Kanizsa Subjective Figures Can Act as Occluding Surfaces at Parallel Stages of Visual Search

Abstract

Four experiments examined whether Kanizsa subjective figures can induce amodal completion of a notched circle at parallel stages of visual search. Search for the notched circle among full circles was slow and inefficient when the notched circle appeared stereoscopically behind an abutting subjective surface, as if occluded by it. However, search became efficient and parallel when the notched and completed circles appeared nearer so that the subjective figures could not act as occluders. Control studies ruled out explanations in terms of low spatial frequencies, grouping of aligned edges, or the depth of the circles per se. Multiple Kanizsa subjective figures can be coded in parallel as occluding surfaces; such coding is obligatory because it arises even when highly detrimental to performance.

Full text

Journal
of
Experimental
Psychology:
Human
Perception
and
Performance
1998,
Vol.
24,
No.
1,169-184
Copyright 1998
by the
American Psychological Association, Inc.
0096-J523/98/S3.00
Kanizsa
Subjective Figures
Can Act as
Occluding Surfaces
at
Parallel
Stages
of
Visual
Search
Greg
Davis
University
of
Cambridge
Jon
Driver
University
College
London
Four experiments examined whether Kanizsa subjective
figures can
induce
amodal
comple-
tion
of a
notched
circle
at
parallel
stages
of
visual
search.
Search
for the
notched circle among
full
circles
was
slow
and
inefficient
when
the
notched circle appeared stereoscopically behind
an
abutting subjective surface,
as if
occluded
by it.
However, search became
efficient
and
parallel when
the
notched
and
completed
circles
appeared nearer
so
that
the
subjective
figures
could
not act as
occluders. Control studies ruled
out
explanations
in
terms
of low
spatial
frequencies,
grouping
of
aligned edges,
or the
depth
of the
circles
per se.
Multiple Kanizsa
subjective
figures can be
coded
in
parallel
as
occluding surfaces; such coding
is
obligatory
because
it
arises even when
highly
detrimental
to
performance.
Subjective
figures
provide
a
well-known visual illusion
that
has
been extensively studied
(see
Petry
&
Meyer,
1987,
for
reviews). Several types
of
subjective
figures are
shown
in
Figure
1.
The
visual mechanisms that underlie
the
various
types
may
differ
somewhat,
but in
each
case,
the
illusory
perception
of
contours
and of
bright surfaces
is
induced
at
areas
of the
stimulus where there
is no
actual luminance
discontinuity.
It has
been widely argued that
the
study
of
such
subjective
figures may
allow
a
privileged view
of the
mechanisms involved
in the
perception
of
contours, bright-
ness,
shapes,
and
surfaces
(e.g.,
Grossberg
&
Mingola,
1985;
Petry
&
Meyer, 1987). More recently,
it has
also been claimed
(FaMe
&
Koch, 1995) that
subjective-figure
perception
affords
a
paradigm
case
of the
visual system binding together separate
elements
in a
scene (such
as the
"pacmen"
inducers
in
Figure
1A)
to
produce
an
integrated
and
coherent object
(in
this
case,
the
subjective square enclosed
by the
pacmen).
Low-Level Versus
High-Level
Accounts
for
Subjective
Figures
An
enduring issue
has
been
the
extent
to
which subjective
figures
reflect
the
operation
of
low-level versus high-level
visual
processes
(see
Petry
&
Meyer,
1987).
This question
has
traditionally been approached
in a
strictly
dichotomous
fashion,
as if
low-level
and
high-level factors were mutually
Greg Davis, Department
of
Experimental Psychology, Univer-
sity
of
Cambridge, Cambridge, United Kingdom;
Jon
Driver,
Department
of
Psychology, University College London, London,
United
Kingdom.
This
work
was
supported
by
Biotechnology
and
Biological
Sciences Research Council (United Kingdom) Grant 27/S06603.
Our
thanks
to
Joseph Lappin
and Jim
Enns
for
helpful
comments
on
an
earlier
version
of
this article.
Correspondence concerning this article should
be
addressed
to
Greg Davis, Department
of
Experimental Psychology, University
of
Cambridge, Downing Street, Cambridge
CB2
3EB,
United
Kingdom.
Electronic mail
may be
sent
via
Internet
to
gjdlOOO®
cus.cam.ac.uk.
exclusive. However,
it now
seems likely that both low-level
and
high-level
processes
often
contribute jointly
to the final
percept
(see
Lesher,
1995,
and
Spillman
&
Dresp,
1995,
for
extensive reviews).
On the one
hand, abundant evidence
has
now
been amassed
to
show that
low-level
stimulus factors
often
influence
subjective
figures. For
instance,
the
per-
ceived strength
of the
subjective percept depends
on the
spatial separation
of the
inducing
elements
and on the
contrast
of
these inducers with their immediate background
(e.g.,
Brigner
&
Gallagher,
1974;
Kennedy
&
Lee, 1976;
Shapley
&
Gordon, 1985).
In
further
apparent support
of
low-level accounts, recent single-cell recordings
in
behaving
monkeys (described
in
more detail later) suggest that
subjective
edges
may be
coded even
at
very early stages
of
cortical visual processing (e.g., Grosof, Shapley,
&
Hawken,
1993;
Peterhans
& von der
Heydt,
1991).
On the
other hand,
further
results seem consistent with
the
traditional
rival to
low-level accounts, namely, theories that regard subjective
figures
as
the
outcome
of
"intelligent"
or
"inferential"
processes operating
at
relatively late stages
of the
visual
system
(e.g.,
Gregory,
1972;
Parks, 1987).
In
apparent
support
of
such accounts, top-down knowledge
or
prior
experience
can
affect
subjective-figure
percepts
in
some
cases
(e.g.,
Bonaiuto,
Giannini,
&
Bonaiuto,
1991;
Bradley
&
Dumais,
1975;
Coren, Porac,
&
Theodor,
1987;
Gellatly
&
Bishop,
1987;
Parks,
1987;
Rock
&
Anson,
1979).
Moreover, depth information
can
apparently
"veto"
the
perception
of
Kanizsa subjective
figures
(e.g., Figure
1 A) in
situations
in
which
the
inducers
are
seen
as in
front
of the
region they surround,
an
arrangement that would contradict
any
perceptual hypothesis that
the
inducers
are
occluded
by
a
central subjective surface
(e.g.,
Gregory
&
Harris,
1974;
Lawson,
Cowan, Gibbs,
&
Whitmore, 1974; Rock
&
Anson,
1979).
Given
the
existing evidence
for
both low-level
and
high-level contributions
to the final
subjective percept,
we
think
it is no
longer
useful
to
oppose low-level
and
high-level accounts
in a
strictly dichotomous fashion.
In-
stead, what
is
needed
is a
more thorough understanding
of
how
the
various levels
of
processing
interact
to
modulate
the
169

170
DAVIS
AND
DRIVER
Figure
1.
Examples
of
several well-known subjective
figures. As
discussed
in the
text,
the
mechanisms underlying them
may
differ.
A: A
Kanizsa
(1955) square.
B: An
Ehrenstein
(1941)
circle.
C: A
rectangle defined
by
offset
gratings.
D: A
Kanizsa triangle,
as
used
by
Grabowecky
and
Treisman (1989)
as a
visual-search target.
E:
An
example
of a
nontarget
from
the
visual-search study
of
Grabowecky
and
Treisman.
percept. This requires
a
more
rigorous
characterization
of
the
various low-level
and
high-level processes themselves.
Much
of the
prior research cited above
has
tended
to
group
many
different
processes together under
a
common low-
level heading (e.g., brightness contrast, low-spatial-fre-
quency
blurring,
and
lateral inhibition); likewise, other
diverse
processes
have been grouped together under
a
high-level heading (e.g., prior experience, depth perception,
and
intention).
In
this article,
we
suggest that
a
more specific
contrast between distinct
levels—namely,
that between
preattentive
and
attentive vision (Julesz
&
Bergen, 1983;
Treisman
&
Gelade, 1980;
Wolfe,
1994)—may
provide
a
useful
fresh
perspective.
We
also suggest that
future
progress
in
characterizing
the
levels
of
processing that influence subjective-figure percepts
will
come primarily
from
studies that
use
objective perfor-
mance measures
of
perception,
in
tasks
with correct
and
incorrect responses.
One
limitation
of the
pioneering studies
cited above
is
that most relied
on
subjective reports
of
what
was
perceived, given unlimited viewing
of a
single display,
in
tasks that
had no
correct
or
incorrect response (such
as
rating
the
perceived strength
of a
subjective
figure;
Warm,
Dember,
Padich,
Beckner,
&
Jones,
1987).
Although such
phenomenal
measures have been used with considerable
ingenuity,
they
ran the risk
that many
levels
of
processing
will
invariably contribute
to the
unspeeded phenomenal
percept.
Certainly,
unspeeded phenomenal judgments
are
quite
unsuitable
for
addressing
the two
main
issues
we
investigate
here.
The first
such issue
is
whether
the
perception
of
subjective
figures
requires
focused
attention
to
each cluster
of
inducing elements,
as
claimed
by
Bradley
and
Dumais
(1975),
Brandeis
and
Lehmann
(1989),
and
Pritchard
and
Warm
(1983).
This issue cannot
be
assessed with standard
phenomenal measures, because these
all
rely
on
unspeeded
judgments
for a
single attended stimulus.
Our
second
question
is
whether
the
efficient
perception
of
subjective
figures
requires
a
deliberate intention
to see
them,
as
claimed
by
Rock
and
Anson
(1979).
Again, this cannot
be
assessed
with
standard phenomenal measures, because once
the
experimenter begins
to
question
the
observer about
the
strength
of any
subjective
figure, the
observer presumably
develops
an
intentional
set to
perceive such
figures. Our
studies
all
relied instead
on
objective performance tasks
rather than
on
subjective reports. These tasks
all
involved
visual
search, which
has
been widely used
to
assess whether
visual
properties require focused attention
for
their percep-
tion,
as
described below.
Attention
and
Subjective
Figures
in
Visual
Search
Several recent
findings
from
human psychophysics (e.g.,
Davis
&
Driver, 1994; Grabowecky
&
Treisman, 1989;
Gurnsey,
Humphrey,
&
Kapitan, 1992)
and
also
from
monkey
neurophysiology
(e.g.,
Peterhans
& von der
Heydt,
1991)
have been taken
as
preliminary evidence that subjec-
tive
figures may be
coded
preattentively.
However,
we
argue
that
on
closer inspection, these existing data actually remain
equivocal
as
regards
the
involvement
of
attention.
The
previous
studies
on
subjective
figures and
human attention
have
all
used
the
visual-search task. This
has
become
a
standard
means
for
assessing whether
a
particular visual
property
(in our
case,
the
presence
of a
subjective
figure) can
be
coded
"preattentively,"
that
is, at
stages
of
vision that
can
operate
efficiently
across
the
visual
field in
parallel.
The
visual-search method
is
well established,
so we
give
only
a
brief overview
of its
logic here.
The
critical measure
is
the
time required
to
detect
a
particular target among
a
varied number
of
nontargets.
If the
target
is
distinguished
by
a
property that
can be
efficiently coded
in
parallel,
it
should
"pop out."
As a
result, reaction time (RT) should
be
scarcely
affected
by the
number
of
nontargets present. This
is
often
found
for
targets
defined
by
simple visual features
(e.g.,
by
substantial differences
in
color,
or in
orientation, etc.;
Treisman
&
Gelade, 1980). More recently,
efficient
parallel
search
has
also been found
for
targets distinguished
by
some
more
complex derived properties (e.g.,
Aks
&
Enns,
1992;
Enns
&
Rensink,
1991).
When
a
search target
is
defined
by an
attribute that cannot
be
processed
in
parallel
(or
which
is
processed
only
ineffi-
ciently
at
parallel stages), then
RT
should increase with
set
size,
in
contrast
to
cases
of
highly
efficient
parallel search.
This
increasing delay with larger
set
sizes
has now
been
observed
for
various targets defined
by
complex differences
from
their nontargets (e.g., Treisman
&
Gelade, 1980;
Wolfe,
1994)
or by
nonsalient
differences
(e.g.,
Treisman
&
Gormican,
1988). When
the
observed increase
in RT
against
set
size
is
linear, with
a
slope that
is
twice
as
great
for
target-absent trials versus target-present trials,
it is
often
concluded that
a
self-terminating serial search took place,
involving inspection
of
each item
in
turn until
the
target
was
found
(e.g.,
Treisman
&
Gelade,
1980).
However, various
complexities
and
qualifications have
now
emerged concern-
ing the
situations
in
which
a
steep
RT
versus
set-size
function
can be
taken
as
unequivocal evidence
for a
strictly
serial search,
as
opposed
to a
very noisy
and
inefficient

PARALLEL
CODING
OF
SUBJECTIVE VISUAL SURFACES
171
parallel
search (see
Miiller,
Heller,
&
Ziegler, 1995; Palmer,
1996;Townsend,
1990; Wolfe,
1994).
For
present purposes,
we
need
not be
concerned with
the
most appropriate interpretation
for
very steep search slopes
(e.g.,
as
reflecting
a
strictly
serial
search versus
a
noisy
parallel search). Instead,
we
simply concentrated
on the
contrast between highly
efficient
searches (yielding
flat
functions)
and
highly
inefficient
searches (yielding steep
and
linear
functions)
in
otherwise similar tasks. Such compari-
sons
remain
useful
for
establishing which visual
properties
can
be
efficiently
extracted
by
parallel vision (see
Theeuwes,
1995; Wolfe, 1994). When characterizing
any
process
as
parallel
rather than
as
serial
in
this
article,
we
have
assumed
only
that entirely
flat
search
functions
can be
taken
as
unambiguous
evidence
for an
efficient
parallel
process.
This
remains
a
straightforward conclusion, regardless
of the
various
interpretations that
are
possible
for
steeper
slopes.
Several studies have already used subjective-figure stimuli
in
visual-search tasks. Grabowecky
and
Treisman
(1989)
used
a
Kanizsa
(1955)
triangle
as the
target (Figure
ID).
The
nontargets
each comprised
the
same three
pacmen,
but now
rearranged
so as not to
form
any
subjective
figure
(Figure
IE).
If
Kanizsa subjective
figures can be
perceived
in
parallel,
the
target ought
to pop out
regardless
of the
number
of
nontargets,
as it
should
be the
only bright subjective
shape.
In
fact, Grabowecky
and
Treisman reported
a
large
effect
of set
size
on RTs
(although their data have only been
presented
in
abstract form). This result suggests that focal
attention
to
each
set of
pacmen
may be
required
to
perceive
a
subjective
figure, in
apparent agreement with
the
claims
of
Brandeis
and
Lehmann
(1989)
and
Pritchard
and
Warm
(1983).
However, Grabowecky
and
Treisman's
(1989)
pioneering
visual-search result
for
humans stands
in
apparent contradic-
tion
to the
claims
of
Peterhans
and von der
Heydt
(1991)
on
the
basis
of
their
single-cell
findings in
behaving monkeys.
They
argued that attention, even
in the
form
of
feedback
from
higher visual areas,
was
unlikely
to
influence
the
response they observed
in V2
cells
when subjective bars
were
presented. Their argument
was
based
on two
main
findings.
First,
the
latency
of the V2
response
to
subjective
bars
was
very brief (around
70
msec) following stimulus
onset, apparently ruling
out
feedback
from
later visual areas.
Second,
at the
time
of
recording,
the
awake monkey
was
engaged
in
performing
a
demanding task (discriminating
central luminance-defined
figures) for
stimuli that were
unrelated
to the
irrelevant
but
effective subjective-figure
displays. Moreover, these target stimuli were spatially
removed
from
the
peripheral location
of the
irrelevant
subjective
figures.
Peterhans
and von der
Heydt accordingly
suggested that
the
existence
of a
subjective
figure and its
orientation
can be
coded
as
early
as V2
without
any
involvement
of
attention. However,
it
should
be
noted that
they
had no
direct
measure
of
where their monkeys were
attending. Moreover, their conclusion
for the
monkeys
is in
apparent
conflict
with Grabowecky
and
Treisman's conclu-
sion
for
humans.
Alternatively,
Gurnsey
et
al.
(1992) have suggested that
the
latter
conclusion
for
humans
may be
misleading.
They
argued
that
in
Grabowecky
and
Treisman's (1989) search
task,
a
fairly
weak signal
for the
relatively faint subjective-
figure
target
may
have been overwhelmed
by a
stronger
signal
corresponding
to the
simultaneous sudden onset
of the
high-contrast-inducing pacmen.
It is
well
established
that
a
relatively
weak target stimulus
can be
hard
to find
among
concurrent
nontarget
stimuli that induce
a
more
powerful
neural
response
(e.g.,
when searching
for a
small target
among
large nontargets; Treisman
&
Gormican,
1988). This
can
lead
to
slow
and
inefficient
search, even though
the
dimension
defining
the
target
(in
this case, size)
can in
principle
be
coded
in
parallel
(as
revealed when
the
roles
of
small
and big
items
are
reversed).
Thus,
it is
possible
that
some activity
was
generated
in
response
to
Grabowecky
and
Treisman's subjective-figure target (analogous
to the V2
response
in
monkeys)
at
parallel stages
of
human
vision
but
that
this signal
was
simply swamped
by the
greater activity
due
to the
high-contrast onset
of the
pacmen inducers
themselves.
On
the
basis
of
this argument, Gurnsey
et al.
(1992)
chose
to
examine human visual search
for a
different
type
of
subjective
figure:
those induced
by
offset
gratings (see
Figure 1C). Using variants
of
such offset-grating
figures,
they
demonstrated
efficient
parallel search
for
vertical
subjective
bars among horizontal subjective bars (Figure
2A),
and
similarly
for the
reverse
case.
These results provide
an
apparent case
of
preattentive parallel coding
for
subjec-
tive
figures in
humans, albeit with stimuli
of a
different
type
to
those investigated
by
Grabowecky
and
Treisman
(1989).
Gurnsey
et al.
also reported
efficient
parallel search
for
subjective
crescents among subjective oblique bars (Figure
IB
Figure
2.
Example target
and
nontarget stimuli
from
the
visual-
search study
of
Gurnsey
et al.
(1992).
A:
Vertical
and
horizontal
bars
denned
by
offset
tilted gratings.
B:
Low-spatial-frequency
version
of the
image
in A. See
text
for
details
of how it was
produced. Note
the
alternating dark
and
light
blobs along
the
borders
of the
vertical
and
horizontal
bars.
C:
Crescent
and
oblique
bar
defined
by
offset
gratings.
D:
Low-spatial-frequency version
of
the
image
in C. See
text
for
details
of how it was
produced. Note
the
alternating
dark
and
light blobs
at the top and
bottom
of the
oblique
bar,
and
likewise
for the
crescent.

172
DAVIS
AND
DRIVER
2C),
but
curiously, they
found
inefficient
and
apparently
serial search
for the
reverse case
of
subjective oblique bars
among subjective
crescents.
Gurnsey
et
al.
(1992) contended that low-spatial-
frequency
blur,
as
originally posited
to
account
for
subjec-
tive figures
by
Ginsberg
(1975),
could
not
play
a
significant
role
in
their displays. Indeed,
it is
usually claimed
(e.g.,
Redies, 1989;
Van der
Zwan
&
Wenderoth,
1994) that
offset-grating
stimuli, such
as
Figure
1C,
provide
a
water-
tight
argument against such low-spatial-frequency accounts,
as
such stimuli supposedly
do not
contain
any
energy
at low
frequencies. However, low-spatial-frequency blurring might
yet
provide
a
full
explanation
for
Gurnsey
et
al.'s
data,
without
any
involvement
of
subjective
figures.
Note that
their displays (Figures
2A and 2C)
differed
from
conven-
tional
offset-grating
displays (such
as
Figure
1C)
because
the
misaligned inducing gratings either
ran at 45° to the
borders between them (Figure 2A),
or the
borders
ran at an
oblique angle
to the
gratings (Figure 2C).
By
contrast,
conventional offset-grating
displays,
which have been
claimed
to
rule
out
low-spatial-frequency artifacts, have
the
offset
gratings running perpendicular
to the
border between
them
(Figure
1C).
We
noted that with
the
Gurnsey
et al.
(1992) type
of
display, dotted
"blobs"
of
alternating contrast
are
experi-
enced
with
unspeeded
viewing,
along
the
border
between
the
offset
gratings, unless this border
is
directly foveated.
This phenomenal observation suggested
to us
that mere
blurring
in
peripheral
vision might
produce
the
discontinui-
ties
on
which search
was
based,
and
that
no
subjective
figures
need have been involved.
To
illustrate this possibil-
ity,
we
reproduced
the
Gurnsey
et al.
stimuli
according
to
their pixel description
(as
shown
in
Figures
2A and 2C) and
then
blurred them with
a
Gaussian
filter,
using Adobe
Photoshop
3.0
software.
The filter was set at 79
cycles/
picture width when applied
to the
display
in
Figure
2A. The
outcome (with contrast enhanced
for
reproduction)
is
shown
in
Figure
2B.
Blobs
of
opposing contrast
are
evident
at
these
low
spatial frequencies, along
the
putatively "subjective"
borders where
the
gratings abut. Search based
on
these blobs
alone could presumably produce
the
parallel result
for
vertical borders among horizontal borders
and for
horizontal
borders among vertical ones. Furthermore, similar
filtering
of
the
crescent stimuli (using
a filter at 59
cycles/picture
width
for the
display
in
Figure
2C)
also reveals blobs (see
Figure 2D). These emerge around
the
entire border
of the
crescent
but are
most apparent where this
border
is
slanted
at
45° to the
offset
gratings
(i.e.,
at the top and
bottom
of the
crescent
in
Figure 2D).
The top and
bottom
of the
crescent
may
thus approximate
two
pairs
of
slanted lines
of
blobs:
one
pair slanting
rightward (at the top right of
Figure
2D)
and
one
slanting
leftward
(bottom
right of
Figure 2D).
The
oblique
bar
(left
of
Figure
2C)
produces
two
rightward-
slanting
arrangements
of
blobs,
one at its top and one at its
bottom (see
left
of
Figure 2D).
Search based merely
on
these slanted groups
of
low-spatial-
frequency
blobs might therefore account
for the
otherwise
curious search asymmetry that Gurnsey
et al.
(1992,
Experi-
ment
2)
found
between
efficient
parallel search
for a
crescent
target among
an
oblique-bar
nontarget
versus
inefficient
search
for the
reverse case.
The
crescent should indeed
pop
out
from
the
oblique
bars
by
virtue
of the
unique leftward-
slanting group
of
low-spatial-frequency blobs
at its
bottom.
By
contrast,
the
oblique
bar
produces only
two rightward-
slanting
groups
of
blobs,
similar
to the rightward-slanting
group
at the top of the
crescent stimulus,
and so the
oblique
bar may
have
no
unique blob
feature
to
support parallel
search.
As
previously shown
by
Treisman
and
Gormican
(1988), search
for the
presence
of a
unique
feature
(such
as
the
leftward-slanting blobs
in the
crescent)
can be
efficiently
parallel, whereas search
for the
absence
of
that same feature
(as in the
oblique bar)
is
slow
and
effortful.
Gurnsey
et al.
(1992)
did
discuss possible low-spatial-
frequency
problems with their stimuli, though
not in the
precise
form
described here. They
ran a
control study (their
Experiment
3) in
which
the
grating stimuli were blurred
on
presentation,
at
just
the
abutting ends
of the
lines.
This
turned
the
efficient
parallel searches into slow
and
inefficient
searches. From this
finding,
Gurnsey
et al.
ruled
out any
low-spatial-frequency
account
for
their original parallel
results. However,
the
blob account described above remains
possible,
as a
similar
exercise
to the filtering in
Figure
2
reveals that low-spatial-frequency blobs
are
absent
in the
stimuli
that were presented with blur. Hence,
the
blob
account
can
again
explain
their
search
results.
This
potential
problem with Gurnsey
et
al.'s stimuli arose because
the
borders were
not
perpendicular
to the
offset
gratings
in
their
displays.
However,
Skotun
(1994)
has
recently overturned
many
previous claims (e.g.,
Peterhans
& von der
Heydt,
1991; Redies, 1989;
Van der
Zwan
&
Wenderoth, 1994)
by
arguing that even
perpendicular
offset-grating stimuli
(e.g.,
Figure
1C)
activate low-spatial-frequency channels, analo-
gous
to
those
in
early human vision, along
the
supposedly
subjective
border.
In any
case,
it is
entirely
possible
that
the
mechanisms
underlying offset-grating subjective stimuli
differ
qualitatively
from
those responsible
for
Kanizsa-type
subjective
figures
(see Grosof
et
al.,
1993,
for
recent
single-cell data
on
this point). Accordingly,
in the
remainder
of
this article,
we
focus
exclusively
on
subjective
figures of
the
Kanizsa
type
(e.g.,
Figure
1A or
ID).
Davis
and
Driver (1994) recently carried
out a
human
visual-search study that also followed
up
Grabowecky
and
Treisman's
(1989)
findings but
used Kanizsa stimuli (shown
in
Figure
3A)
similar
to the
original displays
from
Grabowecky
and
Treisman's study (shown
in
Figures
ID
and
IE).
Like Gurnsey
et al.
(1992), Davis
and
Driver were
concerned that
the
sudden onset
of
high-contrast-inducing
pacmen
may
have overwhelmed
any
signal
for the
subjec-
tive
target
in
Grabowecky
and
Treisman's study. Their
solution
was to
present circular
"placeholders"
in an
immediately preceding display. Clusters
of
these were then
each transformed into either
a
target arrangement
of
pacmen
that
formed
a
subjective square (top
of
Figure
3A)
or a
nontarget arrangement
of
similar
pacmen that formed
no
subjective
figure
(bottom
of
Figure
3
A)
simply
by
removing
an
appropriate
90°
segment
from
each
of the
preceding
circular
placeholders.
As a
result,
the
onset
of the
subjective-
figure
target
did not
have
to
compete with
the
high-contrast

PARALLEL
CODING
OF
SUBJECTIVE VISUAL SURFACES
173
B
Figure
3.
Example target
and
nontarget
stimuli
from
several
previous
visual-search studies. Targets
are
shown
at the top of
each
column,
with
one of
their
associated
nontargets
below.
A:
Stimuli
from
Experiment
1 of
Davis
and
Driver
(1994),
which
found
parallel
search
for the
subjective square.
B:
Stimuli
from
Experi-
ment
2 of
Davis
and
Driver.
The
addition
of the
arcs removes
the
subjective square
in the
target,
and
serial
search
was now
found.
C:
Stimuli
from
Experiment
4 of
Davis
and
Driver. Parallel search
was
found
for the
outline subjective-square target.
D:
Stimuli
from
He
and
Nakayama
(1992).
The
dark regions were either stereoscopi-
cally
in
front
of the
light L-shaped regions
(as
shown
schematically
above)
or
behind them
(as
shown below
in the figure).
Serial search
was
found
for L
shapes when they appeared
in
front
of the
dark
regions,
but
parallel search
was
found
when
the L
shapes appeared
behind
the
dark regions. This
was
attributed
to
amodal completion
of
the L
shape when apparently
lying
behind
a
dark occluder.
See
text
for
more details.
E:
Stimuli
from
Enns
and
Rensink (1992,
Experiment
1,
occlusion condition). Serial search
was
found
for the
notched black square. Control conditions showed that this
was due
to
apparent occlusion
by the
abutting white circle, leading
to
amodal completion
of the
notched target
as a
full
square.
onset
of the
pacmen inducers. Instead, only
the
offset
of the
pacmen
segments took place during
the
search display.
A
second
concern
was
that
efficient
search
for the
subjective
target
in
Grabowecky
and
Treisman's
(1989)
study
may
have been prevented
by
spurious alignments
between
the
pacmen
from
distinct nontargets, which could
induce
partial subjective shapes among
the
nontarget stimuli.
This
was
prevented
in
Davis
and
Driver's
(1994)
study
by
prearranging
the
circular placeholders into spatially distinct
clusters
of
four
circles each, such that
a
subsequent
pacman
from
one
cluster
was
very unlikely
to
group with
any
pacman
from
another cluster. With these
two
main
modifica-
tions,
Davis
and
Driver
found
relatively
flat RT
against
set-size
functions (around
10
ms/eluster),
indicative
of
parallel search
for the
subjective-square
target.
In a
control
study,
arcs were presented across
the
inducing bites
in the
pacmen (see Figure 3B). This eliminated
the
square subjec-
tive figure
with
unrestricted viewing,
and
search rate
now
became very slow
and
inefficient (around
150
ms/cluster).
Finally,
the
observation
of
efficient
parallel search
for
outline subjective-square targets (Figure 3C), with inducers
of
opposite
contrast polarity,
was
held
to
rule
out
accounts
for
the
parallel search
in
terms
of
low-spatial-frequency
artifacts
(Ginsberg,
1975).
Davis
and
Driver's
(1994)
findings
apparently provide
the
strongest evidence
yet
that subjective
figures can be
encoded
in
parallel, without
the
need
for
focal
attention
to
each
inducer,
or to
each cluster
of
inducers. However, potential
criticisms remain.
The
efficient
parallel
search
for the
square
targets
shown
at the top of
Figure
3A and 3C may
indeed
have
been based
on a
subjective-figure
percept,
as
suggested
by
the
shift
to
inefficient
search when arcs were added
(Figure
3B). However,
an
alternative explanation would
simply
be
that parallel search resulted whenever
the
group-
ing
between
the
four
pacmen
in a
target cluster
was
strong.
Abundant
evidence already exists
to
show that visual search
is
easier
when target elements group strongly together,
to
allow
segmentation
from
nontarget elements (e.g., Duncan
&
Humphreys,
1989).
The
vertical
and
horizontal edges
of
the
target inducers
in
Figures
3A and 3C may
simply have
been more
"free"
to
group
with
aligned edges than with
the
equivalent edges
in
Figure
3B,
which were
closed
off
by the
arc.
This essential problem
in
interpreting Davis
and
Driver's
(1994)
results
can be
presented
in
more general
and
philo-
sophical terms.
One can
readily imagine
a
machine-vision
system that could distinguish
the
target
of
Figure
3A
from
the
associated nontargets
in
parallel, without necessarily
having
to
produce
any
illusory edges
or
bright surfaces
within
the
target cluster.
In
fact, participants
in our
previous
experiments
all
reported
on
debriefing that they experienced
bright subjective squares
for the
target stimuli
in
Figures
3A
and
3C
when performing
the
search task. However,
it is
unclear
whether their subjective experiences were based
on
the
parallel stage
of
processing
that evidently
controlled
their
search responses
or on
some later
attentional
stage that
might
follow
detection
of a
target. Thus,
the
evidence that
parallel search
was
actually
based
on a
subjective-figure
percept
in
Davis
and
Driver's (1994) study
was
rather
indirect.
We
sought
to
remedy this deficiency
in the
present series
of
experiments.
We
have also addressed
two
further
possible
shortcomings
in
Davis
and
Driver's
(1994)
study.
First,
even
if
their results could
be
taken
at
face
value,
as
indicating
parallel detection
of a
subjective
figure,
this would
still
not
show
that multiple subjective
figures can be
coded
simulta-
neously.
Their search displays either contained
one
subjec-
tive figure,
or
none,
so the
case
of
multiple subjective
figures
was
never addressed. Second,
the
parallel search
for a
single
subjective
figure was
observed
in
participants
who had the
intention
of
detecting
the
subjective-square target.
This
falls
well
short
of
demonstrating that
the
parallel coding
of
Kanizsa
subjective
figures is
automatic (Schneider
&
Shif-
frin,
1977)
in the
sense
of
being obligatory rather than
merely
an
option that participants
can
exercise when
effi-
cient task performance demands
it.
Rock
and
Anson
(1979)
have
previously argued that
efficient
perception
of
subjec-
tive
figures may
depend
on an
intention
to
perceive them.
In
the
present
series
of
studies
we
sought
to
determine whether
multiple
subjective
figures
still
get
coded
in
parallel even
when
efficient
task performance actually demands that they
should
not be.
Such
a
result would provide much stronger
evidence
that their parallel coding
is
obligatory.

174
DAVIS
AND
DRIVER
Can
Subjective Figures
Act as
Occluding Surfaces
in
Visual Search?
Our
new
experiments examined whether subjective
fig-
ures
can act as
occluding surfaces
at
parallel stages
of
visual
search,
in the
manner recently demonstrated
by He and
Nakayama
(1992)
and
Enns
and
Rensink
(1992)
for
lumi-
nance-defined
surfaces.
He and
Nakayama tested visual
search
for
white
L
shapes among reversed
L
shapes
in
stimuli
such
as
those
in
Figure
3D.
They manipulated
the
stereoscopic
depth
of the
regions shaped
as a
white
L (or a
reversed
L) so
mat
they either appeared
to lie in front of the
abutting
black squares
or
behind them. Search
for the
former
case
was
efficient
and
parallel, whereas
in the
latter
it was
highly inefficient,
yielding
steep
slope
functions.
He and
Nakayama
attributed this result
to
amodal
completion
(Kanizsa,
1979; Sekuler
&
Palmer, 1992)
of the Ls and
reversed
Ls in
parallel vision (both shapes appeared
as
partially occluded white squares with unrestricted viewing).
This
interpretation
was
supported
by
control experiments
in
which
the
same depth relations held,
but the L
shape
no
longer abutted
the
dark region,
thus
breaking
the
impression
of
occlusion.
The
search asymmetry between
the two
depths
was
no
longer apparent
with
this arrangement.
Enns
and
Rensink
(1992)
have similarly concluded that
occlusion
can
induce amodal completion
at
parallel stages
of
visual search.
On the
basis
of
their study, which used only
pictorial cues
to
depth, they
found
efficient
parallel search
for
a
notched-square target among complete-square
nontar-
gets under various conditions. However, when
the
notched
square
was
arranged
so
that
it
abutted
a
circle,
with
the
latter
thus
appearing
to be an
occluder, search became
inefficient
(see Figure
3E;
the
target
is
above
and was
presented among
nontargets
like that shown below
in the figure).
Enns
and
Rensink suggested that
the
difficulty
of
search
in
this
condition arose because
the
notched-square target became
amodally
completed
as a
full
square when apparently
occluded
by the
circle.
As a
result,
the
notched target
was
coded
as
highly similar
to the
nontarget
squares
at
parallel
stages
of
vision,
and
hence focal attention
was now
required
to
distinguish
it from
these
nontarget squares.
If
similar completion results could
be
obtained when
a
subjective
figure
rather than
a
luminance-defined shape
served
as the
potential occluder, this would provide compel-
ling evidence that subjective
figures can
behave
as
occluding
surfaces
in
parallel vision. Note that Kanizsa
figures
could
only
act as
occluders
in
this
way if
there
was
indeed some
construction
of an
illusory
surface
between
the
inducers.
Thus, such
a
result would avoid
the first
shortcoming
of
Davis
and
Driver's (1994) visual-search study, namely, that
no
performance evidence
was
obtained
that directly demon-
strated interpolation
of a
subjective surface between
the
inducers rather than mere grouping between
the
inducers.
Furthermore,
in
search tasks like those used
by
Enns
and
Rensink
(1992)
or He and
Nakayama
(1992),
the
occluding
surface
actually disrupts performance
by
inducing
the
amo-
dal
completion
of the
notched target, which prevents
its
efficient
parallel detection.
If a
similar disruption could
be
produced
by
occluding subjective surfaces, this would
remedy
the
second shortcoming
in
Davis
and
Driver's
study.
It
would show that
the
perception
of
subjective surfaces
is
obligatory rather than merely
an
option that
can be
exercised
when
it
benefits performance.
Experiment
1
In
this study, participants searched
for a
large brown
notched circle with
a 90°
segment taken
out of it
(two
examples
of
targets
are
shown
in the
left
column
of
Figure
4A,
with
hatched shading) among large brown complete
circles
(four
examples
are
shown
in the
middle
and right
columns
of
Figure
4A,
again with hatched shading).
Our
idea
was
that when
the
notched target appeared
to lie
behind
an
abutting subjective-square surface, then
the
incomplete
target
circle
should
become
amodally completed
and
thus
difficult
to
distinguish
from
the
complete brown nontarget
circles
within parallel
vision.
The
potential subjective sur-
faces
were generated
by
small black pacmen (see Figure
4A), which were arranged into
clusters
of
three
or
four.
The
clusters
of
four
pacmen were always arranged
so as to
generate
a
Kanizsa subjective square between them (see
two
examples
in right
column
of
Figure 4A).
The
clusters
of
three pacmen either
had a
complete brown
circle
(i.e.,
a
nontarget)
replacing
a
black
pacman
at one
corner
of the
square (see
two
examples
in
middle column
of
Figure
4A) or
a
notched brown circle
(i.e.,
the
target)
at one
corner (see
two
examples
in
left
column
of
Figure 4A).
In the
latter
case,
the
pacmen were aligned
with
the
notched target
so as to
generate
a
subjective square between them.
The
circular
borders
of all the
large brown stimuli were given
an
uncrossed stereo disparity,
as
indicated schematically
by the
shading
in
Figure
4A, so
that they appeared
farther
away
than
the
black pacmen. Thus,
if any
subjective surfaces were
formed,
the
brown nontargets
and the
target should unambigu-
ously
appear
to lie
behind these surfaces
(as
shown
in
Figure
5A
for a
target cluster, where
the
hypothesized subjective
surface
is
marked with diagonal lines).
The
straight
edges
of
the
notched brown target
had no
artificial
disparity,
as
discussed
in
detail later.
Previous
work
has
found
that search
for a
substantially
notched target among complete targets,
as
with
the
present
brown
stimuli,
is
usually
efficient
and
parallel, yielding
flat
search slopes (Enns
&
Rensink, 1992;
Treisman
&
Gormi-
can,
1988).
We
have
confirmed
this
for our own
particular
stimuli
in
Experiments
2-4;
moreover,
we
have shown
in
those studies that neither possible similarities between
the
large brown notched target
and the
small black pacmen
nor
the
unusual stereo properties
of the
straight edges
on the
notched target
affect
this
efficient
parallel
search.
However,
we
expected
inefficient
search
in the
present task,
for the
following
reasons. Enns
and
Rensink (1992) have observed
that
search
for a
notched target among complete targets
becomes
inefficient
when
the
notched target
is
apparently
occluded
by a
luminance-defined surface (Figure
3E).
This
difficulty
in
search
is
thought
to
arise because
the
notched
target gets amodally completed behind
the
occluder
and
thus
is
treated similarly
to the
modally
complete nontargets
within
parallel
stages
of
vision.
If
subjective surfaces
can

PARALLEL
CODING
OF
SUBJECTIVE
VISUAL SURFACES
175
similarly
act as
occluders
at
parallel
stages
of
vision,
then
the
present
brown
notched
targets
in the
back
plane
should
get
amodally
completed
behind
the
subjective
surfaces
in the
front
plane.
As a
result, serial
search
should
be
found.
Such
an
outcome
would
imply
that
multiple
subjective
surfaces
Figure
4.
Examples
of the
possible target
and
nontarget
stimuli
in
our
visual-search tasks. Each cell depicts
a
stimulus cluster, drawn
to
scale.
The
left
column depicts
the two
possible target clusters
in
each experiment;
the
middle
and right
columns each depict
two
possible nontarget clusters
for the
experiments.
The
hatched
shading indicates
red or
green coloring. Cross-hatching arises
where
these
two
colors were superimposed. Solid shading indicates
a
black stimulus.
A:
Possible stimuli
in
Experiments
1 and 2. The
target
was a
large notched circle,
which
appeared brown when
fused
through
the
red-green
3-D
spectacles.
It was
clustered with
three small
black
pacmen
so as to
form
a
Kanizsa
square
and
appeared
at the top
left
or
bottom
right of
this square.
The
possible
nontargets
had
complete large brown circles, either inside (central
column)
or
outside (right column)
the
cluster
of
pacmen.
In
Experiment
1,
the
brown stimuli were given
an
uncrossed disparity
to
appear behind
the
black pacmen, whereas
in
Experiment
2
they
appeared
in
front.
B: The two
possible target clusters
and
four
possible nontarget clusters
in
Experiment
3. The
brown stimuli
appeared
to lie
behind
the
black crosses.
C: The two
possible target
clusters
and
four
possible nontarget clusters
in
Experiment
4. The
brown
stimuli appeared
to lie
behind
the
rotated black pacmen.
Inducing
Pacmen
Subjective
Figure
Notched
Circle
Target
Figure
5. A:
Schematic depiction
of the
arrangement
in
depth
for
a
target cluster
in
Experiment
1.
The
large brown notched target
lies
in
the
back
plane,
as
indicated
by the
dotted
lines,
with three
black
pacmen
in
front.
The
subjective surface
hypothetically
formed
between them
is
indicated
by
diagonal lines.
It
should lead
the
notched
target
to
appear
as an
occluded complete
circle.
B:
Schematic depiction
of the
reverse arrangement
in
depth
for
Experiment
2. The
notched target should
no
longer appear occluded
by
any
subjective surface.
can
be
formed
at
parallel stages
of
vision;
and
moreover,
it
would
show
that
they
are
formed
in an
obligatory
fashion,
even
when
severely detrimental
to
detection
of the
brown
notched
target.
Method
Participants.
Six
participants
(4
women
and 2
men) were
recruited
by
advertisement. They were each paid
£3.60
on
complet-
ing
the
experimental
session.
At the
beginning
of the
session,
we
checked that each participant reported stereoscopic depth when
viewing
an
example
of our
visual-search displays
and
that their
experience
of
depth reversed with
a
reversal
of
input
to the two
eyes.
This
check
was
also
carried
out for all
participants
in our
subsequent
studies.
The
ages
of
participants ranged
from 21 to 32
years
(M
= 24
years).
Apparatus
and
materials.
All
stimuli were displayed
on a
Sony
Trinitron
12-in.
(31
cm)
color
monitor,
by
means
of
Vsearch
software
(Enns, Ochs,
&
Rensink,
1990) that
was run on an
Apple
Macintosh
Quadra
610
microcomputer.
We
conducted each experi-
ment
in
this series
in a
darkened room, with screen brightness
and
contrast
set to
maximum. Each
of the
large brown
circles
had a
diameter
of
around
1.1°
of
visual angle. Figure
4A
shows each
possible stimulus cluster
to
scale,
so the
other visual angles
can all

176
DAVIS
AND
DRIVER
be
derived
by
comparison
with
the
brown circles. (Note that
the
actual
separation
between
neighboring
clusters
within
one
visual-
search display
is not
depicted
in
Figure
4;
that
is
described below.)
All
displays were viewed through
a
pair
of
red-green
3-D
spectacles
(i.e.,
with
a
green
filter for one eye and a red filter for the
other), mounted
at the fixed
viewing distance
of 85 cm. Any
artificial
disparity
was
always
at 15
min
arc.
Figure
4A
shows
the two
possible target clusters
(at top and
bottom
of the
left
column)
and the
four
possible
nontarget
clusters
(middle
and right
columns). These
nontargets
were designed
to
prevent search strategies
for the
notched brown target based
on
properties other than
its
notch. Specifically, they rendered
the
location
of the
target relative
to the
pacmen
uninformative,
and
likewise
for the
number
of
adjoining pacmen,
or the
presence
of a
square subjective
figure.
The
differently
hatched
shadings
for the
large
"brown"
elements
in
Figure
4A
represent
red and
green coloring
in the
displays
as
presented.
The
crossed hatching arises where these
two
colors were
superimposed. Through
the
red-green
spectacles,
these large
elements appeared brown,
and the
spectacles were arranged
to
yield uncrossed disparity
for
their circular edges,
so
that they
appeared
behind
the
screen
plane
on
which
the
black pacmen fell.
With
unrestricted viewing,
the
notched brown target circle under-
went
powerful
amodal
completion
as a
complete circle that
was
partially occluded
by a
square subjective surface,
as
shown
in
Figure
5A. Our
question
was
whether such coding would also
arise
at
parallel stages
of
visual search. Figure
6A
depicts
a
target-
present display
with
a set
size
of
nine clusters,
which
should
be
viewed
by
placing
a
mirror (reflecting side
to the
left)
and
looking
with
both eyes toward
the right-hand
side
of the
display. This setup
is
illustrated
in
Figure
6B and
described
in the figure
caption.
Readers should
be
able
to
confirm
for
themselves that
the
presence
of
the
notched large circle target
is not
immediately apparent,
because
of
amodal completion
as a
full
circle
behind
the
abutting
subjective
square.
Note once again that
the
straight notched edges
of the
brown
target were
not
given
any
artificial
stereo disparity, unlike
the
curved edges (this
is why the
drawing
of the
arrangement
in
Figure
5A
shows
the
notched edges
of the
target
as
appearing
in the
front
plane with
the
subjective
figure).
Such
a
stereo arrangement
was
necessary
to
allow perfect alignment
of the
target's straight edges
with
the
black
pacmen
in
both
eyes,
so as to
induce
a
subjective
square between
the
pacmen
and the
target. Moreover,
it was
also
essential
to
allow
a
direct comparison with
our
subsequent control
studies,
as we
discuss later. Experiments
3 and 4
show that this
unusual
depth arrangement
of
straight edges relative
to
curved
edges
in the
notched target does
not
determine
the
critical results.
Each visual-search display contained
five,
seven,
or
nine clusters
drawn
from
the six
possibilities
shown
in
Figure
4A; see
Figure
6A
for
an
example
of a
target-present display with
a set
size
of
nine.
Half
the
displays contained
one
target cluster,
and the
remainder
had
no
target.
The two
possible target clusters were used equally
often
overall,
as
were
the
four
possible nontarget clusters. Within
each display, there
was at
least
one of
each
of the
four
possible
nontarget
clusters
shown
in the
middle
and right
columns
of
Figure
4A. The
clusters
in a
display were arranged
at
random within
an
imaginary
4X3
grid, with each imaginary cell subtending 2.8°.
Cells
in the
imaginary grid were either empty
or had a
cluster
at
their
center.
Design.
There were
two
orthogonal within-subject
factors.
Display set-size
had
three equiprobable levels
(five,
seven,
or
nine
clusters), whereas
the
required response
had two
equiprobable
levels (target present
or
target absent).
Procedure.
The
task
was to
detect
the
presence
or
absence
of a
large notched brown circle
as
rapidly
as
possible, pressing
a key
e*
et
**
r*
4.
,%
4>
^^..^
^,
Place
Mirror
Here-*
o
"
0*0
Figure
6. A:
Example
of a
typical target-present display (set size
9) in
Experiments
1 and 2,
with
stereoscopic depth information
included. This should
be
viewed
by
placing
a
mirror
as
indicated
in
the
diagram
in B. To
examine
a
display
from
Experiment
1,
arrange
the
mirror
so
that
its
reflecting surface faces
left.
Then
focus
on the
right
image with both eyes,
as
illustrated
in B. To
examine
a
display
from
Experiment
2,
make
the
mirror's reflecting surface
face
right
and
focus
on the
left
image.
B:
A
plan view
of the
setup
for
viewing
the
stereoscopic displays
in A. C: For
readers
who
experience
difficulty
in
perceiving
the
stereoscopic depth using
our
suggested
arrangement,
a
2-dimensional
(2-D) version
is
included where
strengthened
2-D
cues
to
occlusion
demonstrate
how the
presence
of
a
subjective
figure
makes search
for a
grey
pacman
shape highly
inefficient.
Note
that
this display
is not
like those used
in our
experiments
and is
intended
for
illustration only.
under
the
index
or
middle
finger of the
preferred hand, respectively.
We
emphasized that participants should entirely ignore
the
small
black
pacmen
in
front
and
concentrate
on
just
the
large brown
stimuli
behind.
No
mention
of
possible subjective-figure percepts
was
made,
as we
wished
to
determine whether their perception
arises
spontaneously (see Rock
&
Anson,
1979).
Each participant
underwent
12
blocks
of 60
trials
each.
The first 6
blocks
were
discarded
as
practice.
The six
possible conditions (formed
by
crossing target present
or
absent with
set
size) were equiprobable
in
each block,
but the
order
of
trials
was
otherwise random
for
each
participant. Each trial began
with
a
central
fixation
display,
presented
for
150
ms.
This comprised
a
plus
or a
minus sign, which
also gave feedback
on the
accuracy
of the
immediately preceding
response.
It was
followed
by a
visual-search display that
was
presented
until
the
participant responded,
or for a
maximum
of
4,500
ms.

PARALLEL
CODING
OF
SUBJECTIVE
VISUAL SURFACES
177
Results
We
calculated
the
mean
RTs on
correct trials, plus
percentage error rates,
for
every participant,
at
each
set
size
by
response type.
The
averages across participants
are
shown
in
Figure
7A. It can be
seen that
RT
increased
dramatically with
set
size
on
both target-present
and
target-
absent
trials.
In
addition,
the
error rate also increased
with
set
size. Linear regressions
on the
averaged
RT
data against
set
size gave slopes
of
57.5
ms/cluster
for
target-present
responses,
and
159.1 ms/cluster
for
negative trials (with
ranges
of
19-94
ms/cluster
and
56-244
ms/cluster, respec-
B
Experiment
2
2600-1
2400-
2200-
2000
1800
1600-
1400-
1200-
(10)
7
Set
Size
2000-]
1800-
1600-
1400-
1200-
1000-
800-
600 •
(0)
r...
'
(5)
5
(1)
I
-•J"S
(4)
7
Set
Size
(1)
I
--•5
(5)
9
—•
O—•
Target-Present
—•—
Target-Absent
C
Experiment
3
D
Experiment
4
2000-
1800-
1600-
1400-
1200-
1000-
800
600-
^
(2)
(4)
^
i
fr
.|.
-3
5
(4) (7) (9)
Figure
7.
Average reaction times,
in
milliseconds, across partici-
pants
as a
function
of
display set-size
in
each experiment. Data
for
correct responses
on
target-present trials
are
represented
by
open
circles
and
dotted lines; while data
for
target-absent trials
are
shown with solid symbols
and
lines. Standard error bars
are
also shown.
The
mean percentage
of
incorrect responses
is
given
in
parentheses, next
to the
associated
RT
point. Where
two
such
points coincide,
the
error rate
for
target-absent trials
is
shown
above.
A:
Experiment
1.
Note
the
steeper
functions
and
higher
overall reaction times
for
this experiment, which required
a
shift
in
scale
on the
ordinate.
B:
Experiment
2. C:
Experiment
3. D:
Experiment
4.
lively).
These data
are
inconsistent with
efficient
parallel
search
and
have
all the
hallmarks traditionally associated
with
serial self-terminating search (although
as
noted earlier,
very
inefficient
and
noisy parallel processes
can
also pro-
duce
steep search
slopes).
We
carried
out
separate one-way within-subject analyses
of
variance
(ANOVAs)
on the
target-present
and the
target-
absent
RT
data, with
the
factor
of set
size.
There were main
effects
of set
size
for
both target-present
and
target-absent
trials, Fs(2,
10) =
14.9
and
22.2, respectively,
ps <
.01.
Similar analyses
of
error rates
found
an
increase
in
errors
with
set
size
for
target-present trials,
F(2,10)
=
4.6,
p <
.05,
but
not for
target-absent
trials,
F(2,
10) = 0.0
(ns).
Planned
contrasts
of the
search
slope
data, derived
by
linear regres-
sions
of the RT
means against
set
size
for
each participant,
revealed that
the
target-absent
and the
target-present slopes
differed
significantly
from
each other, F(l,
5) =
8.7,
p <
.03,
but did not
depart
significantly,
F(l,
5) = 1.3
(ns)
from
the
2:1
ratio predicted
by
serial
self-terminating
search
models.
Discussion
Search
for a
large notched brown
circle
among complete
large brown circles
was
highly
inefficient
when these stimuli
appeared
stereoscopically
behind
a
plane containing black
pacmen
that were arranged
so as to
produce subjective
squares,
one of
which abutted
the
notch
in the
target when
present.
Our
explanation
for
this outcome
is
that
the
notched
target became
amodally
completed
at
parallel stages
of
vision because
of the
abutting subjective surface appearing
as an
occluder
in
front
of it. As a
result
of
this completion,
the
notched brown circle would
be
indistinguishable
from
the
complete brown
nontargets
without closer inspection,
leading
to the
slow search rates.
If the
difficulty
of
search
was
indeed caused
by the
subjective surfaces, this would
imply
that such surfaces
are
constructed spontaneously
at
parallel stages
of
vision, even when irrelevant
to the
prescribed task
and
indeed even when highly detrimental
to
efficient
performance
of
that task.
However,
we
must also consider alternative accounts.
It is
possible
that
the
serial
search arose simply because
the
brown
target
was
hard
to
distinguish
from
the
black pacmen,
which
were also notched
circles.
This seems unlikely,
because
the
pacmen were both considerably smaller than
the
target
and in a
different
color
and
depth plane. Nevertheless,
we
considered
it
important
to
rule
out
such
possibilities
empirically.
In
line with
He and
Nakayama
(1992),
a
simple
control experiment allowed
us to
examine whether
the
difficult
search
in
Experiment
1 was
indeed caused
by
subjective
surfaces appearing
in
front
of the
plane that
contained
the
brown stimuli.
By
merely reversing
the red
and
green
filters
across eyes,
we
could
now
present exactly
the
same displays
but
with
crossed disparities
for the
curved
edges
of the
brown stimuli.
As a
result,
the
brown stimuli,
including
the
target,
now
appeared
in
front
of the
black
pacmen
and any
subjective surfaces that these induced.
The
target should therefore
no
longer seem occluded
by any
abutting
subjective
figure
(see Figure
5B, and
note that
the

178
DAVIS
AND
DRIVER
straight
edges
of the
notched brown target again appeared
at
screen
disparity, which
now
lies
behind
the
apparent depth
of
the
curved brown
edges).
With this reversed depth,
the
notched target should
no
longer
be
amodally
completed
behind
a
subjective surface,
and so
efficient
parallel
search
should
now be
found. Readers
can get an
impression
of a
typical display
by
viewing Figure
6A,
again using
the
mirror
setup
depicted
in
Figure
6B,
but
this
time
with
the
reflecting
side
of the
mirror
facing
to the
right,
and
both eyes looking
toward
the
left
of the
display. Readers should
be
able
to
confirm
for
themselves that
the
presence
of the
notched large
circle
target
is now
immediately apparent,
as the
subjective
squares
can no
longer
act as
occluders
for
brown elements
because
the
latter appear
in the
front
plane.
Experiment
2
Method
The
method followed
the
previous study exactly, except
for a
reversal
of the
red-green
3-D
spectacles,
so
that
the
left
eye now
viewed each display through
the filter
previously used
for the right
eye,
and
vice
versa.
Six new
participants
(5
women
and 1
man)
were recruited
from
the
same source
as
before. Their ages ranged
from
17
to 43
years
(M
=21
years).
If the
previous result
was due
to
occlusion
by
subjective
figures,
performance should
now
become
efficient
and
parallel,
as any
subjective
figures
were
now in
the
wrong depth plane
to
produce occlusion.
On the
other hand,
if
the
previous result
was due
merely
to
similarity
in
shape between
the
brown notched target
and the
black pacmen,
it
should
be
found
again,
as any
such similarities remained.
Results
The
mean correct
RTs and
error
rates across participants
for
each condition
are
shown
in
Figure
7B. It can be
seen
that
the
reversal
of the 3-D
spectacles
had a
dramatic impact
on
performance,
as
compared with Experiment
1.
That study
had
found slow search rates (Figure 7A), whereas
the
present
findings
indicated highly
efficient
parallel search.
Linear regressions
on the
averaged
RT
data against
set
size
gave
slopes
of
only
2.8
ms/cluster
for
target-present
re-
sponses
and 9.3
ms/cluster
for
target-absent trials (with
ranges
of
—9-10
ms/cluster
and
-5-22 ms/cluster, respec-
tively).
These
data suggest
an
efficient
parallel
search
and
contrast with
the
steep search slopes
in
Experiment
1.
We
carried
out
separate one-way within-subject
ANOVAs
on the
target-present
and the
target-absent
RT
data, with
the
factor
of
set
size. There
was no
effect
of set
size
on
target-present
trials,
F(2,
10) <
1,
although there
was a
small increase
in
RT
with
set
size
on
target-absent trials,
F(2,
10) =
4.9,
p <
.05.
The
latter
finding is
often observed
for
efficient
parallel
search tasks
(e.g.,
Treisman
&
Gelade,
1980)
and is
usually
attributed
to
checking responses (see Chun
&
Wolfe,
1996).
Similar analyses
of
error
rates
found
no
effects
of set
size
on
target-present
or on
target-absent trials,
Fs(2,
10) = 0.2 and
0.6, respectively
(ns).
Planned contrasts
of the
search
slope
data, derived
by
linear regressions
on the RT
means against
set
size
for
each
participant, revealed that
the
target-absent
and the
target-
present slopes
no
longer
differed
reliably
from
each other,
F(l,
10) <
1.
We
carried
out a
further
analysis
to
examine
the
contrast with Experiment
1. The
target-present
and the
target-absent
slopes
were significantly lower
in
Experiment
2,
Fs(l,
10) =
22.4
and
19.9,
respectively,ps
<
.001.
Discussion
The
simple manipulation
of
reversing
the 3-D
spectacles
from
then-
arrangement
in
Experiment
1,
so
that
the
brown
stimuli
now
appeared stereoscopically
in
front
of the
black
pacmen instead
of
behind,
had a
powerful
impact
on
performance.
The
previously very steep search slopes
now
became
flat. The
efficient
parallel search
found
in
Experi-
ment
2
demonstrates that
our
notched brown circle target
can
be
readily
found
among
the
complete brown circles, even
in
the
presence
of
aligned black pacmen.
The
dramatic change
in
results
from
Experiment
1 is
consistent with occlusion
by
subjective
figures
causing
the
difficulty
of
search
in
that
study.
There should
be no
such occlusion
in the
present
study,
because
the
brown stimuli
now
appeared
in front of
any
subjective surfaces (see Figure
5B for a
representation
of
this situation; view Figure
6A
appropriately
with
a
mirror
for
a
depiction
of the
stereo arrangement).
However,
one
might still suggest alternative accounts
for
these
findings.
Search
for
targets
at the
back
of two
separate
depth planes
(as in
Experiment
1)
might
be
less
efficient
in
general than search
at the
front
of the
same
two
planes
(as in
Experiment
2). We
know
of no
evidence
to
support this
assertion
from
previous studies
in
which participants must
restrict search
to a
particular depth plane (e.g.,
He &
Nakayama,
1992;
Nakayama
&
Silverman,
1986). However,
it
does remain
a
theoretical possibility. Moreover, using
a
different
measure
for the
restriction
of
attention (response
competition
from
irrelevant
distractors),
Andersen
and
Kra-
mer
(1993) have recently argued that
it may be
harder
to
ignore
distractors
in
front
of a
target
(as for the
black pacmen
in
Experiment
1)
than
to
ignore comparable distractors
behind
a
target
(as in
Experiment
2).
If
this alone
is
sufficient
to
explain
the
present pattern
of
results, then
we
should
find
efficient
search whenever
the
brown
targets
are in the
front
plane
but
inefficient
search
whenever
tiiey
appear
in the
back plane
with
black
nontar-
gets
in front.
Alternatively,
if
occlusion
by
subjective
surfaces
is the
correct explanation
for the
difficulty
of
search
in
Experiment
1,
then search
for a
brown notched target
should
be
efficient
even
in the
back plane, provided that
no
occluding subjective surfaces
are
formed
in the
front
plane.
We
examined this
in our
next study while also controlling
for
possible low-spatial-frequency accounts
(e.g.,
Ginsberg,
1975)
of the
subjective surfaces
in
Experiment
1.
Finally,
the
next
study
also permitted
a
test
of
whether
the
unusual
stereo
arrangement
for the
notched target
in
Experiment
1
could
in
any way
have been responsible
for our
results.
Experiment
3
The
stimuli, task,
and
procedure
for
Experiment
3
were
identical
to
Experiment
1,
except that
the
black pacmen were

PARALLEL
CODING
OF
SUBJECTIVE VISUAL SURFACES
179
replaced with black
crosses
that
had
equivalent alignments
of
their inner edges (see Figure
4B;
two
possible
target
clusters
are
shown
in the
left
column, with
the
four
possible
nontarget
clusters
in the
middle
and right
columns).
As in
Experiment
1,
the 3-D
spectacles were arranged
so
that
the
brown
nontargets
and any
target appeared stereoscopically
behind
the
black stimuli.
We
replaced
the
black pacmen
with
black crosses
for the
following reason.
It has
been known
since
the
work
of
Kanizsa
(1955)
that, unlike pacmen,
such
aligned
crosses
do not
produce bright subjective
figures
between them with unrestricted viewing (e.g.,
see the
displays
in the right
columns
of
Figure 4B), even though
their inner aligned edges
are
equivalent
to
those
of the
effective
inducing pacmen. This null
effect
for
crosses
has
been variously attributed
to
their symmetry, their
"goodness
of
figure," and
their familiarity
(e.g.,
Kanizsa, 1979)
or to
the
grouping
of
aligned edges within each cross
(Sajda
&
Finkel,
1995).
All
such accounts agree that
the
crosses
form
well-completed shapes
in
their
own right and
hence
do not
induce
any
perception
of an
occluding subjective
figure.
This
failure
of
aligned
crosses
to
induce subjective
figures
with
unrestricted viewing
has
been taken
(e.g.,
by
Kanizsa,
1979)
as an
important counterexample
to
low-spatial-
frequency
accounts (Ginsberg, 1975)
of the
subjective
figures
seen with comparable pacmen inducers.
It has
been
argued that
any
blurring between
the
aligned edges
of
pacmen
at low
spatial frequencies should apply equally
for
comparable crosses. This should certainly hold
for our
stimuli,
because
we
ensured that
the
crosses were
at
least
as
thick
as the
pacmen around their critical inducing edges
(compare Figures
4A and 4B,
which show
the
clusters
to the
same
scale).
If
the
effective
occluding
surfaces
in
Experiment
1
were
caused merely
by
low-spatial-frequency
blurring, they should
also
be
produced
in the
present cross study
to
yield occlusion
and
thus
inefficient
search once again. However,
if the
surfaces
that
influence
search
hi
our
tasks have more
in
common with
the
subjective
figures
that
are
experienced
phenomenally with unrestricted viewing, then
no
subjective
surfaces
should
be
formed
by the
crosses
in
this task,
and
hence
efficient
parallel search might
be
found,
even though
participants
now had to
search
in the
back plane again.
The
brown
stimuli
all had
uncrossed disparity
in
Experiment
3
just
as in
Experiment
1, so
that they appeared
in the
back
plane. Note also that
as for
Experiments
1 and 2, the
straight
edges
of the
notched circle target
in
Experiment
3
(see
Figure
4B,
left
column)
had no
artificial
stereo disparity
and
thus
appeared
at the
screen depth. Hence
the
straight edges
of
the
notch appeared
in
front
of the
target's
circular edges
in
Experiment
3,
yielding
an
unusual depth arrangement that
tends
to
produce
a
sensation
of a
highlight
in
front
of the
notch with unrestricted viewing. However,
the
crucial point
is
that this applied equally
for the
notched target
in
Experiment
1,
where highly
inefficient
search
had
been
found.
If the
results
of
Experiment
1
were somehow
due
just
to
this unusual depth arrangement within
the
target, then
those results should
be
found
again. Alternatively,
if the
results
of
Experiment
1
were
due to
occlusion
by
subjective
figures
and
no
such
figures are
formed
by
aligned crosses
within
preattentive
vision, then
efficient
parallel search
for
the
notched target should
now be
found
instead.
Method
Seven
new
participants were
recruited from the
same source
as
before.
Four were women
and 3
were
men who
ranged
in age
from
19
to 28
years
(M
= 24
years).
The
method
was
exactly
as for
Experiment
1
except
for the
replacement
of
black pacmen
with
black
crosses,
as
shown
in
Figure
4B.
Results
The
mean correct
RTs and
error rates across participants
for
each condition
are
shown
in
Figure
7C. It can be
seen
that
the
change
from
black pacmen
to
crosses
had a
dramatic
impact
on
performance
as
compared
with
Experiment
1.
That
study
had
found
very slow search rates (Figure 7A),
whereas
the
present
findings
indicated highly
efficient
parallel search. Linear regressions
on the
averaged
RT
data
against
set
size gave
slopes
of
only
3.6
ms/cluster
for
target-present responses
and
10.6 ms/cluster
for
target-
absent
trials
(with
ranges
of
—5-16
ms/cluster
and
—5-36
ms/cluster, respectively).
We
carried
out
separate one-way
within-subject
ANOVAs
on the
target-present
and
target-
absent
RT
data, with
the
factor
of set
size. There
was no
effect
of set
size
on
target-present
or on
target-absent trials,
Fs(2,
12)
=
2.2 and
2.5, respectively (ns). Similar analyses
of
error rates
found
that
the
effects
of set
size
did not
reach
significance
on target-present or on target-absent
trials,
Fs(2,
12) = 3.7 and
3.6, respectively (ns). Planned contrasts
of the
search slope data, derived
by
linear regressions
on the RT
means
against
set
size
for
each participant, revealed that
the
target-absent
and the
target-present
slopes
did not
differ
reliably
from
each other, F(l,
6) < 1
(ns). Moreover,
the
target-present
and the
target-absent
slopes
were significantly
lower
in the
present study than
in
Experiment
1,
Fs(l,
11)
=
25.7
and
22.6, respectively,
ps
<
.001.
Discussion
The
efficient
parallel search
in
this study suggests that
the
presence
of the
small black pacmen,
and the
accompanying
subjective
figure
percepts,
was
essential
for
causing
the
extreme
difficulty
of
search
in
Experiment
1.
Certainly,
the
current
data rule
out
several alternative explanations
for
that
outcome. Mere low-spatial-frequency blur (Ginsberg, 1975)
seems inadequate
to
produce effective occluding surfaces
that
can
disrupt parallel search
for the
abutting notched
target, because such blurring should operate between
the
present cross inducers just
as for the
pacmen inducers
of
Experiment
1.
Equally,
it
cannot
be the
case that search
is
always
serial whenever
the
notched target
has
uncrossed
disparity
for its
circular contours
but no
artificial disparity
for
the
straight edges
of the
notch.
The
target took this
form
hi
both Experiments
1 and 3, yet
highly
inefficient
search
was
found
in the
former study
and
highly
efficient
search
in
the
latter.
We
argue that presenting
the
straight notched
edges
of the
target
in
front
of its
circular edges
in
this
way
leads
to an
illusory highlight
in the
region
of the
notch. This

180
DAVIS
AND
DRIVER
highlight
is
swallowed
up by the
abutting subjective surface
that
was
present
in
Experiment
1, and
because there were
many
such subjective surfaces within each search display
for
that
study, search could
not be
based
on its
presence.
By
contrast,
in
Experiment
3 no
bright subjective surfaces were
formed
between
the
aligned black
crosses,
and
hence
the
notched target produced
the
only highlight
in the
display,
leading
to the
efficient
search
that
was
observed.
Whether
or
not
the
exact details
of
this account
are
accepted,
the
present
parallel result certainly demonstrates that
the
inefficient
search
of
Experiment
1
cannot have been
due to the
unusual
stereo
arrangement within
the
notched target,
as
this same
arrangement
led to
efficient
parallel
search
in
Experiment
3.
The
present results also show that search
for the
brown
notched
circle
does
not
have
to be
inefficient
whenever
it
must
take
place
in the
back plane, with black
nontargets
in
front.
This
arrangement
applied
to
Experiment
3
just
as to
Experiment
1, yet
efficient
parallel search
was now ob-
served.
However,
two
alternatives
to our
account
in
terms
of
occluding
subjective
surfaces remain
possible.
First,
one
might
argue that
a
difficulty
in
searching
for a
notched target
in
the
back plane
may
only become apparent when nontar-
gets
in the
front
plane have
a
very similar shape.
In
other
words,
the
relative depth
of the
target
may
interact with
its
similarity
in
shape
to
nontargets
in
other planes.
The
black
pacmen
in
Experiment
1
were certainly more similar
in
shape
to the
notched target than
to the
present black crosses.
Second,
one
might argue that
the
difficulty
of
searching
for
the
notched
target
in
Experiment
1 did not
reflect genuine
occlusion
by a
subjective surface
but
merely strong grouping
between
the
aligned pacmen
and the
notched edges
of the
target, which impaired segmentation
of the
notched target
as
an
isolated
entity.
Given
the
efficient
parallel
search
in
Experiment
2, any
such argument seems forced
to
concede
that,
for
some unknown reason, grouping between aligned
straight
edges
in a
common plane
is
only detrimental when
the
curved edges
of the
target
lie in the
back plane rather
than
in the
front
plane. Moreover, given
the
results
of
Experiment
3,
such
an
argument would also have
to
concede
that
the
disruptive grouping does
not
arise when crosses
rather than pacmen provide
the
aligned edges.
In
other
words,
the
aligned
edges
of
crosses
must somehow
be
less
"free"
to
group with
the
target notch than
the
equivalent
edges
of
pacmen
are to
group with this notch, perhaps
because
of the
numerous
90°
junctions that
are
present
in the
cross
shapes.
On the one
hand,
the
account
in
terms
of
edge
•
grouping alone starts
to
seem increasingly post
hoc at
this
point.
On the
other hand,
it
should
be
admitted
that
some
such
difference
in
freedom
of
grouping
for the
straight
inducing edges must presumably exist between
crosses
and
pacmen
to
explain
why
subjective
figures
are
induced
by
pacmen
but not by
crosses with unrestricted viewing. Once
this
is
granted,
one
could perhaps argue that
it is the
difference
in
grouping
per se
rather than
in the
consequent
formation
of
subjective
figures
that
dictated
our
visual-
search results.
In
our final
study
we
examined these
two
remaining
alternative accounts
to our
hypothesis
of
occluding subjec-
tive
surfaces.
By
these accounts,
the
critical
factor
is
either
(a)
distraction
from
similar shapes
in the
front
plane
or (b)
grouping between
the
straight notched edges
of the
target
with
aligned
free
edges
in the
front
plane.
Experiment
4
As in
Experiment
1,
participants
searched
for a
large
brown notched circle among complete large brown
circles
in
the
back plane. Also
as in
Experiment
1, the
front
plane
contained black pacmen nontargets, though
now
arranged
so
as
not to
form
any
subjective squares (see Figure 4C).
If the
difficulty
of
search
in
Experiment
1 had
been caused merely
by
problems
in
ignoring small black nontargets
in the
front
plane when these
had a
similar shape
to the
large brown
target
at the
back, then
the
slow search rates
of
Experiment
1
should
be
found
once
again.
A
further similarity
to
Experi-
ment
1 was
that within target clusters, pacmen that neigh-
bored
the
notched target always
had one of
their straight
edges perfectly aligned with
a
straight edge
from
the
target
(see Figure
4C,
left
column). Thus,
if the
serial search
in
Experiment
1 had
been caused simply
by
grouping between
straight
target edges
and
free
straight edges
in the
front
plane, then highly
inefficient
search should
be
found
once
again. However,
if the
outcome
of
Experiment
1 was due to
occlusion
by
subjective surfaces, then
it
should
not be
found
in
the
present study.
The
pacmen were
now
each rotated (see
Figure
4C) so
that
while pacmen that neighbored
the
notched target still
had one of
their edges
in
perfect
alignment
with
it, no
subjective square should
be
formed
with
the
other pacmen.
Our
account therefore predicts
efficient
parallel search, whereas
the two
remaining alterna-
tives
must predict
inefficient
search,
as in
Experiment
1.
Method
The
method followed Experiment
1
exactly except
for the
rotation
of
black pacmen nontargets that
is
illustrated
in
Figure
4C
(which shows
two
possible
target
clusters
in the
left
column
and the
four
possible
nontarget
clusters
in the
middle
and
right columns).
Six
new
participants were recruited
from
the
same source
as
before.
There
were
4
women
and 2 men who
ranged
in age
from
17
to 23
years
(M
=
21
years).
Results
The
mean correct
RTs and
error rates across participants
for
each condition
are
shown
in
Figure
7D. It can be
seen
that
the
rotation
of
pacmen
had a
dramatic impact
on
performance
as
compared
with
Experiment
1
(cf. Figure
7
A).
That study
had
found
very slow search rates, whereas
the
present
findings
indicated
efficient
parallel search.
Linear regressions
on the
averaged
RT
data against
set
size
gave
slopes
of
only
1.1
ms/cluster
for
target-present
re-
sponses
and
23.8 ms/cluster
for
target-absent trials (with
ranges
of
—10-12
ms/cluster
and
—2-104
ms/cluster,
respec-
tively).
The
relatively
steep
mean
slope
for
target-absent
responses
was
largely
due to one
participant
who
appeared
to
check serially when
no
target
was
present (yielding slopes
of
12
ms/cluster
on
target-present trials
but 104
ms/cluster

PARALLEL
CODING
OF
SUBJECTIVE VISUAL SURFACES
181
on
target-absent trials). With this participant excluded,
the
mean
slopes
were
—
1
ins/cluster
on
target-present trials
and
8
ms/cluster
on
target-absent trials (ranging
from
—10-4
ms/cluster
and from
—2-15
ms/cluster,
respectively).
We
carried
out
separate one-way within-subject
ANOVAs
on
the
target-present
and the
target-absent
RT
data
from all 6
participants, with
the
factor
of set
size. There
was no
effect
of
set
size
on
target-present
trials,
F(2,10)
= 0.4
(ns),
or on
the
target-absent trials,
F(2,10)
=
2.2,
p >
.1,
even though
the 1
participant
who
apparently checked serially
was
included.
In
similar analyses
of
error rates
we
found
no
effects
of set
size
on
target-present
or on
target-absent trials,
F(2,
10) = 1.2 and
1.8, respectively (ns), again with every
participant included. Planned contrasts
of the
search slope
data,
derived
by
linear regressions
on the RT
means
for
each
participant, revealed that
the
target-absent
and the
target-
present
slopes
did not
differ
reliably
from
each other,
F(l,
5)
< 1
(ns).
The
target-present slopes were
significantly
lower
in the
present
study
than
in
Experiment
1,
F(l,
10) =
23.8,
p <
.001,
as
were
the
target-absent
slopes,
F(l,
10) =
13.3,
p<.
005.
Discussion
These
findings
provide conclusive evidence that
the
perception
of
occluding subjective surfaces
was
indeed
responsible
for the
difficulty
of
search observed
in
Experi-
ment
1.
Experiment
4 was
identical
to the first
experiment
in
all
respects except
for the
rotation
of
pacmen
nontargets
(cf.
Figures
4A and
4C). This rotation preserved
all the
factors
that
should
be
essential
for
rendering search
difficult
accord-
ing
to
every account
of
Experiment
1
that does
not
invoke
occlusion
by
subjective surfaces.
First,
the
notched target
still
had the
unusual stereo arrangement
of
Experiment
1,
whereby
its
straight notched edges appeared
in front of its
curved
edges.
Second,
the
black pacmen still appeared
in the
front
plane, with
the
notched target behind,
and
these black
pacmen were just
as
similar
to the
target
in
shape
as for the
pacmen
nontargets
of
Experiment
1
(and likewise they were
just
as
distinct
in
terms
of
size, color,
and
depth). Finally,
pacmen which neighbored
the
notched target still
had one
free
straight edge perfectly aligned with
one of the
target's
straight edges. Nevertheless,
efficient
parallel search
was
now
found
rather than
the
very slow search rates
of
Experiment
1.
This
is
just
as we had
expected
by our
account,
because
no
occluding subjective surface could
be
formed
between
the
rotated black pacmen
in the
front
plane.
General
Discussion
We
began
by
considering
the
traditional debate over
whether subjective
figures
reflect
low-level
or
high-level
visual
processes.
Our
brief review suggested that actually
both high-level
and
low-level factors
often
play
a
role
in
determining
the
phenomenal percept obtained
witii
unre-
stricted
and
unspeeded viewing. However,
we
noted that
a
number
of
subtly
different
distinctions have typically been
subsumed together under
the
low-level
and the
high-level
headings
of
previous research that
has
taken
a
dichotomous
approach.
We
argued that
future
progress depends
on
addressing more specific questions about
the
exact
levels
of
processing that influence subjective
figures,
within objective
performance
tasks
with
restricted
viewing under time pres-
sure.
We
then raised
two
such questions, which both relate
to
attentional
issues.
Our first
question
was
whether
Kanizsa
subjective
figures can be
coded
efficiently
in
parallel
"preat-
tentive"
vision.
Our
second
question
was
whether
the
coding
of
Kanizsa
figures is
obligatory, arising spontaneously even
when
participants
do not
have
to
judge
any
subjective
figure
and,
moreover, even when
the
perception
of
subjective
figures
can
only
be
detrimental
to
their prescribed task.
Our
review
of
previous
findings on
these
two
questions (Davis
&
Driver, 1994; Grabowecky
&
Treisman,
1989;
Gurnsey
et
al.,
1992;
Peterhans
& von der
Heydt,
1991)
showed that
the
existing data were equivocal. Davis
and
Driver's
recent
finding
of
pop out in
visual search
for a
subjective-figure
target provided
the
most suggestive prior evidence
for
parallel coding. However, their results
did not
directly
demonstrate that
any
subjective
surface
was
interpolated
between
the
inducers
of the
subjective-figure
target
or
that
parallel coding would arise obligatorily
for
multiple subjec-
tive figures,
even
when participants
had no
intention
of
searching
for
these
figures.
The
results
from
the
present visual-search experiments
thus
provide
the first
unambiguous evidence
for the
parallel
and
obligatory coding
of
multiple Kanizsa subjective
fig-
ures. Experiment
1
found
very slow search rates
for a
notched-circle target when
its
notch abutted
a
subjective
surface
that
lay
stereoscopically
in
front.
In
line
with
the
previous work
of
Enns
and
Rensink
(1992)
and He and
Nakayama
(1992)
with
luminance-defined
occluders,
we
attribute
this outcome
to
amodal completion
of
notched
targets when
the
notch
is
apparently produced
by an
occluding subjective surface. Experiments
2-4
controlled
for
alternative accounts. Consistent
with
our
occlusion
account, Experiment
2
found
efficient
parallel search when
stereoscopic
depth
was
reversed,
so
that
the
target
now lay in
front
of
any
abutting subjective surface. Experiment
3
found
parallel search when
the
notched target
lay in the
back plane,
as
in
Experiment
1, but now
aligned crosses replaced
the
pacmen
that
had
previously induced subjective surfaces
in
the
front
plane. This result rules
out
possible
accounts
for the
occluding subjective surfaces
of
Experiment
1 in
terms
of
low-spatial-frequency
blur.
It
also demonstrates that search
can
be
efficient
for
notched targets
in the
back plane,
provided that there
is no
amodal completion
of the
notched
target
due to
apparent occlusion
by a
subjective surface.
Finally, Experiment
4
found
parallel search
for a
notched
target
at the
back even when
the
notch remained aligned
with
"free"
pacmen edges
at the front, but
with these
now
arranged
so
that
no
subjective surface could
be
formed. This
rules
out any
explanation
of the
difficult
search
in
Experi-
ment
1 in
terms
of
mere edge grouping.
We
think that this
edge-grouping control
is
particularly important,
as
most
previous studies
of
subjective
figures
(see Petty
&
Meyer,
1987) have inadvertently introduced potential
differences
in
edge grouping when comparing subjective
figures
with
control
stimuli.

182
DAVIS
AND
DRIVER
Our
results thus demonstrate obligatory parallel coding
for
multiple
Kanizsa
subjective figures. Unlike Davis
and
Driver's
(1994)
previous visual-search data,
our findings
entail that subjective surfaces
get
interpolated between
the
appropriate inducers
at
parallel stages
of
vision, because
such
surfaces evidently acted
as
occluders
to
disrupt what
should otherwise have been
efficient
parallel search
in
Experiment
1.
Moreover, there were multiple subjective
surfaces
in
each
of the
present displays, whereas Davis
and
Driver presented
at
most
one
subjective
figure
(i.e.,
just their
target). Hence,
our
experiments
are the first to
show that
several concurrent subjective
figures can be
coded together
in
parallel.
Finally,
we
found
parallel emergence
of
occlud-
ing
subjective surfaces even though participants
had no
intention
of
searching
for
subjective surfaces. Moreover,
we
observed this
finding in
Experiment
1 for a
situation
in
which
the
subjective surfaces could only disrupt
the
pre-
scribed task. This implies that
the
parallel coding
of
Kanizsa
subjective
surfaces
is
obligatory rather than optional.
Our
conclusion that Kanizsa
figures can act as
occluding
surfaces,
at
parallel stages
of
vision, corroborates
and
extends
the
recent claims
of He and
Nakayama
(1992)
and
Enns
(1992) concerning
the
visual processes tapped
by
visual search. Enns argued that visual-search tasks
can
reveal much more sophisticated parallel processes than
had
previously been thought.
In
particular, visual-search tasks
reveal parallel processes that deal with
the
scene-based
relations between
3-D
surfaces rather than merely with
the
2-D
properties
of
simple image features (see also Enns
&
Rensink,
1991, 1992;
He &
Nakayama, 1992). Indeed,
parallel vision
may
often
be
unable
to
access
2-D
image
properties directly,
with
the
result that
a
slow
and
inefficient
search
can be
required
to
detect
the
incompleteness
of a
partially occluded shape.
Our
results provide
a
further
demonstration
of
this phenomenon
and
generalize
it to the
case
of
occlusion
by
subjective surfaces.
Earlier,
we
noted that most previous studies
of
subjective-
figure
perception have typically used unspeeded phenom-
enal measures concerning
the
strength
of any
illusory
figure
(e.g.,
Warm
et
al.,
1987).
As
discussed earlier, such measures
have
several shortcomings when issues such
as the
possible
involvement
of
attention
in the
coding
of
subjective
figures
are
examined.
Our
experiments
differed
from
such phenom-
enal techniques
in two
main respects. First,
a
speeded
objective judgment
was
required
(is the
notched target
present?) rather than
an
unspeeded introspective assessment.
Second,
we
measured
the
existence
of any
subjective-figure
percept indirectly
by
means
of its
effect
on
judgments
for a
luminance-defined
stimulus
(i.e.,
the
notched target). This
aspect
of our
method allowed
us to
examine whether
subjective
figures
arise spontaneously rather than merely
in
response
to
leading questions (see Rock
&
Anson,
1979;
Rock
&
Mitchener, 1992). Because
any
effect
of the
subjective
surface
on the
notched target could only disrupt
performance
in
Experiment
1, our
indirect objective mea-
sure
also allowed
us to
conclude that
the
emergence
of
subjective
occluding surfaces
is
obligatory. Below
we
discuss
how
these
findings fit
with previous work
on
subjective
figures and
also
how
they extend those prior
results.
Dresp
and
colleagues
(e.g.,
Dresp, 1993; Dresp
&
Bonnet,
1995) have recently
found
that thresholds
for the
detection
of
a
luminance-defined
edge
can be
affected
by the
presence
of
a
subjective
figure—that is,
thresholds
are
lower
for
probes presented along
a
subjective
edge.
Their studies
are
thus
similar
to
ours
in
using
an
indirect measure, whereby
the
presence
of a
subjective
figure
affects
objective judg-
ments
of a
luminance-defined stimulus. Their studies
differ
from
ours
in the
details
of the
task
and in the
controls that
have been used (typically,
the
Dresp studies compare just
inward-
and
outward-facing pacmen, whereas
we
used
various controls, comprising stereoscopic depth reversals
in
Experiment
2,
cross inducers
in
Experiment
3, and
rotated
but
edge-grouped pacmen
in
Experiment
4).
More impor-
tant,
our
studies also
differ
from
this previous work
in the
specific
conclusions that
can be
drawn concerning
the
role
of
attention.
In the
Dresp studies, only
a
single subjective
figure is
presented
in
each display, within
a
region that
is
known
to be
relevant
for the
target-detection task. Thus,
no
conclusions
can be
drawn
from
the
Dresp studies about
parallel processing without focal attention.
By
contrast,
our
own
studies addressed this
very
issue. However,
in
future
work,
the
probe-detection technique could
be
adapted
to
allow
further
study
of the
role
of
attention
by
varying
the
number
of
subjective-figure stimuli
and
control stimuli
within
a
display
and by
restricting their exposure time prior
to
presentation
of the
detection
probe.
We
turn
now to a
further
aspect
of our
performance
findings:
They
confirm
that
Kanizsa subjective
figures can
act
as
occluding surfaces,
to
induce
amodal
completion
of
abutting
shapes
(as in
Experiment
1).
This
is
consistent with
several previous claims. Kanizsa
(1979)
himself argued that
the
inducing pacmen
in his
displays become
amodally
completed behind
the
subjective surface that they induced.
In the
past, such claims have typically been based solely
on
subjective
reports, which
can be
questioned
as firm
evidence
for
amodal completion (see Sekuler
&
Palmer, 1992).
The
present results provide more objective evidence that subjec-
tive surfaces
can
indeed induce amodal completion behind
them.
Bruno
and
Gerbino (1987)
had
previously produced
some
objective performance data that
seemed
consistent
with
this proposal.
In a
speeded
same-different
matching
task, their participants
had to
match
a
complete shape
to a
subsequent
partial version
of
that shape. This
was
easier
when
the
partial shape
was
occluded
by a
regular luminance-
defined
surface,
or by a
subjective
surface,
than when
no
occluder
was
apparent. However, Bruno
and
Gerbino
did not
implement
as
many controls
as we
have
for the
effect
of
occlusion
by
subjective surfaces. They merely compared
inward-facing
inducers
to
outward-facing inducers
in a
manner that
did not
control
for
possible
low-spatial-
frequency
artifacts
or for
mere edge grouping. Moreover,
their displays contained
at
most only
one
subjective surface,
in
a
location that
was
known
to be
relevant. Hence
the
issue
of
parallel coding could
not be
addressed. Equally, subjec-
tive
figures
aided performance
in
their task
and
might

PARALLEL
CODING
OF
SUBJECTIVE VISUAL SURFACES
183
therefore have been
of
strategic
use,
so the
issue
of
obligatory coding could
not be
addressed either.
Yantis
(1995)
has
recently also suggested that subjective
surfaces
can act as
occluders,
because their presence
can
determine
the
apparent motion
of
stimuli that disappear
briefly,
in a
manner consistent with occlusion during move-
ment. However,
as
with Bruno
and
Gerbino's
(1987)
study,
Yantis's
displays contained
at
most
one
subjective
figure in a
region that
was
relevant
to the
prescribed task. Thus,
although
previous data have produced some suggestive
support
for
amodal
completion behind subjective surfaces,
our
results provide
the first
unequivocal evidence
from
objective performance
to
show that
Kanizsa
subjective
figures can
indeed
act as
obligatory occluding surfaces
at
parallel
stages
of
vision.
The
other aspect
of our
results, namely, that Kanizsa
figures can act in
this
way
without focal attention, makes
considerable sense
from
the
functional perspective advo-
cated
by
Ramachandran
(1987).
Along with many others,
he
noted that
the
contours
of
individual objects
in
real-world
scenes
are
rarely demarcated
in any
simple
fashion
by
continuous
and
constant edges
in the
luminance domain.
Complexities
due to
lighting, shadows, occlusion,
and
intrinsic changes along
an
object's surface
can
result
in
considerable luminance variations
and
discontinuities along
the
contour
of an
object. Moreover, various forms
of
camouflage
in the
natural world
are
designed precisely
to
exacerbate these problems (e.g.,
the
stripes
on a
tiger),
Ramachandran
has
argued that
the
perception
of
subjective
surfaces
may
serve
as an
"anticamouflage"
device that
has
evolved precisely
to
circumvent these
difficulties.
It
allows
real-world contours
to be
extracted
by
nonaccidental
align-
ments
in an
image (e.g.,
the
fact
that
all the
stripes
end at the
occluding edge
of the
tiger),
in the
absence
of
corresponding
continuous luminance edges
in
that image (which
are
broken
up by the
stripes). This account suggests that
far
from
being
a
laboratory curio that arises
in
just
a few
artificial
displays,
the
perception
of
subjective
figures may
serve
a
vital
evolutionary
function
in the
veridical perception
of
natural
images. However, note that
any
such anticamouflage
func-
tion
would
be
largely self-defeating
if
careful
attentional
scrutiny were always required
to
detect
the
camouflaged
object.
Our
evidence
for
efficient
parallel coding
of
subjec-
tive
figures
therefore makes considerable functional sense,
because such parallel coding should allow otherwise camou-
flaged
objects
to pop out
from
their background even when
initially they
are not
focally
attended.
Although
our
results show that subjective surfaces
can be
coded
as
occluders
at
parallel stages
of
vision,
in an
obligatory manner, this does
not
entail that focal attention
will
never have
any
influence
on
subjective-figure percepts.
As
we
noted earlier, there
are
already several demonstrations
of
various high-level influences
on
subjective
figures, and it
is
possible that some
of
these
may
operate only
at
attentive
levels
of
processing.
The
visual-search technique could
be
adapted
to
study whether factors such
as
prior experience
(Coren
et
al.,
1987;
Gellatly
&
Bishop,
1987)
or
perceptual
set
(Rock
&
Anson,
1979)
can
exert their influence
at
parallel stages
of
vision
or
only with focal attention
to the
inducing stimuli.
Our findings
already show that cross
inducers (Experiment
3)
fail
to
induce
a
subjective surface
with
diffuse
attention
in
parallel vision, just
as
when
the
cross inducers
are
given unrestricted viewing with focal
attention (Kanizsa,
1979).
However,
it
remains
to be
seen
whether
all of the
other factors that
can act
against
a
subjective-figure
percept with unrestricted viewing
(see
Perry
&
Meyer,
1987)
will likewise exert
a
comparable
influence
at
parallel
stages
of
preattentive
vision.
In
prin-
ciple,
the
visual-search task could
be
used
to
determine
the
levels
of
processing
at
which every potential
"veto"
on a
subjective
surface
can
operate.
References
Aks,
D. J., &
Enns,
J. T.
(1992). Apparent depth influences visual
search
for the
direction
of
shading.
Perception
&
Psychophysics,
51,
63-74.
Andersen,
G.
J.,
&
Kramer,
A.
(1993). Limits
of
focused attention
in
three-dimensional space.
Perception
&
Psychophysics,
53,
658-667.
Bonaiuto,
P.,
Giannini,
A.
M,
&
Bonaiuto,
M.
(1991).
Visual
illusory productions with
or
without amodal completion. Work-
shop
on new
issues
in the
perception
of
anomalous surfaces
and
subjective
contours conducted
at the
llth
European Conference
on
Visual Perception.
Perception,
20,
243-257.
Bradley,
D.
R.,
&
Dumais,
S. T.
(1975). Ambiguous cognitive
contours.
Nature,
257, 582-584.
Brandeis,
D. U., &
Lehmann,
D.
(1989).
Segments
of
event-related
potential
map
series
reveal landscape changes with visual
attention
and
subjective contours.
Electroencephalography
and
Clinical
Neurophysiology,
73,
507-519.
Brigner,
W.
L.,
&
Gallagher,
M. B.
(1974). Subjective contour:
Apparent depth
or
simultaneous brightness contrast?
Perceptual
&
Motor
Skills,
38,
1047-1053.
Bruno,
N., &
Gerbino,
W.
(1987). Amodal completion
and
illusory
figures:
An
information processing analysis.
In S.
Petry
& G. E.
Meyer
(Eds.),
The
perception
of
illusory
contours (pp.
220-222).
New
York/Berlin:
Springer-Verlag.
Chun,
M. C., &
Wolfe,
J. M.
(1996).
Just
say no: How are
visual
searches terminated when there
is no
target present?
Cognitive
Psychology,
30,
39-78.
Coren,
S.,
Porac,
C.,
&
Theodor,
L. H.
(1987).
Set and
subjective
contour.
In S.
Petry
& G. E.
Meyer
(Eds.),
The
perception
of
illusory
contours
(pp. 237-246).
New
York/Berlin:
Springer-
Verlag.
Davis,
G.,
&
Driver,
J. S.
(1994). Parallel detection
of
Kanizsa
subjective
figures in the
human visual system.
Nature,
371,
791-793.
Dresp,
B.
(1993).
The
Kanizsa square does
not
entail
a
configural
superiority
effect.
Bulletin
of the
Psychonomic
Society,
31,
183-184.
Dresp,
B.,
&
Bonnet,
C.
(1995).
Subthreshold
summation with
illusory
contours.
Vision
Research,
35,
1071-1078.
Duncan,
J.,
&
Humphreys,
G. W.
(1989). Visual search
and
stimulus
similarity.
Psychological
Review,
96,
433-458.
Ehrenstein,
W.
(1941).
Uber
Abwandlungen
der L.
Hermannschen
Helligkeitserscheinung [Modifications
of the
Hermann bright-
ness
phenomenon].
Zeitscriftfur
Psychologie,
150,
83-91.
Enns,
J. T.
(1992).
The
nature
of
selectivity
in
early human vision.
In
B.
Burns
(Eds.),
Percepts,
concepts
and
categories
(pp.
39-74).
Amsterdam: North-Holland.
Enns,
J.
T.,
Ochs,
E. P., &
Rensink,
R. A.
(1990).
Vsearch:

184
DAVIS
AND
DRIVER
Macintosh software
for
experiments
in
visual search. Behav-
ioural
Research
Methods,
Instruments,
and
Computers,
22,
118-122.
Enns,
J. T., &
Rensink,
R. A.
(1991).
Preattentive
recovery
of
three-dimensional orientation
from
line drawings. Psychological
Review,
98,
101-118.
Enns,
J.
T.,
&
Rensink,
R. A.
(1992).
An
object completion process
in
early vision. Investigative
Opthalmology
&
Visual
Science,
33,
1263.
Fahle,
M., &
Koch,
C.
(1995).
Spatial displacement
but not
temporal asynchrony destroys temporal binding.
Vision
Re-
search,
35,
491-494.
Gellatly,
A.,
&
Bishop,
M.
(1987).
The
perception
of
illusory
contours:
A
skills analysis.
In S.
Petry
& G. E.
Meyer
(Eds.),
The
perception
of
illusory
contours (pp.
262-265).
New
York/Berlin:
Springer-Verlag.
Ginsberg,
A. P.
(1975).
Is the
illusory triangle real
or
imaginary?
Nature,
257,
215-220.
Grabowecky,
M.,
&
Treisman,
A.
(1989).
Attention
and fixation in
subjective contour perception. Investigative
Opthalmology
&
Visual
Science,
30,
457.
Gregory,
R. L.
(1972). Cognitive contours. Nature, 238,
51-52.
Gregory,
R.
L.,
&
Harris,
J.
(1974). Illusory contours
and
stereo
depth. Perception
&
Psychophysics,
15,
411-416.
Grosof,
D. H.,
Shapley,
R.
M.,
&
Hawken,
M. J.
(1993).
Maccaque
VI
neurons
can
signal
"illusory"
contours. Nature, 365,
550-
552.
Grossberg,
S.,
&
Mingola,
E.
(1985).
Neural dynamics
of
percep-
tual grouping: Textures, boundaries
and
emergent segmenta-
tions. Perception
&
Psychophysics,
38,
141-171.
Gurnsey,
R.,
Humphrey,
G. K., &
Kapitan,
P.
(1992). Parallel
discrimination
of
subjective contours
defined
by
offset
gratings.
Perception
&
Psychophysics,
52,
263-276.
He,
Z.
J.,
&
Nakayama,
K.
(1992).
Surfaces versus features
in
visual-search. Nature, 359,
231-233.
Julesz,
B.,
&
Bergen,
J. R.
(1983). Parallel versus serial processing
in
rapid pattern discrimination. Nature, 303,
696-698.
Kanizsa,
G.
(1955).
Margini
quasi-percettivi
in
campi
con
stimola-
zione
omogenea
[Quasi-perceptual margins
in
homogeneously
stimulated
fields].
Rivista
di
Psicologia,
49,
7-30.
Kanizsa,
G.
(1979). Organization
in
vision.
New
York: Praeger.
Kennedy,
J.
M.,
&
Lee,
H.
(1976).
A figure-density
hypothesis
and
illusory contour brightness. Perception,
5,
387-392.
Lawson,
R.
B.,
Cowan,
E.,
Gibbs,
T.
D.,
&
Whitmore,
C. G.
(1974).
Stereoscopic enhancement
and
erasure
of
subjective contours.
Journal
of
Experimental
Psychology,
103,
1142-1146.
Lesher,
G.
W.
(1995).
Illusory contours: Towards
a
neurally based
perceptual theory.
Psychonomic
Bulletin
&
Review,
2,
279-321.
Miiller,
J.,
Heller,
D.,
&
Ziegler,
J.
(1995). Visual search
for
singleton feature targets
within
and
across
feature
dimensions.
Perception
&
Psychophysics,
57,
1-17.
Nakayama,
K.,
&
Silverman,
G. H.
(1986).
Serial
and
parallel
processing
of
visual feature conjunctions. Nature, 320,
264-265.
Palmer,
J.
(1996). Attention
in
visual search: Distinguishing
four
causes
of a
set-size
effect.
Current Directions
in
Psychological
Science,
4,
118-123.
Parks,
T. E.
(1987).
Illusory
figures and
pictorial objects.
In S.
Petry
& G. E.
Meyer
(Eds.),
The
perception
of
illusory
contours (pp.
76-79).
New
York/Berlin:
Springer-Verlag.
Peterhans,
E.,
& von der
Heydt,
R.
(1991).
Subjective
contours—
Bridging
the gap
between
psychophysics
and
physiology.
T.I.N.S.,
14,
112-119.
Petry,
S.,
&
Meyer,
G. E.
(Eds.).
(1987).
The
perception
of
illusory
contours.
New
York/Berlin:
Springer-Verlag.
Pritchard,
W.
S.,
&
Warm,
J. S.
(1983).
Attentional processing
and
the
subjective contour
illusion.
Journal
of
Experimental
Psychol-
ogy:
General, 112,
145-175.
Ramachandran,
V. S.
(1987).
Visual perception
of
surfaces:
A
biological theory.
In S.
Petry
& G. E.
Meyer
(Eds.),
The
perception
of
illusory
contours (pp.
93-108).
New
York/Berlin:
Springer-Verlag.
Redies,
C.
(1989).
Discontinuities along lines: Psychophysics
and
neurophysiology.
Neuroscience
&
Biobehavioral
Reviews,
13,
17-22.
Rock,
L, &
Anson,
R.
(1979). Illusory contours
as the
solution
to a
problem. Perception,
8,
665-681.
Rock,
L, &
Mitchener,
K.
(1992).
Further evidence
of
failure
of
reversal
of
ambiguous
figures by
uninformed subjects.
Percep-
tion,
21,
39-45.
Sajda,
P., &
Finkel,
L. H.
(1995). Intermediate-level visual
representations
and the
construction
of
surface perception.
Journal
of
Cognitive
Neuroscience,
7,
267-291.
Schneider,
R.
M.,
&
Schiffrin,
W.
(1977).
Controlled
and
automatic
processing:
II.
Perceptual learning, automatic attending,
and a
general theory.
Psychological
Review,
84,
127-190.
Sekuler,
A.
B.,
&
Palmer,
S. E.
(1992). Perception
of
partly
occluded objects:
A
microgenetic
analysis.
Journal
of
Experimen-
tal
Psychology:
General, 121,
95-111.
Shapley,
R.,
&
Gordon,
J.
(1985).
Nonlinearity
in the
perception
of
form.
Perception
&
Psychophysics,
37,
84—88.
Skotun,
B.
C.
(1994).
Illusory contours
and
linear
filters.
Experimen-
tal
Brain Research, 100,
360-364.
Spillman,
L.,
&
Dresp,
B.
(1995).
Phenomena
of
illusory form:
Can
we
bridge
the gap
between levels
of
explanation?
Perception,
24,
1353-1364.
Theeuwes,
J.
(1995).
Abrupt luminance change pops out; abrupt
color change does not. Perception
&
Psychophysics,
57,
637—
644.
Townsend,
J. T.
(1990). Serial
vs.
parallel processing: Sometimes
they
look like Tweedledum
and
Tweedledee
but
they
can
(and
should)
be
distinguished.
Psychological
Science,
I,
46-53.
Treisman,
A.,
&
Gelade,
G.
(1980).
A
feature integration theory
of
attention.
Cognitive
Psychology,
12,
97-136.
Treisman,
A.,
&
Gormican,
S.
(1988). Feature analysis
in
early
vision: Evidence
from
search asymmetries. Psychological
Re-
view,
95,
15-48.
Van
der
Zwan,
R.,
&
Wenderoth,
P.
(1994).
Psychophysical
evidence
for
area
V2
involvement
in the
reduction
of
subjective
contour
tilt
aftereffects
by
binocular
rivalry.
Visual
Neurosci-
ence,
11,
823-830.
Warm,
J.
S.,
Dember,
W. N.,
Padich,
R.
A.,
Beckner,
W. N., &
Jones,
S.
(1987).
The
role
of
illumination level
in the
strength
of
subjective
contours.
In S.
Petry
& G. E.
Meyer
(Eds.),
The
perception
of
illusory
contours (pp.
176-182).
New
York/Berlin:
Springer-Verlag.
Wolfe,
J.
(1994). Guided search 2.0: Revised model
of
visual
search.
Psychonomic
Bulletin
&
Review,
1,
202-238.
Yantis,
S.
(1995). Perceived continuity
of
occluded visual objects.
Psychological
Science,
6,
182-186.
Received
August
14,
1995
Revision received
July
11,1996
Accepted December
2,1996