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Probability summation of acuity in the human infant
Vision Res. Vol. 32. No. Printed in Great Britain.
IO, pp. 1999-2003, All rights reserved
1992
Copyright
Probability Summation Human Infant EILEEN
E. BIRCH,*t$
WILLIAM
0042-6989/92 $5.00 + 0.00 CI 1992 Pergamon Press Ltd
of Acuity in the
H. SWANSON*t
Received 16 July 1991
Raw data from two studies of monocular and binocular acuity development were used to determine whether a binocular acuity advantage as a function of age is predicted by probability summation and whether these predictions accurately describe the course of binocular acuity development. Two decision rules for the combination of the outputs of right eye and left eye “channels” were evaluated, the decision-threshold rule and the integration rule. Both decision rules predicted a binocular acuity advantage for infants and children aged O-60 months. However, both rules failed to adequately describe the normal course of monocular and binocular acuity development. No binocular acuity advantage was found prior to 6 months of age while, after 6 months of age, binocular acuity was superior to monocular acuity by 0.12 log unit (0.4 octave). The absence of binocular acuity superiority prior to 6 months of age is consistent with suggestions by other authors that the immature human visual system combines information from the two eyes nonselectively. Acuity
Probability
summation
Visual development
Preferential
In the human infant, fusion and stereopsis have an abrupt onset at 4-6 months of age (Birch, Gwiazda & Held, 1982; Birch, Shimojo & Held, 1985; Braddick, Wattam-Bell, Day & Atkinson, 1983; Fox, Aslin, Shea & Dumais, 1980; Gwiazda, Bauer & Held, 1989; Held, Birch & Gwiazda, 1980; Petrig, Julesz, Kropfl, Baumgartner & Anliker, 1981; Reuss, 1981; Shimojo, Bauer, O’Connell & Held, 1986) and stereoacuity improves rapidly during months 6-12 (Birch ef al., 1982; Held et al., 1980). The rates of visual acuity development and of binocular function development are relatively independent. Acuity develops at a different rate than stereoacuity (Birch, 1985; Birch & Hale, 1988), shows no sudden change at the age of onset for fusion or stereopsis (Birch, 1985, 1992), and may be limited by retinal development while fusion and stereopsis may be limited by cortical maturation (Wilson, 1988). Binocular acuity has been shown to be superior to monocular acuity after &6 months of age; i.e. after the onset of stereopsis (Birch, 1985; Birch & Hale, 1988; Dobson, 1983; McDonald, Sebris, Mohn, Teller & Dobson, 1986; Thompson & Drasdo, 1988). While at first glance the development of binocular superiority appears to fall neatly into the general finding of the emergence of binocularity at &6 months of age, it is in fact difficult to reconcile with probability summation.
*Retina Foundation of the Southwest, 9900 North Central Expressway, Suite 400, Dallas, TX 75231, U.S.A. tDepartment of Ophthalmology, University of Texas Southwestern Medical Center, Dallas, Texas, U.S.A. $To whom all correspondence should be addressed at the Retina Foundation of the Southwest.
looking
Models of probability summation predict a binocular acuity advantage for adults based on two assumptions. First, the two eyes must have similar acuities; use of a fellow eye with very poor acuity along with an eye with good acuity will yield little or no binocular advantage. Second, the two eyes must function as independent detectors (or “separate analyzers” in the terminology of Graham, 1989); i.e. there must be separate right and left eye “channels” with statistically independent noise (Green & Swets, 1966). Since no superiority of binocular acuity over monocular acuity has been found during the first few months of life, one or both of these assumptions must be incorrect for early human development. That is, the two eyes must have greatly different acuities and/or the two eyes must not function independently prior to the onset of fusion and stereopsis. Indeed, there is preliminary evidence to suggest that both of these assumptions may be incorrect. Significant interocular differences in acuity have been documented in approx. 40% of infants age O-2 months (Birch, 1985; Birch & Hale, 1988; Dobson, 1983; Thompson & Drasdo, 1988), raising the possibility that probability summation may not predict a significant binocular advantage in this age range. In addition, data from a study of fusion in pre-stereoptic infants suggests a nonselective combination of information from the two eyes; i.e. the two images are superimposed without regard to content (Held, 1985, 1988; Shimojo et al., 1986). The aims of the present study were: (1) to evaluate whether a binocular acuity advantage as a function of age is predicted by probability summation and (2) to determine whether these predictions adequately describe human monocular and binocular acuity development.
1999
2000
EILEEN E. BIRCH and WILLIAM H. SWANSON MATERIALS
AND METHODS
Forced-choice preferential-looking acuity data were taken from two previously published reports (Birch, 1985; Birch & Hale, 1988). One study used a constant stimulus paradigm to obtain percent correct as a function of spatial frequency (Birch, 1985). The second study used a staircase procedure with at least eight reversals (Birch & Hale, 1988). Raw data from these studies were fit by maximum likelihood estimation to a psychometric function of the form: P(x) = yD(x) + 0.5 [l -D(x)]
(1)
where P(x) is the probability of a correct response, D(x) is the probability of detecting stimulus x (with x in min of arc), and y is the probability of a correct response when D(x) = 1.O (Swanson & Birch, 1992). For D(x), the approximation of the cumulant of the normal distribution described by Quick (1974) was used: D(x) = 1 - 2+/4a
(2)
where a is the value of stimulus x for which D(x) = 0.5, and fi is a constant which is inversely proportional to the slope of the function, Maximum likelihood estimates for tl, fl and y were obtained by solving for the maximum in a grid of seventy-five 0.03 log unit steps of c(, eleven 0.10 log unit steps of /?, and thirteen 2% steps of y. For each stimulus x, the likelihood L(x) that correct responses were given on k of n trials is: L(x) = n !/[k!(n - k)!][P(x)lk[ 1 - P(x)1” - k
(3)
and the likelihood of a complete data set is the product of the likelihoods for all of the stimuli used to generate that data set. Nine data sets from infants who had acuities outside the range of stimuli for either of the monocular tests or the binocular test were not included in the present study, leaving complete data sets (OD, OS, and OU) from 79 infants for analysis.* Infants were assigned to age groups
*Twelve of the total of 264 acuity estimates (88 each for OD, OS and OU) were outside of the range of stimuli tested, 6.8% of constant stimulus acuity estimates and 2.3% of staircase acuity estimates. This resulted in a total of 9 full data sets (OD, OS and OU) being excluded from analysis, 13.6% of constant stimulus data sets and 6.8% of staircase acuity estimates. The 9 excluded data sets were from subjects over a wide range of age groups (3, 6, 9, 10, 11, 11, 29, 43 and 49 months). The 9 excluded data sets (27 acuity estimates) were comprised of 15 acuity estimates which were within the range of stimuli tested and 12 acuity estimates which were outside of the range of stimuli tested. Acuity estimates which were within the range of stimuli tested were similar to those obtained from age-matched infants who were not excluded from the analyses. Therefore, it is unlikely that the exclusion of these data sets led to a significant bias since only a small percentage of the total data set were excluded, excluded data sets were not limited to a single age range, and “useable” acuities from the excluded data sets were similar to those of included infants. tDistinguishing between these two decision rules is not an aim of this report. Both decision rules are included to illustrate that, in this case,their predictions are quite close and that neither rule provides an adequate prediction of binocular acuity for infants aged o-6 months.
on the basis of post-term age (average of 13 infants per age group): O-6 months; 7-12 months; 13-24 months: 25-36 months; 37-48 months; or 49-60 months. Two decision rules for the combination of the outputs from right eye and left eye “channels” were used to predict binocular acuities from monocular acuities.? The decision-threshold model describes the probability of detection based on multiple observations as equal to one minus the product of the probabilities that detection does not occur in any of the observations (Green & Swets, 1966; similar to the maximum-output decision rule described by Graham, 1989): Do,(x) =
1 - u - a&N[l
- &S(X)l~
(4)
The integration model assumes that the information in multiple observations is pooled and that the sum of the information determines the overall decision based on the product of likelihood ratios (Gorea & Tyler, 1986; Green & Swets, 1966; similar to the sum-of-outputs rule described by Graham, 1989): &u(x) = [&&)*
+
&,(~)210.5
(5)
where R(x) = (cx/x)~. Each infant included in the study contributed two monocular acuity data sets (OD and OS) and a binocular acuity data set (OU). For each infant, the maximum likelihood estimates for CL,/I and y obtained for OD and OS were used to generate predicted binocular psychometric functions under the decision threshold and integration rules. In addition, the binocular acuities predicted by each decision rule were compared with the infant’s measured binocular acuity to obtain difference scores for each infant. RESULTS
Model predictions Monocular acuities obtained from the maximum likelihood estimation procedure are shown in Fig. 1. In this figure, each infant contributed a mean monocular /
1.2 1 .o 0.8 $ r 0.6 =$ .r” 0.4
0’ q
0.2 0.0
0
10
20
30
40
50
60
Age (months) FIGURE I. Measured monocular FPL grating acuities (solid symbols f 1 SE) and predictions for binocular grating acuity based on two rules of probability summation, the decision-threshold rule (solid line) and the integration rule (dotted line). Acuities are plotted as log min of arc resolution (log MAR).
PROBABILITY
SUMMATION
acuity to the calculation of a grand mean for the age group. For the six age groups, monocular acuity estimates obtained by maximum likelihood estimation did not differ significantly from the acuities originally reported (mean difference = 0.00 + 0.17 log unit). Also shown in Fig. 1 are the predicted binocular acuities from the two decision rules. Each infant contributed a predicted binocular acuity based on its monocular acuities to the calculation of a grand mean for the age group. Predictions of binocular acuity from the decisionthreshold rule and from the integration rule were similar; both decision rules predicted a superiority of binocular over monocular acuity at all ages. Averaged over all age groups, the decision-threshold rule predicted a binocular advantage of 0.12 log unit (0.40 octave) and the integration rule predicted a binocular advantage of 0.10 log unit (0.33 octave). Adequacy
IN INFANTS
2001
.
.Y
1.2
0
0
10
20
Decision-threshold Integration
30
40
50
60
Age (months) FIGURE 3. Error from predictions (actual binocular acuity minus predicted binocular acuity for the decision-threshold rule (solid symbols) and the integration rule (open symbols). Each data point represents one infant.
of the models
Predicted and measured binocular acuities are shown as a function of age in Fig. 2. Both decision rules failed to adequately predict binocular acuity in the O-6 month age range, predicting better acuity than was obtained. In all remaining age groups (7-60 months), both decision rules gave reasonable predictions of binocular acuity. The difference between predicted and measured binocular acuity was calculated by taking a difference score for each infant (actual binocular acuity minus the binocular acuity predicted from that individual’s monocular acuities) and then computing the mean difference score for each age group (Fig. 3). For infants aged G-6 months, the mean difference score was 0.21 + 0.05 log unit (0.70 octave) using the decision-threshold rule and 0.17 _+0.0 1 log unit (0.57 octave) using the integration rule. While the two models accurately predicted binocular acuity for some individual infants, binocular acuity was over-predicted by 0.3 log unit (1 octave) or more in 33 and 27% of CM month olds, respectively. In older age groups, difference scores were much smaller; mean differences between measured binocular acuity and predicted binocular acuity ranged from -0.05 to 0.01 log unit (-0.17 1.2 1 .o
65
0
. .. .
0.8
Binocular Decision-threshold Integration
5 0.6 $ = " 0.4 0' 4 0.2
to 0.03 octave; mean = -0.02 & 0.01 log unit) for the decision-threshold rule and from -0.08 to -0.01 log unit (-0.26 to -0.03 octave; mean = - 0.04 + 0.01 log unit) for the integration rule. All individual infants’ binocular acuities were within 0.3 log unit (1 octave) of predicted binocular acuity. To verify that the age dependence of the binocular advantage was not due to changes in the shape of the psychometric function (other than acuity) or changes in the likelihood of the fitted psychometric function, the relationship between parameters of the psychometric functions fit by maximum likelihood estimation and age was examined. While these parameters differed between the constant stimulus and staircase procedures, within each procedure the upper asymptote (y), the slope (log/I), and the likelihood (log L), did not correlate significantly with age (r2 < 0.057 in all cases; summarized in Table 1). Nor did y or log /3 differ significantly between the O-6 months and 7-12 months age groups for OD (t,. = 0.108; tS = 0.735), OS (ty = 0.517; to = 0.194), or OU (tr = 0.520; tg = 0.137). In each age group, the mean acuity estimates obtained with the maximum likelihood fitting procedure did not differ significantly from the published acuities, which were obtained by graphical interpolation or staircase reversal averages. Differences between the published means and the TABLE 1. Correlations between ameters of the psychometric
0
10
20
30
40
50
60
Eye
Parameter
OD
log B Y log L
OS
log B Y log L
ou
log B )’ log L
Age (months) FIGURE 2. Actual binocular grating acuities (solid symbols + 1 SE) vs predicted binocular grating acuities from the decision-threshold rule (solid line) and the integration rule (dotted line). Acuities are plotted as log min of arc resolution (log MAR).
age and function
Constant stimulus rz
Staircase
0.001 0.057 0.004 0.005 0.003 0.015 0.008 0.007 0.014
0.033 0.000 0.001 0.002 0.000 0.035 0.002 0.000 0.003
r’
par-
2002
EILEEN E. BIRCH and WILLIAM
maximum likelihood estimates ranged from -0.04 to 0.03 log unit (-0.13 to 0.10 octave) in the various age groups, with a mean difference of 0.00 If: 0.03 log unit. DISCUSSION Both decision rules predicted a binocular acuity advantage in all age groups. This result suggests that the interocular differences in acuity which are present for some infants during the first 6 months of life do not preclude a binocular acuity advantage. In the present study, interocular differences of 1.0-2.3 octaves were present in 19% of infants; all but one of these infants were in the O-6 month age group. Despite the high prevalence of signi~cant intero~ular differences in the youngest age group, a binocular acuity advantage was predicted for this age group by both decision rules (Fig. 1). When the data are examined on an individual basis, approximately the same percentage of infants with interocular differences of 1.0 octave or greater (89O/) and of infants with interocular differences < 1.O octave (88%) had a predicted binocular acuity advantage (using the d~ision-threshold rule). This somewhat unexpected finding may be explained by the fact that the monocular psychometric functions of infants with interocular differences less than one octave had significantly steeper slopes than those of infants with interocular differences greater than one octave (mean log b = 0.68 and 0.54, respectively; f = 2.29, P < 0,025). Thus, while significant interocular differences in acuity reduce the expected binocular advantage, shailower slopes of monocular psychometric functions may act to increase the expected amount of binocular acuity advantage. Both decision rules are poor predictors of binocular acuity during the first 6 months of life but accurately predict binocular acuity during months 7-60. The failure to accurately predict binocular acuity during early months is not att~butable to age-related di~eren~s in the shape of the psychometric function, as indexed by the upper asymptote or slope parameters, or to age-related differences in the ability to make threshold estimates, as indexed by likelihood of fits and by agreement between different threshold estimation procedures. The integration rule as expressed in equation (5) is based on the common assumption of near-threshold linearity (Cornsweet, 1970; Massof, 1985). However, it is possible that an essential nonlinearity makes the assumption invalid during early visual development. Therefore, a more general formulation for the integration rule was evaluated, for which the only assumption was that the standard deviations of the signal and noise distributions are the same. For this formulation (Green & Swets, 1966), d’ was derived directly from P(X). Predictions from the nonlinear formulation had a mean signed difference of 0.001 log unit (0.004 octave) from the predictions of the linear formulation and a mean unsigned difference of 0.006 log unit (0.019 octave). Thus, while a nonlinear formulation led to a slight improvement in agreement between predicted
H. SWANSON
and measured binocular acuities, it was not sutlicient to account for the 0.17 log unit (0.57 octave) discrepancy. Modei ofhuman visual dewfopment The absence of probability summation during months O-6 is consistent with other suggestions that information from the two eyes is combined nonselectively prior to the onset of fusion and stereopsis. Prior to the onset of fusion, the human infant appears to have a primitive form of binocularity in which the visual system superimposes the inputs from the two retinas regardless of image content (Held, 1985, 1988; Shimojo er al., 1986). One model of the development of human binocular function suggests that the immature primary visual cortex lacks segregation into ocular dominance columns, so that both retinas provide inputs to comma cells (Held, 1985; Hickey & Peduzzi, 1987; LeVay & Voight, 1988; LeVay, Wiesel & Hubel, 1980; LeVay. Stryker & Shatz, 1978). The convergent of monocular inputs onto common cortical cells may offer no opportunity for binocular advantage due to probability summation if two assumptions are met. First, the inputs to the cortex from the two monocular channels must be summed linearly. This assumption appears reasonable if the convergence of monocular inputs onto common cells is indeed an accurate description of the immature primary visual cortex. Second, noise must be perfectly correIated. This assumption is almost certainly incorrect. At least some of the noise in the monocular channels (e.g. photon noise, intrinsic photoreceptor noise) is uncorreiated. Other sources of noise are likely to be correlated, including stimulus-related noise in the monocular channels and extraneous noise from the infant or observer in FPL testing. Moreover, noise arising at the cortical level must be perfectly correlated if monocular inputs converge onto common cells. To the extent that noise in the monocular channels is correlated, little or no binocular advantage is predicted [or, in Graham’s (1989) “summation square” terminology, “no summation” of the monocular components is predicted]. As the primary visual cortex matures. segregation of ocular dominance columns occurs and provides for separate left and right eye “channels” (LeVay et al., 1980, 1978; Poggio & Fischer, 1977). Noise in separate cortica1 left and right eye channels is likely to he uncorrelated. Segregation into ocular dominance columns also provides for the preservation of eye of origin information required for stereopsis and has been shown to coincide with the onset of stereopsis in kittens (Timney, 1988). The independence of right eye and left eye channels following ocular dominance column segregation may provide an anatomical basis for the nonlinear combination of signal -t noise from each eye which characterizes probability summation. An alternative explanation of the failure to find evidence of probability summation in the youngest age group is that, in the t3-6 month group, the primary source of noise is extraneous noise from the infant and/or observer in the FPL test situation and that
PROBABILITY
SUMMATION
extraneous noise decreases with age, making the independent noise in the two monocular channels more evident in later age groups. Within the FPL protocol, extraneous noise may result in inappropriate responses to stimuli when the infant responds to an irrelevant aspect of the test situation or when the observer responds to an irrelevant aspect of the infant’s behavior. The findings that neither the upper asymptote (y) nor the slope (log b) of the psychometric functions correlated with age and that neither ?/ or log fl differed significantly between the G-6 months and 7-12 months age groups argues against this alternative. Clinical implications The absence of binocular acuity superiority appears to be the norm for healthy infants under 6 months of age. For healthy infants over 6 months of age, probability summation results in an advantage in binocular acuity of 0.1 O-O. 12 log unit over monocular acuity. This binocular advantage makes the use of binocular normative data as a “gold standard” inappropriate for comparison with monocular acuity data from pediatric patients aged 6 months or older. The finding of binocular acuity superiority may suggest mature cortical organization, e.g. segregation into ocular dominance columns, but does not necessarily imply the capability for stereopsis. Failure to find binocular acuity superiority in an infant over 6 months of age may suggest immature cortical organization, e.g. lack of segregation into separate right and left eye channels, or may suggest that one of the monocular channels is so weak that its contribution to probability summation does not result in a binocular acuity advantage.
REFERENCES Birch, E. E. (1985). Infant interocular acuity differences and binocular vision. Vision Research, 25, 511L576. Birch, E. E. (1992). Stereopsis in infants and its developmental relationship to visual acuity. In Infanr oision. New York: Oxford University Press. In press. Birch, E. E. & Hale, L. A. (1988). Criteria for monocular acuity deficit in infancy and early childhood. Innestigatioe Ophthalmology und Visual Science, 29. 636643. Birch, E. E., Gwiazda, J. & Held, R. (1982). Stereoacuity development for crossed and uncrossed disparities in human infants. Vision Research, 22, 507-5 13. Birch, E. E., Shimojo, S. & Held, R. (1985). Preferential-looking assessment of fusion and stereopsis in infants aged l-6 months. Investigative Ophthalmology and Visual Science, 26, 366370. Braddick, O., Wattam-Bell, J., Day, J. &Atkinson, J. (1983). The onset of binocular function in human infants. Human Neurobiology, 2, 65-69. Cornsweet. T. N. (1970). Visual perception (p. 334). New York: Academic Press. Dobson, V. (1983). Clinical applications of preferential looking measures of visual acuity. Behavioral Brain Research, 10, 25-38. Fox, R., Aslin, R. N.. Shea, S. L. & Dumais, S. T. (1980). Stereopsis in human infants. Science, 207, 323-324. Gorea, A. &Tyler, C. W. (1986). New look at Bloch’s law for contrast. Journal of the Opiical Society qf America, A3, 5241.
IN INFANTS
2003
Graham, N. (1989). Visual pattern analyzers (pp. 1533154, 280-285). New York: Oxford University Press. Green, D. M. & Swets, J. A. (1966). Signal detection theory and psychophysics (pp. 2355240). New York: Kreiger. Gwiazda, J., Bauer, J. A. Jr & Held, R. (1989). Binocular function in human infants: Correlation of stereoptic and fusion-rivalry discriminations. Journal of Pediutric Ophthalmology and Strubismus. 26, 128-132. Held, R. (1985). Binocular vision-behavioral and neural development. In Meher, V. & Fox, R. (Eds). Neonatal cognition: Beyond rhe blooming, buzzing confusion (pp. 37-44). Held. R. (1988). Developmental of cortically mediated visual processes in human infants. In von Euler. C., Forssberg, H. & Lagercrantz, H. (Eds), Neurobiology q/early it&n/ behavior (pp. 155-l 64). Stockholm: Stockton Press. Held, R., Birch, E. E. & Gwiazda. J. (1980). Stereoacuity of human infants. Proceedings qf the National Academy qf.Science, U.S.A., 77, 5512~ 5514. Hickey, J. L. & Peduzzi, J. D. (1987). Structure and development of the visual system. In Salapatek, P. & Cohen. L. (Eds), Hundhook of infanr perception (pp. 142). New York: Academic Press. LeVay, S. & Voight, T. (1988). Ocular dominance and disparity coding in cat visual cortex. Visual Neuroscience, I, 395414. LeVay. S., Stryker, M. P. & Shatz, C. J. (1978). Ocular dominance columns and their development in layer IV of the cat’s visual cortex. A quantitative study. Journul (?f Comparative Neurolog],. 179, 223-244. LeVay, S.. Wiesel, T. N. & Hubel, D. H. (1980). The development of ocular dominance columns in normal and visually deprived monkeys. Journal of Comparo/ir.e Neurology, 161, I 5 1. Massof. R. W. (1985). Color-vision theory and linear models of color vision. Color Reseurch and Applications, IO, 133-146. McDonald, M., Sebris, S. L.. Mohn. G., Teller, D. Y. & Dobson, V. (1986). Monocular acuity in normal infants: The acuity card procedure. American Journal of’Oprometry and Physiological Optics, 63, 127-134. Petrig, 9.. Julesz, B., Kropfl. W., Baumgartner, G. & Anliker, M. (1981). Development of stereopsis and cortical binocularity in human infants: Electrophysiological evidence. Science, 213, 1402~1405. Poggio, G. F. & Fischer, 9. (1977). Binocular interaction and depth sensitivity of striate and prestriate cortical neurons of the behaving rhesus monkey. Journal qf Neurophysiology, 40, 1392- 1405. Quick, R. F. (1974). A vector-magnitude model of contrast detection. Kybernetik. 16, 65-61. Reuss, J. (1981). Human stereopsis: Detection and development. Disserlaiion Abstracts Inrernutional, 42, 19619. Shimojo, S., Bauer, J., O’Connell, K. M. & Held. R. (1986). Prestereoptic binocular vision in infants. Vision Research, 26, 501-510. Swanson. W. H. & Birch, E. E. (1992). Extracting thresholds from noisy psychophysical data. Perception and P.rychophysics. 51, 409-422. Thompson, C. & Drasdo, N. (1988). Clinical experience with preferential looking acuity tests in infants and young children. Ophthalmology and Physiological Optics, 8, 309-321. Timney. 9. N. (1988). The development of depth perception. In Shinkman, P. G. (Ed.), Advances in neurul and behaGoral deoelopment (pp. 1533207). New Jersey: Ablex Publishing. Wilson, H. R. (1988). Development of spatiotemporal mechanisms in the human infant. Vision Research, 28, 611-628.
Acknowledgements-This project was supported in part by grants from the National Institutes of Health (EY05236, EY07716) and from the James R. Dougherty Jr Foundation. The authors wish to thank Christopher W. Tyler for initially prodding us to examine the contribution of probability summation to monocular-binocular differences in infant acuity and Wilson S. Geisler for helpful suggestions on the analysis.
IO, pp. 1999-2003, All rights reserved
1992
Copyright
Probability Summation Human Infant EILEEN
E. BIRCH,*t$
WILLIAM
0042-6989/92 $5.00 + 0.00 CI 1992 Pergamon Press Ltd
of Acuity in the
H. SWANSON*t
Received 16 July 1991
Raw data from two studies of monocular and binocular acuity development were used to determine whether a binocular acuity advantage as a function of age is predicted by probability summation and whether these predictions accurately describe the course of binocular acuity development. Two decision rules for the combination of the outputs of right eye and left eye “channels” were evaluated, the decision-threshold rule and the integration rule. Both decision rules predicted a binocular acuity advantage for infants and children aged O-60 months. However, both rules failed to adequately describe the normal course of monocular and binocular acuity development. No binocular acuity advantage was found prior to 6 months of age while, after 6 months of age, binocular acuity was superior to monocular acuity by 0.12 log unit (0.4 octave). The absence of binocular acuity superiority prior to 6 months of age is consistent with suggestions by other authors that the immature human visual system combines information from the two eyes nonselectively. Acuity
Probability
summation
Visual development
Preferential
In the human infant, fusion and stereopsis have an abrupt onset at 4-6 months of age (Birch, Gwiazda & Held, 1982; Birch, Shimojo & Held, 1985; Braddick, Wattam-Bell, Day & Atkinson, 1983; Fox, Aslin, Shea & Dumais, 1980; Gwiazda, Bauer & Held, 1989; Held, Birch & Gwiazda, 1980; Petrig, Julesz, Kropfl, Baumgartner & Anliker, 1981; Reuss, 1981; Shimojo, Bauer, O’Connell & Held, 1986) and stereoacuity improves rapidly during months 6-12 (Birch ef al., 1982; Held et al., 1980). The rates of visual acuity development and of binocular function development are relatively independent. Acuity develops at a different rate than stereoacuity (Birch, 1985; Birch & Hale, 1988), shows no sudden change at the age of onset for fusion or stereopsis (Birch, 1985, 1992), and may be limited by retinal development while fusion and stereopsis may be limited by cortical maturation (Wilson, 1988). Binocular acuity has been shown to be superior to monocular acuity after &6 months of age; i.e. after the onset of stereopsis (Birch, 1985; Birch & Hale, 1988; Dobson, 1983; McDonald, Sebris, Mohn, Teller & Dobson, 1986; Thompson & Drasdo, 1988). While at first glance the development of binocular superiority appears to fall neatly into the general finding of the emergence of binocularity at &6 months of age, it is in fact difficult to reconcile with probability summation.
*Retina Foundation of the Southwest, 9900 North Central Expressway, Suite 400, Dallas, TX 75231, U.S.A. tDepartment of Ophthalmology, University of Texas Southwestern Medical Center, Dallas, Texas, U.S.A. $To whom all correspondence should be addressed at the Retina Foundation of the Southwest.
looking
Models of probability summation predict a binocular acuity advantage for adults based on two assumptions. First, the two eyes must have similar acuities; use of a fellow eye with very poor acuity along with an eye with good acuity will yield little or no binocular advantage. Second, the two eyes must function as independent detectors (or “separate analyzers” in the terminology of Graham, 1989); i.e. there must be separate right and left eye “channels” with statistically independent noise (Green & Swets, 1966). Since no superiority of binocular acuity over monocular acuity has been found during the first few months of life, one or both of these assumptions must be incorrect for early human development. That is, the two eyes must have greatly different acuities and/or the two eyes must not function independently prior to the onset of fusion and stereopsis. Indeed, there is preliminary evidence to suggest that both of these assumptions may be incorrect. Significant interocular differences in acuity have been documented in approx. 40% of infants age O-2 months (Birch, 1985; Birch & Hale, 1988; Dobson, 1983; Thompson & Drasdo, 1988), raising the possibility that probability summation may not predict a significant binocular advantage in this age range. In addition, data from a study of fusion in pre-stereoptic infants suggests a nonselective combination of information from the two eyes; i.e. the two images are superimposed without regard to content (Held, 1985, 1988; Shimojo et al., 1986). The aims of the present study were: (1) to evaluate whether a binocular acuity advantage as a function of age is predicted by probability summation and (2) to determine whether these predictions adequately describe human monocular and binocular acuity development.
1999
2000
EILEEN E. BIRCH and WILLIAM H. SWANSON MATERIALS
AND METHODS
Forced-choice preferential-looking acuity data were taken from two previously published reports (Birch, 1985; Birch & Hale, 1988). One study used a constant stimulus paradigm to obtain percent correct as a function of spatial frequency (Birch, 1985). The second study used a staircase procedure with at least eight reversals (Birch & Hale, 1988). Raw data from these studies were fit by maximum likelihood estimation to a psychometric function of the form: P(x) = yD(x) + 0.5 [l -D(x)]
(1)
where P(x) is the probability of a correct response, D(x) is the probability of detecting stimulus x (with x in min of arc), and y is the probability of a correct response when D(x) = 1.O (Swanson & Birch, 1992). For D(x), the approximation of the cumulant of the normal distribution described by Quick (1974) was used: D(x) = 1 - 2+/4a
(2)
where a is the value of stimulus x for which D(x) = 0.5, and fi is a constant which is inversely proportional to the slope of the function, Maximum likelihood estimates for tl, fl and y were obtained by solving for the maximum in a grid of seventy-five 0.03 log unit steps of c(, eleven 0.10 log unit steps of /?, and thirteen 2% steps of y. For each stimulus x, the likelihood L(x) that correct responses were given on k of n trials is: L(x) = n !/[k!(n - k)!][P(x)lk[ 1 - P(x)1” - k
(3)
and the likelihood of a complete data set is the product of the likelihoods for all of the stimuli used to generate that data set. Nine data sets from infants who had acuities outside the range of stimuli for either of the monocular tests or the binocular test were not included in the present study, leaving complete data sets (OD, OS, and OU) from 79 infants for analysis.* Infants were assigned to age groups
*Twelve of the total of 264 acuity estimates (88 each for OD, OS and OU) were outside of the range of stimuli tested, 6.8% of constant stimulus acuity estimates and 2.3% of staircase acuity estimates. This resulted in a total of 9 full data sets (OD, OS and OU) being excluded from analysis, 13.6% of constant stimulus data sets and 6.8% of staircase acuity estimates. The 9 excluded data sets were from subjects over a wide range of age groups (3, 6, 9, 10, 11, 11, 29, 43 and 49 months). The 9 excluded data sets (27 acuity estimates) were comprised of 15 acuity estimates which were within the range of stimuli tested and 12 acuity estimates which were outside of the range of stimuli tested. Acuity estimates which were within the range of stimuli tested were similar to those obtained from age-matched infants who were not excluded from the analyses. Therefore, it is unlikely that the exclusion of these data sets led to a significant bias since only a small percentage of the total data set were excluded, excluded data sets were not limited to a single age range, and “useable” acuities from the excluded data sets were similar to those of included infants. tDistinguishing between these two decision rules is not an aim of this report. Both decision rules are included to illustrate that, in this case,their predictions are quite close and that neither rule provides an adequate prediction of binocular acuity for infants aged o-6 months.
on the basis of post-term age (average of 13 infants per age group): O-6 months; 7-12 months; 13-24 months: 25-36 months; 37-48 months; or 49-60 months. Two decision rules for the combination of the outputs from right eye and left eye “channels” were used to predict binocular acuities from monocular acuities.? The decision-threshold model describes the probability of detection based on multiple observations as equal to one minus the product of the probabilities that detection does not occur in any of the observations (Green & Swets, 1966; similar to the maximum-output decision rule described by Graham, 1989): Do,(x) =
1 - u - a&N[l
- &S(X)l~
(4)
The integration model assumes that the information in multiple observations is pooled and that the sum of the information determines the overall decision based on the product of likelihood ratios (Gorea & Tyler, 1986; Green & Swets, 1966; similar to the sum-of-outputs rule described by Graham, 1989): &u(x) = [&&)*
+
&,(~)210.5
(5)
where R(x) = (cx/x)~. Each infant included in the study contributed two monocular acuity data sets (OD and OS) and a binocular acuity data set (OU). For each infant, the maximum likelihood estimates for CL,/I and y obtained for OD and OS were used to generate predicted binocular psychometric functions under the decision threshold and integration rules. In addition, the binocular acuities predicted by each decision rule were compared with the infant’s measured binocular acuity to obtain difference scores for each infant. RESULTS
Model predictions Monocular acuities obtained from the maximum likelihood estimation procedure are shown in Fig. 1. In this figure, each infant contributed a mean monocular /
1.2 1 .o 0.8 $ r 0.6 =$ .r” 0.4
0’ q
0.2 0.0
0
10
20
30
40
50
60
Age (months) FIGURE I. Measured monocular FPL grating acuities (solid symbols f 1 SE) and predictions for binocular grating acuity based on two rules of probability summation, the decision-threshold rule (solid line) and the integration rule (dotted line). Acuities are plotted as log min of arc resolution (log MAR).
PROBABILITY
SUMMATION
acuity to the calculation of a grand mean for the age group. For the six age groups, monocular acuity estimates obtained by maximum likelihood estimation did not differ significantly from the acuities originally reported (mean difference = 0.00 + 0.17 log unit). Also shown in Fig. 1 are the predicted binocular acuities from the two decision rules. Each infant contributed a predicted binocular acuity based on its monocular acuities to the calculation of a grand mean for the age group. Predictions of binocular acuity from the decisionthreshold rule and from the integration rule were similar; both decision rules predicted a superiority of binocular over monocular acuity at all ages. Averaged over all age groups, the decision-threshold rule predicted a binocular advantage of 0.12 log unit (0.40 octave) and the integration rule predicted a binocular advantage of 0.10 log unit (0.33 octave). Adequacy
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.
.Y
1.2
0
0
10
20
Decision-threshold Integration
30
40
50
60
Age (months) FIGURE 3. Error from predictions (actual binocular acuity minus predicted binocular acuity for the decision-threshold rule (solid symbols) and the integration rule (open symbols). Each data point represents one infant.
of the models
Predicted and measured binocular acuities are shown as a function of age in Fig. 2. Both decision rules failed to adequately predict binocular acuity in the O-6 month age range, predicting better acuity than was obtained. In all remaining age groups (7-60 months), both decision rules gave reasonable predictions of binocular acuity. The difference between predicted and measured binocular acuity was calculated by taking a difference score for each infant (actual binocular acuity minus the binocular acuity predicted from that individual’s monocular acuities) and then computing the mean difference score for each age group (Fig. 3). For infants aged G-6 months, the mean difference score was 0.21 + 0.05 log unit (0.70 octave) using the decision-threshold rule and 0.17 _+0.0 1 log unit (0.57 octave) using the integration rule. While the two models accurately predicted binocular acuity for some individual infants, binocular acuity was over-predicted by 0.3 log unit (1 octave) or more in 33 and 27% of CM month olds, respectively. In older age groups, difference scores were much smaller; mean differences between measured binocular acuity and predicted binocular acuity ranged from -0.05 to 0.01 log unit (-0.17 1.2 1 .o
65
0
. .. .
0.8
Binocular Decision-threshold Integration
5 0.6 $ = " 0.4 0' 4 0.2
to 0.03 octave; mean = -0.02 & 0.01 log unit) for the decision-threshold rule and from -0.08 to -0.01 log unit (-0.26 to -0.03 octave; mean = - 0.04 + 0.01 log unit) for the integration rule. All individual infants’ binocular acuities were within 0.3 log unit (1 octave) of predicted binocular acuity. To verify that the age dependence of the binocular advantage was not due to changes in the shape of the psychometric function (other than acuity) or changes in the likelihood of the fitted psychometric function, the relationship between parameters of the psychometric functions fit by maximum likelihood estimation and age was examined. While these parameters differed between the constant stimulus and staircase procedures, within each procedure the upper asymptote (y), the slope (log/I), and the likelihood (log L), did not correlate significantly with age (r2 < 0.057 in all cases; summarized in Table 1). Nor did y or log /3 differ significantly between the O-6 months and 7-12 months age groups for OD (t,. = 0.108; tS = 0.735), OS (ty = 0.517; to = 0.194), or OU (tr = 0.520; tg = 0.137). In each age group, the mean acuity estimates obtained with the maximum likelihood fitting procedure did not differ significantly from the published acuities, which were obtained by graphical interpolation or staircase reversal averages. Differences between the published means and the TABLE 1. Correlations between ameters of the psychometric
0
10
20
30
40
50
60
Eye
Parameter
OD
log B Y log L
OS
log B Y log L
ou
log B )’ log L
Age (months) FIGURE 2. Actual binocular grating acuities (solid symbols + 1 SE) vs predicted binocular grating acuities from the decision-threshold rule (solid line) and the integration rule (dotted line). Acuities are plotted as log min of arc resolution (log MAR).
age and function
Constant stimulus rz
Staircase
0.001 0.057 0.004 0.005 0.003 0.015 0.008 0.007 0.014
0.033 0.000 0.001 0.002 0.000 0.035 0.002 0.000 0.003
r’
par-
2002
EILEEN E. BIRCH and WILLIAM
maximum likelihood estimates ranged from -0.04 to 0.03 log unit (-0.13 to 0.10 octave) in the various age groups, with a mean difference of 0.00 If: 0.03 log unit. DISCUSSION Both decision rules predicted a binocular acuity advantage in all age groups. This result suggests that the interocular differences in acuity which are present for some infants during the first 6 months of life do not preclude a binocular acuity advantage. In the present study, interocular differences of 1.0-2.3 octaves were present in 19% of infants; all but one of these infants were in the O-6 month age group. Despite the high prevalence of signi~cant intero~ular differences in the youngest age group, a binocular acuity advantage was predicted for this age group by both decision rules (Fig. 1). When the data are examined on an individual basis, approximately the same percentage of infants with interocular differences of 1.0 octave or greater (89O/) and of infants with interocular differences < 1.O octave (88%) had a predicted binocular acuity advantage (using the d~ision-threshold rule). This somewhat unexpected finding may be explained by the fact that the monocular psychometric functions of infants with interocular differences less than one octave had significantly steeper slopes than those of infants with interocular differences greater than one octave (mean log b = 0.68 and 0.54, respectively; f = 2.29, P < 0,025). Thus, while significant interocular differences in acuity reduce the expected binocular advantage, shailower slopes of monocular psychometric functions may act to increase the expected amount of binocular acuity advantage. Both decision rules are poor predictors of binocular acuity during the first 6 months of life but accurately predict binocular acuity during months 7-60. The failure to accurately predict binocular acuity during early months is not att~butable to age-related di~eren~s in the shape of the psychometric function, as indexed by the upper asymptote or slope parameters, or to age-related differences in the ability to make threshold estimates, as indexed by likelihood of fits and by agreement between different threshold estimation procedures. The integration rule as expressed in equation (5) is based on the common assumption of near-threshold linearity (Cornsweet, 1970; Massof, 1985). However, it is possible that an essential nonlinearity makes the assumption invalid during early visual development. Therefore, a more general formulation for the integration rule was evaluated, for which the only assumption was that the standard deviations of the signal and noise distributions are the same. For this formulation (Green & Swets, 1966), d’ was derived directly from P(X). Predictions from the nonlinear formulation had a mean signed difference of 0.001 log unit (0.004 octave) from the predictions of the linear formulation and a mean unsigned difference of 0.006 log unit (0.019 octave). Thus, while a nonlinear formulation led to a slight improvement in agreement between predicted
H. SWANSON
and measured binocular acuities, it was not sutlicient to account for the 0.17 log unit (0.57 octave) discrepancy. Modei ofhuman visual dewfopment The absence of probability summation during months O-6 is consistent with other suggestions that information from the two eyes is combined nonselectively prior to the onset of fusion and stereopsis. Prior to the onset of fusion, the human infant appears to have a primitive form of binocularity in which the visual system superimposes the inputs from the two retinas regardless of image content (Held, 1985, 1988; Shimojo er al., 1986). One model of the development of human binocular function suggests that the immature primary visual cortex lacks segregation into ocular dominance columns, so that both retinas provide inputs to comma cells (Held, 1985; Hickey & Peduzzi, 1987; LeVay & Voight, 1988; LeVay, Wiesel & Hubel, 1980; LeVay. Stryker & Shatz, 1978). The convergent of monocular inputs onto common cortical cells may offer no opportunity for binocular advantage due to probability summation if two assumptions are met. First, the inputs to the cortex from the two monocular channels must be summed linearly. This assumption appears reasonable if the convergence of monocular inputs onto common cells is indeed an accurate description of the immature primary visual cortex. Second, noise must be perfectly correIated. This assumption is almost certainly incorrect. At least some of the noise in the monocular channels (e.g. photon noise, intrinsic photoreceptor noise) is uncorreiated. Other sources of noise are likely to be correlated, including stimulus-related noise in the monocular channels and extraneous noise from the infant or observer in FPL testing. Moreover, noise arising at the cortical level must be perfectly correlated if monocular inputs converge onto common cells. To the extent that noise in the monocular channels is correlated, little or no binocular advantage is predicted [or, in Graham’s (1989) “summation square” terminology, “no summation” of the monocular components is predicted]. As the primary visual cortex matures. segregation of ocular dominance columns occurs and provides for separate left and right eye “channels” (LeVay et al., 1980, 1978; Poggio & Fischer, 1977). Noise in separate cortica1 left and right eye channels is likely to he uncorrelated. Segregation into ocular dominance columns also provides for the preservation of eye of origin information required for stereopsis and has been shown to coincide with the onset of stereopsis in kittens (Timney, 1988). The independence of right eye and left eye channels following ocular dominance column segregation may provide an anatomical basis for the nonlinear combination of signal -t noise from each eye which characterizes probability summation. An alternative explanation of the failure to find evidence of probability summation in the youngest age group is that, in the t3-6 month group, the primary source of noise is extraneous noise from the infant and/or observer in the FPL test situation and that
PROBABILITY
SUMMATION
extraneous noise decreases with age, making the independent noise in the two monocular channels more evident in later age groups. Within the FPL protocol, extraneous noise may result in inappropriate responses to stimuli when the infant responds to an irrelevant aspect of the test situation or when the observer responds to an irrelevant aspect of the infant’s behavior. The findings that neither the upper asymptote (y) nor the slope (log b) of the psychometric functions correlated with age and that neither ?/ or log fl differed significantly between the G-6 months and 7-12 months age groups argues against this alternative. Clinical implications The absence of binocular acuity superiority appears to be the norm for healthy infants under 6 months of age. For healthy infants over 6 months of age, probability summation results in an advantage in binocular acuity of 0.1 O-O. 12 log unit over monocular acuity. This binocular advantage makes the use of binocular normative data as a “gold standard” inappropriate for comparison with monocular acuity data from pediatric patients aged 6 months or older. The finding of binocular acuity superiority may suggest mature cortical organization, e.g. segregation into ocular dominance columns, but does not necessarily imply the capability for stereopsis. Failure to find binocular acuity superiority in an infant over 6 months of age may suggest immature cortical organization, e.g. lack of segregation into separate right and left eye channels, or may suggest that one of the monocular channels is so weak that its contribution to probability summation does not result in a binocular acuity advantage.
REFERENCES Birch, E. E. (1985). Infant interocular acuity differences and binocular vision. Vision Research, 25, 511L576. Birch, E. E. (1992). Stereopsis in infants and its developmental relationship to visual acuity. In Infanr oision. New York: Oxford University Press. In press. Birch, E. E. & Hale, L. A. (1988). Criteria for monocular acuity deficit in infancy and early childhood. Innestigatioe Ophthalmology und Visual Science, 29. 636643. Birch, E. E., Gwiazda, J. & Held, R. (1982). Stereoacuity development for crossed and uncrossed disparities in human infants. Vision Research, 22, 507-5 13. Birch, E. E., Shimojo, S. & Held, R. (1985). Preferential-looking assessment of fusion and stereopsis in infants aged l-6 months. Investigative Ophthalmology and Visual Science, 26, 366370. Braddick, O., Wattam-Bell, J., Day, J. &Atkinson, J. (1983). The onset of binocular function in human infants. Human Neurobiology, 2, 65-69. Cornsweet. T. N. (1970). Visual perception (p. 334). New York: Academic Press. Dobson, V. (1983). Clinical applications of preferential looking measures of visual acuity. Behavioral Brain Research, 10, 25-38. Fox, R., Aslin, R. N.. Shea, S. L. & Dumais, S. T. (1980). Stereopsis in human infants. Science, 207, 323-324. Gorea, A. &Tyler, C. W. (1986). New look at Bloch’s law for contrast. Journal of the Opiical Society qf America, A3, 5241.
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Graham, N. (1989). Visual pattern analyzers (pp. 1533154, 280-285). New York: Oxford University Press. Green, D. M. & Swets, J. A. (1966). Signal detection theory and psychophysics (pp. 2355240). New York: Kreiger. Gwiazda, J., Bauer, J. A. Jr & Held, R. (1989). Binocular function in human infants: Correlation of stereoptic and fusion-rivalry discriminations. Journal of Pediutric Ophthalmology and Strubismus. 26, 128-132. Held, R. (1985). Binocular vision-behavioral and neural development. In Meher, V. & Fox, R. (Eds). Neonatal cognition: Beyond rhe blooming, buzzing confusion (pp. 37-44). Held. R. (1988). Developmental of cortically mediated visual processes in human infants. In von Euler. C., Forssberg, H. & Lagercrantz, H. (Eds), Neurobiology q/early it&n/ behavior (pp. 155-l 64). Stockholm: Stockton Press. Held, R., Birch, E. E. & Gwiazda. J. (1980). Stereoacuity of human infants. Proceedings qf the National Academy qf.Science, U.S.A., 77, 5512~ 5514. Hickey, J. L. & Peduzzi, J. D. (1987). Structure and development of the visual system. In Salapatek, P. & Cohen. L. (Eds), Hundhook of infanr perception (pp. 142). New York: Academic Press. LeVay, S. & Voight, T. (1988). Ocular dominance and disparity coding in cat visual cortex. Visual Neuroscience, I, 395414. LeVay. S., Stryker, M. P. & Shatz, C. J. (1978). Ocular dominance columns and their development in layer IV of the cat’s visual cortex. A quantitative study. Journul (?f Comparative Neurolog],. 179, 223-244. LeVay, S.. Wiesel, T. N. & Hubel, D. H. (1980). The development of ocular dominance columns in normal and visually deprived monkeys. Journal of Comparo/ir.e Neurology, 161, I 5 1. Massof. R. W. (1985). Color-vision theory and linear models of color vision. Color Reseurch and Applications, IO, 133-146. McDonald, M., Sebris, S. L.. Mohn. G., Teller, D. Y. & Dobson, V. (1986). Monocular acuity in normal infants: The acuity card procedure. American Journal of’Oprometry and Physiological Optics, 63, 127-134. Petrig, 9.. Julesz, B., Kropfl. W., Baumgartner, G. & Anliker, M. (1981). Development of stereopsis and cortical binocularity in human infants: Electrophysiological evidence. Science, 213, 1402~1405. Poggio, G. F. & Fischer, 9. (1977). Binocular interaction and depth sensitivity of striate and prestriate cortical neurons of the behaving rhesus monkey. Journal qf Neurophysiology, 40, 1392- 1405. Quick, R. F. (1974). A vector-magnitude model of contrast detection. Kybernetik. 16, 65-61. Reuss, J. (1981). Human stereopsis: Detection and development. Disserlaiion Abstracts Inrernutional, 42, 19619. Shimojo, S., Bauer, J., O’Connell, K. M. & Held. R. (1986). Prestereoptic binocular vision in infants. Vision Research, 26, 501-510. Swanson. W. H. & Birch, E. E. (1992). Extracting thresholds from noisy psychophysical data. Perception and P.rychophysics. 51, 409-422. Thompson, C. & Drasdo, N. (1988). Clinical experience with preferential looking acuity tests in infants and young children. Ophthalmology and Physiological Optics, 8, 309-321. Timney. 9. N. (1988). The development of depth perception. In Shinkman, P. G. (Ed.), Advances in neurul and behaGoral deoelopment (pp. 1533207). New Jersey: Ablex Publishing. Wilson, H. R. (1988). Development of spatiotemporal mechanisms in the human infant. Vision Research, 28, 611-628.
Acknowledgements-This project was supported in part by grants from the National Institutes of Health (EY05236, EY07716) and from the James R. Dougherty Jr Foundation. The authors wish to thank Christopher W. Tyler for initially prodding us to examine the contribution of probability summation to monocular-binocular differences in infant acuity and Wilson S. Geisler for helpful suggestions on the analysis.