Yirlon Res. Vol. 31. No. 5. pp. 805-813. 1991
Printed in Great Britain. All rights mcrvai
mM2-6989:91 53.00 f 0.00
Copyright6 1991 PergamonRW
DEPTH ATTRACTION AND REPULSION
DOT STEREOGRAMS
SCOrr B. STEVENSON, LAURENCE
K.
CORMACK
and
pk
IN RANDOM
CLETON
M. SCH~R
School of Optometry, University of California. Rerkeley, CA 94720, U.S.A.
(Receired 31 January 1990; in reuircd form 19 July
l9!20)
At&met-Ptevious
studies of perceived attraction or repulsion of adjacent visual targets have used local
targets whose positions were varied in both depth and direction. We have measured these effects in three
subjects using dynamic random-dot stereograms to isolate depth-axis effects. Results show that both
attraction and repulsion effects can occur for overlapping, positively correlated. randomdot surfaces. The
results were quantitatively similar to those reported previously for local targets. Manipulation of
interocular correlation confirmed that the effects are produced by binocular interactions. Results are
explained as accurate judgments based on the stimulus at the cyclopean ievel.
Stereopsis
Random dots
Cross-correlation
INTRODUCTION
When visual targets are placed in close proximity to one another, whether in depth or in
direction, their perccivcd positions arc shifted
relative to their actual positions by as much as
I min arc. These effects have been termed
attractions and repulsions (Canz, 1964; Westheimcr, 1986), indicating the shift of a test target
toward or away from an inducing target. While
results vary with the individual subject, there is
generally an attraction effect for test and inducing separations of less than 5 min arc, and a
repulsion efTeet for larger separations.
Westheimer (1986) and Westheimer and Levi
(1987) have specilically addressed the question
of whether the effects seen in the depth domain
are completely accounted for by monocular
effects which shift the visual direction of targets
before they are combined at a subsequent binocular stage. Their results indicate that a depth
axis effect occurs in addition to the changes in
monocular visual direction, but their studies all
involved local targets (points or lines) which
necessarily have a combination of lateral separations and depth separations.
We sought to examine the depth-axis
component of attraction and repulsion effects
with a stimulus-the
dynamic random-dot
stereogram-that
allows for changes in target
depth without changes in the monocular stimulus. We produced stereograms which portrayed
two overlapped surfaces of random dots in the
bottom half of the visual field serving as test and
Disparity
Averaging
inducing targets. A single surface in the top half
served as an adjustable probe target (Fig. I).
Changes in the disparity of thcsc surfaces are
visible only in the binocular view. The monocular stimuli remain virtually unchanged, because
each frame displays a new, random pattern of
dots, providing no info~ation about the lateral
image shifts which produce disparity (Julcsz,
1971). Thus, if any interactions occur between
individual dots in the monocular stimuli, they
will be constant across all binocular conditions
and so any attraction or repulsion effects
measured will reflect depth-axis inte~ctions
only.
The manipulation of interocular correlation
provides another means of ensuring that
binocular effects are isolated from monocular
ones since it alters the visibility of binocular
(cyclopean) surfaces without changing the monocular images in any detectable way.
Interocular correlation is a measure of the
degree to which the two monocular views match
one another at a particular disparity. It is
essentially a description of the signal strength of
a random-dot surface. An interocular correlation of zero means that matches between the
two monocular views are completely random.
An interocular correlation of positive one
means that the monocular views match exactly.
An interocular correlation of negative one
means that the monocular views are exactly
opposite (every black dot is matched to a white
dot and vice versa).
Scol-r 8.
806
SEVENSON
Fig. 1. Schematic depiction of subject’s task. Subject viewed
a dynamic random-dot stereogram display containing three
surfaces. labelled “adjustable probe.” “test” and “inducing”
in the figure. The test and inducing surfaces were overlaid
and appeared in the lower half of a circular 1I deg field. The
depth separation of the test and inducing surfaces. and the
correlation of the inducing surface were set by the experimenter. Probe and test surfaces were always positively
correlated. The probe appeared in the upper half of the
display and was adjusted by the subject to match the depth
of the test surface. Configuration for the “inducing far”
condition is shown.
EXPERIMENT
1
We began our studies by testing for attraction
and repulsion cffccts with positively correiatcd
random-dot surfaces.
Stimuli. The stimuli used in ail our stud&
wcrc dynamic random-dot stcrcograms which
were displayed on video monitors (TSD modci
HR,M, 60 Hz nonintcrlaccd) and viewed in a
front-surface mirror haploscope. The dots wcrc
generated by a pseudo-random noise generator
that consisted of a 32 bit shift register, running
at 7 MHz. with a NOT XOR combination of
bits 23 and 30 fed back to the input. In this
configuration, the resulting stream of bits repeats itself about every 2 min with equal numbers of on and off bits. Positive interocular
correlation
was produced by sending identical
bit streams to the two video monitors. Negative
interocular correlation was produced by inverting the sign of one of these bit streams. Zero
interocular correlation was produced by sending
independent bit streams to the two monitors.
Disparity was manipulated by introducing a
variable delay into the bit stream going to the
left monitor. The output of the shift register was
delay line (Data Delay
fed into a programmable
Devices model PDU- 13256). and the amount of
delay was controlled by an AT clone computer.
Upper and lower half-fields of the display
were independently controlled by changing disparity and correlation at a fixed location in each
video frame. OverIapped surfaces with different
et
al.
depths were independently controlled by alternating between two values of disparity and
correlation on alternate video frames. The rapid
(60 Hz) exchange between two disparity values
which produced overlapped surfaces was never
visible to the subject as such: neither motion in
depth nor flicker were ever perceived. The resuiting stereograms portrayed three independent surfaces: a single one in the upper half-field
and two overlapped ones in the lower half-field.
Figure I shows a cartoon intended to represent
approximately what the subjects saw when viewing the display.
Appmzrus. The stereograms were viewed in a
mirror haploscope arrangement at a distance of
57.3 cm. Convergence angle was set to match
the viewing distance. Opaque circular apertures
Ii deg in diameter masked the edges of the
display. A horizontal black line subtending
3 min arc covered the center of the field where
depth and correlation transitions occurred. The
dots were 5 min arc wide, the contrast was about
80% (measured on a static dot pattern) and the
mean luminance was about SOcd/m*. The AT
computer controlled the disparity and correlation of the three surfaces and subjects made
~~~ijustm~nt settings by pressing keys on the
computer keyboard.
Prodwe.
The apparent attraction or repuision of the overiappcd test and inducing surfaces in the lower half-field was measured by
having subjects adjust the disparity of the probe
surface in the upper half-field so that there
appeared to be no depth difference between the
probe and the test sufaccs. Ten adjustment
settings were made for each depth separation of
test and inducing surfaces. Each setting began
with the probe at a randomly selected disparity.
The difference between the mean of the 10
settings of the probe surface and the actual
disparity of the test surface was used as an index
of the attraction or repulsion for that condition.
For most conditions, separate runs were made
with the inducing surface nearer than and farther than the test surface.
For small depth separations of the test and
inducing surfaces, the gap between them is not
visible and they appear as a single, thick surface
(Stevenson, Cormack & Schor, 1989). In these
situations the subjects were instructed to adjust
the probe to match the depth of this single
surface.
Subjects. Subjects were two of the authors
(SBS and LKC) and an undergraduate who was
naive to the purpose of the experiments
Depth attraction and repulsion
(GSEG). Two were emmetropic and one wore
contact lens correction. Complete data sets were
collected on SBS and GSEG, and the basic
results for expts I and III were confirmed on
subject LKC.
Results
The attraction and repulsion effects measured
in expt I are shown in Fig. 2. For each subject,
the disparity difference between the test surface
and the mean of the probe surface settings is
plotted against the disparity difference between
test and inducing surfaces. Attraction is represented as positive values on the vertical axis,
repulsion as negative values. The horizontal line
807
which intersects the vertical axis at zero represents the expected result if no attraction or
repulsion occurred. Symbols represent the mean
of the 10 settings and error bars represent
f 1 SD. The open and solid symbols represent
the conditions in which the inducing surface was
near and far, respectively.
From all three subjects’ data it is clear that
both attraction and repulsion effects occur
under the conditions we have used. When the
depth separation is zero, subjects align the
probe to the same disparity as the combined test
and inducing surfaces with high precision and
accuracy. As the separation is increased, the
probe settings indicate an attraction effect which
Interaction
of random-dot
surfaces
both positive correlation
1
LKC
.o
05
^u
b
.s
E
1.0
0.5
.A
0
z5
0
u
._,
-0.5
z
;
-1.0
0.
1.0
-
0.5
-
GSEG
Oj
-1.5+
0
,
,
,
)
2
4
6
6
Separation
Fig. 2. Data
.
(
,
10
12
.
,
14
_
16
(min arc)
for three subjects from cxpt I. in which the inducing
surface was positively correlated.
Perceived shift of test surface is plotted on the vertical axis against disparity separation of test and inducing
surfaces on the horizontal
are for “inducing
disparity
near.”
axis. Solid symbols show data for “inducing
Attraction
specifies. are plotted as positive values on the vertical
negative values. Error
far” configuration,
open symbols
effects, in which test is perceived as closer to inducing surface than
bars represent
axis. Repulsion
f I SD of the IO adjustment
efkcts
settings.
are plotted
as
SCOTT
808
8. %TW!BsoN
peaks at 2-3 min arc of sepaqtion and returns
to baseline at 4-6 min arc. Further separations
reveal a repulsion effect which is maximum at
6-8 min arc of separation and returns to baseline at lO-12min arc.
While there are some individual differences
apparent in these data, the general result is the
same for all three subjects. In addition, these
results are in agreement with results reported
previously for attraction and repulsion interactions for targets separated in depth and/or in
visual direction (Westheimer, 1986; Westheimer
& Levi, 1987).
EXPERIMENT
et
al.
Intrmctionof rundam-dot
zero correlation
swkcas
control
15,
4
1.0
1
.r
0
f
-0.5
f
-151
II
Methods
The next experiment was conducted as a
control to ensure that the effects measured in
expt I were due to binocular interactions, and
not to interactions among elements in the monocular stimuli. While the use of random-dot
stercograms should ensure this, we took the
conservative approach of testing this assumption with a control experiment. The conditions
were the same as in expt I except that the
inducing surface was given zero correlation
instead of positive corrciation. Thus, our procedure went through all the manipulations for
prcscnting an inducing surface, but there was no
binocular information to specify the surface.
Under these conditions we expect no attraction
or repulsion effects.
Stimrli.
The stimuli were the same as in expt
I, except that the left and right monitors received statistically independent bit streams
while the inducing surface was being displayed.
This was achieved by having the computer
switch an electronic gate at the same time it
changed the disparity to that of the inducing
surface. The gate determined whether the right
monitor received the same bit stream as the left
monitor or received a bit stream generated by an
XOR combination of two different bits of the
shift register.
Subjects and apparatus were the same as in
expt I.
Proced4re.
Since the inducing surface had
zero correlation, it was not visible to the subject
and therefore the lower half-field of the display
always had a single, unambiguous surface to
which the probe could be matched.
Reslrlts
The results of expt II are shown in Fig. 3,
plotted on the same axes as in Fig. 2. It is clear
-1.5-I
1
0
1
,
2
4
,
6
,
,
e
10
Separation (mln arc)
Fig. 3. Data
for two subjects from cxpt II, in which the
inducing surface had zero correlation.
Axes and symbols are
the same as in Fig. 2.
from these results that no attraction or repulsion effects occurred when a zero-correlation
inducing surface was used. Subjects always
made an accurate and precise match of the
probe and test disparities for all separations of
test and inducing surfaces, with no evidence of
any constant errors that would indicate attraction or repulsion.
EXPERIMENT
III
The next experiment sought to further explore
the role of interocular correlation in the generation of the attraction and repulsion effects.
Instead of a positively correlated inducing surface, we used a negatively correlated inducing
surface. The probe and test surfaces were positively correlated as before. While we had no
specific predictions of the outcome of this experiment, we reasoned that if interocular correlation is an accurate descriptor of the binocular
stimuli whose interactions we measured in expt
I, then a negative inducing stimulus should
produce essentially opposite results.
Depth attraction
Metho&
Stimuli. The stimuli were the same as in expt
I and II except that the left and right monitors
received exactly opposite bit streams while the
inducing surface was being displayed. As before.
the computer switched an electronic gate at the
same time it changed the disparity to that of the
inducing surface. This gate determined whether
the right monitor received the same bit stream
as the left monitor or received a digitally inverted version of the bit stream.
Subjects and apparatus were the same as in
expts I and II.
Procedure. For small separations of test and
inducing surfaces, the presence of the negatively
correlated inducing surface tended to cancel the
positively correlated test surface, making it
and repulsion
809
difficult or impossible for the subjects to perform the task. This was generally true for
separations below l-2 min arc. so settings were
not made for separations in this range. For
larger separations, the positively correlated test
surface was not cancelled by the negatively
correlated inducing surface and the standard
procedure was used.
Results
The results from expt III are shown in Fig. 4,
plotted on the same axes as in Figs 2 and 3
except that the scale has changed on the vertical
axis. All three subjects show a repulsion effect
that is greatest for small separations of test and
inducing surfaces and tapers off to baseline at
about 10 min arc. Note that the results are
Intoration
of random-dot surfacer
positive and negative correlation
21
,
1
LKC
-
-31
=a
-1
2
s
a;
-2
-3
2
GSEG
1
0
-1
-2
0
2
4
6
a
10
12
14
?6
Separation Imin arc)
Fig. 4. Data for three subjects from expt Ill, in which the inducing surface was negatively correlated.
and symbols are the same as for Figs 2 and 3. except for the vertical scale.
Axes
?iCOl-K
8. STEVENSON
et d.
810
generally but not exactly the opposite of the
results from expt I. Small separations produce a
repulsion effect instead of an attraction effect,
but in most cases, larger separations do not
produce an attraction effect where repulsion
occurred in expt I. Note also that the variability
of the settings, as indicated by the error bars, is
very high for small separations. This is in agreement with the observation that the test and
inducing surface tend to cancel at small separations, making the task more difficult.
lus, the visual system responds to a proximal
one that has been filtered by the optics of the eye
and, in this case, processed by monocular stages
of vision before some matching process extracts
the information required to perform the task.
With this in mind we performed a computer
simulation designed to describe the information
available to the “cyclopean retina” (Julesz,
1971) under the conditions of our experiments.
This information was then used to determine
how subjects would be expected to perform in
the tasks based on the information provided to
their binocular visual mechanisms. Any departure from this performance would indicate central interactions among the processes involved,
assuming an accurate stimulus description.
DISCUSSION
The results of these three experiments indicate
that attraction and repulsion effects do occur for
stimuli which isolate depth-axis changes from
monocular
visual direction changes. This
confirms the conclusions of Westheimer (1986)
and Westheimer and Levi (1987) that the depthaxis effects are not due simply to monocular
interactions, and it extends the generality of
their findings to include random dot stereograms in the list of stimuli which show these
interactions. In particular, the powerful effect of
intcrocular correlation on these interactions is
strong cvidcncc that the interactions arc occurring in the cyclopean domain; that is. at the level
of binocular interaction in the visual system.
HIMULATION
Methods
Figure 5 illustrates our approach to the simulation. On the left-hand side is a cartoon intended to represent the stages of vision involved.
The images are generated on the video monitors, blurred by optics, imaged on the two
retinas, processed through some monocular
stages of vision, combined by binocular mechanisms and then analyzed by “downstream processcs” to dctcrmine the relative depths of image
fcaturcs.
On the right-hand side of Fig. 5 is a parallel
structure describing our simulation of thcsc
events. First, left- and right-eye “image” arrays
of 5 min arc dots were constructed with a
simulation of the pseudo-random noise generator. These were then smoothed (blurred) with
a sine-squared function and added to a realvalued “retinal” array with 0.5 min arc receptor
I
In order to better understand these effects. it
is necessary to start with a complete description
of the stimulus to the cyclopean Icvel of vision.
While our methodology specifies a distal stimu-
Simulatron
Visual Stages
E!!!La
Image
Array
Smoothing
Optics
Monocular
Differencing,
Call.S
Averaging
Binocular
Cross
Correlation
Cells
Localization
Decision
I
Fig. 5. Schematic
outline of rationale
for simulation.
processing presumed to occur on viewing a dynamic
stages of the computer
simulation
The left panel represents stages of visual image
random-dot
intended
stereogram.
to parallel
The right panel represents
the visual stages.
Depth
5
E.,.,1
c
Cm*r-cormlaUontunctlon
mlnsre dots. 4 mtnsm blur
0
-10
dlrpsrlly
Fig. 6. Cross-correlation
ated random-dot
in depth.
10
In
function
mln
of smoothed,
images which portray
Interocular
attraction
correlation
vertical axis against disparity
differenti-
a single. flat surface
product
is plotted on the
in min arc on the horizontal
axis. Dot size for this simulation
was 5 min arc, as in the
actual
were
experiments.
sine-squared
Dot
function
arrays
smoothed
with
a
whose full width was 4 min arc.
spacing. This process was repeated for 1 set of
model time, to simulate time-averaging over
several video frames. These arrays were then
converted to their first-difference functions, to
simulate edge extraction in the visual system.
The resulting left- and right-eye arrays were
cross-correlated over a range of horizontal disparity to yield functions of intcrocular correlation vs horizontal disparity. Finally, statistics
arc computed on thcsc functions to localize
fcaturcs in them.
Figure 6 shows the result of this simulation
for the case in which test and inducing surfaces
were both positively correlated and had zero
separation. (This is equivalent to a single, flat,
positively correlated random-dot surface.) Interocular correlation. or matching strength of the
random-dot pattern is plotted on the vertical
axis as a function of horizontal disparity on the
horizontal axis. The function shows a broad
peak of correlation at zero disparity, negative
side-lobes at a distance of one pixel on either
side of the peak, and zero correlation for all
other disparities.
The breadth of the cross-correlation function
on the disparity axis is largely determined by the
amount of blur introduced by the optics, which
we have simulated by smoothing the image
arrays. The high correlation at zero disparity
occurs because identical patterns were used for
the right and left eye images. The zero correlation at most other disparities occurs because
the dot patterns are random and the simulation
averaged over a large enough region that spurious matches (“false targets”) were cancelled
out.
and repulsion
811
The side-lobes of negative correlation are the
result of having matched edge information in
the random dot stereograms. Binary-valued
random-dot
patterns have two constraints
which give rise to these negative side-lobes.
First, the spatial quantization into pixels constrains the shortest distance between edges in
the random dot image. Second, a rising (or
falling) luminance edge in the image is always
adjacent to either no edge (0 correlation) or a
falling (rising) edge (- 1 correlation) one pixel
away. Thus, at a disparity equal to one pixel’s
width on either side of a correlated surface
where all edges match, on average there is a
correlation of -0.5.
Side-lobes with some amount of negative correlation usually occur (when edge information is
matched) for images that have been quantized
into pixels. They also occur for spatially broadband natural images that have been low-pass
filtered, by optics for example (Nishihara. 1989).
Negative side-lobes do not usually occur if
gray-level (zero order) luminance information in
the images are matched, instead of edge (first
order) information. A bright dot is always adjacent to either a bright dot (+ I correlation) or
to a dark dot (- I correlation), producing an
average correlation of zero.
The function in Fig. 6 simulates the information available to the subjects in our task to
specify the location in depth of a single randomdot surface. Figure 7 shows a series of cross-
-10
10
0
Disparity IminI
Fig.
7. Series of cross-correlation
two overlaid,
positively correlated
varying disparity separation.
The
top-most
function
functions
representing
random-dot
surfaces of
Axes are the same as in Fig. 6.
represents
surfaces with zero dis-
parity difference, and is the same as the function in Fig. 6.
Functions
for progressively
larger separations
are plotted
with vertical offsets for clarity. One surface is placed at zero
disparity
in every function,
while
the other
is placed at
successively larger negative disparity values in steps of
arc. The simulated
I min
subject’s task was to locate the “test
surface” peak near zero disparity
in each function without
regard to the position of the “inducing
surface.”
2 shows good agreement between our simulation and the data collected in expt 1. The
simulation shows an attraction effect for small
separations of test and inducing surface, a crossover at about 5 min arc of disparity separation
and a repulsion for still larger separations.
Slmulrtlon
SIML‘LATION
0
2
4
6
SeporatIon
6
10
12
14
16
fmln ofd
Fig. 8. Results of Simulation I in which test and inducing
surfaces are both positively correlated. The predicted shift
of the test surface in min arc is plotted on the vertical axis
against the disparity separation of test and inducing surfaces
on the horizontal axis. E&h function represents the value of
a statistic computed on the cross-correlation functions
shown in Fig. 7 to localize the peak near zero disparity.
Heavy curve represents the location of local maximum
(mode) nearest zero disparity in eztch cross-correlation
function. Lighter curves represent mean and median values
computed for the region bounded by nearest minima in the
cross-correlation functions. Comparison to Fig. 2 shows
goad agrrrment between data and simulation.
correlation functions simulating two randomdot surfaces with varying amounts of depth
separation. The function at the top of the figure
is the same as that plotted in Fig. 6, and
represents zero disparity dilTerence between test
and inducing surface. The placement of the
functions is such that the component produced
by the test surface is always in the same position, running straight down the page, while the
component produced by the inducing surface is
displaced incr~~lsingly to the left in steps of
I min arc of disparity.
As the depth separation between test and
inducing surface is increased, the cross-correlation function becomes broader and then splits
into two clearly discriminablc components.
Since the subjects’ task was to locate the position of the test surface, the last stage of our
simulation was to localize the test component in
the cross-corrclotion functions of Fig. 7. We
computed the mean, median and mode of each
function in the region surrounding zero disparity. The mean and median were computed
for the region bounded by local minima on
either side of zero disparity.
Figure 8 shows the location of the computed
mean, median and mode values as a function of
the disparity difference between test and inducing surfaces in our simulation. The mode values
are plotted with a heavier line for emphasis
because they involve fewer assumptions than the
mean and median values and because they seem
to fit the data best. A comparison of Figs 8 and
II
Experiment II, the control condition in which
the inducing surface had zero correlation, was
not simulated. Since the zero-correlated inducing surface produces no signal in the crosscorrelation function, only the test surface is
visible and no attraction or repulsion effects are
expected.
SIhllJLATfON
iI1
in order to simulate the results of expt III, in
which a negatively correlated inducing surface
was used, we followed all the same steps as
above except that the image array values for one
eye were inverted on the appropriate frames.
The cross-correlation
function for a single,
negatively correlated random-dot surface is exactly the inverse of the function shown in Fig. 6,
with high negative correlation at the disparity of
the surface and positive side-lobes on either
side. The simulation was carried out for a range
of disparity separations of the positive test and
negative inducing surfaces. The same rules described above for Simulation I were applied in
order to localize the test component for each
separation of test and inducing surface.
RWdlS
Figure 9 shows a series of cross-correlation
functions representing a positively correlated
o-2
-
-4
-6
-
-8
+
0
-30
Disparity
30
lminl
Fig. 9. Series of cross-correlation functions as in Fig. 7. but
with a negatively correlated inducing surface. Test surface
is placed at zero disparity in each function, while inducing
surface is placed at successively larger negative disparity
values in steps of I min arc. Note that the top-most function
is flat. due to complete cancellation of overlaid positive test
and negative inducing surfaces at zero disparity separation.
Depth
Sepomtlon
Fig. 10. Results of Simulation
attraction
(mtn an)
111 in which inducing surface
was negatively correlated, for comparison to data in Fig. 3.
Axes and functions are the same as in Fig. 8.
test surface with fixed disparity and a negatively
correlated inducing surface which is displaced
increasingly to the right in steps of 1 min arc of
disparity.
Figure IO is a plot of the mean, median and
mode values as a function of the disparity
separation of the two components. The values
for the mode are once again plotted with a
heavier line for emphasis. A comparison to the
data in Fig. 4 indicates that the experimental
and simulation results arc in good agreement for
expt 111as they were for expt I. The simulation
shows the most repulsion for small separations
and shows a gradual decrease in the effect up to
8-10 min arc of separation.
DISCUSSION
Given the assumptions of our simulation, that
the visual system matches edge information in
blurred images averaged over space and time, it
appears that subjects made accurate judgments
of the location of the test surfaces. That is, their
responses reflect the information they were
given. We have found no evidence of a shifting
of perceived position due to central interactions.
The attraction and repulsion effects seen in the
data are consistent with identification of the
peak or some other centroid in the cross-correlation function, with the effects being caused by
the interaction of the profiles of the two component cross-correlation functions.
In particular. the negative side-lobes in these
profiles give rise to the repulsion effects found in
the data. Perhaps previous suggestions of lateral
inhibition were based on an intuitive realization
that some negative side-lobes were required in
order to account for repulsions. Our finding is
that these side-lobes occur in the stimulus, if one
and repulsion
813
assumes that edge information is used in the
binocular matching process. If one assumes
instead that gray-level (zero order) luminance
information is used, these side-lobes do not
occur and the repulsion effects are not predicted. Such a model might then involve inhibition among central, binocular units in order to
account for all the experimental results. Given
that cortical visual neurons in nonhuman primates are known to respond to edge information, our assumptions seem most reasonable
in this regard. Thus, while inhibitory interactions certainly occur at many levels of the
visual system (probably including the processes
which extract edge information), our results
suggest that inhibitory interactions at the central level are not causing the depth attraction
and repulsion effects we have measured.
In summary, we have measured the perceived
position of a test surface in random-dot
stereograms in the presence of an inducing
surface whose depth and correlation were
varied. We found attraction and repulsion
effects like those reported by others for local
targets, confirming that the interactions which
produce these effects occur at binocular levels of
the visual system in the disparity domain. A
simulation of the information available to this
level of the visual system suggests that the
interactions occur due to summation of the
cross-correlation profiles of the surfaces.
Acknow/e&e~enr~-The
her cooperation.
authors thanks subject GSEG
This work was supported
for
by NE1 NRSA
grant no. EY-06045.
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