 |
 Previous Article
The Journal of Neuroscience, June 15, 2000, 20(12):4758-4767
Local Disparity Not Perceived Depth Is Signaled by Binocular
Neurons in Cortical Area V1 of the Macaque
Bruce G.
Cumming and
Andrew J.
Parker
University Laboratory of Physiology, Oxford, United Kingdom OX1 3PT
 |
ABSTRACT |
Binocular neurons that are closely related to depth perception
should respond selectively for stimuli eliciting an appropriate depth
sensation. To separate perceived depth from local disparity within the
receptive field, sinusoidal luminance gratings were presented within a
circular aperture. The disparity of the aperture was coupled to that of
the grating, thereby rendering unambiguous the psychophysical matching
between repeating cycles of the grating. In cases in which the stimulus
disparity differs by one horizontal period of the grating, the portion
of the grating that locally covers a receptive field is binocularly
identical, but the depth sensation is very different because of the
aperture. For 117 disparity-selective V1 neurons tested in two monkeys,
the overwhelming majority responded equally well to configurations that
were locally identical but led to different perceptions of depth.
Because the psychophysical sensation is not reflected in the firing
rate of V1 neurons, the signals that make stereo matches explicit are
most likely elaborated in extrastriate cortex.
Key words:
primary visual cortex; binocular disparity; stereopsis; correspondence problem; depth perception; behaving monkey
| |
INTRODUCTION |
The extent to which the properties
of disparity-selective cortical neurons match those of psychophysical
depth perception remains unclear. Most existing data are compatible
with the view that disparity-selective neurons in primary visual cortex
(V1) perform a simple calculation of the disparity of features within their receptive fields (Ohzawa, 1998 ), yet several
psychophysical properties of stereopsis require more complex
processing. One of these is the ability to solve the stereo
correspondence problem: image features on the left retina must be
matched with appropriate features on the right retina before depth is
perceived (Julesz, 1971; Marr and Poggio,
1979).
Whether single neurons respond only to appropriately matching stimuli
is therefore an important test of how well they account for depth
perception. The complexity of natural images is such that locally a
binocular receptive field may receive stimulation from image features
that fall in appropriate locations on each retina. On some occasions,
those features are generated by a single object in the
three-dimensional world (globally correct matches) and on other
occasions not (false matches). If some disparity-selective neurons
respond to these false matches, it suggests that an additional processing stage is required to understand why the false match is not
perceived psychophysically. It has been argued that disparity selectivity in the response of complex cells to random dot stereograms (RDS; Poggio, 1984; Poggio et al., 1985)
"assigns to the complex cell the unique property of solving the
correspondence problem" (Poggio and Poggio, 1984). It
has subsequently been pointed out that such responses to random dot
stimuli are well explained on the basis of local matches alone
(Qian, 1994; Fleet et al., 1996; Cumming and Parker, 1997), so by itself this test does
not establish whether V1 neurons distinguish global from false matches.
Many neurons show disparity selectivity when stimulated by
anticorrelated RDS (Cumming and Parker, 1997), which
produce no sensation of depth (Julesz, 1971;
Cogan et al., 1993; Cumming et al.,
1998). This suggests that V1 neurons are not exclusively selective for psychophysically perceived matches. However, the majority
of these neurons modulated their firing less strongly for
anticorrelated RDS than for correlated RDS. This is at odds with
predictions based on the simplest versions of local processing, but
refinements of such local models may be able to accommodate this
result. Thus the data need not imply a general ability to distinguish
false matches from global matches. Rather, the interpretation depends
on detailed comparisons of quantitative models.
These uncertainties could be avoided if it were possible to present
identical features locally in the receptive field and yet
arrange that these features were sometimes false matches but at other
times globally correct matches. Psychophysically it is possible to
arrange this by using a horizontal row of identical elements. When a
disparity is applied to the whole row, depth is perceived at this
disparity, even when the disparity is as large as the spacing between
elements (McKee and Mitchison, 1988). Under these
circumstances, the disparity measured between nearest identical
elements on the retinas is different from the global disparity
(perceived by the observer).
We used a modified version of this stimulus, consisting of circular
patches of sinusoidal gratings, applying disparity to both the grating
and the circular aperture. This produces a stable and robust sensation
of depth (see Figure 1) and is highly effective in activating V1
neurons. With this stimulus, the distinction between globally correct
and false matches can only be made by reference to the location of the
aperture, which we arranged should lie outside the classical receptive
field. Thus, binocular V1 neurons could make the distinction only if
modulatory influences from beyond the classical receptive field (RF)
(Maffei and Fiorentini, 1976; Gilbert and Wiesel,
1990; Sillito et al., 1995; Levitt and Lund, 1997) influence binocular interactions. This would allow disparity-selective neurons to respond preferentially to globally correct matches, as pointed out by Mitchison (1988).
| |
MATERIALS AND METHODS |
A detailed description of the recording techniques has been
given elsewhere (Cumming and Parker, 1999). In brief,
monkeys were trained to fixate for fluid reward while viewing binocular stimuli via a mirror stereoscope. The positions of both eyes were recorded with scleral search coils. Extracellular action potentials were recorded via tungsten-in-glass microelectrodes (Merrill and Ainsworth, 1972), which were inserted transdurally before each recording session. Necessary surgery was performed under general anaesthetic, and all of the procedures complied with the UK Home Office
regulations on animal experimentation.
Stimulus generation and selection. Stimuli consisted of
high-contrast (99%), sinusoidal luminance modulations within a
circular aperture. The rest of the screen was a uniform gray equal to
the mean luminance of the grating (188 cd/m2).
Linearity of the response of the display was measured with a Tektronix
(Wilsonville, OR) J16 Photometer, and appropriate gamma correction was
applied to ensure a linear response. The aperture was made sufficiently
large to ensure that, at the largest disparity used, the minimum
response field (MRF; determined with a binocular flashing bar at the
optimal orientation) was covered by the grating in both eyes. The
aperture was made no larger than this to ensure that the psychophysical
percept remained robust: when a large number of grating cycles is
visible there is an increased chance of perceiving matches at
disparities other than that of the aperture (Hess and Wilcox,
1994; Prince and Eagle, 2000).
Typical stimulus configurations are shown in Figure
1, which shows two different disparities,
differing by one spatial period of the grating. Although the stimulus
within a putative receptive field is identical, one of the stimuli
appears in front of the fixation marker, and one appears behind. Note
that with this arrangement the disparity of the bars of the grating is
always consistent with the disparity of the aperture. Nonetheless, the
local disparity of the bars has several alternative interpretations
depending on how they are matched binocularly.
View larger version (127K):
[in this window]
[in a new window]
|
Figure 1.
Example stimuli for free fusion. The
rectangle shows diagrammatically the location of a putative
receptive field. In A, corresponding parts of the stimulus
overlie the receptive field. In B, the stimulus within the
receptive field is identical to A, but noncorresponding
parts of the stimulus are within the receptive field. Despite the fact
that one of these stimuli is seen in front of the fixation cross and
one is seen behind, the stimulus within the putative receptive field is
the same. For clarity of exposition, the disparity is applied by
translating only the left image in this diagram. During recording,
disparity was applied with a symmetrical displacement of both monocular
half images.
|
|
Before measuring responses to disparity, tuning curves were constructed
for orientation, spatial frequency, and temporal frequency. The optimal
values for each of these parameters were then used when constructing a
disparity tuning curve (except that we did not use temporal frequencies
>16 Hz, to keep temporal frequency substantially lower than the 72 Hz
monitor refresh rate). The disparities tested were determined by the
orientation and spatial frequency of the stimulus. First, the
horizontal spatial period was calculated (the repeat period of a
horizontal section through the stimulus). The disparity spacing was
then set to one-fifth of this angle, and a minimum of seven (median,
nine) stimuli were tested. The range of disparities included both the
preferred disparity and one that differed from the preferred disparity
by one horizontal period of the stimulus. Each stimulus was presented
at least twice (median, five times).
The majority of neurons (106 of 117) were also tested with dynamic RDS
presented against a midgray background. These were constructed with
equal numbers of black and white square dots with dimensions 0.08 × 0.08° at an overall density of 25% and the same contrast (99%)
as the gratings. Each stimulus consisted of a circular central region,
which varied in disparity, and an annular surround region of fixed
disparity. The central region was matched in size to the measured
minimum response field (for details, see Cumming and Parker,
1999).
Data analysis and curve fitting. The measure of neural
response used throughout was the mean firing rate over the 2 sec
stimulus presentation (spikes were counted from 50 msec after the first video frame until 50 msec after the last video frame). The firing rate
as a function of disparity was then fit with two curves. First, the
data were fit with a sinusoid. If the firing rate were determined only
by the local matches within the RF, the frequency of the fitted
sinusoid would be predicted by the properties of the grating stimulus
used (Ohzawa and Freeman, 1986a,Ohzawa
and Freeman, 1986b). The second fit was intended to allow
for the possibility that cells responded to both types of match but
responded more strongly to the global match than to the false match.
This curve was a sinusoid whose amplitude was modulated by a Gaussian envelope (an even-symmetric Gabor function; Figure
2). For both curves, a least squares fit
was produced by nonlinear regression (Numerical Algorithms Group,
Oxford, UK).
View larger version (24K):
[in this window]
[in a new window]
|
Figure 2.
Disparity selectivity of one neuron and the
corresponding Gabor fit. The Gabor fit is constrained to be
even-symmetric (the Gaussian is always centered at the peak). This fit
is then used to compare the magnitudes of responses to locally
identical stimuli (differing in disparity by one period of a horizontal
cross section through the stimulus). The stimulus here was a 4 cycles
per degree (cpd) grating oriented 70° from vertical, so the
horizontal period was 0.25/cos(70°) = 0.73°. The
peak-to-trough amplitude at the preferred disparity (A1) is
compared with the peak-to-trough amplitude for the response to a
disparity differing by one stimulus period (A2). This is
expressed in percent attenuation: 100 * (A1  A2)/A1, and in this example is 15%. Note that if the period of
the fitted Gabor is different from the stimulus period, the second peak
in the Gabor fit is not at the disparity one stimulus period
away from the peak. A2 is then smaller than the amplitude of
the second peak in the Gabor fit.
|
|
An important assumption of regression analysis is that the residuals
are constant. For the majority of cortical neurons, in which
variability increases with mean firing rate (Dean, 1981; Tolhurst et al., 1981; Britten et al.,
1993; Geisler and Albrecht, 1997), a simple
least squares regression is inappropriate. Before using regression
analysis, a transformation should be applied to the firing rates to
render the residuals constant (Draper and Smith, 1998).
Geisler and Albrecht (1997) have argued that the variance of firing in V1 is adequately described as linearly
proportional to the mean, an observation we have confirmed for
disparity-selective neurons in awake monkey V1 (Parker et al.,
1998). Under these circumstances, the square root of the mean
firing rate ( ) is the variable whose variance
is constant (Armitage and Berry, 1994). Consequently all
regression analysis (including ANOVA) was performed on
. Note that the fitted curve was similarly
transformed, so that the fitted sinusoid is =  , where  is
disparity, and m is the mean of the responses to all disparities. Thus firing rate is modeled as a linear sinusoidal function of disparity, but the transformation has the effect of reducing the weight given to the higher firing rates, compared with no
transformation. (In practice, for this data set, using untransformed
rates gives similar fits.)
Psychophysical training. Both animals were trained to make
psychophysical judgments of depth. Initially, they were trained with
random dot stimuli (Prince et al., 2000), consisting of
a central region whose disparity was varied from trial to trial, and a
surrounding annulus with a disparity that remained fixed at zero. If
the animal successfully maintained fixation for the stimulus
presentation period, the stimulus and fixation marker were replaced by
two markers symmetrically above and below the former position of the
fixation point. The animal signified whether the stimulus had a crossed
or uncrossed disparity by moving fixation to the lower or upper marker,
respectively. Only correct responses were rewarded. Once the animals
performed this task reliably, they were tested with grating patches.
Here, the task required a report of whether the grating patch was in
front of or behind the fixation marker.
| |
RESULTS |
Psychophysical responses
First, we wished to confirm that the binocular matching of
features in stimuli such as those shown in Figure 1 was perceptually unambiguous, for the animals from whom neurons were recorded. Some care
is required in the choice of a stimulus configuration, particularly the
size of the aperture. If the aperture is large relative to the period
of the grating (i.e., many cycles of the grating are present), there is
an increased possibility of some ambiguity in the psychophysical
matching. In the extreme case of an infinitely large aperture, the
matching becomes totally ambiguous. Human psychophysical studies have
confirmed the importance of aperture size in controlling how features
are matched in stimuli such as those used here (Hess and Wilcox,
1994; Prince and Eagle, 2000). To ensure that
the matching was unambiguous, the aperture was made as small as
possible while still ensuring that the region of overlap still covered
the neuronal minimum response fields, even at the largest disparities used.
The psychophysical responses were measured with configurations
identical to those used for some of the unit recordings. The results
are shown in Figure 3, where it is clear
that both animals successfully discriminate two configurations in which
the central region is identical (see Fig. 1). These locally similar
features do not produce a perception of depth at the equivalent
disparity, so they are therefore "false" matches. With this
distinction made on psychophysical grounds, it is then possible to
consider whether disparity-selective neurons in the same animals
respond to such false matches.
View larger version (20K):
[in this window]
[in a new window]
|
Figure 3.
Psychophysical responses to gratings of the two
monkeys used in this study. For all near (positive) disparities the
animals consistently report seeing the grating patch in front of the
fixation marker. Similarly, far disparities are consistently reported
as behind. Error bars show SDs of the binomial distributions. Each
stimulus was presented 50 times.
|
|
Single neuron responses
In recordings from 628 neurons in two animals (303 in Monkey Hg
and 325 in Monkey Rb), we completed this experiment in 117 neurons (56 and 61 in Hg and Rb, respectively). One-way ANOVA showed a significant
(p < 0.05) effect of disparity on
in all these neurons. The receptive fields
had eccentricities between 1 and 5°, and the mean receptive field
diameter was 0.68°. Almost all of these neurons showed some
orientation selectivity, and quantitative data on orientation tuning
were analyzed for 83 of 117 neurons. The mean orientation bandwidth
(half-width at half-height) was 23°, and there was a slight bias
toward near-vertical orientations (47 of 83 neurons had preferred
orientations within ±45° of vertical). At least one reason for this
bias results from the stimuli used: if the preferred orientation had
been near-horizontal, large disparities would have been required. This
would have required the use of large stimuli, which has two hazards.
First, large stimuli might overlap the fixation point, consequently
disrupting the animals' control of vergence. Second, large stimuli
would have many cycles of the grating within the aperture so that the perceptual response might become ambiguous. Of the 117 neurons, 37 were
classified as simple, and 80 were classified as complex, on the basis
of the modulation in their firing rate in response to the grating
stimuli (Skottun et al., 1991; as modified by
Cumming et al., 1999).
The effect of disparity on firing rate is shown for one neuron from
each animal in Figure 4. This shows the
disparity tuning measured with both sinusoidal gratings and RDS. There
are clearly two peaks in the tuning curves for sinusoidal stimuli, and
only one peak in response to RDS. Thus one of the peaks represents activation by a false match. The responses were quantified by fitting a
sinusoidal function to the firing rates. The period of the best-fitting
sinusoid should equal the period of a horizontal cross section through
the stimulus, i.e.:
|
|
where  is the angle of the stimulus away from vertical.
View larger version (16K):
[in this window]
[in a new window]
|
Figure 4.
Responses of complex cells from each animal to
both RDS and grating stimuli. The responses to random dot stimuli show
one peak, whereas the responses to sinusoidal stimuli show two peaks.
The responses to RDS are fitted with a Gabor function; the responses to
gratings are fitted with a sinusoid. The spatial frequency of the
sinusoid was free to vary, and the best fitting periods (1.21 and
0.263°) were very close to the respective horizontal periods of the
stimuli (rb590: 4 cpd grating, oriented 78° away from vertical,
horizontal period = 1.18°; Hg246: 4 cpd vertical grating,
horizontal period = 0.25°). Error bars show SEM.
|
|
In 12 cells we also measured the response to stimuli of two different
spatial frequencies (usually with a ratio 2:1), as illustrated in
Figure 5. The period of the disparity
tuning function changed in the same way as the period of the stimulus.
We compared the ratio of the fitted periods with the ratio of the
stimulus periods. The expected value of this is unity, and the
experimentally observed value was 0.95 (±0.11 SD). Thus the period of
the fitted sinusoid reflects the horizontal period of the stimulus
and is not determined by the receptive field structure. This is exactly
what is expected if the neurons respond only to the disparity of the
portion of the stimulus that falls within the classical receptive
field.
View larger version (27K):
[in this window]
[in a new window]
|
Figure 5.
Responses of one complex cell to circular
patches of sinusoidal grating at different disparities. The stimulus
orientation was vertical, and data were collected for two spatial
frequencies. Both disparity tuning curves show two peaks, and the
separation of the peaks is approximately equal to the spatial period of
the stimulus. The continuous lines show sinusoidal functions
fitted to the data. The spatial frequency of the fitted sinusoid was
free to vary, so the best fitting frequency gives a measure of how
closely the separation of the peaks matches the predicted
value.
|
|
The results of fitting sinusoids to the data for all 117 cells are
shown in Figure 6. Two points are
contributed to this plot by each of the 12 cells for which the
experiment was repeated at two spatial frequencies. There is clearly a
very strong correlation between the period of the best-fitting sinusoid
and the horizontal period of the stimulus, as expected if the neurons
are activated by false matches in these stimuli.
View larger version (11K):
[in this window]
[in a new window]
|
Figure 6.
Disparity modulation is sinusoidal with the
spatial period predicted by local matching. The period of the best
fitting sinusoid is plotted against the horizontal spatial period of
the stimulus. Results of 129 experiments are plotted from 117 neurons.
Responses were measured at two spatial frequencies in 12 neurons. Most
neurons show a close agreement between the expected and observed
spatial period (solid line). Small deviations above this
line could be the result of vergence eye movements (see
Results). The open symbol shows the most extreme
deviation (hg186), for which the tuning curve is shown in Figure
8.
|
|
Note that small deviations from the predicted periodicity might occur
as a result of vergence eye movements. If the animals tend to adjust
vergence in response to the stimulus disparities, then the retinal
disparity will be smaller than the nominal stimulus disparity. In this
case, the tuning would be expected to modulate with a longer period
than that specified by the stimulus. For each experiment we performed a
linear regression of vergence angle on stimulus disparity. This
revealed a small but highly significant tendency for the animals to
converge with the stimulus disparity: the mean of the regression slopes
was 0.027 (degrees of vergence per degree of disparity), with an SEM of
0.006 (n = 129; t test p < 0.0001).
Some of the scatter of points around the identity line in Figure 6,
particularly points that deviate slightly upward toward a longer fitted
period, might therefore reflect the effect of vergence eye movements. A
few neurons show large deviations from the predicted modulation as a
function of disparity: for 6 of 129 cases, the fitted period is more
than twice the predicted period. This size of deviation is much too
large to be explained by random error or vergence eye movements, and
other explanations must be sought.
The data in Figure 6 demonstrate that the overwhelming majority of
neurons show periodic modulations in their disparity tuning, like those
shown in Figures 2, 4, and 5. The spatial period of this modulation is
close to that predicted from the orientation and spatial frequency of
the stimulus. These tuning curves show multiple peaks, and the
locations of the extra peaks correspond to disparities that place false
matches within the receptive field. Although the locations of the extra
peaks are well explained by this argument, this analysis does not
address the question of whether the magnitude of the
responses to false matches is the same as the response to globally
correct matches. To examine this, even-symmetric Gabor functions were
fit to the data, as shown in Figure 2.
The spatial frequency of the fitted Gabor was free to vary, so that all
of the tuning curves we saw could be well fit by this function. (On
average, the Gabor accounted for 94% of the variance in the data
sets.) The magnitude of the response at the center of the Gabor was
then compared with the response to a disparity that differed by exactly
one period of the stimulus (i.e., a stimulus that is identical within
the minimum response field). The extent to which this second response
was attenuated relative to the peak provides a measure of how far the
tuning curves deviate from the simplest prediction. The example in
Figure 2 shows an attenuation of 15%, slightly larger than the median
of the population (14%). Figure 7 shows
the distribution of this attenuation measure across the population of
neurons recorded here. The great majority of neurons follow the simple
pattern illustrated in Figures 2, 4, and 5: there is a periodic
modulation at the predicted spatial frequency, and the responses to
false matches are similar in magnitude to the responses to
psychophysically perceived matches (81 of 129 experiments showed <20%
attenuation).
View larger version (14K):
[in this window]
[in a new window]
|
Figure 7.
Frequency distribution of response
attenuation. This compares the response at the peak of the Gabor with
the response to a stimulus differing in disparity by exactly one period
of the stimulus. This is expressed as a percentage attenuation relative
to the peak response. There is a large clustering of neurons in the
region of zero attenuation. Note that attenuation is always calculated
relative to the peak of the fitted Gabor, even though this peak could
have occurred in response to a false match. Indeed
comparison with the responses to RDS stimuli suggested that for many
cells the largest peak was in response to a false match. Solid
symbols show the data for strongly disparity-selective neurons
(maximum response >20 spikes/sec and maximum response > twice
minimum response). Open symbols show the remaining
data.
|
|
Note that if the fitted period of modulation does not correspond to the
horizontal period of the stimulus, then this analysis inevitably
assigns the measured attenuation as large. This is because the
attenuation is calculated for a disparity one stimulus period away from the Gabor center. In the specific case, when the
fitted period is more than twice the stimulus period, there is no
minimum in the region between the peak and the first false match, so
the attenuation is 100%. All of the neurons for which the ratio
(fitted period)/(predicted period) was >1.2 had attenuation values
>35%. Hence, the attenuation measure captures both deviations from
the expected period of the fit and variations in the amplitude of the
peaks. The attenuation is always calculated relative to the largest
peak (the center of the Gabor), wherever that happens to be. In some
cases this peak appears to occur in response to false
matches (see Figure 8), so that by itself a substantial attenuation
value does not necessarily indicate a preference for global matches
over false matches.
The data in Figure 7 show that the great majority of neurons show
periodic modulation in their disparity tuning, and that both the
location and magnitude of the multiple peaks are as predicted on the
basis that these neurons respond only to the disparity of local
features within the receptive field. The distribution does show a small
number of neurons that show substantial deviations from this pattern
(large attenuation values), so it is possible that this represents a
subgroup that is selective for global disparity matches.
Close inspection of the tuning curves suggests an alternative
explanation. These large values of attenuation are all consistent with
a possible failure to cover the receptive field fully with the
binocular stimulus. When the responses to RDS stimuli are also
examined, this explanation frequently turns out to be the more
plausible. Figure 8 shows the data for
gratings and RDS from three neurons with large attenuation values. All
three neurons show a preferred disparity for the windowed grating
stimulus that is different from the preferred disparity for the random
dot stimuli. Thus, none of these data is consistent with a specific
selectivity for globally correct binocular disparities. In all
three cases, the pattern of results can actually be better explained by
supposing that the area over which binocular interaction occurred was
larger than our estimate of the classical receptive field. Using these stimuli, changes in disparity necessarily cause changes in the location
of monocular stimuli: in the extreme, if the disparity was made very
large, the stimulus might be moved off the monocular receptive field
altogether. Such monocular artifacts are particularly hazardous here,
because we tried to keep the stimuli as small as possible to ensure
that the psychophysical sensation of depth was unambiguous. Because our
estimate of RF size was the MRF (determined by hand plotting with a
bar), it is quite possible that the area over which binocular
interaction occurs was underestimated.
View larger version (16K):
[in this window]
[in a new window]
|
Figure 8.
Responses of three neurons illustrating extreme
deviations from simple sinusoidal tuning functions. In all three cases,
the attenuation is much larger than the median of the population
(14%), so these represent extreme examples. Nonetheless, when the
responses to RDS are considered, it is hard to reconcile any of these
cases with a specific selectivity for global matches. In each case, the
solid line shows the Gabor fit to the disparity tuning
measured with gratings (solid symbols), and the dashed
line shows a Gabor function fit to the disparity tuning measured
with RDS (open symbols). A, Most extreme
deviation observed in the entire data set (100% attenuation). The
repeat period of the grating tuning curve is much larger than the
stimulus period (ratio 7.8, shown with an open symbol in
Fig. 6). The pattern of disparity selectivity for gratings is quite
different from that observed in response to RDS. Note that the response
to large positive disparities is similar to that for right eye
monocular stimulation (dashed line), as if the grating patch
no longer covered the RF in the left eye. B, Example in
which the tuning function shows the expected periodicity but shows
changes in the depth of modulation (27% attenuation). Note that the
greatest firing rate is in response to a false match
(assuming that the response to RDS indicates the global match normally
signaled by this neuron). C, Example in which responses on
either side of the central peak are attenuated (43%), yet once again
the value of the preferred disparity is different from that shown in
response to RDS. The pattern seen in response to the grating could
occur if the area of binocular overlap in the stimulus no longer covers
the neuron's binocular summation area. In all three cases shown here,
the comparison of responses to gratings and RDS does not support the
view that these neurons fire selectively for global stereoscopic
matches.
|
|
Figure 7 shows no evidence of two distinct groups of neurons. Neurons
that respond differentially to identical stimuli within the receptive
field frequently a show different disparity preference when tested with
random dot patterns (Fig. 8). This group also tends to be less strongly
modulated by disparity than the neurons that show more similar
responses to false matches. (The solid symbols show neurons
whose maximum response was >20 spikes/sec and more than double the
minimum response.) Taken together, these observations suggest that the
data in Figure 7 are best explained by supposing that, for these few
neurons, our hand plotting of minimum response fields underestimated
the area over which these neurons integrated binocular information. The
available evidence strongly indicates that V1 neurons respond equally
well to either false matches or globally correct matches provided that
they adequately cover the binocular receptive field.
Responses to compound gratings
One feature of the grating stimuli deserves further consideration.
Within the bounds of the MRF, the false matches and the global matches
are identical. From one perspective it may seem unsurprising that
identical stimuli within the MRF produce similar responses. An
alternative view would be that, because stimuli outside the MRF can
influence the activity of many V1 neurons (Maffei and
Fiorentini, 1976; Gilbert and Wiesel, 1990;
Sillito et al., 1995; Levitt and Lund,
1997), such influences might be critical in binocular vision.
The present results demonstrate that such interactions are not
exploited in solving the stereo correspondence problem. Whatever
processes underlie our ability to perceive the stimuli in Figure 1 at
different depths, they appear not to be reflected in the firing rate of
disparity-selective neurons in V1.
This still leaves open the possibility that there are other
circumstances in which V1 neurons might respond in a way that more
closely resembles the psychophysical correspondence process. To examine
this possibility, we investigated a subset of neurons with compound
gratings composed of two spatial frequencies, as shown in Figure
9. Now, when the whole pattern is
displayed with a disparity equal to the spatial period of one
sinusoidal component, the other sinusoidal component is at a different
phase in the two eyes. Potentially, the information from the two
spatial frequencies could be combined to assist in distinguishing
global from false matches.
View larger version (70K):
[in this window]
[in a new window]
|
Figure 9.
Example binocular compound grating. This is
the sum of two gratings, with spatial frequencies in the ratio 3:4.
These were chosen to ensure that both component gratings produced
disparity-selective responses in the neuron. The stimulus is shown here
with a disparity equal to the spatial period of one of the component
gratings. Thus, within the RF, one of the grating components is exactly
aligned, but the other is not.
|
|
The most robust way to produce this effect psychophysically would be to
add a component at a much lower spatial frequency than the optimum.
However, if such a frequency was outside the spatial frequency pass
band of the neuron, it is possible that it would be just as invisible
to the receptive field as the aperture in the previous experiments. For
all the cases examined here, we took the precaution of verifying that
both component spatial frequencies were independently capable of
exciting the neuron. Consequently, we chose two spatial frequencies
close to the optimal, with frequencies in the ratio 3:4, as
illustrated in Figure 9. Human psychophysical experiments suggest that
the information available in this kind of stimulus is sufficient to
allow unambiguous stereo matching (Hess and Wilcox,
1994).
We investigated the psychophysical performance of human observers, as
well as the two monkeys, using a modified version of the stimulus shown
in Figure 9. The modification was required because the data in Figure 3
demonstrate that the aperture effectively constrains matching, even for
a single sinusoid. Clearly then, the psychophysical matches will be
equally unambiguous with the stimuli illustrated in Figure 9. Because
the intention of this experiment was to test the neurons with
information within the receptive field that rendered the
matches unambiguous, we tested observers with a stimulus that limited
them to the same type of information. A compound grating was multiplied
by a broad Gaussian envelope (SD = 3°), and disparities were
applied only to the grating, not the envelope. In this stimulus the
only information that distinguishes false from globally correct matches
is the phase relationship between the two frequency components. For
each stimulus, the animal made a forced choice front-back judgment.
When the stimulus within the envelope was a single sinusoid, the
animals' responses showed a periodicity at the spatial frequency of
the stimulus. Figure 10 shows the
responses to compound gratings. The animals are able to identify
correctly the disparity of stimuli when either sinusoidal component
alone would be unreliable, indicating that the information available to
single neurons in Figure 11 is
sufficient to disambiguate some stereo matches psychophysically. We
have confirmed this result in three human observers.
View larger version (17K):
[in this window]
[in a new window]
|
Figure 10.
Psychophysical responses to compound gratings,
for the two animals from which neurons were recorded. The stimulus was
a vertical compound grating multiplied by a Gaussian with an SD of
3°. The two component gratings had spatial frequencies of 3 and 4 cpd
for monkey Rb and 6 and 8 cpd for monkey Hg. The disparity is expressed
in multiples of the period of the grating of lower spatial frequency.
Both animals correctly discriminate stimuli at ±0.5 cycles of
disparity, indicating that they combine information across the two
spatial frequencies to solve the correspondence problem.
|
|
View larger version (14K):
[in this window]
[in a new window]
|
Figure 11.
Effects of stimulating two disparity selective
neurons with compound gratings. Left graph, Responses
of one neuron to the two component gratings presented individually. The
fitted curves are sinusoids in which the spatial period is fixed at the
horizontal period of the stimulus. Center graph, Responses
of the same cell to a stimulus that was the sum of the two stimuli in
the left graph. The fitted curve shows a weighted linear sum
of the two sinusoids fitted to the data in the left graph
and accounts for 85% of the variance induced by disparity. Right
graph, Responses to the compound grating of the cell for which the
fitted curve was the worst in the data set. Despite this,
the data are qualitatively similar to those in the center
graph. There is a second peak in the tuning curve, which is
smaller and broader than the peak near 0 disparity.
|
|
For recording experiments, stimuli like those in Figure 9 were used, in
which both the aperture (outside the MRF) and the combination of the
two gratings (inside the MRF) make the matches unambiguous. Disparity
tuning curves were constructed for each component grating individually
and for the compound gratings; all three stimulus types were
interleaved. The compound gratings provide adequate information within
the receptive field to distinguish false from global matches, so there
should only be one peak in the disparity tuning curves for these
stimuli, if these neurons are making use of this information. Figure 11
illustrates the results for two cells, where it is clear that there are
two peaks in the tuning curves, but the peaks are of different
magnitudes. One would expect this difference in magnitude even if the
neurons were simply signaling local matches: the large peak occurs
where both grating components are at the optimal disparity, whereas at
other disparities only one of the two components is at the optimal
disparity. We attempted to describe the responses to the compound
gratings by the weighted sum of the responses to the component
gratings:
|
|
where is the stimulus disparity, A1,
 1, A2, and
2 are the amplitude and phase of the sinusoids fitted to
the component gratings, 2  1 and 22
are the horizontal periods of the component gratings, k is a
weighting factor, and m is the mean rate about which the
function modulates. Despite the fact that only two additional parameters (k and m) are introduced to fit the
responses to compound gratings, the resulting fits describe the data
well (see Figure 11). This experiment was performed on 13 cells, and on
average the fit accounted for 80% of the variance in
. Even in cases in which the fit was
relatively poor, the data showed the same qualitative pattern: the
second peak was smaller and broader than the peak nearer 0. This can be
seen in Figure 11, right graph, which shows the worst fit in
the data set (accounting for 64% of the variance in
). Even in this case there are clearly two
peaks in the tuning curve, so qualitatively it appears as if the neuron
responds to the false matches. The poor fit reflects only a
quantitative failure to match the data exactly in this example. The
data do not indicate any genuine ability to distinguish false matches
from global ones.
The responses of single V1 neurons to disparity in compound gratings
are well predicted by a linear combination of the responses to
disparity in the component gratings. The psychophysical ability to
combine information across components to disambiguate stereo matches
reflects a nonlinear combination of the component gratings. This
nonlinear combination is not reflected in the activity of single V1 neurons.
| |
DISCUSSION |
Stereo matching with extended sinusoidal gratings is inherently
ambiguous: applying a disparity equal to the period of the grating
produces an identical stimulus. We used an aperture to render the
matching unambiguous in small circular patches of sinusoidal gratings.
This was effective psychophysically for the animals used here and for
human observers. We find that the response of the great majority of
disparity-selective neurons in area V1 depends only on the local
disparity of the stimulus within the RF, regardless of the position of
the aperture. Thus these neurons are unable to distinguish false
matches from global matches in these stimuli.
Several earlier studies have also demonstrated that gratings elicit
periodic disparity responses (Ohzawa and Freeman,
1986a,Ohzawa and Freeman, 1986b;
Wagner and Frost, 1994; Smith et al.,
1997). However, in most cases this simply reflects the periodic
nature of the stimulus: stimuli with disparities differing by one
spatial period were identical stimuli. It is only the use of an
aperture that renders these disparities discriminable and hence permits the distinction between psychophysical and neuronal responses. Wagner and Frost (1994) used an aperture in their study
of neurons in the Wulst of the anesthetized barn owl. Usually, the
aperture was fixed in size (10°), substantially larger than typical
receptive fields. The stimuli therefore typically contained many cycles of grating, so it is not known whether they would have supported unambiguous psychophysical matching (the animals were not tested psychophysically).
In a small number of neurons, the responses did appear to distinguish
between two configurations that were identical within the bounds of the
receptive field. However, this interpretation depends critically on our
assessment of the receptive field size. If we had underestimated the
size of the receptive field, then it is quite possible that neural
responses to two stimuli were different, because the stimulus within
the real receptive field was different. Because our measure of
receptive field extent depended on hand plotting with a bar, it is
quite possible that MRF size was underestimated in this small fraction
of neurons. Furthermore, recent studies have shown that RF size depends
on the stimulus that is used to assess it (Sceniak et al.,
1999). Thus there may be a discrepancy between the area over
which binocular interaction occurs and the MRF measured with a bar,
even if the latter is determined quantitatively.
Another discrepancy may arise from interactions along the length of the
classical receptive field, parallel to the preferred orientation.
Consider a neuron that shows end stopping (in both eyes). For the
windowed grating stimuli, it is inevitable that globally correct
matches correspond to elements of the same length in both eyes, whereas
the false matches correspond to elements of different lengths. If
neurons responded preferentially to stimuli that elicited similar
degrees of end stopping in the two eyes, they could discriminate the
false matches in this stimulus from the global matches. This is of
especial concern with special complex cells (Palmer and
Rosenquist, 1974; Gilbert, 1976), which respond preferentially to stimuli of a length shorter than the total spatial elongation of the receptive field. A more extensive comparison of
receptive fields and summation areas for monocular and binocular stimuli would be necessary to substantiate this interpretation. The
current data do not differentiate between this explanation and a simple
failure to fill the monocular receptive fields.
In any case, the great majority of neurons show little attenuation, so
these alternative mechanisms need not be invoked. These data indicate
that the perceptual process that differentiates the stimulus
configurations shown in Figure 1 is not reflected in the activity of
disparity-selective neurons in primate V1. The parts of the stimulus
that determine this psychophysical response lie outside the classical
receptive field, so this result shows that the modulations produced by
the nonclassical surround are not exploited to constrain stereo matching.
The present results complement our earlier study using anticorrelated
RDS (Cumming and Parker, 1997), in which the false
matches within the RF were quite different from the global matches.
That study demonstrated that V1 neurons show disparity selectivity for
these false matches, but the amplitude of the modulation was generally
lower than for correlated RDS. Although this deviates from the
predictions of a simple energy model (Ohzawa et al., 1990; Fleet et al., 1996; Cumming and
Parker, 1997), it seems unlikely to reflect a mechanism that
can identify false matches in correlated stereograms. A possible
mechanism of this type is a "top-down" influence that reduces the
response modulation because the animals do not perceive depth. The
present results with grating patches argue against the presence of such
a mechanism, because the majority of neurons respond equally well to
the false matches.
The results reported here, combined with the earlier study of
anticorrelated RDS, argue strongly that at least some of the psychophysical processes that solve the stereo correspondence problem
are completed outside V1. This is important not only for depth
perception but also for maintaining binocular single vision. Thus V1
neurons seem to be at best a preliminary stage in the representation of
stereo disparity, analogous to their role in motion processing. For
example, few neurons in V1 show pattern-motion selectivity when tested
with plaid patterns, whereas a substantial fraction of neurons in
MT do show selectivity for pattern motion (Movshon et al.,
1985). It may be that for stereo, as for motion, responses in
extrastriate cortical areas are able to match psychophysical responses
more closely than responses in V1.
| |
FOOTNOTES |
Received Feb. 7, 2000; revised April 5, 2000; accepted April 6, 2000.
This work was supported by the Wellcome Trust. B.G.C. is a Royal
Society University research fellow. We thank Owen Thomas for
contribution to the psychophysical work and Simon Prince for critical
evaluation of this paper.
Correspondence should be addressed to Dr. Bruce G. Cumming, University
Laboratory of Physiology, Parks Road, Oxford, UK OX1 3PT. E-mail:
bruce.cumming{at}physiol.ox.ac.uk.
| |
REFERENCES |
-
Armitage P,
Berry G
(1994)
In: Statistical methods in medical research. Oxford: Blackwell.
-
Britten KH,
Shadlen MN,
Newsome WT,
Movshon JA
(1993)
Responses of neurons in macaque MT to stochastic motion signals.
Vis Neurosci
10:1157-1169[Web of Science][Medline].
-
Cogan A,
Lomakin A,
Rossi A
(1993)
Depth in anticorrelated stereograms.
Vision Res
33:1959-1975[Web of Science][Medline].
-
Cumming BG,
Parker AJ
(1997)
Responses of primary visual cortical neurons to binocular disparity without the perception of depth.
Nature
389:280-283[Medline].
-
Cumming BG,
Parker AJ
(1999)
Binocular neurons in V1 of awake monkeys are selective for absolute, not relative, disparity.
J Neurosci
19:5602-5618[Abstract/Free Full Text].
-
Cumming BG,
Shapiro SE,
Parker AJ
(1998)
Disparity detection in anticorrelated stereograms.
Perception
27:1367-1377[Web of Science][Medline].
-
Cumming BG,
Thomas OM,
Parker AJ,
Hawken MJ
(1999)
Classification of simple and complex cells in V1 of the awake monkey.
Soc Neurosci Abstr
25:1548.
-
Dean AF
(1981)
The variability of discharge of simple cells in the cat striate cortex.
Exp Brain Res
44:437-40[Web of Science][Medline].
-
Draper NR,
Smith H
(1998)
In: Applied regression analysis, Ed 3. New York: Wiley.
-
Fleet DJ,
Wagner H,
Heeger DJ
(1996)
Neural encoding of binocular disparity: energy models, positions shifts and phase shifts.
Vision Res
36:1839-1857[Web of Science][Medline].
-
Geisler WS,
Albrecht DG
(1997)
Visual cortex neurons in monkeys and cats: detection, discrimination, and identification.
Vis Neurosci
14:897-919[Web of Science][Medline].
-
Gilbert CD
(1976)
Laminar differences in receptive field properties of cells in cat primary visual cortex.
J Physiol (Lond)
268:391-421[Abstract/Free Full Text].
-
Gilbert CD,
Wiesel TN
(1990)
The influence of contextual stimuli on the orientation selectivity of cells in primary visual cortex of the cat.
Vision Res
30:1689-701[Web of Science][Medline].
-
Hess RF,
Wilcox LM
(1994)
Linear and non-linear contributions to stereopsis.
Vision Res
34:2431-2438[Web of Science][Medline].
-
Julesz B
(1971)
In: Foundations of cyclopean perception. Chicago: University of Chicago.
-
Levitt JB,
Lund JS
(1997)
Contrast dependence of contextual effects in primate visual cortex.
Nature
387:73-76[Medline].
-
Maffei L,
Fiorentini A
(1976)
The unresponsive regions of visual cortical receptive fields.
Vision Res
16:1131-1139[Web of Science][Medline].
-
Marr D,
Poggio T
(1979)
A computational theory of human stereo vision.
Proc R Soc Lond B Biol Sci
204:301-328[Medline].
-
McKee SP,
Mitchison GJ
(1988)
The role of retinal correspondence in stereoscopic matching.
Vision Res
28:1001-1012[Medline].
-
Merrill EG,
Ainsworth A
(1972)
Glass-coated platinum-plated tungsten electrodes.
Med Biol Eng
10:662-672[Web of Science][Medline].
-
Mitchison GJ
(1988)
Planarity and segmentation in stereoscopic matching.
Perception
17:753-782[Medline].
-
Movshon JA,
Adelson EH,
Gizzi MS,
Newsome WT
(1985)
The analysis of moving visual patterns.
Exp Brain Res [Suppl]
11:117-151.
-
Ohzawa I
(1998)
Mechanisms of stereoscopic vision: the disparity energy model.
Curr Opin Biol
8:509-515.
-
Ohzawa I,
Freeman RD
(1986a)
The binocular organization of simple cells in the cat's visual cortex.
J Neurophysiol
56:221-242[Abstract/Free Full Text].
-
Ohzawa I,
Freeman RD
(1986b)
The binocular organization of complex cells in the cat's visual cortex.
J Neurophysiol
56:243-259[Abstract/Free Full Text].
-
Ohzawa I,
DeAngelis GC,
Freeman RD
(1990)
Stereoscopic depth discrimination in the visual cortex: neurons ideally suited as disparity detectors.
Science
249:1037-1041[Abstract/Free Full Text].
-
Palmer LA,
Rosenquist AC
(1974)
Visual receptive fields of single striate cortical units projecting to the superior colliculus in the cat.
Brain Res
67:27-42[Web of Science][Medline].
-
Parker AJ,
Pointon AD,
Cumming BG
(1998)
The variability of neuronal firing in cortical area V1 of awake, behaving monkeys.
Perception [Suppl]
27:9.
-
Poggio GF
(1984)
Processing of stereoscopic information in primate visual cortex.
In: Dynamic aspects of neocortical function (Edelman G,
Cowan WM,
Gall WE,
eds), pp 613-635. New York: Wiley.
-
Poggio GF,
Poggio T
(1984)
The analysis of stereopsis.
Annu Rev Neurosci
7:379-412[Web of Science][Medline].
-
Poggio GF,
Motter BC,
Squatrito S,
Trotter Y
(1985)
Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random dot stereograms.
Vision Res
25:397-406[Web of Science][Medline].
-
Prince SJD,
Eagle RA
(2000)
Stereo correspondence in one-dimensional Gabor stimuli.
Vision Res
40:913-924[Medline].
-
Prince SJD,
Pointon AD,
Cumming BG,
Parker AJ
(2000)
The precision of single neuron responses in V1 during stereoscopic depth judgments.
J Neurosci
20:3387-3400[Abstract/Free Full Text].
-
Qian N
(1994)
Computing stereo disparity and motion with known binocular properties.
Neural Comput
6:390-404.
-
Sceniak MP,
Ringach DL,
Hawken MJ,
Shapley R
(1999)
Contrast's effect on spatial summation by macaque V1 neurons.
Nat Neurosci
2:733-739[Web of Science][Medline].
-
Sillito AM,
Grieve KL,
Jones HE,
Cudeiro J,
Davies J
(1995)
Visual cortical mechanisms detecting focal orientation discontinuities.
Nature
378:492-496[Medline].
-
Skottun B,
DeValois R,
Grosof D,
Movshon J,
Albrecht D,
Bonds A
(1991)
Classifying simple and complex cells on the basis of response modulation.
Vision Res
31:1079-1086[Web of Science][Medline].
-
Smith EL,
Chino YM,
Ni J,
Ridder WH,
Crawford M
(1997)
Binocular spatial phase tuning characteristics of neurons in the macaque striate cortex.
J Neurophysiol
78:351-365[Abstract/Free Full Text].
-
Tolhurst DJ,
Movshon JA,
Thompson ID
(1981)
The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast.
Exp Brain Res
41:414-419[Web of Science][Medline].
-
Wagner H,
Frost B
(1994)
Binocular responses of neurons in the barn owl's visual Wulst.
J Comp Physiol [A]
174:661-670.
Copyright © 2000 Society for Neuroscience 0270-6474/00/20124758-10$05.00/0
This article has been cited by other articles:
|
|
|
|
 
A. W. Roe, A. J. Parker, R. T. Born, and G. C. DeAngelis
Disparity Channels in Early Vision
J. Neurosci.,
October 31, 2007;
27(44):
11820 - 11831.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
C. Chandrasekaran, V. Canon, J. C. Dahmen, Z. Kourtzi, and A. E. Welchman
Neural Correlates of Disparity-Defined Shape Discrimination in the Human Brain
J Neurophysiol,
February 1, 2007;
97(2):
1553 - 1565.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
P. D. L. Howe and M. S. Livingstone
V1 Partially Solves the Stereo Aperture Problem
Cereb Cortex,
September 1, 2006;
16(9):
1332 - 1337.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Tanaka and I. Ohzawa
Neural basis for stereopsis from second-order contrast cues.
J. Neurosci.,
April 19, 2006;
26(16):
4370 - 4382.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Nienborg, H. Bridge, A. J. Parker, and B. G. Cumming
Neuronal Computation of Disparity in V1 Limits Temporal Resolution for Detecting Disparity Modulation
J. Neurosci.,
November 2, 2005;
25(44):
10207 - 10219.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
K. Krug, B. G. Cumming, and A. J. Parker
Comparing Perceptual Signals of Single V5/MT Neurons in Two Binocular Depth Tasks
J Neurophysiol,
September 1, 2004;
92(3):
1586 - 1596.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
P. Neri, H. Bridge, and D. J. Heeger
Stereoscopic Processing of Absolute and Relative Disparity in Human Visual Cortex
J Neurophysiol,
September 1, 2004;
92(3):
1880 - 1891.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. D. Menz and R. D. Freeman
Functional Connectivity of Disparity-Tuned Neurons in the Visual Cortex
J Neurophysiol,
April 1, 2004;
91(4):
1794 - 1807.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Nienborg, H. Bridge, A. J. Parker, and B. G. Cumming
Receptive Field Size in V1 Neurons Limits Acuity for Perceiving Disparity Modulation
J. Neurosci.,
March 3, 2004;
24(9):
2065 - 2076.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
B. Zhang, K. Matsuura, T. Mori, J. M. Wensveen, R. S. Harwerth, E. L. Smith III, and Y. Chino
Binocular Deficits Associated With Early Alternating Monocular Defocus. II. Neurophysiological Observations
J Neurophysiol,
November 1, 2003;
90(5):
3012 - 3023.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
J. C. A. Read and B. G. Cumming
Testing Quantitative Models of Binocular Disparity Selectivity in Primary Visual Cortex
J Neurophysiol,
November 1, 2003;
90(5):
2795 - 2817.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
Z. Kourtzi, M. Erb, W. Grodd, and H. H. Bulthoff
Representation of the Perceived 3-D Object Shape in the Human Lateral Occipital Complex
Cereb Cortex,
September 1, 2003;
13(9):
911 - 920.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S. Grossberg
How does the cerebral cortex work? development, learning, attention, and 3-D vision by laminar circuits of visual cortex.
Behav Cogn Neurosci Rev,
March 1, 2003;
2(1):
47 - 76.
[Abstract]
[PDF]
|
|
|
|
|
|
|
G. C. DeAngelis and T. Uka
Coding of Horizontal Disparity and Velocity by MT Neurons in the Alert Macaque
J Neurophysiol,
February 1, 2003;
89(2):
1094 - 1111.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
A. Grunewald, D. C. Bradley, and R. A. Andersen
Neural Correlates of Structure-from-Motion Perception in Macaque V1 and MT
J. Neurosci.,
July 15, 2002;
22(14):
6195 - 6207.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
S.J.D. Prince, A. D. Pointon, B. G. Cumming, and A. J. Parker
Quantitative Analysis of the Responses of V1 Neurons to Horizontal Disparity in Dynamic Random-Dot Stereograms
J Neurophysiol,
January 1, 2002;
87(1):
191 - 208.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
B. T. Backus, D. J. Fleet, A. J. Parker, and D. J. Heeger
Human Cortical Activity Correlates With Stereoscopic Depth Perception
J Neurophysiol,
October 1, 2001;
86(4):
2054 - 2068.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Bridge and B. G. Cumming
Responses of Macaque V1 Neurons to Binocular Orientation Differences
J. Neurosci.,
September 15, 2001;
21(18):
7293 - 7302.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
A. Nieder and H. Wagner
Hierarchical Processing of Horizontal Disparity Information in the Visual Forebrain of Behaving Owls
J. Neurosci.,
June 15, 2001;
21(12):
4514 - 4522.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Tanaka, T. Uka, K. Yoshiyama, M. Kato, and I. Fujita
Processing of Shape Defined by Disparity in Monkey Inferior Temporal Cortex
J Neurophysiol,
February 1, 2001;
85(2):
735 - 744.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
M. Endo, J. H. Kaas, N. Jain, E. L. Smith III, and Y. Chino
Binocular Cross-Orientation Suppression in the Primary Visual Cortex (V1) of Infant Rhesus Monkeys
Invest. Ophthalmol. Vis. Sci.,
November 1, 2000;
41(12):
4022 - 4031.
[Abstract]
[Full Text]
|
|
|
|
|
|
|
J. S. Bakin, K. Nakayama, and C. D. Gilbert
Visual Responses in Monkey Areas V1 and V2 to Three-Dimensional Surface Configurations
J. Neurosci.,
November 1, 2000;
20(21):
8188 - 8198.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
TOP
ABSTRACT
INTRODUCTION
