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Research Article  |   June 2009
Stereo and motion Dmax in infants
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Journal of Vision June 2009, Vol.9, 9. doi:10.1167/9.6.9
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      John Wattam-Bell; Stereo and motion Dmax in infants. Journal of Vision 2009;9(6):9. doi: 10.1167/9.6.9.

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Abstract

These experiments compared the maximum displacement and disparity limits (Dmax) for apparent motion and stereopsis in random-dot displays in adult and 12–28 week-old infant subjects. Both stereo and motion Dmax increased during development, from about 0.3 deg in the youngest infants to 2 deg in adults. Some of the younger infants (12–14 weeks) did not give a stereo threshold, probably because stereopsis had not yet developed; but otherwise, the values of Dmax in the two domains were close to each other throughout the age range. These results suggest that both stereo and motion Dmax are limited by some common factor. Possible factors include receptive field sizes and internal noise. Simulations in which these were varied showed that while changes in both could contribute to the development of Dmax, only an increase in receptive field size can fully account for the rise in Dmax with age.

Introduction
A superficial comparison between the visual processing of stereoscopic disparity and apparent motion suggests a number of similarities. Perhaps the most obvious is that they both face the correspondence problem. In each case, the minimum input is a pair of images which are identical apart from a spatial offset: the visual system's task is to identify the direction and size of this offset, and this depends on correctly matching the features of one image with their partners in the other. This similarity of task suggests that the visual system may use essentially the same method for solving it in the two domains. Physiological evidence supports this idea: the mechanisms underlying disparity and direction selectivity in V1 seem to involve very similar computations which are well described by the standard energy model (Anzai, Ohzawa, & Freeman, 1999; Emerson, Bergen, & Adelson, 1992; see also 1); while area MT, in which cells typically show sensitivity to both motion and disparity (Maunsell & Van Essen, 1983a, 1983b), provides a common neural substrate for processing in the two domains. 
Stereograms and kinetograms constructed from random-dot patterns (RDPs) illustrate the ease with which the visual system solves the correspondence problem. Braddick (1974) found that there is an upper displacement limit for apparent motion in RDPs (motion Dmax), beyond which the motion became incoherent, and over the last 35 years there has been a large amount of research into the factors that affect motion Dmax. There is also an equivalent maximum disparity limit for stereopsis in RDPs (stereo Dmax). This has received much less attention, but recently Glennerster ( 1998) made a direct comparison between stereo & motion Dmax, and found that they were identical over a wide range of stimulus parameters—further evidence for a common style, if not site, of processing. 
In an experiment on infant subjects, Wattam-Bell (1992) showed that motion Dmax increases during the course of development, and suggested that infants had low values of Dmax because they lacked directional detectors with large receptive fields. The discussion above suggests there will be a similar developmental increase in stereo Dmax. The strongest prediction is that at any age, stereo and motion Dmax are the same, which would imply a rather specific common factor, rather than a general one such as variation in motivation or attention. Equality of Dmax cannot be true for the youngest infants, however—it is known that sensitivity to stereo disparity emerges at around 3–4 months (Birch, 1993; Braddick, 1996), by which time sensitivity to motion direction is well established (Wattam-Bell, 1996a, 1996b). When stereopsis first appears, does it have the same Dmax as motion, or is there a period in which it lags behind? The experiments reported here addressed this question by measuring stereo and motion Dmax under similar conditions in infants aged 12–28 weeks. 
An important issue for these experiments is how to equate the stimuli in the two domains. The problem is that although stereopsis and motion perception may be quite similar, they are not identical. Locally, the ‘natural’ stimulus for stereo can only be a single displacement (i.e. the difference between the two eyes’ views), while for motion it is the limiting case of a sequence of displacements (i.e. continuous motion). 
One solution is to use impulse-like stimuli—short trials consisting of a single displacement. This was Glennerster's ( 1998) approach, and it yielded almost identical values of Dmax for stereo and motion. However, infant testing requires long trial durations, with information relevant to the task present throughout a trial. To achieve this, the motion stimulus must consist of a sequence of displacements. The current study used stimuli of indefinite duration in which the direction of motion or disparity reversed periodically. While it is perhaps not so obvious that the stereo and motion stimuli will be well matched under these conditions, data from adult subjects described below show that over a wide range of reversal intervals, stereo and motion Dmax are indeed the same. 
Methods
Stimuli
The motion and stereo stimuli were random-dot patterns (RDPs), made up of 0.25 deg square elements, with a density of 50% (i.e. half the squares were bright and half dark). Two such patterns were displayed side-by side on a 26 inch video monitor (Mitsubishi HC3505, 640 × 512 pixels, 50 Hz refresh). At the viewing distance of 50 cm, the patterns were 16.9 deg wide by 39.5 deg high, and were separated by 8.8 deg ( Figure 1). 
Figure 1
 
The random dot stimuli. See text for description.
Figure 1
 
The random dot stimuli. See text for description.
Separate copies of the RDPs were fed to the red and green inputs of the monitor. Subjects viewed them through red (right eye) and green (left eye) filters. We used the method described by Mulligan ( 1986) to minimize the cross-talk between the eyes that results from the mismatch between the filters and the phosphors of the monitor. This procedure reduces stimulus contrast: measured through the red filter, the minimum and maximum luminances were 0.32 cd/m2 and 3.7 cd/m2 (84% contrast), while through the green filter they were 0.38 cd/m2 and 4.1 cd/m2 (83% contrast). 
Displacements of the RDPs were always fully coherent, and resulted in dots wrapping round, but over a virtual width twice as great as the visible pattern width. Hence dots falling off one edge did not immediately appear at the opposite edge, which allowed displacements of unambiguous direction up to just short of the full pattern width (16.9 deg). 
In the motion stimulus, disparity was zero, and the dots were displaced coherently in the horizontal direction between every video frame (every 20 msec). On one side of the screen, the RDP was segregated horizontally into alternate regions of leftwards and rightwards motion, while on the other side the pattern was uniform; all the dots moved in the same direction ( Figure 1). In any one trial, the absolute displacement was constant in all parts of the display, but its direction reversed periodically—regions of leftwards motion switched to rightwards, and vice-versa. Each time direction reversed, the patterns were replaced by a new, uncorrelated set of dots. 
For the stereo stimulus, disparity was produced by varying the relative horizontal positions of the red and green dots in the RDP. The segregated pattern was divided horizontally into alternate regions of crossed and uncrossed disparity, while the uniform pattern contained only one of these disparities. Absolute disparity was constant during a trial, but its sign reversed periodically—regions of crossed disparity switched to uncrossed, and vice-versa. As in the motion stimulus, reversals were accompanied by random replacement of the RDPs; this was to eliminate the coherent apparent motion that occurs when disparity switches, which is visible monocularly. 
Between both motion and stereo trials, the RDPs were stationary and disparity was zero, and there was a fixation marker—a rectangle, which was stationary for adults, but oscillated vertically for infants—in the center of the screen. 
All trials started and finished with a random replacement of the RDPs; this is necessary with the stereo stimulus to mask the monocularly-visible apparent motion that accompanies the transition from zero to non-zero disparity. 
Procedure
Dmax was measured with forced-choice preferential looking (i.e. preference for the segregated pattern) in infants, and 2AFC in adults, using a 2-up 1-down staircase. Staircases started at 0.24 deg disparity/displacement size, which varied in steps of 0.12 deg for the first two reversals, and 0.06 deg for the final six. Thresholds were estimated from the mean disparity/displacement size of these last 6 reversals. If at any time the 2-up 1-down staircase drove the stimulus level below 0.12 deg, it was abandoned, and instead, testing continued at that level until 20 trials had been gathered. If performance was at or above 70%, the level was increased by 0.12 deg, otherwise it was decreased by the same amount, and a further 20 trials gathered. This procedure continued until (a) a pair of stimulus levels (0.12 deg apart) were found that bracketed 70% correct, with the lower level producing the higher performance, in which case the threshold was estimated by linear interpolation to the 70% point; or (b) performance remained below 70% down to the lowest level (0.06 deg), leading to an undefined threshold. 
This procedure was designed to ensure that if an infant had no overall preference for the segregated pattern at any displacement, the staircase would fail. In practice this only happened with a subset of the youngest infants, and only for the stereo stimulus, which probably reflects a lack of stereopsis in these infants. Overall, infants showed a robust preference for the segregated pattern that was sufficient to allow thresholds to be measured. 
Subjects
The author was the main adult subject, but key aspects of his results were confirmed in one other subject. Both adults had normal vision. The infant subjects were all born within 14 days of their expected date, and had no known ocular or other medical problems. Infant ages reported here were based on expected date of birth. 
Results
Adults
The first experiment examined the effect of disparity/direction reversal interval (0.08–0.48 sec) for indefinite-duration trials (i.e. until the subject responded) in adults. Dmax was reduced at the shorter intervals ( Figure 2), but for one subject at least appeared to reach a plateau beyond 0.12 sec; and more importantly, stereo and motion Dmax were essentially the same throughout the range. 
Figure 2
 
Adult motion (blue line) and stereo (red line) Dmax as a function of reversal interval. The circles show results for subject JWB. An additional subject was tested at both extremes of the reversal interval range (squares): for clarity their results have been moved sideways. Each of the data points shows the mean and standard error of four threshold estimates.
Figure 2
 
Adult motion (blue line) and stereo (red line) Dmax as a function of reversal interval. The circles show results for subject JWB. An additional subject was tested at both extremes of the reversal interval range (squares): for clarity their results have been moved sideways. Each of the data points shows the mean and standard error of four threshold estimates.
Infants
The infant experiments used a disparity/direction reversal interval of 0.48 sec; the adult data ( Figure 2) suggest that any value will suit the purpose of minimizing differences between stereo and motion thresholds, and 0.48 sec was chosen because it is well into the region where reversal interval has no effect on adult Dmax or infant motion coherence thresholds (Mason, Braddick, & Wattam-Bell, 2003; Wattam-Bell, 1994). Trial duration was unlimited, but in practice no trial lasted more than 10 sec, and the majority were less than 5 sec. A total of 86 infants were tested; 12 of these failed to provide any results because of fussing, sleep etc. Of 64 infants who contributed to the results reported here, 26 gave both stereo and motion data (12 did motion first, 14 stereo first), while the remainder only managed one test (again due to fussing or sleep): 13 for motion, and 25 for stereo. The infants were divided into five age groups; Table 1 shows the distribution of infant numbers across age groups and conditions. Each infant was tested on a single occasion only, contributing results to single age group. 
Table 1
 
Distribution of infant numbers across age groups and conditions.
Table 1
 
Distribution of infant numbers across age groups and conditions.
Motion + stereo Motion only Stereo only Motion total Stereo total
12–14 weeks 10 2 6 12 16
15–17 weeks 4 4 6 8 10
18–20 weeks 5 2 3 7 8
21–23 weeks 7 5 2 12 9
24–28 weeks 0 0 8 0 8
Figure 3 shows the results for motion Dmax. As in previous experiments (Wattam-Bell, 1992, 1996a), Dmax increased with age, and ANOVA revealed that this effect was significant (F(3, 37) = 6.01, P < 0.01). 
Figure 3
 
Infant motion Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group.
Figure 3
 
Infant motion Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group.
The infant's stereo Dmax results are summarized in Figure 4. Ten of the 51 infants tested for stereo gave an undefined threshold (see Methods), indicating either an absence of stereopsis or a Dmax < 0.06 deg. Since all of these infants were in the youngest (12–14 week) age group, their undefined thresholds probably imply a lack of stereopsis; a number of studies agree that its onset (defined as the age at which 50% of infants show stereopsis) is at about 14 weeks (Birch, 1993; Braddick, 1996). In Figure 4, two results are given for the 12–14 week group; the open bar is the mean Dmax of those infants who produced a defined threshold, while the filled bar is the mean of all the infants in the group, which was calculated by setting undefined thresholds to zero. 
Figure 4
 
Infant stereo Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group. For the 12–14 week group, the unfilled column shows the mean Dmax of those infants who gave a defined stereo threshold (see text for details), while the filled column includes all the infants in this group; undefined thresholds were assigned a value of 0 deg.
Figure 4
 
Infant stereo Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group. For the 12–14 week group, the unfilled column shows the mean Dmax of those infants who gave a defined stereo threshold (see text for details), while the filled column includes all the infants in this group; undefined thresholds were assigned a value of 0 deg.
The results plotted in Figure 4 indicate that like motion Dmax, stereo Dmax increases with age. Anova across all age groups (but including only those infants in the 12–14 week group who gave a defined threshold) showed a significant effect of age ( F(4, 32) = 6.15, P < 0.001), as did an analysis that excluded the youngest group entirely ( F(3, 28) = 5.63, P < 0.005). 
Figure 5 plots motion vs. stereo Dmax for 20 of the infants who did both conditions (the other 6 had undefined stereo thresholds). There was no significant difference between the two thresholds in this group (mean thresholds were 0.45 deg (motion), and 0.40 deg (stereo); t = 1.31, P = 0.21). The regression line in Figure 2 has a slope of 0.74 (95% confidence interval: 0.3–1.2), and an intercept of 0.06 (95% confidence interval −0.14–0.28). Thus the two thresholds are significantly correlated. By itself, a correlation is but weak evidence for a common mechanism; any two visual functions that improve with age are liable to be correlated, whether or not they share a common neural substrate. However, the fact that the regression intercept and slope are not significantly different from zero and one, respectively, is consistent with the hypothesis that in infants stereo and motion Dmax are not just correlated, but are equal to each other (as they are in adults). Equality of thresholds provides rather stronger evidence in favor of a common substrate. 
Figure 5
 
Infants' stereo Dmax vs. motion Dmax. These data are from 20 infants who were tested for both thresholds, and gave a defined stereo threshold.
Figure 5
 
Infants' stereo Dmax vs. motion Dmax. These data are from 20 infants who were tested for both thresholds, and gave a defined stereo threshold.
If there is more to the correlation between thresholds than a non-specific effect of age, then it should remain significant after removing this effect. Here, however, the result is rather inconclusive; the partial correlation coefficient between stereo and motion Dmax for the data in Figure 5 is 0.43, which is not quite significantly different from zero ( P = 0.066). 
Discussion
The main finding from the infant experiment was that stereo Dmax, like motion Dmax, increases during development. In addition, there is no real evidence of any quantitative difference between the two thresholds, except in the youngest age group; and even in this group the thresholds are similar when the infants who appear to have not yet developed stereopsis are excluded. 
A developmental increase in motion Dmax was also reported by Wattam-Bell (1992). The two studies tested different but overlapping age ranges. In the region of overlap (12–15 weeks), motion Dmax in the present study was about 30% lower than in Wattam-Bell (1992), and this difference is significant (t = −2.21, p = 0.044). The reasons for this discrepancy are not clear; while there are a number of stimulus differences that might affect Dmax, adults gave similar results in the two studies. However, it might be that infants were more affected by some of the differences, in particular stimulus luminance, which was considerably lower in the current study because the stimuli were viewed through the red/green filters. 
A tentative extrapolation of the development of Dmax reported here suggests it could reach adult levels by about 1 year. However, Parrish, Giaschi, Boden, and Dougherty (2005) found that for motion, Dmax continues to increase until 7 years, though more slowly than found here, while motion coherence thresholds were already adult-like at 3 years (though see Gunn et al., 2002). This developmental dissociation could arise if, as argued below, Dmax primarily reflects the properties of local mechanisms, whereas global integration of local responses is critical for coherence thresholds. 
Kiorpes and Movshon ( 2004a) measured the development of motion sensitivity (inverse coherence thresholds) in macaques over a wide range of spatiotemporal displacements. They found that after about 14 weeks the main change was a vertical shift in the motion sensitivity function (i.e. sensitivity as a function of spatial displacement), and that this was sufficient to account for the rather modest rise in upper displacement limit (Dmax) that they observed. Given the usual translation of macaque weeks to human months, their findings are not incompatible with the present results, which imply that the most rapid change in Dmax occurs in the first year of life (for humans). 
Dmax for the youngest macaques tested by Kiorpes and Movshon (2004a)—2 weeks and up, thus approximately equivalent to the infants tested here—was similar to that for older macaques, which does contrast strongly with the present results. However, this is probably a consequence of the way younger infants were tested; whereas the older subjects made a perceptual choice, the youngest subjects’ thresholds were measured mainly from the OKN evoked by the stimulus. In young infants, OKN is largely a subcortical reflex, and thus probably does not reflect the properties of cortical motion mechanisms that contribute to perceptual choices. Indeed, human newborns readily produce OKN (Atkinson, 1979; Naegle & Held, 1982), even though it has so far proved impossible to find any evidence for perceptual discrimination of direction before about 7–8 weeks (Wattam-Bell, 1996a, 1996b). Moreover, in older infants, coherence thresholds for OKN develop earlier than thresholds for a perceptual task (Mason et al., 2003). 
Cortical motion processing in the primate visual system starts with local measurements by directionally-selective neurons in early visual cortex (V1, and perhaps V2: De Valois, Yund, & Helper, 1982; Priebe, Lisberger, & Movshon, 2006). Global properties of the motion are then recovered by pooling the local signals in extrastriate cortical areas, in particular V5/MT (Born & Bradley, 2005). In this system, Dmax is likely to be dominated by the properties of the local detectors. Local responses to displacements that are much larger than the largest local receptive fields (RFs) will be pure noise, and no amount of subsequent pooling will extract a meaningful signal. For displacements comparable to the largest RF sizes, local signals will be noisy and pooling will improve detection—but note that Dmax will still be essentially determined by local RF size, with subsequent pooling playing a secondary role. 
1 describes simulations, based on such a two stage model (local detection followed by global integration), which broadly support this conclusion. Briefly, the simulations indicate that while changes in first-stage RF size can readily explain the 6-fold increase in Dmax between infants and adults, variations in either internal noise or the extent of second-stage spatial pooling can account for little more than a two-fold increase. Moreover, the available evidence suggests that in early infancy these last two factors develop in the wrong direction: first, responses of visual neurons in infant macaques are more reliable (i.e. less noisy, although also less sensitive) than in adults (Rust, Schultz, & Movshon, 2002). Second, a number of infant motion studies suggest that the spatial extent of second-stage integration may actually shrink during the first months of life (Banton & Bertenthal, 1995; Banton, Bertenthal, & Seaks, 1999; Dobkins, Fine, Hsueh, & Vitten, 2004; Roessler & Dannemiller, 1995; Wattam-Bell, 1994). 
Hence, although changes in noise and/or pooling may be important for the relatively slow improvement in Dmax in later development (Kiorpes & Movshon, 2004a; Parrish et al., 2005), an increase in local RF sizes remains the most plausible explanation for the rapid development of Dmax in the first year of life. This seems at odds with the generally accepted view that RF sizes decrease during development. Measurements of neuronal acuity in monkeys (Blakemore & Vital-Durand, 1983) suggest that the smallest RFs get smaller, while more direct measures of RF sizes (e.g. Movshon, Kiorpes, Cavanaugh, and Hawken (2000) in infant monkeys; Freeman and Ohzawa ( 1992) in kittens) indicate that average sizes also decrease. 
However, in V1 these effects are largely a result of increasing photoreceptor density in the fovea (Hendrickson & Drucker, 1992; Kiorpes & Movshon, 2004b), and since this is mainly due to photoreceptor migration, peripheral density should if anything decrease, leading to larger peripheral RFs, though this effect may be rather small (and is not offered as an explanation for the development of Dmax). More generally, the decrease in average RF size doesn't have strong implications for the development of the largest RFs. Even if the range of RF sizes expands in both directions (which is basically what is being proposed here) average sizes will still decrease, simply because smaller RFs are more numerous—more of them are needed to adequately sample a given region of the visual field. 
This discussion has so far focused on motion processing simply because there are many more relevant studies than for stereopsis. However, the similarity of motion and stereo Dmax in adults and infants suggests that much of the discussion can be carried over directly to the stereo domain, and that the development of stereo Dmax is also a result of an increase in the size of the largest low-level disparity detectors. However, recent physiological studies have highlighted important differences between motion and stereo that are likely to be relevant here. The properties of V1 motion mechanisms projecting directly to area MT can adequately account for velocity tuning in MT. But the properties of V1 disparity detectors cannot fully explain MT disparity tuning—among other things, there is a shortfall at large disparities (Roe, Parker, Born, & DeAngelis, 2007). One suggestion is that the gap is filled by the indirect pathway via V2, where sensitivity to large disparities is created de novo from non-selective V1 inputs (Roe et al., 2007). Interestingly, in the model described in 1, RF sizes for disparity/motion energy mechanisms are determined by the sizes of the non-selective subunits forming their inputs. If such subunits in V1 (essentially simple cells) provide the input both to motion mechanisms in V1 and to disparity mechanisms in V2, then they would provide the common substrate which could explain the parallel development of stereo and motion Dmax. 
Appendix A
This appendix outlines the results of simulations exploring the effects on Dmax of (a) emergence of larger receptive fields (RFs), and (b) a decrease in internal noise. 
The focus is on local, low-level motion/stereo mechanisms such as those found in V1. The assumption is that these provide the inputs to a later stage which is responsible for detecting the relative motion of the segregated stimulus, but that Dmax for this task is primarily limited by the properties of the low-level mechanisms. In support of this, Baker and Braddick ( 1982) have shown that segregation in motion stimuli depends on absolute displacement, which implies that the motion is first detected by mechanisms operating separately in each region of the stimulus. 
The simulations were based on the disparity energy model, which accurately mimics the behavior of binocular complex cells in V1 (Ohzawa, 1998). Strictly, the motion domain requires a full spatiotemporal energy model (Adelson & Bergen, 1985), but in situations where performance is limited by spatial displacement, as is the case for apparent motion Dmax in both adults and infants (Wattam-Bell, 1992), a good approximation can be achieved by reducing the temporal dimension to two points, one before and one after the displacement of the stimulus. The motion model then becomes equivalent to the disparity model—a general spatial-displacement energy detector, sensitive to displacements of a stimulus between two points in time (motion) or between the two eyes at one point in time (stereo). 
The energy mechanisms were constructed along the lines proposed by Adelson and Bergen ( 1985). Arrays of Gabor filters, with spatial phase varying in steps of 90 deg., sampled the stimulus at each time point (or eye). These filters were combined linearly to produce quadrature pairs of leftwards and rightwards space-time (or space-eye) oriented filters, whose outputs were squared and summed to form leftwards and rightwards displacement energy mechanisms. 
For any one energy mechanism, the input Gabors all had the same size Gaussian envelope, which thus defined the receptive field size of the mechanism as a whole. Different receptive field sizes were created by spatial scaling of the Gabor filters. 
The outputs of the leftwards and rightwards energy mechanisms were separately pooled across the different receptive field sizes and over space (five distinct stimulus locations were used in most of the simulations; this is not a critical parameter). Finally, a decision about the direction of the stimulus displacement was derived from the relative strength of the leftwards vs. rightwards pooled responses. 
The performance of the model was assessed as percent correct direction decisions, over 5000–20000 trials, as a function of stimulus displacement in the range 0.1–3.0 deg. Dmax was estimated as the displacement giving 70% correct performance on the upper limb of the function. 
The first set of simulations explored the effect of adding larger receptive fields to the pool of displacement detectors ( Figure A1). 
Figure A1
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of adding mechanisms with progressively larger receptive fields: (a) one RF size of 0.31 deg. (b) two sizes spanning 0.31–0.62 deg. (c) four sizes spanning 0.31–1.25 deg. (d) eight sizes spanning 0.31–2.50 deg. The dashed curve (e) shows performance for the same range of RFs as (d), but with a 10-fold increase in the extent of second stage spatial pooling.
Figure A1
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of adding mechanisms with progressively larger receptive fields: (a) one RF size of 0.31 deg. (b) two sizes spanning 0.31–0.62 deg. (c) four sizes spanning 0.31–1.25 deg. (d) eight sizes spanning 0.31–2.50 deg. The dashed curve (e) shows performance for the same range of RFs as (d), but with a 10-fold increase in the extent of second stage spatial pooling.
Dmax increased from 0.34 deg for a model with one 0.32 deg RF to 2.2 deg for a model with RF sizes spanning 0.32–2.5 deg. When the larger RFs are added, Dmax doesn’t quite keep up with the size of largest. This is because the responses of all sizes of RF are pooled; at large displacements, close to Dmax, the smaller RFs are just generating noise, which degrades the performance of the model. Nevertheless, Dmax was increased by a factor of 6.5: it is clear that adding larger RFs can in principle explain the increase in Dmax with age found in this study. 
Figure A1, curve (e) illustrates the effect of increasing the extent of spatial pooling by a factor of 10. The response function becomes steeper, which does increase Dmax, but only by about 15%. 
The second set of simulations explored the effect of adding internal noise on performance of the model with RF sizes spanning 0.32–2.5 deg. ( Figure A2). 
Figure A2
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of internal noise on performance. The noise levels indicated on the graph are standard deviations of Gaussian noise added to the outputs of the displacement energy mechanisms.
Figure A2
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of internal noise on performance. The noise levels indicated on the graph are standard deviations of Gaussian noise added to the outputs of the displacement energy mechanisms.
Internal noise reduces Dmax; but it also reduces performance at all displacements. For the highest noise level depicted in Figure A2, performance only just reaches 70%, at a displacement of about 0.8 deg. Taking this as Dmax, it represents a factor of 2.8 reduction over Dmax for the zero noise case, rather less than the developmental change to be accounted for. Moreover, the noise = 3 case is unlikely to be representative of the even the youngest infants’ performance: in the motion task, this group averaged 78% correct at 0.12 deg displacement. It is apparent from Figure A1 that any response function whose peak is appreciably higher than 70% correct will have a Dmax of at least 1 deg: overall, it seems that changes in internal noise can’t account for much more than a twofold change in Dmax. 
These results were checked for a range of model parameters (Gabor bandwidth, and a linear vs. quadratic pooling rule). In all cases the same pattern of results emerged, leading to the same conclusion: adding larger RFs shifts the response function sideways and can readily account for large changes in Dmax, whereas internal noise squashes the response functions vertically and can only account for a twofold variation in Dmax. 
Acknowledgments
This research was supported by a Medical Research Council program grant (G7908507). 
Commercial relationships: none. 
Corresponding author: John Wattam-Bell. 
Email: j.wattam-bell@ucl.ac.uk. 
Address: Visual Development Unit, Department of Developmental Science, UCL, Gower Street, London, WC1E 6BT, UK. 
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Figure 1
 
The random dot stimuli. See text for description.
Figure 1
 
The random dot stimuli. See text for description.
Figure 2
 
Adult motion (blue line) and stereo (red line) Dmax as a function of reversal interval. The circles show results for subject JWB. An additional subject was tested at both extremes of the reversal interval range (squares): for clarity their results have been moved sideways. Each of the data points shows the mean and standard error of four threshold estimates.
Figure 2
 
Adult motion (blue line) and stereo (red line) Dmax as a function of reversal interval. The circles show results for subject JWB. An additional subject was tested at both extremes of the reversal interval range (squares): for clarity their results have been moved sideways. Each of the data points shows the mean and standard error of four threshold estimates.
Figure 3
 
Infant motion Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group.
Figure 3
 
Infant motion Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group.
Figure 4
 
Infant stereo Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group. For the 12–14 week group, the unfilled column shows the mean Dmax of those infants who gave a defined stereo threshold (see text for details), while the filled column includes all the infants in this group; undefined thresholds were assigned a value of 0 deg.
Figure 4
 
Infant stereo Dmax: mean and standard error for each age group. See Table 1 for infant numbers in each group. For the 12–14 week group, the unfilled column shows the mean Dmax of those infants who gave a defined stereo threshold (see text for details), while the filled column includes all the infants in this group; undefined thresholds were assigned a value of 0 deg.
Figure 5
 
Infants' stereo Dmax vs. motion Dmax. These data are from 20 infants who were tested for both thresholds, and gave a defined stereo threshold.
Figure 5
 
Infants' stereo Dmax vs. motion Dmax. These data are from 20 infants who were tested for both thresholds, and gave a defined stereo threshold.
Figure A1
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of adding mechanisms with progressively larger receptive fields: (a) one RF size of 0.31 deg. (b) two sizes spanning 0.31–0.62 deg. (c) four sizes spanning 0.31–1.25 deg. (d) eight sizes spanning 0.31–2.50 deg. The dashed curve (e) shows performance for the same range of RFs as (d), but with a 10-fold increase in the extent of second stage spatial pooling.
Figure A1
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of adding mechanisms with progressively larger receptive fields: (a) one RF size of 0.31 deg. (b) two sizes spanning 0.31–0.62 deg. (c) four sizes spanning 0.31–1.25 deg. (d) eight sizes spanning 0.31–2.50 deg. The dashed curve (e) shows performance for the same range of RFs as (d), but with a 10-fold increase in the extent of second stage spatial pooling.
Figure A2
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of internal noise on performance. The noise levels indicated on the graph are standard deviations of Gaussian noise added to the outputs of the displacement energy mechanisms.
Figure A2
 
Percent correct direction discrimination as a function of stimulus displacement, showing the effect of internal noise on performance. The noise levels indicated on the graph are standard deviations of Gaussian noise added to the outputs of the displacement energy mechanisms.
Table 1
 
Distribution of infant numbers across age groups and conditions.
Table 1
 
Distribution of infant numbers across age groups and conditions.
Motion + stereo Motion only Stereo only Motion total Stereo total
12–14 weeks 10 2 6 12 16
15–17 weeks 4 4 6 8 10
18–20 weeks 5 2 3 7 8
21–23 weeks 7 5 2 12 9
24–28 weeks 0 0 8 0 8
© 2009 ARVO
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