Vision Res., Vol.37, No. 20, pp. 2849-2869, 1997
Pergamon
PII: S0042-6989(97)00086-2
© 1997ElsevierScienceLtd.All rightsreserved
Printedin GreatBritain
0042-6989/97 $17.00+ 0.00
Similar Mechanisms Underlie Simultaneous
Brightness Contrast and Grating Induction
BARBARA BLAKESLEE,*J" MARK E. McCOURT*
Received 15 October 1996; in revised form 18 March 1997
The experiments explore whether the mechanism(s) underlying grating induction (GI) can also
account for simultaneous brightness contrast (SBC). At each of three test field heights (1, 3 and
6 deg), point-by-point brightness matches were obtained from two subjects for test field widths of
32 deg (GI condition), 14, 12, 8, 6, 3 and 1 deg. The point-by-point brightness matches were
quantitatively compared, using GI condition matches as a standard, to assess systematic alterations
in the structure and average magnitude of brightness and darkness induction within the test fields
as a function of changing test field height and width. In the wider test fields induction structure was
present and was generally well-accounted for by the GI condition sinewave predictions. As test field
width decreased the sinewave amplitude of the induced structure in the test field decreased (i.e.,
flattened), and eventually became negative (i.e., showed a reverse cusping) at the narrower test field
widths. As expected, both subjects showed a decrease in overall levels of brightness and darkness
induction with increasing test field height. For any particular test field height, however, relative
brightness increased with decreasing test field width. This brightness increase began at larger test
field widths as test field height increased. The results are parsimoniously accounted for by the
output of a weighted, octave-interval array of seven difference-of-gaussian filters. This array of
filters differs from those previously employed to model various aspects of spatial vision in that it
includes filters tuned to much lower spatial frequencies. The two-dimensional output of this same
array of filters also accounts for the GI demonstrations of Zaidi [(1989) Vision Research, 29, 691697], Shapley and Reid's [(1985) Proceedings of the National Academy of Sciences USA, 82, 59835986] contrast and assimilation demonstration, and the induced spots seen at the street intersections
of the Hermann Grid. The physiological plausibility of the filter array explanation of brightness
induction is discussed, along with a consideration of its relationship to other models of brightness
perception. © 1997 Elsevier Science Ltd
Brightness
Induction
Grating induction Filling-in
INTRODUCTION
Simultaneous brightness contrast
Classical brightness contrast
(DeValois & Pease, 1971; Yund et al., 1977; DeValois &
DeValois,
1988), a common explanation for SBC is that
It has long been known that the brightness of a region of
the
brightness
of the test field must be determined by the
visual space is not related solely to that region's
information
at
the edges of the bounded region (for
luminance, but depends also upon the luminances of
example,
by
average
perimeter contrast) and is subseadjacent regions. Simultaneous brightness contrast (SBC)
produces a homogeneous brightness change within an quently filled-in or assigned to the entire enclosed area
enclosed test field, such that a gray patch on a white (Shapley & Enroth-Cugell, 1984; Cornsweet & Teller,
background looks darker than an equiluminant gray patch 1965; Grossberg & Todorovic, 1988; Paradiso &
on a black background. This effect has been well- Nakayama, 1991; Rossi & Paradiso, 1996; Paradiso &
quantified with respect to inducing background and test Hahn, 1996; for review see Kingdom & Moulden, 1988).
field luminance (Heinemann, 1955). Although SBC It is becoming clear, however, that this explanation is
decreases with increasing test field size, brightness too simple and that distal factors must also play a role in
induction occurs for test fields as large as 10 deg (Yund SBC (Arend et al., 1971; Land & McCann, 1971;
& Armington, 1975). Since this distance far exceeds the Heinemann, 1972; Shapley & Reid, 1985; Reid &
dimensions of retinal or LGN receptive fields in monkey Shapley, 1988).
Grating induction (GI) is a brightness effect that
produces a spatial brightness variation (a grating) in an
*Department of Psychology,North Dakota State University,Fargo,
extended test field (McCourt, 1982). The perceived
ND 58105-5075, U.S.A.
tTo whomall correspondenceshouldbe addressed[Fax:+1-701-231- contrast of the induced grating decreases with increasing
8426; Email: blakesle@prairie.nodak.edu].
inducing grating frequency and with increasing test field
2849
2850
B. BLAKESLEEand M. E. McCOURT
height (McCourt, 1982), such that canceling contrast is
constant for a constant product of inducing frequency and
test field height (McCourt, 1982; Foley & McCourt,
1985). Although not formally reported for test fields
larger than 3 deg, where at low frequencies the
percentage of inducing grating contrast required to
cancel the induced grating may still exceed 30%
(McCourt, 1982), GI is observed in test fields at least as
large as 6 deg (see Fig. 4). Although GI may extend over
large distances, homogeneous brightness fill-in cannot
account for GI. For example, a fill-in mechanism
dependent on average perimeter contrast does not predict
the appearance of a pattern in a GI test field because only
a single value (average perimeter contrast) determines the
assignment of brightness. A homogeneous fill-in mechanism which computes brightness based on local contrast
rather than on average perimeter contrast (and which can
therefore produce both positive and negative brightness
signals originating from the opposite-polarity test field
edges) still cannot produce a patterned test field (i.e., an
induced grating). This is so because, without boundaries
within the test field to arrest the propagation of these
putative brightness signals, induced brightness and
darkness will diffuse and average to produce the percept
of a homogeneous test field. Several more complex
brightness models have been proposed that incorporate
non-homogeneous fill-in mechanisms (Grossberg &
Mingolla, 1987; Pessoa et al., 1995), but these have not
yet been applied to GI.
It has been suggested that GI might be understood in
terms of the output of parallel spatial filtering across
multiple spatial scales (Moulden & Kingdom, 1991 ). An
attractive feature of this approach is that both the lowpass spatial frequency response of GI, and the invariance
of induction magnitude with viewing distance (i.e., the
direct tradeoff between the effects of inducing grating
spatial frequency and test field height), can be parsimoniously accounted for by multiple-channel isotropic
spatial filtering.
Despite the fact that SBC is typically considered a
homogeneous brightness effect dependent on homogeneous brightness fill-in, whereas the defining characteristic of grating induction is that it possesses spatial
structure and cannot be produced by a homogeneous fillin mechanism, it has nevertheless been suggested both
that SBC is a special low frequency instance of grating
induction (McCourt, 1982), and that GI is a particular
case of SBC (Zaidi, 1989; Moulden & Kingdom, 1991).
The present experiment explores this issue, asking
whether the mechanism(s) underlying GI can account
for SBC as well, or if fundamentally different brightness
mechanisms are required to explain these effects. The
structure and magnitude of induction in both GI and SBC
stimuli were measured, where the inducing conditions for
the two effects were rendered as similar as possible by
employing one cycle of a low frequency sinewave grating
as the inducer. Test field dimensions spanned a range that
incorporated both classic SBC and GI configurations.
Point-by-point brightness matches were quantitatively
compared, using GI matches as a standard, to assess
systematic changes in induction structure and magnitude
as a function of changing test field height and width.
Predictions from homogeneous brightness fill-in mechanisms as opposed to linear filtering mechanisms were
compared. The results are most simply accounted for by
the output of a weighted octave-interval array of
difference-of-gaussian (DOG) filters. This array of filters
differs from those previously employed to model various
aspects of spatial vision in that it includes filters tuned to
much lower spatial frequencies.
METHODS
Subjects
Two subjects (the authors BB and MM) participated in
the study. Both subjects were well-practiced psychophysical observers and possessed normal or correctedto-normal vision.
Instrumentation
Stimuli were generated using a PC-compatible microcomputer (486/66 MHz) with a custom-modified TIGA
(Texas Instruments Graphics Architecture) graphics
controller (Vision Research Graphics, Inc.). Images were
presented on a high-resolution display monitor (21"
IDEK Iiyama Vision Master, model MF-8221). Display
format was 1024 (w) x 768 (h) pixels. Frame refresh rate
was 97 Hz (non-interlaced). All images could possess 2 s
simultaneously presentable linearized intensity levels
selected from a palette of approximately 2 ~5.
Stimuli
Viewed from a distance of 60.7 cm the stimulus field
subtended 24.2 deg in height and 32 deg in width;
individual pixels measured 0.031 deg x 0.031 deg. Mean
display luminance was 50cd/m 2. Inducing patterns
appeared in the lower half of the stimulus field. The
inducing patterns for all stimuli consisted of one cycle of
a vertical sinewave grating (presented in sine phase) with
a spatial frequency of 0.03125 cycles/degree (c/d).
Inducing grating Michelson contrast was constant at
0.75. The test and comparison patches of classical SBC
are both referred to here as test fields. The test fields were
centered vertically within the inducing field and horizontally with respect to the half cycle of the sinewave in
which they were inserted, e.g., Fig. 1(g). The luminance
of the test fields was set to the mean luminance of the
display (50 cd/m2). GI test fields [see Fig. l(a)] were
unitary and extended the full width of the display
(32 deg).
The height of the SBC and GI test fields assumed three
values (1, 3 and 6 deg). Although increases in test field
height resulted in decreases in inducing field height, the
height of the upper and lower inducing fields was never
less than 3 deg. Foley & McCourt (1985) demonstrated
that GI magnitude remains constant until the sizes of the
upper and lower inducing fields fall below this value.
Therefore, the decreases in inducing field height
SBC AND GI
2851
14 °
32 °
o
12 °
Stimuli (1 ° test field height)
FIGURE l(a-d).
produced by increasing test field height are not expected
to alter GI magnitude. At each test field height the
following test field widths were examined: 1, 3, 6, 8, 12,
14 and 32 deg. See Fig. l(a-g) for illustrations of the
stimuli used in the 1 deg test field height condition. The
upper half of the stimulus display contained a matching
stimulus of adjustable luminance surrounded by a
homogeneous field which was also set to the mean
luminance of the display (50 cd/m2). The matching
stimulus measured 0.25 deg in width and either 1, 3 or
Caption overleaf
6 deg in height, such that it was always matched in height
to the test field under study.
Procedures
All stimuli were viewed binocularly through natural
pupils in a dimly lit room. Each subject's head was
positioned relative to the display with a chin and forehead
rest. Eye movements were restricted only in that subjects
were instructed to maintain their gaze within the display
in order to hold adaptation state stable. Induction
2852
B. BLAKESLEE and M. E. McCOURT
6°
3 °
lO
Stimuli (1° test field height)
FIGURE I. Stimuli used to measure the effect of test field width on induction magnitude. Test field widths of 32, 14, 12, 8, 6, 3
and 1 deg were tested at each of three test field heights (1. 3 and 6 deg). Only the stimuli from the 1 deg test field height
condition are illustrated. Inducing contrast was constant at 0.75. Test field luminance was set to the mean of the display (50 cd/
m2). Note that the 32 deg stimulus is a standard GI stimulus (one unitary test field), the 1 deg stimulus is a "classical" SBC
stimulus (two 1 deg×l deg test fields). In the 3 and 6 deg test field height conditions the "classical" SBC stimulus is represented
by the 3 and 6 deg test field width conditions, respectively.
magnitude was measured using a point-by-point brightness matching technique (Heinemann, 1972; McCourt,
1994). A thin bright line (1 pixel wide, 0.031 deg) served
as a pointer. Subjects adjusted the luminance of the
matching field (located several degrees directly above the
pointer), until it matched the brightness of that region of
the display (test field or inducing grating) to which the
pointer referred. This region was located several degrees
below the pointer (at the level of the test fields). Each trial
was initiated by the subject. The initial luminance of the
SBC AND GI
(a)
0.9
i
1° test field height, 32 o test field width
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2853
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F I G U R E 2 (a---d).
Caption overleaf.
,
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2854
B. BLAKESLEE and M. E. McCOURT
(e) 1 o test field height, 6 ° test field width
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FIGURE 2. Complete sets of point-by-point brightness matches lor subjects BB and MM are illustrated for the 1 deg test field
height condition. Open symbols refer to brightness matches made to the test field(s); filled symbols are brightness matches to the
inducing grating. The dotted line depicts the veridical luminance profile of the stimulus display along the vertical center of the
test field. Mean luminance matches for each observer in the GI condition (32 deg test field width) were fit using a nonlinear
regression procedure (method of least-squares) to a sinewave grating [Eq. (1)]. This optimized function is depicted by the solid
line. The amplitude and offset parameters obtained from the 32 deg test field condition (GI) are referred to as the "grating
induction prediction" and were used as a baseline to compare induction structure and magnitude for the narrower test field
widths. These values are indicated in the panel for the 32 deg test field condition. Mean luminance matches in the 14, 12, 8, 6
and 3 deg test field conditions were modeled using a four-parameter version of Eq. (1). Eq. (2) permits independent amplitude
variations within the dark and bright test fields. Parameters ~ and 7~ refer to the amplitudes of the best-fitting sinewave
functions to the mean luminance match values in the dark and bright half-cycles, respectively. Parameters 6d and 5b permit
compensatory offset changes which accommodate magnitude changes produced by variations in parameters c~aand c~h. The bestfitting functions (solid lines) obtained for each stimulus configuration are indicated in each panel.
matching field was randomized at the beginning of each
adjustment trial and subjects controlled subsequent
increments and decrements in matching luminance by
depressing appropriate response buttons. Each button
press resulted in a matching field luminance change of
l cd/m 2 (1.0% maximum luminance). No time limits
SBC AND GI
2855
(a) 3 ° test field height, 32 ° test field width
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FIGURE 3 (a--d).
Captionoverleaf
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2856
B. BLAKESLEEand M. E. McCOURT
(e) 3 ° test field height, 6 ° test field width
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FIGURE 3. Complete set of point-by-point brightness matches for subjects BB and MM for the 3 deg test field height condition.
See Fig. 2 for details.
were imposed, and the adjustment interval for each trial
lasted until terminated by the subject. Final adjustment
settings were recorded by computer, which also randomized the location of the matching field from trial to
trial. Between five and ten matches were obtained from
each subject in each experimental condition.
Under the conditions of the present experiment the
percepts of brightness and lightness are not separable
(Arend & Spehar, 1993a,b) and the term brightness is
employed throughout when discussing the experimental
results.
RESULTS
Mean matching luminance was compared across all
stimuli. Complete sets of point-by-point brightness
matches for the 1, 3 and 6 deg test field height conditions
are illustrated for observers MM and BB in Figs 2-4.
Open symbols refer to brightness matches made to the
test field(s); filled symbols [Fig. 2(g)] are brightness
matches to the inducing grating. The dotted line in each
panel depicts the veridical luminance profile of the
stimulus display along the vertical center of the test field.
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2858
B. B L A K E S L E E and M. E. M c C O U R T
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(e) 6 ° test field height, 6 ° test field width
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FIGURE 4. Complete set of point-by-point brightness matches lor subjects BB and MM for the 6 deg test field height condition.
See Fig. 2 for details.
Note that although the magnitude of GI decreases with
increasing test field height (McCourt, 1982; Foley &
McCourt, 1985), it is still clearly evident even in the
6 deg test field height condition. Similarly, brightness
induction in SBC stimuli also decreases with increasing
test field height and width (Yund & Armington, 1975). It
is also of interest that both subjects show consistent
undermatching to the inducing grating [see Fig. 2(g)].
Mean matching luminance values obtained from the
point-by-point brightness matching procedure were
analyzed to extract and quantify two key items of
information: (1) Are changes in test field height and
width accompanied by systematic alterations in the
structure of the brightness variations within the test
fields?; and (2) Do these changes cause systematic
alterations in the average magnitude of brightness or
darkness induction within the test fields?
The mean luminance matches of each observer in the
G! condition (32 deg test field width) were fit using a
nonlinear regression procedure (method of least-squares)
to a sinusoidal function of the form:
LM(C~, 6,x)
----
-~[sin(x) + 6]
(1)
where the parameters c~ and & refer to the amplitude and
SBC AND GI
0.9
I
I
BB
I
•"!
2859
I
[
I
I
6 ° test field height
3 ° test field width
:',,.
0.8
\
i
E
-i
0.7
/
i
/
X
/
E
0.6
inducing grating I
urn nanca prof e I
V
/
._E
c-
\
",,
"
/
i
\
32 ° test field: be6t fit to
prediction)
( Eq.
G I1
(brightness)
nduction I
additional
O
t~
2
v
O
o
e"
incluction
0.5
/
e'-
E
._J
0,4
--
additional (darkness)
ee--
nduction
\
]
/
/
best fit to Eq. 2 J
N
0.3
A
!
i
/
/
!
0.2
/
i/
0.1
0
I
I
I
I
I
I
I
128
256
384
512
640
768
896
1024
Match Position (pixels)
FIGURE 5. Illustration of the data analysis used to extract changes in the magnitude of induction which might accompany
variations in test field width. The area between the veridical luminance distribution and the grating induction prediction [Eq. (l)]
was numerically integrated for each observer. This area is illustrated by the bold hatched region. For each test field width the
area between the grating induction prediction and the fit to the four-parameter function for that test field width [Eq. (2)] was also
numerically integrated. The ratio of these two areas provides a comprehensive index of the average change in induction
magnitude as a function of changing test field width.
offset of the matching function, respectively, and x
refers to the spatial position of the brightness match.
This optimized function is depicted by the solid line in
Fig. 5 which illustrates the analysis, and by the solid lines
in Figs 2(a), 3(a) and 4(a). The optimal parameter values
obtained from the 32 deg test field (GI) condition are
referred to as the "grating induction prediction". These
parameter values are indicated in the legends of Figs 2(a),
3(a) and 4(a), and were used as a baseline to compare
induction structure and magnitude in conditions where
test field width was varied. To quantify changes in the
structure of induction that occur with decreasing test field
width, mean luminance matches in the 14, 12, 8, 6 and
3 deg test field conditions were modeled using a fourparameter version of Eq. (1):
L M ( a d , O~b, tSd, tSb,X) ---- --
ad[sin(x) +
6d],X <_ 7r radians
- ab[sin(x) + 6b],X > 7rradians
(2)
Eq. (2) permits independent amplitude variations
within the dark and bright test fields. Parameters ~d and
ab refer to the amplitudes of the best-fitting sinewave
functions to the mean luminance match values in the dark
and bright half-cycles, respectively. Parameter x refers to
the spatial position of the brightness match. Parameters
~d and ~b permit compensatory offset changes which
accommodate magnitude changes produced by variations
in parameters 0~d and ~b. The best-fitting functions (solid
lines) obtained for each stimulus configuration are
2860
B. BLAKESLEE and M. E. McCOURT
1 o Test Field Height
.25 ~
i ....
150
q ~ - ~
I ....
3 o Test Field Height
'
.....
~~
'
- ~7
25
~!
BB
i
? '~T
~-~
b ....
150
I '
-.25
i
~' -.so ~
I
'~
~++-,- . . . . I . . . . ,,!
!
.25~
MM 1
=E ~_
--a ~, o ~
~-,,,_ __~
":,--~
~g
::
MM .
q)
==E
MM-
"Fo
MM 1
100
o~
v13
L,_
-~
o
rj
ii/
ot
-50
b
~
[ i i i iJ
0
5
10
15
0
.....
5
: .
iO
s ~ [ t
c~
15
5
10
indicated in Figs 2 ( b - g ) , 3(b-g) and 4(b-g). Note that if
the brightness variation within a test field is unchanged
from the grating induction prediction, then the values of
parameters ~d and :~b will equal ~. If the brightness
variations are "flattened" (i.e., are more squarewavc than
sinewave), however, then the values of ~d and cq~ will
approach zero. Finally, if the brightness variations within
the test fields are opposite in spatial phase to those
observed in the 32 deg wide grating induction test fields
(i.e., if a reverse phase "cusping" occurs, such as in a
missing-fundamental squarewave stimulus), such "cusping" will be indexed by negative values of parameters ~,t
and XbFigures 6(left), 7(left) and 8(left) summarize the
amplitude data. The structure o f both brightness and
darkness induction is generally well-accounted for by the
GI predictions (horizontal dotted line) for test field
widths of 14, 12 and 8 deg at all three test field heights.
For test fields narrower than 8 deg in width, however, the
tendency was for the amplitude parameters (~d and ~b) to
decrease and eventually assume negative values. This
appears in the matching data as a flattening of the
sinewave structure in the test fields [see Figs 2(e), 3(e)
and 4(e)] followed by a reverse cusping [see Figs 2(1),
3(f) and 4(f)]. The 1 deg test field width condition was
excluded from the amplitude analysis because the
number of brightness matches (sampling rate) within
0
15
5
10
15
Test Field Width (deg)
Test Field Width (deg)
FIGURE 6. Sununary of the matching data for ~,ubiccts BP, alid MM
obtained lor the I deg test field height conditions nsing lhc best-fitting
amplitude paraineter and the index of reduction magnitude. The lell
panels plot fitted sinewaxe amplitudes as a function of test field x~idth
lot brightness induction (open symbols) and darkness induction tlilled
symbols). The dotted line represents the amplitude of the GI
prediction. A decrease in the amplitude o1 the smewave l:rom the GI
prediction indicates a flattening of the structure of the induction.
Negative amplitudes indicate a reverse cusping ill the structure of the
induction relative to the GI prediction. The right panels summarize the
matching data with respect to induction magnitude hy plotting mean
matching luminance (the % change l:rom the GI predictiont a~, a
function of test field width.
i
//
-25 ~
g
-.50
l
J'E~
i
25 ;
o
I '/
"5
:5
~_ -25 k
0...
E
"~,:1; -50
i ~='
100 ~
/ . . . . .~. . . . . . . . . . . . . .
r
~.
i ....
BB
J
0'{--I
100 i
....
BB
t'IG[;RE 7. Summary o1 the matching data obtained for the 3 deg tesi
field height. See Fig. 6 fl)r details:.
this lest field size was insufficient to assess structure in
any meaningful way.
In order to index changes in the magnitude of induction
which might accompany variations in test field width, the
area between veridical matching (i.e., mean luminance)
and the grating induction prediction [Eq. (1)] was
numerically integrated for each observer at each test
field height. This area is illustrated by the bold hatched
region in Fig. 5. For each test field width the area between
the grating induction prediction and the optimal fit to the
four-parameter function for that test field width [Eq. (2)]
was also numerically integrated. The ratio of these two
areas provides a comprehensive index of the average
change in induction magnitude as a function of changing
6 o Test Field Height
150
251
BB -
oi
........................ 2
....
i ....
i ....
i
....
i ....
i ....
i
....
I,IIii
10
100
8g
~
<E
g
so
-.25 i
•J ' ~
25
0
MM"
~
"
0
..c: ,,-,
N®
Zi =~1oo
:~o~
° 50
LL
-.25
-.50
i i i i [ I t i i I i i r i I
5
10
,,,i
15
5
15
Test Field Width (deg)
FIGURE 8. Summary of the matching data obtained for the 6 deg test
field height. See Fig. 6 for details.
SBC AND GI
test field width. Although excluded from the amplitude
analysis, the 1 deg test field condition was included in the
induction magnitude analysis by setting the values of
parameters ~a and ~b equal to 0 (i.e., by assuming a flat
brightness profile across the test field). Hence, for this
condition the values of parameters 60 and fib alone index
induction magnitude.
With respect to induction magnitude, Figs 6(right),
7(right) and 8(right) reveal that both subjects displayed a
relative increase in both brightness and darkness induction with decreasing test field width. There was, in
addition, a tendency for this relative increase in induction
magnitude to be greater, and to begin at increasingly
larger test field widths as test field height increased. Note
that GI magnitude decreases with increasing test field
height and that the increases in induction magnitude with
decreasing test field width are relative to the GI
prediction for that particular test field height. It is
interesting that whereas for one subject the relative
magnitude of brightness induction exceeded that of
darkness induction, the opposite pattem was obtained
for the second subject. This asymmetry is also obvious in
the point-by-point brightness matching data of these
subjects [see Figs 2-4]. These differences suggest that the
relative gain of the "on" and "off" pathways in individual
observers may differ in subtle, but perhaps meaningful
ways. Further consideration of these intriguing differences is, however, beyond the scope of the present paper.
DISCUSSION
The mechanisms of induction
As discussed earlier, a homogeneous fill-in mechanism
does not predict GI. In addition, the point-by-point
matching data from the present study reveal no
discontinuities in either the structure or magnitude of
induction as the test field is transformed from the GI
configuration (32 deg continuous test field) in which the
mean perimeter luminance is equal to the mean, to the
elongated but separate test fields (14 and 12 deg) in
which mean perimeter luminance is substantially different for the two test fields situated on the bright and dark
phases of the inducing grating. Clearly, a homogeneous
fill-in mechanism cannot predict either the observed
induction structure or the lack of a change in induction
magnitude from the GI prediction in the elongated, but
separate, test fields [see Figs 2(b, c), 3(b, c) and 4(b, c)].
These data are consistent, however, with the hypothesis
that a single mechanism (which is not a homogeneous
fill-in mechanism) underlies brightness induction in these
elongated test field stimuli.
Consider next the change from the GI prediction in
both structure (flattening) and magnitude (increase) that
occurs with further decreases in test field width. Figure 9
indexes induction magnitude by plotting mean matching
luminance (as a percent change from the GI prediction) as
a function of mean test field perimeter luminance. It is
clear for both darkness (filled symbols) and brightness
(open symbols) induction that a large change in mean test
2861
150
i
. . . .
i
. . . .
,
BB
,00
50
"8
150
t-
"~
100
...1
50
0
0.25
0.50
0.75
M e a n T e s t Field P e r i m e t e r L u m i n a n c e
(% m a x i m u m )
FIGURE 9. Mean matching luminance (the % change from the GI
prediction) is plotted as a function of mean test field perimeter
luminance for subjects BB and MM at three test field heights: 1 deg
(circles), 3 deg (triangles) and 6 deg (squares). It is clear for both
darkness (filledsymbols)and brightness(open symbols)inductionthat
a large change in mean test field perimeter luminance occurs before
there is any correspondingshift in mean matchingluminancefrom the
GI prediction. Note that the curves representing the three test field
height conditionsare not congruent.
field perimeter luminance occurs before there is any
corresponding shift in mean matching luminance from
the GI prediction. If a fill-in mechanism dependent on
mean perimeter luminance is responsible for these
systematic changes in induction magnitude as test field
width decreases, it would have to possess a high contrast
threshold (and/or a strongly accelerating continuous
response nonlinearity), since a substantial change
( _ 25%) in mean perimeter luminance is required before
induction magnitude departs significantly from the GI
prediction. This is inconsistent with results which
indicate that the border contrast-dependent fill-in mechanism responsible for the missing-fundamental illusion
possesses a low contrast threshold (Burr, 1987), and that
induced brightness in the missing-fundamental squarewave illusion increases only for border contrasts up to
0.02, and actually declines with increasing contrast. A
further difficulty for a fill-in explanation based solely on
mean perimeter luminance is that the curves representing
the three test field height conditions are not congruent
(Fig. 9). Thus, to account for the differences in perceived
brightness which are associated with regions possessing
identical mean perimeter luminance, the putative homogeneous fill-in mechanism must assign brightness based
2862
B. BLAKESLEE and M. E. McCOURT
not only on mean perimeter luminance, but also on the
geometry of the enclosed region. Even if such a
homogeneous high-threshold fill-in mechanism could
explain the increased magnitude of induction and the
decreased amplitude (i.e., the "flattening") of induction
structure at intermediate test field widths, it still cannot
account for the reverse phase "cusping" observed at the
narrower test field widths. Indeed, such "cusping" has
almost universally been attributed to an edge or border
contrast mechanism whose response decreases in strength
with distance from the edge as, for example, in Mach or
Hering inhibition (Fiorentini et al., 1990). In summary, a
possible, albeit cumbersome, account for the observed
changes in the structure and magnitude of brightness
induction as a function of test field height and width
might include three mechanisms: (1) a GI mechanism
(that is not a homogeneous fill-in mechanism) which
accounts for patterned induction in the elongated test
fields; (2) a homogeneous high-threshold fill-in mechanism which accounts for both the progressive flattening of
the structure and the increasing magnitude of induction
that begins at intermediate test field widths; and (3) an
edge or border contrast mechanism that accounts for the
"cusping" seen at the narrower test field widths.
A multiscale filtering explanation oJ" GI and SBC
Perhaps a simpler and more plausible idea is that a
mechanism dependent on the distribution of luminance
over a broader area, not simply perimeter or border
luminance, determines brightness induction. This hypothesis is consistent with the large number of studies
which have indicated that regions removed from the test
field edge play a significant role in both SBC (Heinemann, 1972; Arend et al., 1971 ; Land & McCann, 1971 :
Shapley & Reid, 1985; Reid & Shapley, 1988) and GI
(Foley & McCourt, 1985; Zaidi, 1989; Moulden &
Kingdom, 1991; McCourt & Blakeslee, 1993). The
convolution of a GI stimulus with a suitably chosen
DOG weighting function will produce opposite-phase
induced gratings. However, no single concentric weighting function produces counterphase induction across the
combination of test field heights and inducing spatial
frequencies for which it is observed (Foley & McCourt,
1985). Moulden & Kingdom (1991) suggested that a
multiscale array of DOG filters could, however, explain
many aspects of GI, including the discriminability of the
inducing and induced stripes, and the rapid fall-off of
induced grating amplitude with increasing inducing
grating spatial frequency (McCourt, 1982) and test field
height (McCourt, 1982; Foley & McCourt, 1985).
We revisit these ideas by posing the question: How
accurately can the pooled output of DOG filters across
multiple spatial scales account for the brightness
matching data of the present experiment? To answer this
question we selected an array of seven isotropic twodimensional DOG filters whose center frequencies were
arranged at octave intervals (see Table 1). The ratio of
center-surround space constants was 1:2, producing
filters whose spatial frequency bandwidth (lull-width at
TABLE 1. Difference of gaussian space constants
Space constant (deg)
Mechanism
Center
Surround
1
2
3
4
5
6
7
0.047
0.094
0.188
0.375
0.75
1.5
3
0.093
0.188
0.375
0.75
1.5
3
6
Moulden & Kingdom ( 1991 )
1
2
3
4
0.033
0.065
0.130
0.262
0.052
0.104
0,208
0.419
half-height) was 1.9 octaves. Center-surround volumes
were equal, such that the response of each DOG to a
homogeneous field was zero. The particular filters
employed were chosen by first setting the center size
(zero-crossing to zero-crossing) of one of the filters of the
array to 3deg, thus matching the height of the
intermediate test field (mechanism 5 of Table 1). Four
additional filters (also arranged at octave intervals--two
above and two below the 3 deg filter) were added to the
array to ensure that the ensemble as a whole captured the
majority of the Fourier energy contained in all of our
stimuli at all test field heights (mechanisms 3, 4, 6 and 7).
Finally, two high frequency filters (mechanisms 1 and 2)
were added such that the array encompassed the high
frequency range typically used in modeling the early
filtering stages of the visual system (Wilson & Bergen,
1979; Watt & Morgan, 1985; Moulden & Kingdom,
1991: Kingdom & Moulden, 1992). The spatial parameters of our mechanisms, as well as those used in
Moulden and Kingdom's (1991) model of grating
induction, appear in Table 1. Note that the present filter
10
---~
----
5
~:
¢:~
slope
slope
slope
slope
3
=
=
=
=
1.0
0.5
0.25
0.1
J
/
j /
U-
>
•.~
~ 0.5
~
~
/..J
~ 0.3
/
/
0.1
0.1
0.3 0.5
1
3
5
10
DOG Center Frequency (cpd)
FIGURE 10. Potential weighting functions for combining filter outputs
are illustrated by the power functions describing log filter weight as a
function of log center frequency. A slope of 1.0 corresponds to the lowfrequency fall-off of the human contrast sensitivity function at
threshold (Campbell & Robson, 1969). Successively shallower slopes
approximate the reduced low-frequency fall-off at suprathreshold
contrast levels, as determined by contrast matching (Georgeson &
Sullivan, 1975).
SBC AND GI
2863
1 degree test field height
i
75
i
i
3 degree test field height
i
•
l
i
'
75
-
14o
50
50
25
25
0
0
-25
-25
-50
-5O
-75
(a)
i
75
I
i
i
t
h
i
i
(b)
i
I
'
I
i
I
i
i
-75
I
I
i
~.
I
I
I
3~
i
0 ,
'
.
(b)
l
l
l
l
i
75
i
14"
(a)
i
i
l
,
l
l
i
'
I
i
8"
5O
5O
25
25
0
0
-25
"4
~-~
~
-75
~
75
(c)
[.."'
(d)
i
i
i
6o
7".
•"
o Z
~_5o
~
-25
~
-75
~
75
-50
ID
I~ 25
~5o
~: 2s
0
o
-25
-25
-50
-75
i
(a)
I
I
I
I
,
I
,
I
,
I
,
o
I
,
256
I
512
i
I
768
-75
t
'
'
'
I°
50
25
25
0
0
-25
-25
-5O
': ~i
g
,
256
..'/
, "...i,!........
512
768
I
i
I
'6o
'
Spatial Position (pixels)
FIGURE 11. A slice through the summed convolution output of the
weighted filter array (combined with a weighting slope of 0.1) for each
of the test field widths in the 1 deg test field height condition. The
dotted line depicts the veridical luminance profile of the stimulus
display taken at the vertical center of the test field. The solid line is the
summed convolution output along this same line.
array extends to much lower spatial frequencies (by over
an order of magnitude) than those used by Moulden &
Kingdom (1991), who were modeling GI stimuli with
both smaller test field heights (ranging between 0.2 and
1.6 deg), and higher spatial frequency inducing gratings
(between 0.1 and 1.6 c/d). It should be noted that the
particular filter center frequencies we have selected are
not critical: any octave-interval (or denser) array of filters
which spans a comparable range of frequency will
produce essentially identical pooled responses.
How should the outputs of the different filters in the
array be summed? A number of potential weighting
functions are illustrated by the power functions depicted
in Fig. 10, where log filter weight is plotted as a function
of log center frequency. A weighting slope of 1.0
corresponds to the linear low-frequency fall-off of the
,
;
'
i
'
.
3°
_.....
•i
(e)
i/
i
o
•
.1.
'
i
I
i
256
I
512
A
I
768
;
1024
'
./" i "".
1°-
-50
-75
1024
I
..."i ?..
1024
75
'/i'i'.,'
i
I
-50
(o)
75
-75
(c)
,
,
256
i......Jl......512
768
10~4
Spatial Position (pixels)
FIGURE 12. A slice through the summed convolution output of the
weighted filter array (combined with a weighting slope = 0.1) for each
of the test field widths in the 3 deg test field height condition. See Fig.
11 for details.
human threshold contrast sensitivity function (Campbell
& Robson, 1968; Laming, 1991). Successively shallower
slopes approximate the reduced low-frequency fall-off in
sensitivity observed at suprathreshold contrast levels, as
determined by contrast matching (Georgeson & Sullivan,
1975). A comparison of the convolutions of filter arrays
combined with weights ranging between 0 and 1.0 with
the point-by-point brightness matching data of Figs 2-4
revealed that a weighting slope of 0.1 was optimal. This
slope is quite consistent with the shallow low-frequency
fall-off of the suprathreshold CSF, which is expected to
be associated with our high suprathreshold contrast
stimulus (0.75 contrast inducing grating, 0.00 contrast
test field).
Figures 11-13 illustrate the summed output of the
weighted filter array when convolved with the inducing
stimuli. These profiles are taken along a line correspond-
2864
B. BLAKESLEEand M. E. McCOURT
6 degree test field height
75
i
i
i
'
_
I
I
I
'
•
14"
32*
50
25
0
-25
-50
(b)
(a)
-75
i
75
i
i
' _
12"
i
i
J
'
8. -
50
25
0
-'.t
-25
o
~
-75
LL
75
(C),
i
i
.-> 50
•
rr
i
,~
,
(d)i ,
i
E
i
,
,
I
512
L
768
,
..
6 °
t
25
0
-25
-50
".,?
-75
I
75
'
I.
I
'
J
i
~
........
(,)
7
,
J
I
256
~
1024
'
," ii -.
1°
50
25
0
-25
-50
........ ....
(g)
-75
I
0
256
I
512
i
":[ "
768
i
1024
Spatial Position (pixels)
FIGURE 13. A slice throughthe summedconvolutionoutput of the
weightedfilterarray(combinedwith a weightingslope= 0.1) for each
of the test fieldwidthsin the 6 deg test fieldheightcondition.See Fig.
11 for details.
ing to the vertical center of the test field. A comparison of
these convolutions with the matching data of Figs 2-4
clearly indicates that multiscale, weighted linear filtering
captures all of the essential features of the matching data,
in terms of both structure and magnitude, Notice that the
predicted overall magnitude of induction decreases with
increasing test field height, however, within each test
field height the magnitude of induction increases with
decreasing test field width. The filtering operation also
captures the flattening and reverse cusping of the
sinewave structure in the test fields that occurs with
decreasing test field width, and the test field widths at
which these structural changes occur. It is particularly
noteworthy that the linear weighted combination of filter
outputs simultaneously captures the undermatching to the
inducing grating.
Applying the multiscale filtering explanation to other
brightness phenomena
In order to test the generality of this simple filtering
explanation we convolved this same filter set (using the
identical weighting function) with the GI demonstrations
of Zaidi (1989). Although intriguing, these observations
have never been adequately explained. In one demonstration Zaidi (1989) showed that the orientation of induced
gratings depended, not on the orientation of the inducing
grating, but on the relative phase of the upper and lower
inducing gratings. In the standard grating induction
stimulus the upper and lower inducing gratings are in
phase and the induced grating is a counterphase grating of
the same orientation as the inducing grating [see Fig.
l(a)]. Zaidi (1989) found, however, that when the phase
of the upper and lower gratings was slightly offset, the
test field appeared to contain a tilted induced grating. The
most pronounced orientation change occurred for upper
and lower inducing gratings whose phase was offset by
90 deg [left panel of Fig. 14(a)]. When inducing gratings
were offset by 180 deg the test field appeared to contain
light and dark meniscuses, but no cohesive grating was
perceived [left panel of Fig. 14(b)]. The right-hand panels
of Fig. 14(a, b) are 3D mesh plots which show (in
magnified view) the weighted test field output of the filter
array following convolution with these stimuli. It is clear
that the filter array produces an output which closely
resembles the appearance of these two test fields.
In a second demonstration Zaidi (1989) showed that if
the orientation and phase of four different spatial
frequency inducing gratings were adjusted such that the
horizontal spatial frequency at the test fieJd edges was
identical in all conditions, the gratings induced in the
homogeneous test field were vertically oriented and
possessed the same spatial frequency. Zaidi (1989)
concluded that whereas the orientation and spatial
frequency of the induced grating appeared to be governed
by the proximal cues, GI magnitude depended on distal
portions of the inducing grating as well, since the
amplitude of induction increased markedly with increasing inducing grating elevation (i.e., as the orientation of
the inducing grating became perpendicular to the test
field). The left-hand panels of Fig. 15(a, b) illustrate
examples of these stimuli for two inducing grating
orientations (90 and 45 deg elevations, respectively). The
right-hand panels again show 3D mesh plots which
illustrate (in magnified view) the weighted test field
output of the filter array following convolution with these
stimuli. The output of this array of filters closely
resembles the appearance of the test fields. Figure 16
plots the output of the weighted filter array (as relative
test field contrast) as a function of inducing grating
elevation. The systematic decrease in induction magnitude with decreasing inducing grating elevation produced
by the linear array is strikingly similar to the data of Zaidi
(1989).
To further test the generality of the weighted filter
explanation we convolved the array with a stimulus
similar to that used by Shapley & Reid (1985) and Reid &
SBC AND GI
2865
(a)
1
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(b)
• ............... -J -5o
1
\
X Position
1o24
-'-"-'
FIGURE 14. Zaidi's (1989) grating induction demonstration showing that (a, left panel) when the phase of the upper and lower
inducing gratings is offset by 90 deg the test field appears to contain a tilted induced grating and (b, left panel) when the inducing
gratings are offset by 180 deg the test field appears to consist of light and dark meniscuses, but no cohesive grating is perceived.
The right-hand panels of (a) and (b) are 3D mesh plots which show (in magnified view) the weighted output of the filter array
(weighting slope = 0.1) following convolution with the stimuli shown in the respective left-hand panels. It is clear that the filter
array produces an output which closely resembles the appearance of the induced brightness in the two test fields.
Shapley (1988) to demonstrate the existence o f brightness contrast and "assimilation". Assimilation is interpreted and modeled by these investigators as the
summation of local contrasts across space. The left-hand
panel of Fig, 17 presents a version o f the stimulus used by
Shapley & Reid (1985). The right-hand panel contains
the luminance profile o f this stimulus (dotted line), along
the vertical center o f the test fields. The solid line
represents a slice o f the weighted filter convolution
output at the same location. The filter array produces
output which accords with the appearance of both the
equiluminant central test fields and the equiluminant
surrounds.
Finally, the same weighted filter array also produces
output which agrees with the appearance of the Hermann
Grid stimulus across a variety of spatial scales. Figure 18
shows one o f the stimulus configurations examined and a
mesh plot o f the weighted array output at one of the grid
2866
B. BLAKESLEE and M. E. McCOURT
(a)
1
(b)
1
\
"~ Position
1024
v ~
FIGURE 15. Two stimuli (left-hand panels a, b) like those used by Zaidi (1989) demonstrating that the orientation and spatial
frequency of the induced grating appear to be governed by proximal cues. The spatial frequency of the gratings in (a) and (b) are
different but their orientation and phase have been adjusted such that the horizontal spatial frequency at the test field edges is
identical in both conditions. The gratings induced in the homogeneous test fields are vertically oriented and possess the same spatial
frequency. The right-hand panels of (a) and (b) are 3D mesh plots of the weighted array output (weighting slope = 0.1) following
convolution with the stimuli shown in the respective left-hand panels. The output of weighted filter array closely resembles the
appearance of the induced brightness in the test fields.
intersections. The filter array produces localized output
minima at the same locations where h u m a n observers see
dark spots at the intersections of the "streets" o f the grid.
In the interests o f brevity (and because the linear
filtering results appear to account so well for our
observations) we have not attempted in this paper to
refine the multiscale filter array explanation by attaching
plausible response nonlinearities (such as a sigmoidal
contrast transduction stage) to the filter outputs, or to
explore nonlinear combination rules (such as Minkowski
pooling) with regard to pooling filter outputs. Such
extensions o f the present explanation can, however, if
merely by virtue o f the greater n u m b e r o f degrees o f
freedom these added stages afford, only enhance the
explanatory p o w e r o f this general approach. W e should
note, however, that such response nonlinearities will be
required to explain other salient intensive aspects o f
brightness induction, such as the saturation o f induced
SBC AND GI
encompassing salient features of induction in SBC,
brightness assimilation and Hermann Grid stimuli. Since
most brightness models (indeed, most models of spatial
vision) incorporate spatial filtering at an early stage to
extract information about luminance changes, it seems
useful to categorize brightness phenomena according to
which can or cannot be accounted for by multiscale
filtering. For example, our multiscale filtering explanation cannot account for effects like the Craik-O'BrienCornsweet illusion or the appearance of the missingfundamental squarewave at low contrasts. These types of
brightness effects may indeed depend on a low-threshold
border-dependent brightness fill-in mechanism such as
that discussed by Burr (1987), or on more complex fill-in
mechanisms or brightness assignment rules such as those
incorporated in a number of other models (Grossberg &
Todorovic, 1988; Kingdom & Moulden, 1992; Heinemann & Chase, 1995; Pessoa et al., 1995).
Some brightness models exist which incorporate nonhomogeneous fill-in mechanisms (Grossberg & Mingolla, 1987; Pessoa et al., 1995). These models are based on
the boundary contour system/feature contour system first
proposed by Cohen & Grossberg (1984) and later
elaborated by Grossberg and Mingolla (Grossberg &
Mingolla, 1985, 1987). In these models, as in homogeneous fill-in models, boundary signals are used to
generate fill-in compartments within which brightness is
diffused or spread such that, at equilibrium, the diffused
activities correspond to perceived brightness. The most
recent versions of these models, however, have been
modified such that the boundary signals may be
generated either by luminance "edges" or by continuous
luminance gradients. In the latter case, luminance
1.0
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0.8
i.r.~ o.6
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.~
N
o.4
0.2
I
I
I
I
I
I
I
30
40
50
60
70
80
90
Inducing
2867
Grating Elevation (deg)
FIGURE 16. The output of the weighted filter array (weighting
slope = 0.1) predicts the systematic decrease in induction magnitude
which Zaidi (1989) reported occurred with decreasing inducing grating
elevation. The stimuli were produced like those previously described
and depicted in the left-hand panels of Fig. 15(a) 90 deg elevation and
Fig. 15(b) 45 deg elevation, but included two additional stimuli with
elevations of 30 and 60 deg.
contrast with increasing inducing grating contrast, the
nonlinear relationship between matching contrast and test
field contrast in GI displays (McCourt & Blakeslee,
1994), and the "crispening effect" (Whittle, 1992).
Utility of a multiscale filtering explanation
It would appear that a multiscale array of twodimensional DOG filters whose outputs are weighted in
accord with suprathreshold contrast sensitivity provides a
powerful heuristic towards explaining a number of
seemingly complex features of GI, while simultaneously
0.6
/
0.4
23
0
LL
0.2
I
e~
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I
p
i
b
0.0
>
-0.2
¢D
n."
-0.4
q
,
:° °
-0.6
0
I
I
I
256
512
768
Spatial Position (pixels)
FIGURE 17. A version of the stimulus used by Shapley & Reid (1985) to demonstrate brightness contrast and "assimilation"
(left-hand panel). In the fight-hand panel the luminance profile of this stimulus taken at the vertical center of the test fields is
depicted by the dotted line. The solid line represents a slice (taken at the same location) of the output of the weighted filter array
(weighting slope = 0.1) following convolution with this stimulus. It is clear that the output of the weighted filter array predicts
the appearance of both the equlluminant central test fields and the equiluminant surrounds.
1024
2868
B. BLAKESLEE and M. E. McCOURT
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/ i l l l l l i
/:
n
:
i l U l l l i l
ii
4O
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i
c~
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v
X Positron
FIGURE 18. This example of the Hermann Grid stimulus (left-hand panel) was conw)lved with the weighted filter array
(weighting slope = 0.1 ). The right-hand panel shows a mesh plot of the weighted filter array output at one of the intersections.
The filter array produces localized output minima at the same locations where human observers see dark spots at the
intersections of the "streets" of the grid.
gradients produce "boundary webs" which may partially
or totally arrest diffusion within specified regions, thus
allowing fill-in to account for gradual changes in
brightness across space (Grossberg & Mingolla, 1987:
Pessoa et al., 1995). Interestingly, while in regions of
zero boundary activity brightness is free to diffuse (as in
the original homogeneous fill-in models), diffusion is
inhibited in regions where boundary web signals are
dense, and the predicted brightness distribution reverts to
that produced by the outputs of the initial filtering
operations (Pessoa et al., 1995). While it is possible that
these more complex models may also account for
brightness induction in the present study, it is clear that
understanding these effects does not require an explanation beyond multiscale spatial filtering.
Physiological plausibility
Although center-surround filtering is one of the oldest
and most frequently invoked mechanisms used to explain
induction effects (Kingdom et al., 1997: for review see
Fiorentini et al., 1990) it is often dismissed as an
explanation for long-range effects such as SBC [and
Shapley and Reid's (1985) demonstration of assimilation] because physiological evidence has indicated that
retinal and/or LGN receptive fields are [oo small to
account for the distances over which these brightness
effects occur (Shapley & Enroth-Cugell, 1984: Cornsweet & Teller, 1965; Reid & Shapley, 1988; Grossberg
& Todorovic, 1988; Rossi & Paradiso, 1996; Paradiso
& Hahn, 1996; for reviews see Kingdom & Moulden,
1988; Fiorentini et al., 1990). While the receptive fields
corresponding to the largest DOG filters used in this
study do not appear to exist at the level of the retina, it
may be premature to altogether reject the notion that such
filters might exist at those levels of the nervous system
where brightness percepts are determined. Recent
evidence in fact suggests that a significant number of
cells in cat primary visual cortex respond in a manner
correlated with perceived brightness, and that they do so
over distances far exceeding the size of their "classical"
receptive fields mapped using conventional techniques
(Rossi et al., 1996). This was demonstrated using a
dynamic version of brightness induction in which a
central gray test patch was flanked by a surround whose
luminance was temporally modulated. In human observers this stimulus gives rise to a strong brightness
modulation of the test patch (DeValois et al., 1986). Even
under conditions in which the central test patch extended
3 deg or more to either side of the "classical" receptive
field borders, inclusive of any end-stopping regions, such
that the receptive field of the cortical cell fell entirely
within the homogeneous test field, the cell's output
correlated with test patch brightness (as opposed to
luminance). Interestingly, these are precisely the conditions under which it has long been assumed that a cell
would not respond to a SBC stimulus and which
necessitated the proposal of explanatory mechanisms
such as border-dependent brightness fill-in over large
regions. The results of Rossi et al. (1996) suggest that
brightness may be synthesized at an early stage in the
striate cortex, and that extensive "silent surrounds" may
contribute to brightness processing. Importantly, the
authors note that these neurons should not be regarded as
"brightness detectors" p e r se, but rather as multiplexing
brightness information alor,g with o~her stimulus attributes such as orientation and spatial frequency. Recent
SBC AND GI
evidence from primate anatomy and physiology also
indicates that at the earliest cortical levels (V1) the
substrate exists for providing cells with input from
relatively large regions of the visual field, and that the
response properties of cells are modulated by stimuli
lying far outside the "classical" receptive field (Gilbert et
al., 1996). Thus, it appears that heretofore unappreciated
lateral interactions in early visual processing may provide
an order-of-magnitude-larger area of visual integration
than that revealed by the "classical" receptive field,
making the inclusion of large filters in a multiscale array
less implausible than previously believed.
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Acknowledgements--Supported by grants from NSF to B. Blakeslee
(IBN-9306776 and IBN-9514201) and by grants from NIH (EY1013301) to M. McCourt and B. Blakeslee and AFOSR (F49620-94-10445).