Vision Res. Vol. 32, No. 9, pp. 1685-1694, 1992
Printed in Great Britain. All rights reserved
0042-6989/92 $5.00 + 0.00
Copyright 0 1992 Pergamon Press Ltd
Disparity Tuning in Mechanisms
Stereopsis
SCOTT B. STEVENSON,*1 LAWRENCE
CHRISTOPHER
W. TYLER?
K. CORMACK,*
CLIFTON
of Human
M. SCHOR,*
Received 30 December 1991; in revised form 19 February 1992
The change in sensitivity across some stimulus dimension which follows adaptation to a particular
stimulus can reveal a great deal about the tuning characteristics of underlying sensory/perceptual
mechanisms. In this study, a psychophysical adaptation paradigm was employed to characterize the
disparity tuning of perceptual mechanisms involved in stereopsis. The stimulus was a dynamic
random-dot stereogram (DRDS) portraying a surface which varied in interocular correlation (IOC)
and retinal disparity. Adaptation to a fully correlated DRDS surface produced an elevation in IOC
threshold over a relatively narrow range of disparities, with maximum effect at the disparity of the
adapting stimulus. The width of these disparity tuning functions varied from 5 arc min for adaptation
at the horopter to 20 arc min for adaptation at 20 arc min disparity. Frequently, IOC sensitivity was
enhanced for disparities on either side of the adapted disparity, suggesting that an opponent
center-surround organization operates at an early level of disparity processing. A model of underlying
channel structure consistent with these data is presented.
Stereopsis
Disparity tuning
Stereo matching
INTRODUCTION
A common finding in visual psychophysics is that
stimulus dimensions are processed through “channels”
or “filters”: perceptual mechanisms whose selectivity on
a visual dimension is narrow relative to the overall
sensitivity function for that dimension, but whose selectivity is often broad relative to the discrimination function for that dimension. The trichromacy of color vision
provides the classic example of channeling in human
vision. The photopic spectral sensitivity function reflects
a weighted sum of somewhat narrower cone sensitivity
functions, or wavelength channels. Comparison of the
activity in these cone types in turn produces very precise
wavelength discrimination.
Evidence for channels has been found for a number of
visual dimensions including grating spatial frequency
and orientation (Blakemore & Campbell, 1969), lateral
motion (Levinson & Sekuler, 1980), motion in depth
(Beverley & Regan, 1975) and static retinal disparity
(Felton, Richards & Smith, 1972). In a review of such
evidence, Regan (1982) offers a list of defining characteristics of a “visual channel” which restricts the term to
mechanisms that are tuned for one, and only one, visual
*School of Optometry,
University of California at Berkeley, Berkeley,
CA 94720, U.S.A.
tSmith-Kettlewell
Eye Research Institute, 2232 Webster Street, San
Francisco,
CA 94115, U.S.A.
$To whom all correspondence
should be addressed.
Channels
dimension. This paper concerns the tuning characteristics of mechanisms sensitive to static retinal disparity,
and while we refer to “channels,” it should be clear that
we have not determined whether the mechanisms are
tuned on other visual dimensions.
Early evidence for disparity tuned mechanisms in
human vision was reported by Blakemore and Julesz
(1971), who found that adaptation to a random-dot
stereogram produced shifts in the apparent depth of
subsequently viewed stereograms. They argued that
these shifts indicated that relatively narrow disparity
tuned mechanisms had been adapted. Further psychophysical evidence for disparity tuning was provided by
Felton et al. (1972) and by Blakemore and Hague (1972)
in experiments that revealed disparity-specific elevation
of contrast threshold after adaptation to a sine-wave
grating. Thresholds were typically elevated the most at
the disparity of adaptation, supporting the theory that
the visual system includes a number of disparity-tuned
mechanisms with peak sensitivities covering a range of
disparities around the horopter.
The “many narrow channels” view of disparity processing can be contrasted with Richards (1971) threepool hypothesis. He found, and Jones (1977) confirmed
that certain “stereoanomalous” individuals were unable
to make accurate disparity discriminations over a relatively broad range of disparities. Consistent with the
pattern of deficits found, Richards proposed the existence of three pools of disparity detectors: a fine pool for
1685
1686
SCOTT
B. STEVENSON
small disparities, and near and far pools for larger
crossed and uncrossed disparities, respectively.
Recent evidence from single cell recordings in monkey
(Poggio, Gonzalez & Krause, 1988) provides some support for both of the above models of disparity channeling. Some cortical neurons (“tuned”) exhibit narrow
disparity tuning, with peaks distributed across a range
of disparities. Others exhibit broad tuning functions
(“Near/Far”), being excited only by either crossed or
uncrossed disparity but not both. The difficulty in
linking human stereopsis with the single cell results
is that these disparity tuning profiles are found for
both horizontal and vertical disparity. While sensory
and motor fusion operates on both axes of disparity,
stereoscopic depth occurs only for horizontal disparity.
Therefore, it is difficult to know if all, or only a subset
of these cell types might represent the neural basis of
stereopsis.
Our purpose in these experiments was to examine
the disparity tuning of human perceptual mechanisms
processing interocular correlation (i.e. “solving the
stereo-matching problem”). We used an adaptation
paradigm to study the characteristics of visual mechanisms tuned to disparities in the range of 0.5 deg crossed
to 0.5 deg uncrossed disparity. In order to target dis-
e/ ul.
parity processing mechanisms specifically, we have used
dynamic random dot stereogram stimuli that varied in
interocular correlation (IOC): that is, the proportion of
left and right image dots which match each other at the
target disparity (Julesz & Tyler, 1976). We began by
measuring thresholds for detecting IOC over a range of
disparities, and then determined the elevation in these
thresholds which occurred after adaptation at a particular disparity. Finally, we generated a multichannel model
to simulate a set of underlying mechanisms consistent
with our results.
GENERAL
Stimuli
The dynamic random dot patterns were generated
by special-purpose electronics that allowed for precise
control of disparity and interocular correlation. Figure 1
is a schematic diagram of the stimulus generation system. Pseudo-random binary noise was generated by a 32
bit shift register with XOR feedback from bits 23 and
30. A second, uncorrelated noise source was produced
with an XOR combination of bits 25 and 26. (Extensive
computer simulation of the shift register system
confirmed that these noise streams are uncorrelated.)
f-
‘_
Delay
circuit
METHODS
Video
__)
Hor. Sync -*
FIGURE
1. Schematic
of display apparatus.
Subjects viewed display monitors
in a mirror
haploscope
setup with
accommodation
and convergence
set to a distance of 57.3 cm. A hardware
device based on shift registers generated
two
independent
streams of one-bit noise (Dot streams 1 and 2) and an AT computer controlled the routing of the noise sources
to the displays (represented
by a switch in the diagram). When the same noise source went to both displays, IGC was + 1.
When independent
noise was sent to each, IGC was 0. When the AT switched rapidly between the states, IGC was at an
intermediate
level determined by the duty cycle of the mixture. Disparity was controlled by routing one horizontal sync signal
(solid lines) through a programmable
digital delay device under control of the AT. Subjects made responses by pressing keys
on the AT keyboard.
Inset: Schematic of left and right views with 11 deg aperture, dark surround,
fixation dot and nonius
lines. Free fusion of these images yields a percept similar to that experienced
in our setup under conditions
of 100%
correlationPnonius
lines superimposed
on a random-dot
surface in depth.
DISPARITY
TUNING
IN HUMAN
Zero interocular correlation was produced by directing
one noise source to the left monitor and the other to the
right monitor and a positive 1.0 interocular correlation
was produced by directing the same noise source to both
monitors. Various inte~ediate
levels of interocular
correlation were produced by switching rapidly between
the two sources of noise and sending the result to the
left monitor’s image, while always directing the first
source to the right monitor.* For example, at the lowest
IOC level used (2%) one fiftieth of the dots were forced
to be perfectly correlated in the two views (same noise
source) while the remainder were randomly correlated or
anti-correlated (independent noise sources). Although
the percent correlation is small in this example, the
actual number of matching dots is quite high since each
frame of the display had over 18,000 dots visible to the
subject.
Disparity was produced and controlled by directing
the horizontal sync signal going to the left monitor
through a programmable digital delay device. Delay of
the sync resulted in a lateral shift of the noise pattern,
producing a disparity of the noise with respect to the
fixation dot. In our configuration, each unit of delay
(nominally 5 nsecs) resulted in a disparity change of
about 0.27 arc min. The full 255 steps of delay allowed
for a disparity range of about 70 arc min.
All stimuli in these experiments were viewed in a
mirror haploscope at a distance of 57 cm. Convergence
was adjusted for normal viewing at this distance. A chin
rest and forehead rest stabilized the subject’s head. The
display luminance (measured through the haploscope
mirrors) was 40cd/m2 and the contrast (measured on a
static pattern) was 80%. A pair of 9 deg circular apertures concealed the edges of the display, producing a
dark surround. The display dots were 5 arc min wide by
2 arc min tall. A black circle subtending 9 arc min served
as a fixation dot. Vertical nonius lines subtending 3 by
40 arc min provided a reference for maintaining constant
convergence. We estimate that convergence accuracy is
kept to within 1 arc min by this method.7
The appearance of the display varied with IOC from
a flat, opaque plane of dynamic dots at positive 1.OIOC
*Creating intermediate correlations with this method is analogous to
creating intermediate gray-levels with only black and white pixels
by half-toning or dithering. As long as the mixture is beyond the
spatial (and/or temporal) resolution of the eye, the viewer cannot
discriminate between halftone grays and true grays. In random dot
stereograms, individual dot pairs are always either + 1 or - 1
correlated, so intermediate levels of interocular correlation necessarily reflect a mixture of +l and -1 across space and time.
Our mixture rate was chosen so as to exceed both the spatial
and temporal resolution limits of correlation processing. Further
treatment of this topic is given in Cormack et al. (1991b).
$Sensitivity to nonius offset was measured by having subjects fixate the
random noise with all other fusible contours removed. Dichoptic
misalignment thresholds were at or below 30 arc set for our three
subjects in agreement with McKee and Levi (1987). Assuming
that subjects maintained nonius alignment to within twice the
misalignment detection threshold, vergence fixation errors in our
experiments never exceeded 1 arc min. In debriefing, subjects
reported that the nonius lines always appeared aligned, supporting
that assumption.
STEREOPSIS
1687
to a dynamic, space-filling swarm of dots at many depths
at 0.0 IOC. Intermediate levels appeared as a surface
embedded in the swarm, with the apparent density of
the surface being monotonically, if not linearly, related
to the level of IOC. Except for correlations right at
threshold, subjects agreed that when the surface was
visible its depth relative to the fixation mark was also
evident.
Procedure
Thresholds for detection of interocular correlation
were measured in three subjects using a method of
constant stimuli and a temporal two alternative forced
choice procedure. Subjects viewed a zero correlation
pattern at all times except during the signal presentation.
Each trial began with a tone to signal the first interval,
a 500 msec pause, a 200 msec signal (or blank), and
another 500 msec pause. The second interval followed
the same sequence. Subjects then indicated which of the
two intervals contained non-zero correlation by pressing
a key on the keyboard. The next trial followed immediately after each key press. When fixation wandered or a
blank or saccade interrupted a trial, it could be repeated,
with a new random interval order, by pressing the space
bar.
A set of 4--7 IOC levels presented in random order
composed a block of trials and 30 blocks composed a
single threshold dete~ination.
Threshold was defined as
the level producing 75% correct performance, as interpolated from a linear regression between stimulus level
and Z-transform of proportion correct.
Subjects
Subjects for these experiments were three of the
authors of this paper. All had corrected to optimal visual
resolution acuity and excellent stereoacuity for this
stimulus, as reported previously (Stevenson, Cormack
& Schor, 1989).
EXPERIMENT I: BASELINE CORRELATION
SENSITIVITY
We began our experiments by establishing baseline
performance in the correlation detection task, for purposes of comparison to adapted performance.
Five threshold measures for each of 17 disparity levels
(0, 2.5, 5, 10, 15, 20, 25, 30 and 35 arc min for both
crossed and uncrossed directions, and additionally 40
and 45 arc min uncrossed for SBS) composed a complete
baseline correlation sensitivity function. Prior to each
run, subjects were shown a fully correlated surface at the
disparity to be tested in order to minimize uncertainty
about where test stimuli would appear.
Results
The results from the baseline measures of correlation
sensitivity are plotted in Fig. 2. Disparity of the stimulus
relative to fixation is plotted on the horizontal axis
1688
SCOTT
B. STEVENSON
0.0
0 correlation. We measured the UDL for both crossed
and uncrossed disparity in all three subjects.
Methods
-0.5
-1.0
8
A
et trl
1*-
I
-1.d
-60
I
LKC
8
-60
f
-40
-20
Test
0
Disparity
r
20
r
40
(arc
min)
8
60
1
60
FIGURE 2. Baseline correlation
thresholds for three subjects. The log
of interocular
correlation
at threshold
is plotted against horizontal
disparity of the test surface relative to fixation. Negative values of
disparity indicate near (crossed) disparity. A value of 0.0 on the vertical
axis represents
a correlation
of 1.0, the maximum
possible. The
intersection
of each subject’s curve with the line at 0.0 indicates the
upper disparity limits for correlation detection in our task. Correlation
thresholds
were measured
for each subject out to +35 arc min
disparity,
with each point representing
the mean of 5 runs. Upper
disparity limits were measured in a separate experiment.
The general
trend can be characterized
as being symmetric
about 0 disparity,
with an exponential
relationship
between
correlation
threshold
and disparity.
Each subject showed idiosyncratic
departures
from
this exponential
trend, such as the bumps at 0 disparity for SBS, at
+ 5 arc min for CMS and at + 10 for LKC.
against interocular correlation at threshold (log scale).
Correlation
detection thresholds vary from about
0.10 at the horopter to 1.O at about 1 deg of crossed
or uncrossed disparity, the upper disparity limit (see
below). In general, all three subjects show a logarithmic
increase in correlation threshold with linear increases
in disparity away from zero. However, each subject’s
function shows localized irregularities and extensive
baseline measurements made in the context of a followup study (Cormack, Stevenson & Schor, l99la; in
preparation) reveal that the coarser features are stable
over time (e.g. the plateau from + 10 to + 20 arc min the
data for LKC). Of course, some of these features are due
to normal statistical variation and were not replicated
exactly in the follow-up (e.g. the bump at 0 arc min
in the data for SBS).
Figure 3 shows the baseline data replotted to
compare sensitivity for near and far disparities. Data
for the three subjects have been displaced vertically
for clarity. Error bars represent
f 1 SE. Subject
CMS shows a small but consistent difference in sensitivity between near and far disparity values, being more
sensitive to near (crossed) disparity over the range tested.
The other two subjects show no overall difference
between near and far sensitivity, although LKC tends
to be more sensitive to far for disparities greater than
15 arc min.
Upper disparity limits for correlation detection were
determined with a variant on the baseline procedure in
which the correlation was kept at 100% and the disparity
was varied according to the method of constant stimuli.
Otherwise, the trial sequence was the same as described
above for baseline measures. The resulting psychometric
functions were used to determine a threshold value
reflecting the largest disparity for which a 1.O correlated
surface is discriminable from 0.0 correlation.
Results
The upper disparity limits are plotted in Fig. 2
as the intersection between the sensitivity curves and
the horizontal line at 0.0 on the vertical axis. They are
between 45 and 65 arc min for all three subjects and
both directions of disparity, and are consistent with
the exponential trend in the baseline data for each
subject.
EXPERIMENT
III:
The effect of adaptation on correlation sensitivity was
determined for all three subjects and compared to the
baseline measures in order to reveal the extent to which
adaptation at a particular disparity affects sensitivity
over the visible disparity range revealed in the data of
Fig. 2.
Methods
Adaptation trials followed the same sequence as baseline trials except that a 1 min adaptation interval preceded each threshold determination and a 500 msec
“refresher” adaptation interval preceded each interval
of each trial. The adaptation stimulus was a 1.0 correlated surface at some fixed disparity. Three threshold
Near/Far
Baseline
Disparity
EXPERIMENT
II:
UPPER
DISPARITY
LIMIT
The upper disparity limit (UDL) for detecting correlation under our conditions is the disparity at which
correlation threshold reaches 100% and beyond which
even fully correlated surfaces are indistinguishable from
ADAPTATION
Comparison
(arc min)
FIGURE
3. Baseline correlation
thresholds
replotted for purposes
of near/far comparison.
Absolute value of the disparity of the test
stimulus is plotted horizontally
against the log of the correlation
at
threshold, with data from each subject displaced vertically for clarity
(0.5 log units for LKC. 0.8 for CMS). Open symbols plot data for
far (uncrossed)
disparity,
solid symbols for near (crossed) disparity.
Error bars indicate i 1 SE.
DISPARITY
TUNING
IN HUMAN
1689
STEREOPSIS
SAMPLE PSYCHOMETRIC FUNCTIONS
test and adapt both at +20 aranin
adaptation, and the horizontal line at 0 on each vertical
axis indicates a ratio of one (no effect of adaptation).
Values above the line reflect a loss of sensitivity due to
adaptation, and values below it reflect an enhanced
sensitivity due to adaptation. In the bottom panel,
results are shown for two subjects adapting at 20 arc min
far and for one subject adapting at 20 arc min near
disparity.
0.34---6=~ a . *
f
’
In most cases, the tuning functions obtained show the
a5
0.4
0.3
0.2
0.1
0.0
greatest threshold elevation at the disparity of adapCorrelation
tation. An exception to this general rule occurred for
FIGURE 4. Sample psychometric functions showing proportion
subject
LKC (dashed line): the tuning function for
correct responses in a two alternative forced choice paradigm as a
adaptation to 10 arc min far disparity showed maximum
function of the ~nter~ular correlation of a DRDS surfaced presented
at 20 arc min relative to fixation. Open symbols show performance
threshold elevation at 20 arc min. In the same plot,
without adaptation, solid symbols show performance after adapting
subject CMS (dotted line) shows a smaller shift, with
to a fully correlated surface at the same (20arcmin) disparity.
threshold elevation peaking at 15 arc min. In most cases,
Thresholds were determined by fitting the psychometric functions
the
tuning functions show facilitation for disparities on
with a cumulative normal and inter~lating to find the correlation
yielding 75% correct performance.
either side of the adaptation locus. In some cases, where
the data set is sufficiently extensive, there is an indication
that performance returns to baseline for more distant
measures for disparities at and surrounding the site disparity values.
The full width at half height of these disparity tuning
of adaptation composed a single adapted sensitivity
function. Functions were measured for adaptation at functions was measured directly from these plots and the
four values of disparity for each subject (0, + 10, - 10, results are shown in Fig. 7. The horizontal axis plots
+20 arc min for SBS and LKC, and 0, + 10, - 10, the absolute value of the disparity at which threshold
-20 arc min for CMS). Disparity tuning functions were elevation is maximum (which was not always the locus
calculated by taking the log of the ratio of adapted to of adaptation, as noted above). The vertical axis plots
baseline threshold for each test disparity.
the full width at half height of each tuning function
obtained. The best fitting line, its equation and R2 value
Results
Sample psychometric functions for correlation detection at 20 arc min far are shown in Fig. 4 for one subject
before (open symbols) and after (solid symbols) adaptation to a fully correlated surface at the same disparity.
The effect of adaptation on correlation sensitivity across
the range of disparities used is shown in Fig. 5 for
two adaptation conditions for subject SBS. The baseline
data (open symbols) are replotted from Fig. 2, the solid
symbols show correlation thresholds measured after
adaptation to a zero disparity (panel A) and a 10 arc min
near (panel B) surface. Error bars represent f 1 SE.
In both panels of Fig. 5, threshold is elevated at the
disparity of adaptation by about a factor of two, and
the range of disparities for which threshold is elevated
is relatively narrow. The adaptation curve crosses
the baseline curve 5-10arc min on either side of the
adaptation locus and is below baseline for relative
disparities greater than IO-20 arc min in both directions.
The principal difference between the results presented in
panels A and B of Fig. 5 is that adaptation at 10 arc
min near produces a somewhat broader and asymmetric
threshold elevation.
Disparity tuning functions were obtained from these
data by plotting the log of the ratio of adapted to
baseline threshold, and the results are shown in Fig. 6
for all three subjects and all values of adapting disparity.
The horizontal axis plots disparity in arc min, the
vertical axis plots threshold ratio on a log scale. The
arrow on the horizontal axis indicates the disparity of
-40
-140
0
20
40
-20
0
20
40
Test
Disparity (arc
-20
min)
FIGURE 5. Effect of adaptation for two adapting disparities for
subject SBS. Axes are the same as for Fig. 2, but expanded to show
more detail. Open symbols show baseline data replotted from Fig. 2.
Solid symbols show correlation sensitivity after adaptation to a 100%
correlated surface. Error bars indicate &I SE. Panel A: adaptation
at 0 disparity. Panel B: adaptation at -10 arc min. Note that in
both panels, thresholds are elevated at the disparity of adaptation,
and lowered for most disparities outside a relatively narrow region
surrounding it. A plot of the ratio of adapted to baseline threshold
yields the disparity tuning functions shown in Fig. 6.
I690
SCOTT
B. STEVENSON
0.6 1
-
SBS
LKC
as
-----..,....”......
-40
-20
Test
disparity
0
20
( arc
min
40
)
FIGURE
6. Disparity tuning functions for three subjects after adaptation at (A) 0, (B) -10, (C) + 10, (D) + 20 (two subjects) and -20 (one
subject) arc min disparity. The log of threshold ratio (adapt/baseline)
is plotted against the disparity of the test surface in each panel. Arrows
on disparity axis indicate the disparity of the adapting surface. The
solid curve in panel A plots the difference between the two functions shown in Fig. 5(a) for SBS, the solid curve in panel B plots the
difference between the two functions shown in Fig. 5(b). In general, the
disparity tuning functions show the greatest elevation at the locus of
adaptation,
with facilitation for more distal disparities. Note, however,
the peak at +20 for LKC after adaptation
to + 10 arc min (dashed
curve in panel C).
6’1(I/
follow an exponential
relationship
to the magnitude
of the pedestal (but see also Badcock & Schor. 1985;
Regan & Beverley, 1973). Since the fixation reference
was a pair of nonius lines, a disparity value of /ero on
the horizontal
axis of Fig. 2 indicates
the nonius
horopter and sensitivity to correlation
was greatest at
or near this point. One might alternatively
measure a
correlation
horopter,
i.e. the locus of disparities
for
which correlation
threshold is at a minimum.
For our
subjects, this appears to be within 2- 3 arc min of the
nonius horopter.
The bumps and dips in the baseline data of Fig. 3
produce some local asymmetries
between crossed and
uncrossed
disparities
of the same value: for example,
a comparison
of 20 Near vs 20 Far for subject LKC in
Fig. 3 shows about a 0.2 log unit difference in threshold.
Subject CMS shows an asymmetry
in the opposite
direction over most of the disparity range tested, but
the magnitude
of the difference varies considerably.
Considering
all three subjects, these data indicate no
overall difference in sensitivity
between near and far
mechanisms,
particularly
if the correlation
horopter
is used as the reference. This localized, mild form of
“stereoanomaly”
is more consistent
with a model of
many narrow band disparity channels, some of which
may be relatively insensitive,
than with the Richards
(1971) pooling hypothesis.
The effects are not robust
enough in these subjects to be conclusive. but it suggests
that further study may turn up individuals
with pronounced deficits in correlation
sensitivity at a particular
disparity--a
kind of correlation
scotoma.
For each subject, the triangular area in Fig. 2 bounded
by the baseline
sensitivity
curve and the horizontal
line at 0.0 on the vertical axis (top of Fig. 2) represents
those combinations
of disparity and correlation
values
which are distinguishable
from 0.0 correlation.
Everything outside that area has the appearance
of 0.0 correlation: a dynamic
swarm of dots filling a volume in
depth. Values inside the triangle produce the percept of
a stable surface
in depth, floating amidst a less dense
swarm.
The baseline
values of Fig. 2 are specific to the
conditions we tested under and should not be generalized
beyond them. In particular,
correlation
threshold
at
0
E
are shown in the figure. The tuning widths are well fit
by a line with intercept at about 5 arc min (indicating
the average tuning width at the horopter) and slope of
about 0.8.
DISCUSSION
Disparity range of interocular correlation detection
The results of the baseline and upper disparity limit
experiments
indicate that, in general, correlation
sensitivity follows an exponential
relationship
to disparity.
This is reminiscent
of the finding by Blakemore (1970)
that relative depth judgments
on a disparity
pedestal
.P
20
I"=
r 'E
'g
G - 10
AZ
5
3
y I
=
I:
0
4.5584
0
Location
+ 0.80779X
R”2
10
of Tuning
= 0.846
20
Peak
(arc mln)
FIGURE
7. Width of disparity
tuning functions
plotted against
locus of peak elevation. Each point represents the full width at half
height of a tuning function, measured directly from the curves plotted
in Fig. 6. Tuning width is approximately
a linear function of peak
disparity. with an intercept of about 5 arc min.
DISPARITY
TUNING
IN HUMAN
zero disparity varies with stimulus area, duration (Tyler
& Julesz, 1978) and contrast (Cormack, Stevenson &
Schor, 199lb). One would also expect the upper disparity limit to change with these variables, so that
the figure of 1 deg might be exceeded under different
conditions. In general, we chose values that optimize
performance in the tasks so most alterations in the
configuration of our stimuli would result in lowered
correlation sensitivity.
Disparity -speciJic adaptation
The results of the adaptation experiments indicate that
those visual mechanisms which process interocular correlation are sharply tuned for retinal disparity, both at
and away from the horopter. While our data set is not
sufficiently extensive to make a definitive statement, it
appears that a relatively large number of “channels”
exist based on the fact that threshold was usually most
elevated at the locus of adaptation. Had there been
only a few (e.g. 3 or 4) channels mediating correlation
detection, adaptation would have produced the same
elevation profile for a range of adapted disparities. Our
data indicate that there are a large number, if not a
continuum of channels, but a precise estimate of how
many and where they peak would require an order of
magnitude more data than we have presented here.
The finding of facilitation for disparity values distant
from the locus of adaptation suggests that adaptation
weakened an inhibitory mechanism that affects sensitivity under baseline conditions. One explanation, which
has been used to explain facilitory effects in spatial
frequency channels (DeValois, 1977) is that channels are
mutually inhibitory and that adaptation of a channel
releases neighboring channels from inhibition. This assumes that surrounding channels which are not excited
by test stimuli are significantly inhibiting those which
are, thus implying a relatively high, constant level of
activity in all channels. However, in the current context,
the spurious matches which occur at random at all
disparities in a DRDS stimulus might excite surrounding
channels.
A somewhat different explanation holds that each
channel has an opponent, center-surround organization
due to its inputs from earlier levels of processing rather
than from inhibitory interactions at the same level. In
this case, adaptation in the surround region produces
enhanced sensitivity of the channel more directly,
perhaps by adaptation of subunits in the inhibitory
surround. This puts the inhibitory mechanism at an
earlier stage in visual processing and requires no spontaneous activity in surround channels, but retains
the intuitive notion that facilitation comes from a
release of inhibition. Both models yield the same
opponent center-surround characteristics and may be
equivalent at the computational level despite differences
in implementation.
*Wiebull fits to our psychometric
functions
exactly 2.0, so a vector sum is equivalent
across channels.
show that Beta is almost
to probability
summation
STEREOPSIS
1691
Disparity channels model: assumptions
It is important to note that the tuning functions shown
in Fig. 6 are not necessarily plots of disparity-tuned
channels, but may be the result of adapting many
overlapping channels, each with sensitivity to the disparity of the adapting surface. To understand better the
implications of our results, we have developed a model
of underlying channel structure which produces similar
results and have explored some boundary conditions to
limit the possibilities. Our search is by no means exhaustive and our model is by no means definitive, but we have
been able to rule out some general schemes that have
been proposed elsewhere.
We constructed the model according to the general
form of the results presented above, with a number of
tuned mechnisms whose sensitivity decreases with disparity and whose tuning width increases with disparity
such that the area under the channel profile is constant
for all channels. We chose a difference of Gaussians as
the response profile of each mechanism, with an excitatory central region and a broader, inibitory surround
that exactly balances the overall function. The reponse
of the visual system to a pulse of interocular correlation
was modeled as the vector sum of the individual
responses.* The effect of adaptation on an individual
mechanism was assumed to be proportional to its sensitivity to the adapting stimulus. Figure 8 shows the
channel profiles used in the modeling, after several
channels have been desensitized by adaptation to a
stimulus at f 10 arc min. One channel has been plotted
more darkly to illustrate the form of the profile.
The stimulus is represented as being at a single
disparity value in the modeling. In actuality, the energy
of the stimulus is distributed across disparity by some
combination of optical, neural and oculomotor factors
(Stevenson, Cormack & Schor, 1989; 1991). To simplify
the model, we consider the channel profiles to be the
response across disparity of each channel to the stimulus,
without specifying the stimulus profile exactly.
Quantitative agreement between the human data
and the modeling results was achieved by adjusting the
number of channels and eight constants in relatively
simple formulas which determined the location, sensitivity, breadth and inhibitory sidelobe extent of each
channel. In the configuration presented here, there are
21 channels, peak sensitivity falls off as the square root
of disparity from the horopter, the space constant
is inversely proportional to sensitivity, the inhibitory
surround has six times the spatial extent of the excitatory center and the peak separation increases exponentially with disparity. The use of formulas to specify
these variables served to reduce the number of free
parameters considerably, given the large number of
channels used.
Disparity channels model: results
The results of our simulations are shown in Figs 9, 10
and 11. Figure 9 shows simulated pre-adaptation performance for this set of mechanisms (solid curve), with
16Y2
SCOTT
B. STEVENSON
c/ al.
Disparity Channel Profiles
(after adaptation to
0.6
-20
0
Disparity
20
40
(arc min)
FIGURE
8. Sensitivity profiles for hypothetical
disparity tuned correlation
detectors in visual system with difference of
Gaussians profiles. Sensitivity to correlation
is plotted vertically against retinal disparity. Plots reflect channel sensitivity after
adaptation
to a fully correlated
surface at + 10 arc min (indicated by arrow), causing a depression of sensitivity for several
channels peaking near that value. The effect of adaptation
on each channel is assumed to be proportional
to its unadapted
sensitivity to the adapting stimulus. Before adaptation,
the channel profiles are arranged symmetrically
about zero disparity
and have sensitivity which is inversely proportional
to tuning width.
log threshold plotted vertically against disparity. For
comparison, the baseline data from two subjects have
been replotted from Fig. 2. The model baseline captures
the basic form of the human data, absent the idiosyncratic bumps and dips. These variations can be
reproduced in the model by adjustment of individual
channel sensitivities. Figure 10 shows the same model
baseline data (solid curve) along with the postadaptation model baseline (dashed curve), obtained after
adaptation to a stimulus at + 10 arc min. Note that
the adapted baseline drops below the unadapted baseline for disparities that are distant from the locus of
adaptation. Figure 11 shows the difference between
these curves (dotted curve in Fig. 1I), plotted in the same
way as the tuning functions of Fig. 6, with the log of
Comparison
of baseline data
subiects with multlchannel
-40
-20
0
20
from two
model
the threshold ratio plotted vertically against the disparity
of the test stimulus. Also plotted in Fig. 11 are
model threshold elevation curves for adaptation at 0
and 20 arc min disparity. While the profiles do not
match exactly to those found experimentally, they
capture four important characteristics: they peak at
the disparity of adaptation, are narrowly tuned, show
facilitation for surrounding disparities and the offhoropter functions are slightly asymmetric in form.
Note that the asymmetry is not a property of the
individual channels, but of the channel distribution
overall. Note also that the facilitation observed at large
disparities after adaptation to zero disparity (solid curve
in Fig. 11) is produced by the sidelobes of channels
peaking at large disparities not by the sidelobe of the
channel peaking at zero disparity. Thus, the disparity
tuning profile produced by adaptation to a particular
disparity does not accurately reflect the channel profile
of a single mechanism which peaks at that disparity.
40
DISPARITY
FIGURE
9. Baseline data for two subjects and model. Model baseline reflects the vector-summed
output of the channel array shown in
Fig. 8 when presented with correlation
stimuli. Log of correlation
required to reach a criterion (“threshold”)
response is plotted vertically
against disparity of the test pulse. The pattern of detector sensitivity
and tuning width was adjusted in order to produce results like those
exhibited by the human subjects.
8
2
-1.4
-40
-20
0
Disparity
20
40
FIGURE
10. Model baseline replotted along with model correlation
thresholds
after adaptation
to stimulus at + 10 arc min. Note that
threshold is elevated most at the disparity of adaptation.
returns to
baseline on either side and drops below baseline for more distant
disparities.
Axes are the same as in Fig. 9
DISPARITY
TUNING
IN NUMAN
FIGURE
11. Model tuning functions, obtained by taking the
threshold ratio from the model baseline and post adaptation model
sensitivity. Log of the threshold ratio is plotted vertically against the
disparity of the test p&e. Functions are shown for adaptation at 0
(solid curve), + IO arc min (dotted curve) and +20 arc min (dashed
curve). Note the similarity of these functions to the tuning functions
plotted in Fig. 6(b) and 6(c).
Rather, it is a reflection of the aggregate activity of
many channels.
This configuration of the model we present was chosen
to so as to capture both the baseline and the tuning
behavior of the human data and some parameters are
more critical than others. For exampie, as few as 10
channels could be used to match the overall baseline and
tuning characteristics, but then the baseline data showed
considerable bumpiness due to gaps between channels.
ftroadening these 10 channels removed the bumps but
then made the tuning functions broader than the human
data. Using more than 21 channels does not significantly
alter the behavior of the model, so our configuration is
close to the minimum needed to get the idealized baselines and tuning functions shown.
The baseline irregularities and the peak shift from the
human data (seen for LKC adapting at 10 arc min)
suggest that the mechanisms tapped by our experiments
depart from these ideals. These were successfuly simulated by simply adjusting the sensitivity of individual
channels to make localized regions of higher or lower
sensitivity, resulting in an idiosyncratic set of channels.
Thus the model could be easily tuned to capture the
in~vidual differences seen in the data.
The results of our modeling serve to confirm what
was implied by our data concerning the narrow tuning
of multiple underlying mechanisms subserving correlation and disparity processing. Wowever, much is also
revealed by the models we constructed that didn’t work,
Unfortunately, there is always the possibility that a more
creative design might have made these alternatives work.
Our conclusions from these negative results are therefore
tentative.
That being said, we conclude that narrowly tuned
threshold elevation profiles cannot arise from a scheme
based solely on broadly tuned underlying mechanisms
such as the Near and Far neural mechanisms of Foggio
et aE. (1988) or the Near and Far pools of Richards
(1971) The models which produce the kind of functions
we obtained require narrowly tuned mechanisms off
the horopter, more like the Tuned Near and Tuned
Far neural mechanisms of Poggio et al. (1988), the
STEREOPSIS
1693
continuum of disparity tuned mechanisms proposed by
LeVay and Voigt (1988) or the disparity tuned mechanisms proposed by Lehky and Sejnowski (1990). In
particular, one cannot account for the fact that tuning
functions return to baseiine on both sides of their peak
without invoking the existence of a tuned mechanism, off
the horopter, with a relatively narrow profile. We found
that models based on channels with broad sensitivity
profiles extending out to large disparity values (Near/Far
channels) always produced very broad threshold
elevation functions. It is still possible that very broadly
tuned channels are operative in processing correlation
but their contribution is not apparent in our data due to
the ove~helming
influence of more narrowly tuned
channels.
The magnitude of side-lobe facilitation in Fig. 11 is
somewhat less than in the data. It is likely that the data
of Fig. 6 could be more faithfully reproduced by varying
the profiles of the individual mechanisms. Additionally~
as discussed above, it is possible that the oppanent
center/surround behavior could be captured by using
mechanisms without side lobes and then invoking
mutual inhibition at a later stage. However it is implemented, we conclude from our simulations that
inhibitory interactions between test and surrounding
disparities are required to account for the facilitation
effects.
Finally, while the model we present has accounted for
the data by assuming many channels along a line of
sight, it is possible that these data resulted fram the
aggregate response of many channels distributed across
the visual field, with only a small number representing
any given visual direction. The data we present show
that there are a number of channels available to process
correlation over the 9 deg field size we used, but the
distribution of these channels within that field is unknown. The luminance spatiaf frequency tuning of these
channels is likewise open to speculation, since the stimulus we used was spatially broad band.
Thresholds for detecting pulses of positive interocular
correlation against a background of zero correlation
were found to increase logarithmically with linear increases in both crossed and uncrossed retinal disparity.
While signi~~nt irregularities occurred in the functions
for our individual subjects, only one subject shawed
an overall difference between the two directions of
disparity.
Adaptation to 100% correlation at several different
disparity levels revealed threshold elevation tuning functions that were relatively narrow and usually peaked at
the locus of adaptation. More distant disparities showed
a facilitation effect after adaptation.
Efforts to model these results suggest that they are
most likely the result of a large number of disparity
channels, with relatively narrow tuning, broad inhibitory
sidelobes and peak sensitivities that are distributed
about the horopter.
1694
SCOTT
B. STEVENSON
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Acknowledgement-Supported
EY-08883 from the National
by NRSA
Eye Institute.
grant
EY-06045
and