-order sensitivity has already been validated (Lesmes et al., 2010; Reynaud et al., 2014). In the first section, we demonstrated that the truncated log-parabola model (Ahumada & Peterson, 1992; Watson & Ahumada, 2005) accurately describes the disparity sensitivity as well. We confirmed that the qDSF and the MCS lead to slightly but not significantly different results. Indeed, it is not surprising that different psychophysical estimation procedures lead to different results (Kingdom & Prins, 2010; Leek, 2001). The constrained shape of the qDSF reduces the risk of outliers, whereas with the MCS, subjects might have attentional benefits due to its prior knowledge of the appearance of the stimulus (Davis & Graham, 1981; Woods, 1996). The standard procedures are time consuming, however the qDSF method requires approximately 10 times less trials and is optimally suitable for large sample sizes and clinical studies (Gao et al., 2014; Hou et al., 2010; Kalia et al., 2012). 4.2. Large variability of the disparity sensitivity between subjects
Fig. 5. Relationship between the peak frequency and the maximum gain of the disparity sensitivity for each subject. Each point represents the peak frequency and maximum gain for each sensitivity function in Fig. 4b with the same color. The black dotted line represents the best-fit linear regression. The histograms of the distribution of the peak frequencies and maximum gains for all subject are respectively represented above and aside of the graph. Note that the gain is represented on a log-scale. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
To study variability and achieve high statistical significance, we built our normative dataset on a large pool of subjects. We decided to focus on a group of younger adults (see Section 2), with not much variability in the age range in order to avoid any age-induced and acuity-induced artifacts. In this normative dataset, we observed a large variability among the observers associated with a significant correlation between the peak frequency and maximum gain of the disparity sensitivity. Such a correlation has already been observed for contrast sensitivity as a function of luminance (Cox, Norman, & Norman, 1999; Rovamo, Mustonen, & Näsänen, 1994) and eccentricity (Pointer & Hess, 1989), or for aging population (Owsley, Sekuler, & Siemsen, 1983) and also for second-order stimuli (Tang & Zhou, 2009). This correlation is not surprising given the unimodal shape of the disparity sensitivity function which increases to a peak and then decreases as a function of spatial frequency (Barten, 1999). This peak occurs at different spatial frequencies for each subjects and leads to either low, medium, or high spatial frequency tuning profiles (Fig. 3). This implies that for the general population, the disparity sensitivity is similar at low disparity spatial frequency, but variable at high disparity spatial frequencies. (Fig. 4b, see also Legge & Yuanchao, 1989).
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