Subthreshold summation with illusory contours

Abstract

Results from three experiments using spatial forced-choice techniques show that an illusory contour improves the detectability of a spatially superimposed, thin subthreshold line of either contrast polarity. Furthermore, the subthreshold line is found to enhance the visibility of the illusory contour. Stimuli which do not induce illusory contours, but reduce uncertainty about the spatial position of the line, give rise to a slight detection facilitation, but the threshold of 75% correct responses is not attained. The data indicate that superimposing illusory contours and subthreshold lines produces interactions which are similar to classic subthreshold summation. They thus provide psychophysical evidence for the functional equivalence of illusory contours and real lines suggested by recent neurophysiological findings.

Full text

Pergamon 0042-6989(94)00204-5
Vision Res. Vol.
35, No. 8, 1071-1078, 1995
pp.
Copyright 0 1995 Elsevier Science Ltd
Printed in Great Britain. All rights reserved
0042-6989/95 $9.50 + 0.00
Research Note
Subthreshold Summation with Illusory Contours
BIRGITTA DRESP,* CLAUDE BONNET*
Received 17 March 1994; in revised form 10 August 1994
Results from three experiments using spatial forced-choice techniques show that an illusory contour
improves the detectability of a spatially superimposed, thin suhthreshold line of either contrast
polarity. Furthermore, the subthreshold line is found to enhance the visibility of the illusory contour.
Stimuli which do not induce illusory contours, but reduce uncertainty about the spatial position of the
line, give rise to a slight detection facilitation, but the threshold of 75% correct responses is not
attained. The data indicate that superimposing illusory contours and subthreshold lines produces
interactions which are similar to classic subthreshold summation. They thus provide psychophysical
evidence for the functional equivalence of illusory contours and real lines suggested by recent
neurophysiological findings.
Contour Illusory contours Threshold Subthreshold summation
INTRODUCTION
Illusory contours are fine apparent lines or edges
which cannot be defined in terms of local variations in
luminance, as shown on the example of the
Kanizsa square (Fig. 1). Recently, an increasing number
of authors have emphasized the possible significance
of these phenomena with regard to adaptive neuro-
physiological processes, and the evidence that neurons in
the visual cortex of the monkey start firing when an
illusory contour is presented within their receptive field
(Peterhans & Von der Heydt, 1989; Von der Heydt &
Peterhans, 1989; Grosof, Shapley & Hawken, 1993)
suggests that these contours are functionally equivalent
to real lines or edges.
Data from psychophysical studies using increment
threshold techniques to measure the detection of small,
non-oriented, light targets presented upon and alongside
illusory contours (Dresp & Bonnet, 1991, 1993), have
suggested that facilitatory neural interactions may be
the key to a deeper understanding of how these illusory
perceptions are generated in the human brain. The most
striking result of these experiments was that the
threshold for the detection of the target was lowered
when the latter was presented on an illusory contour as
defined by the prolongation of the lines of pixels which
constitute the inner borders of two collinear inducing
elements in the Kanizsa figure.
*Laboratoire de Psychophysique Sensorielle L.N.B.C., UPR 419
C.N.R.S., Universitk Louis Pasteur, 12, rue Goethe, 67000
Strasbourg, France.
It appears that the nature of the effects which deter-
mine increment detection facilitation should be investi-
gated further, given that the previous results obtained
in the Kanizsa square strongly suggest that the facilita-
tory effects are a consequence of the mechanism that
underlies illusory contour formation. Some earlier
psychophysical experiments (Kulikowski & King-Smith,
1977) have revealed that the contrast threshold at which
a fine line target is detected by human observers is
reduced when the target is superimposed on an invisible
line of the same orientation. This threshold facilitation
effect has become widely known as “subthreshold sum-
mation”, and is interpreted in terms of additive neural
activity in the visual cortex. Although it is not con-
sciously perceived, the subthreshold line is effectively
processed in the brain by the same neurons as those that
respond to the target line. When both lines are strictly
superimposed, the neural responses to these two stimuli
add together and a lower contrast is needed for a
threshold response.
The assumption of a functional equivalence of real
lines and illusory contours, and the similarity between
line summation effects and the increment threshold
facilitation effects briefly described above suggest that
a subthreshold technique similar to the one used
by
Kulikowski and King-Smith (1972) might provide fur-
ther insight into the functional characteristics of the
mechanisms that generate illusory contour formation.
In the present study, we investigated the spatial inter-
actions that may occur between subthreshold lines and
illusory contours. In fact, if the hypothesis of a func-
tional equivalence of real and illusory lines holds, a
1071

1072 RESEARCH NOTE
FIGURE 1. A Kanizsa square induced by stimulus elements of
opposite contrast polarity. Although there is no physical difference in
luminance between the figure in the centre of the stimulus and the
background, four illusory contours, delineating an apparent square,
are perceived.
subthreshold line should sum with an illusory contour in
a similar way as it does with a real one. We tested both
the effects of a subthreshold line on the strength of an
illusory contour, and the effects of an illusory contour on
the detectability of a subthreshold line.
EXPERIMENT 1
A first question that arises with this approach is the
one of contrast polarity of an illusory contour. Since
such contours cannot be defined physically in terms
of differences in luminance, this issue appears to be
somewhat problematic. The naive observer might say
that white inducing elements should engender a dark
illusory contour, and black inducing elements should
give rise to a light illusory contour, but in fact, as the
example given in Fig. 1 shows, the inducing elements do
not have to share the same contrast polarity to produce
the phenomenon. Is the illusory contour that results
from such a combination of black and white inducing
elements a dark, or a light one?
The observation that illusory contours can arise from
configurations with inducers of alternating pola#y has
been discussed earlier by Prazdny (1983), and it has been
suggested that their genesis must therefore, at some
stage, involve mechanisms that are insensitive to the sign
of contrast (e.g. Grossberg, 1994; Shapley & Gordon,
1987). Neurophysiological data tend to support this
assumption, given that a certain number of the neurons
in V2 of the macaque monkey which responded to
stimuli eliciting the perception of illusory contours
were reported to respond equally well to bars or edges
of either contrast polarity (e.g. Peterhans & Von der
Heydt, 1989).
If the genesis of illusory contours does not depend
on contrast polarity, we predict that the effect of a
subthreshold line of any polairty should sum with the
effect of an illusory line. In a first experiment, we
determined whether a dark subthreshold line would
enhance the visibility of an illusory contour induced by
white stimulus elements.
Subjects
Two observers, both trained in psychophysics Ll
tasks and naive to the purpose of the present study
participated in the experiment. They both had norma il
vision.
Stimuli
The stimuli (see Fig. 2) were presented binocularly on
a monochrome computerscreen (60 Hz, non-interlaced).
They were generated with an IBM compatible PC (HP
486), equipped with a VGA Trident graphic card. The
size of the white inducing elements was 30 min arc, and
their luminance 20 cd/m2. The edges of two collinear
inducers were separated by a gap of 1 deg of visual angle.
Background luminance was 6.7 cd/m*. The subthreshold
line had the same length as the illusory contour upon
which it was added (1 deg of visual angle), and five
different luminance intensities, presented in random
order within an experimental session according to the
method of constant stimuli. The five luminance levels
of the subthreshold line were: 6.7, 6.6, 6.5, 6.4 and
6.3 cd/m2. The illusory contours and the subthreshold
line appeared simultaneously on the screen for about
350 msec at each trial. The inter-stimulus interval was
about 800 msec.
Procedure
The dark subthreshold line was added randomly to
one of two illusory contours presented simultaneously
on the screen (see again Fig. 2), and the observers
had to press one of two response buttons to indicate
whether it was the left, or the right illusory contour that
appeared more visible to them. Each response that
corresponded to the perception of a stronger illusory
contour on the side where the subthreshold line was
FIGURE 2. In the first experiment, we added a dark subthreshold line
to one of two illusory contours induced by white stimulus elements.
The subthreshold line and the figural context were flashed simul-
taneously for a brief duration. Naive observers had to decide whether
the illusory contour was stronger to the right, or to the left of the
fixation mark. In a preliminary experiment we had verified that the
subthreshold line was not detectable when presented out of context.

RESEARCH NOTE 1073
added, was counted as a “correct detection”. The lumi-
nance of the subthreshold line varied randomly within
an experimental session, which consisted of 50 trials.
Each observer went through 10 sessions. In a pre-
liminary experiment, with the same observers, we had
verified that the subthreshold line could not be detected
when it was presented alone.
Results and discussion
The results are shown in Fig. 3(a) (subject CM) and
Fig. 3(b) (subject VF). When the subthreshold line is
presented out of context on a plain background, the
percentage of correct detections, computed for each of
the five lumininance levels, is situated around 50%
(chance level). When the line is presented on an illusory
contour, performance rises, as a function of the intensity
of the subthreshold line, from chance level to 95%
100 - +
(a)
Subject VF
90 -
??
Line alone + /
5 + Line on illusory contour
t: 80- + /
3
6
z 70-
%
a +-+
/
/
.
60- ./=-------¤-.
40 ((I,
-1 0 1 2 3 4 5 6 I
Subthreshold contrast (%)
@I
Subject CM
??
Line alone
80 + Line on illusory contour
2
/
f
::
z
2 70
8
ki
a 60
5o
40
/;I’yy.<‘,
-1 0 1 2 3 4 5 6 7
Subthreshold contrast (%)
FIGURE 3. These figures show percentages of “correct detections” as
a function of the contrast intensity of the subthreshold line, presented
out of context (m), and presented upon an illusory contour ( + ). (a)
Data for VF, (b) data for CM. When the subthreshold line is presented
alone on a plain background, performances do not exceed the chance
level. When it is presented upon an illusory contour, performance rises,
as a function of the intensity of the subthreshold line, from 50%
(chance level) to 82% (subject CM), and 95% (subject VF) “correct
detections”.
correct detections. These data indicate that the presence
of the subthreshold line enhances the visibility of the
illusory contour.
One possible explanation of this finding would be
that the luminance contrast of the inducing elements,
and not the illusory contour, determines the effect. Such
an interpretation is, however, unlikely to hold here.
Luminance contrasts of opposite polarity are known to
trigger suppressive spatial interactions rather than facili-
tation, as demonstrated by results from spatial prob-
ability summation experiments (e.g. Wilson, Phillips,
Rentschler & Hilz, 1979), studies using lateral masking
techniques to investigate the detection of fovea1 Gabor
signals (Polat & Sagi, 1993), or from more recent
work investigating the effects of ‘luminance pedestals’ on
increment detection of small, non-oriented light targets
presented at the ends of lines (Dresp, 1993; Morgan &
Dresp, 1995).
A more likely explanation for the effect observed in
the present experiment is that the subthreshold line adds
some kind of energy to the illusory contour and thus
enhances its visibility. This would imply that the illusory
contour and the subthreshold line are detected by a
common mechanism, and that the latter is insensitive
to contrast polarity. We ran a second experiment to
investigate this issue further.
EXPERIMENT 2
If the mechanism that generates the illusory contour
is insensitive to the polarity of contrast, and if the
subthreshold line adds energy to specifically that mech-
anism, it should be expected that a line of any polarity
would do so, regardless of the contrast sign of the
inducers. In this experiment we presented dark and light
subthreshold lines on illusory contours induced by black
or white stimulus elements. We furthermore investigated
the effect of lineillusory contour length on both the
detectability of the lines and the strength of the illusory
contour.
Subjects
Two trained observers, including the first author,
participated in this experiment. Both had normal, or
corrected-to-normal vision. One subject was naive to
the purpose of the study.
Stimuli
The stimuli were generated with the same display as
described above. The size of the stimulus elements which
induced the illusory contours was maintained. They were
either white (11 cd/m*), or black (4 cd/m’), and presented
in random order to the left or to the right of the fixation
mark (see Fig. 4). The luminance of the gray background
was 6.73 cd/m2. The 12 luminance intensities of the dark
and light subthreshold lines, randomly presented on one
of the two illusory contours, were 6.15, 6.20, 6.26, 6.32,
6.37, 6.43, 7.03, 7.09, 7.15, 7.21, 7.28 and 7.34cd/m2 for
subject IM, and 6.26, 6.32, 6.37, 6.43, 6.49, 6.55, 6.91,
6.97, 7.03, 7.09, 7.15 and 7.21 cd/m2 for subject BD.

1074 RESEARCH NOTE
FIGURE 4. In the second experiment, we randomly presented sub-
threshold lines of either contrast polarity on illusory contours induced
by stimulus elements of either sign. As in the first experiment, the
subthreshold line appeared either on the contour to the left, or on
the contour to the right of the fixation mark.
The length of the lines was identical to the length of the
illusory contours, and varied within an experimental
session. Five parameters, were used: 37.5, 52.5,67.5,82.5
and 97.5 arc min. As in the previous experiment, the
illusory contours and the subthreshold line appeared
simultaneously on the screen for about 350 msec on each
trial. The duration of the inter-stimulus interval was the
same (about 800 msec).
Procedure
The procedure was similar to the one used in the first
experiment. However, this time the observers, neither
of whom had participated in the first study, had
to accomplish different tasks. Subject IM (the naive
observer) was asked to indicate whether the left or the
right illusory contour appeared stronger to her, whereas
subject BD (the first author) had to detect the contour
on which the subthreshold line was presented. In the
control condition, both observers had to detect the
subthreshold line presented on a plain grey background,
and appearing randomly to the left or to the right of the
fixation mark.
Results and discussion
Generally, the results of this experiment show that
presenting a subthreshold line of any contrast polarity
upon an illusory contour induced by stimulus elements
of any contrast polarity both enhances the visibility of
the illusory contour (task of subject IM), and facilitates
the detectability of the line itself (task of subject BD).
The effects of the subthreshold line on both types
of performance, identification and detection, are very
similar.
The data from the contour enhancement task (subject
IM) are represented in Fig. 5(a, b, c). When the sub-
threshold line was presented alone (the control condition
for both the contour enhancement task, and the detec-
tion task), both subjects accomplished, in fact, a detec-
tion task. The data of subject IM show that, in the
90 - Subject IM
x Dark line alone
# White inducers
t 80 - 0 Black inducers
iY
E
o 70 -
6
d
2
a 60 - x
40
1 I I I I I I I
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
D Lum (cdlm*)
(b)
Subject IM
Dark line alone
White inducers
Black inducers
40
1 I I I I I I I
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
D
Lum
(cdlm*)
100 -
x
90- 0
80 -
50 -
40
’ I I
I I
I
37.5 52.5 67.5 82.5 97.5
Length of subthreshold line (arc min)
FIGURE 5. The results of subject IM, who had to decide on illusory
contour strength, in the second experiment. (b,c) The percentage
of “correct responses” is plotted as a function of the differ-
ence in luminance between the subthreshold line and the back-
ground in the different experimental conditions. (c) Percentages
of “correct responses” as a function of the length of the subthreshold
line.

RESEARCH NOTE 1075
control condition, the white line is detected only at the
two highest luminance intensities, the dark line only
at its lowest intensity, the threshold being defined at
75% correct detections. However, when the lines are
presented on the illusory contours, the visibility of the
latter is enhanced by all intensities, including the sub-
threshold levels. Mean performances in the contour
enhancement task increase from 80% to 90% “correct
detections” for a white line presented on illusory con-
tours [Fig. 5(a)], and from 70% to 92% for a dark line
presented on illusory contours [Fig. 5(b)]. The perform-
ances reveal that the effect of the subthreshold line on
illusory contour enhancement is systematically stronger
when the line and the stimulus elements which induce the
illusory contour have the same contrast polarity. Very
similar results are observed with subject BD in the
detection task, as can be seen in Fig. 6(a, b).
Effects of line length on performances in the
contour enhancement task are shown in Fig. 5(c), effects
on performances in the detection task are shown in
Fig. 6(c). When the subthreshold line is presented alone,
its detectability slightly increases with the length of the
line until an optimum is reached at a length of approx.
1.3 deg of visual angle, but the threshold of 75% correct
detections is never attained. When the subthreshold
line is presented upon an illusory contour, mean per-
formances increase with line/illusory contour length
from below 70% to over 90% in both the contour
enhancement task, and the detection task. Moreover, the
effect of line/illusory contour length persists at 1.3 deg of
visual angle. We assume that this result can be related
to the size of the receptive field of the mechanisms
that generates the illusory contour. Such an interpret-
ation is consistent with neurophysiological and psycho-
physical findings indicating that the spatial limits of
illusory contour integration are beyond 2 deg of visual
angle (e.g. Von der Heydt & Peterhans, 1989; Dresp,
Lorenceau & Bonnet, 1990; Dresp, 1992; Lesher &
Mingolla, 1993).
The results shown in Figs 5(a, b) and 6(a, b) also
reveal that the visibility of an illusory contour is even
further enhanced when the subthreshold line and the
stimulus elements which induce the contour have the
same contrast polarity. Furthermore, the subthreshold
line itself becomes even more detectable. These findings
are likely to be explained by a specific effect of the
inducing elements which seem to provide a ‘luminance
pedestal’ (e.g. Foley & Legge, 1981) facilitating even
more the discrimination of both the illusory contour and
the subthreshold line added on that contour. Such
pedestal effects occur with targets and inducing stimuli
of the same polarity and low contrast intensity, and it
has recently been found that they contribute to lower
increment thresholds for small targets presented at the
ends of lines (Morgan 8z Dresp, 1995).
However, the facilitatory interaction between the
subthreshold line and the illusory contour is clearly not
reducible to a simple pedestal contrast effect generated
by the inducing elements. Pedestal effects are polarity
specific, the one observed in our experiment is not.
100
r (a)
90 -
t; 80 -
2
s
o 70 -
z
:
:
a 60 -
Subject BD
x Dark line alone
+ White inducers
0 Black inducers
401
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
D Lum (cd/m*)
100
r
(b)
90
Subject BD
x Light line alone *
* White inducers *
x
x
1 0 Black i;q
x
50
/
40
1
I
x
I I I I I
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
D Lum (cd/m*)
Subject BD
x Line alone
0 Line on illusory contour
37.5 52.5 67.5 82.5 97.5
Length of subthreshold line (arc min)
FIGURE 6. The results of subject BD, who always had to detect the
subthreshold line, in the second experiment. The graphs reveal similar
tendencies in the results of the two observers, who had been given
different instructions in the experimental condition where the sub-
threshold line was presented on the illusory contour. A subthreshold
line of any contrast polarity is found to enhance the strength of an
illusory contour (IM’s data), and to be better detected when presented
on an illusory contour (BD’s data). This holds for contours induced
by stimulus elements of any contrast polarity.

1076 RESEARCH NOTE
Subthreshold lines of any polarity are better detected
when presented on an illusory contour, regardless of the
polarity of the stimulus elements which induce that
contour.
It might still be objected that the mere presence of
the inducing elements at positions adjacent to the sub-
threshold line reduces uncertainty about the spatial
location of the line, and thus facilitates its detection.
Although we think that such an interpretation can
hardly explain why the subthreshold line enhances
the strength of the illusory contour on which it is added
(results of subject IM), we ran a third experiment to
evaluate the extent to which reduced spatial uncertainty
may account for the data of our first two experiments.
EXPERIMENT 3
To test whether the mere presence of stimulus
elements at positions adjacent to the ends of the sub-
threshold line can explain why the latter becomes
detectable, we used a control configuration which does
not generate illusory contours but should reduce spatial
uncertainty in the same way as the illusory contour
configuration may do. We compared performances
in three experimental conditions: (1) subthreshold line
presented alone; (2) subthreshold line added on an
illusory contour; and (3) subthreshold line presented in
the control configuration. Since we wanted to avoid the
pedestal effect observed in Expt 2, which would only
have added unnecessary noise to the results in this
control experiment, we left out the conditions where
the subthreshold line and the inducing elements have
the same contrast polarity. As in the first study, we
presented a dark subthreshold line, either alone or
within configurations made of white stimulus elements,
generating or not illusory contours.
Subjects
The subjects (IM and BD) were the same as in
Expt 2.
Stimuli
The size and the luminance of the white inducing
elements of the illusory contour configuration were the
same as in the previous experiments. The control
configuration (see Fig. 7) was made of two collinear
“V” stimuli with the same luminance as that of the
inducing elements of the illusory contour configuration.
The stimulus elements in all figure conditions were
separated by a gap of approx. 80 arc min. The length
of the subthreshold line was identical to that gap size.
The luminance levels of the dark subthreshold line were
6.37, 6.43, 6.49, 6.55 and 6.61 cd/m* for subject BD and
6.26, 6.32, 6.37, 6.43 and 6.49 cd/m2 for subject IM. The
luminance of the background on which all stimuli were
presented was 6.73 cd/m2.
Procedure
The procedure was basically the same as in Expt 2.
In the condition where the subthreshold line was pre-
FIGURE 7. In the third experiment, we tested the extent to which
reduced uncertainty about the spatial position of the subthreshold
line may account for the results in Expts 1 and 2. Therefore, we
added a control condition with stimulus elements that induced local
reference contrasts at the ends of the subthreshold line, but no illusory
contour.
sented on the illusory contour, subject IM had to
accomplish the contour enhancement task, as in the
previous experiment, and subject BD the detection task.
In the other conditions, both observers had to detect the
subthreshold line, randomly presented to the left or to
the right of the fixation mark. In addition to the number
of correct detections, we also recorded response times in
this experiment.
Results and discussion
The percentage of correct detections was calculated
for each observer and experimental condition. The prob-
abilities where then transformed into logit values and
plotted as logistic functions of the difference between the
luminance intensity of the subthreshold line and the
luminance intensity of the background. For the trans-
formation of the data, the following formula was used:
logit, = In rr/l - rc, where x is the probability of correct
detection of the subthreshold line for a given observer
within a given experimental condition.
The data of subject IM, who had to decide on
the strength of the illusory contours, are shown in the
Fig. 8(a, b). The data of BD, who accomplished
a detection task in all experimental conditions, are
represented in Fig. 9(a, b). The psychometric functions
relating the transformed probabilities of correct detec-
tion to the differences between the luminance intensity of
the subthreshold line and the luminance intensity of
the background reveal that the best performances are
obtained when the subthreshold line is presented on an
illusory contour, regardless of the instructions given to
the observer [cf. Figs 8(a) and 9(a)]. In this condition, the
theoretical threshold where n = 0.75, in other words the
point where the subthreshold line is, or would be,
detected correctly in 75% of the trials, corresponds to
a luminance difference of 0.23 cd/m* for observer BD
and to a difference of 0.39 cd/m* for observer IM.
In the control condition where the subthreshold line is

RESEARCH NOTE 1077
2.0
(4
Subject IM
No inducers
Illusory contour
v-stimuli
2.0
D
Lum
(cd/m2)
(b)
Subject BD
_
??
No inducers
0 Illusory contour
+ v-stimuli
0
-0.2 0.3 0.4 0.5
D
Lum
(cdlm2)
FIGURE 8. The data from the third experiment. (a) Results of subject
IM, who had to decide on illusory contour strength. The data of
subject BD who accomplished a detection task in all conditions. The
probability of “correct detection” of the subthreshold line is plotted as
a logistic function of the difference in luminance between the line and
the background (a). The graphs indicate that performances are slightly
better when a reference contrast is added at the ends of the line (the
control condition with the “V-stimuli”), however, they are far from
being as accurate as in the condition where the subthreshold line is
presented on the illusory contour. Response times as a function of the
difference in luminance between the subthreshold line and the back-
ground (b), reveal a consistent relation between speed and accuracy,
comparing the different experimental conditions: when the percentage
of correct detections is higher, response times are found to be
systematically shorter.
presented within stimulus elements which induce local
contrast but no illusory contour, the theoretical
threshold lies, for both observers, beyond the luminance
values used in this experiment. For subject BD, it
corresponds to a luminance difference (between sub-
threshold line and background) of 0.43 cd/m2, and
for subject IM to a difference of 0.60 cd/m2. As shown
in the graphs, the slopes of the psychometric func-
tions fitted to the data of the illusory contour condition
and the control condition are roughly parallel. In
the condition where the subthreshold line was presented
alone, performances are situated around chance level
for all the luminance intensities of the subthreshold
line that were used in this experiment.
Figures 8(b) and 9(b) show response times of each
observer in the different experimental conditions. The
graphs reveal a consistent relation between speed and
accuracy: response times are the longest in the condition
that yields the lowest percentages of correct detections
(i.e. when the subthreshold line is presented alone),
and the shortest in the condition that yields the highest
percentages of correct detections (i.e. when the sub-
threshold line is presented on an illusory contour).
The results of this third experiment show that the
facilitatory effect of illusory contour configuration on
both the detectability of a subthreshold line and the
strength of the illusory contour upon which the line
is added cannot be explained solely in terms of reduced
uncertainty about the spatial position of the line.
Although the mere presence of contrast elements at
positions adjacent to the ends of the subthreshold line
slightly improves detection performances, as compared
to the situation where the line is presented alone, it
does not engender a facilitation effect as strong as the
one produced by the illusory contour configuration.
1000 - .-¤ \.-¤
950 - (a) \ .
;; 900
Subject IM
- . No inducers
1 850 - 0 Illusory contour
4 + v-stimuli 800 -
2
s 4 750 -
e: 700 -
+-+
650 -
600 0.2
f ‘.h
I I I
0.3 0.4 0.5
D Lum (cd/m21
850 + -
650 -
600 I
0.1
I I I
0.2 0.3 0.4
D Lum (cd/m2)
FIGURE 9. See caption to Fig. 8.

1078 RESEARCH NOTE
CONCLUSIONS
Dresp, B., Lorenceau, J. & Bonnet, C. (1990). Apparent brightness
The data from our three experiments suggest
enhancement in the Kanizsa Square with and without illusory
contour formation. Perceprion, 19, 483489.
that illusory contours and subthreshold lines tend to sum
Foley, J. M. & Legge, G. E. (1981). Contrast detection and near-
their energies in the same way as real lines and sub-
threshold lines, as demonstrated in the original sub-
threshold summation experiments by Kulikowski and
King-Smith (1972). Their subthreshold line technique
appears to provide an indirect measure of illusory con-
tour integration, showing that “illusory contour detec-
tors” are insensitive to contrast polarity and integrate
over larger distances than classic line detectors. These
observations are consistent with neurophysiological
findings (e.g. Von der Heydt & Peterhans, 1989),
and they support models of form perception which
emphasize the role of polarity insensitive processes in
contour completion (e.g. Grossberg, 1994).
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