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Event-related brain potentials and the efficiency of visual search for vertically and horizontally oriented stimuli

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Reports that visual search is more efficient for vertically than for horizontally shaded objects suggested that search is influenced by a priori knowledge about the source of light. In this study, we examined search for targets defined by the orientation of luminance gradients and measured event-related brain potentials (ERPs). In Experiment 1, we examined search for stimuli that comprised gradual luminance differences. Response times showed the expected orientation anisotropy effect. ERP amplitudes in the P1 latency range were slightly more positive in response to horizontally oriented stimuli, whereas P3 amplitudes were more positive in response to nonsingleton vertically oriented stimuli. Experiment 2 compared search for stimuli that comprised gradual versus step differences in luminance. All the anisotropies that we observed in Experiment 1 could be replicated in Experiment 2. Moreover, these anisotropies were not dependent on the type of the luminance gradient. This finding is inconsistent with the view that search efficiency is influenced by a priori knowledge about the source of light. The behavioral and electrophysiological data are consistent with a context model of visual search. We propose that contextual modulation reduces redundancy and contributes to computing the saliency of visual information by implementing divisive normalization and multiplicative filtering.
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Investigating the efficiency of visual search (VS) is a
popular method that is employed by many students of cog-
nitive processes related to visual perception (for reviews,
see Wolfe, 1998; Wolfe & Horowitz, 2004). VS typically
requires searching through a display for a particular ob-
ject (the target item) among other objects (the distractor
items). Wolfe (2007) specified a number of basic phenom-
ena of VS. Among the most important VS phenomena are
(1) search response times (RTs) are often longer when the
search display contains more distractor items (Palmer,
1995); (2) the average RT is typically longer when no tar-
get is present (Chun & Wolfe, 1996); and (3) a limited set
of visual features support very efficient VS (see Wolfe &
Horowitz, 2004, for a review). As a rule, VS is more effi-
cient the lesser the similarity between target items and dis-
tractor items (Duncan & Humphreys, 1989). Conversely,
VS is less efficient the more heterogeneous the distractor
items (Duncan & Humphreys, 1989).
The direction of curvature is one of the basic features
that support efficient VS (Treisman & Gormican, 1988;
Wolfe, Yee, & Friedman-Hill, 1992). If the curves are part
of the bounding contour of an object, this induces concav-
ity or convexity, with observers possibly preferring con-
cavities (Barenholtz, Cohen, Feldman, & Singh, 2003).
Taken into three dimensions, the concavity and convexity
of surfaces might be basic features for studies that argue
that shading is a discrete feature for VS (Aks & Enns,
1992; Kleffner & Ramachandran, 1992; Ramachandran,
1988; Ramachandran & Rogers-Ramachandran, 2008).
Smooth shading gradients—that is, continuous changes
in luminance—provide the visual system with informa-
tion concerning the surface shape of objects with respect
to the source of light. Shape-from-shading describes the
phenomenon in which the visual system discerns the
three-dimensional shape of an object from the shading
on its surface (Prados & Faugeras, 2006). For example,
observers usually see three of the objects in the upper left
panel of Figure 1 as concave and the lower left object as
convex. In several studies, the effects of the orientation of
shading gradients on the efficiency of VS have been ex-
amined (Adams, 2007; Kleffner & Ramachandran, 1992;
Sun & Perona, 1998; Thornton & Gilden, 2007; Wolfe,
Klempen, & Shulman, 1999). In these studies, empiri-
cal evidence of an orientation anisotropy was repeatedly
found: VS is more efficient when the shading gradients
of targets and distractors are vertically oriented (cf. the
upper left panel of Figure 1), whereas VS becomes more
difficult when shading gradients are horizontally oriented
(cf. the upper right panel of Figure 1).
Standard theories of VS cannot account for the ob-
served orientation anisotropy in these shape-from- shading
VS studies. Feature integration theory, for example, was
proposed to explain different RT slopes for feature and
conjunction searches (Treisman & Gelade, 1980). Ac-
523 © 2010 The Psychonomic Society, Inc.
Event-related brain potentials and the
efficiency of visual search for vertically
and horizontally oriented stimuli
Br u n o Ko p p , Ja s m i n Ki z i l i r m a K , Ca r o l i n li e B s C h e r , Ju l i a ru n g e , a n d Ka r l W e s s e l
University of Technology Carolo-Wilhelmina Braunschweig, Braunschweig, Germany
and Braunschweig Hospital, Braunschweig, Germany
Reports that visual search is more efficient for vertically than for horizontally shaded objects suggested that
search is influenced by a priori knowledge about the source of light. In this study, we examined search for tar-
gets defined by the orientation of luminance gradients and measured event-related brain potentials (ERPs). In
Experiment 1, we examined search for stimuli that comprised gradual luminance differences. Response times
showed the expected orientation anisotropy effect. ERP amplitudes in the P1 latency range were slightly more
positive in response to horizontally oriented stimuli, whereas P3 amplitudes were more positive in response
to nonsingleton vertically oriented stimuli. Experiment 2 compared search for stimuli that comprised gradual
versus step differences in luminance. All the anisotropies that we observed in Experiment 1 could be replicated
in Experiment 2. Moreover, these anisotropies were not dependent on the type of the luminance gradient. This
finding is inconsistent with the view that search efficiency is influenced by a priori knowledge about the source
of light. The behavioral and electrophysiological data are consistent with a context model of visual search. We
propose that contextual modulation reduces redundancy and contributes to computing the saliency of visual
information by implementing divisive normalization and multiplicative filtering.
Cognitive, Affective, & Behavioral Neuroscience
2010, 10 (4), 523-540
doi:10.3758/CABN.10.4.523
B. Kopp, b.kopp@klinikum-braunschweig.de
524 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
cally, one of the best-known examples of a prior belief in
visual perception is the assumption that light is coming
from above (Kersten, Mamassian, & Yuille, 2004). This
light-from-above prior is used to recover shape from oth-
erwise ambiguous shading (Brewster, 1826; Ramachan-
dran, 1988; Ramachandran & Rogers-Ramachandran,
2008). According to the light-from-above account, the
orientation anisotropy arises because the assumption of
overhead lighting aids one to perceive 3-D shape more
vividly in the case of vertical than in the case of horizontal
shading gradients (Adams, Graf, & Ernst, 2004). Thus,
implementing a priori knowledge provides visual percep-
tion with additional cues (i.e., concavity, convexity) when
shading gradients are vertically oriented, in contrast to
when they are horizontally oriented.
We performed two experiments. In the first one of
these, event-related brain potentials (ERPs) were mea-
sured in a study in which shape-from-shading stimuli
were presented and in which orientation anisotropy could
be replicated successfully. The second experiment was
specifically designed to evaluate a theoretical alternative
to the light-from-above account for orientation anisotropy.
Rather than conceptualizing anisotropy as reflecting the
incorporation of prior knowledge into visual perception,
the newly developed context model of anisotropy is based
cording to this theory, basic visual features are processed
automatically and in parallel without focal attention (i.e.,
preattentively). In contrast, when two or more visual fea-
tures belonging to the same object have to be integrated,
an additional process is required that is serial in nature
and comprises focal attention. There is, however, no obvi-
ous rationale for why the perpendicular stimulus rotation
discussed above should lead to two qualitatively differ-
ent ways of visual processing, all other things being equal
(i.e., psychophysical stimulus and task variables). In an-
other popular VS theory, preattentive processes direct the
deployment of attention to interesting spatial locations in
the visual field (Wolfe, 2007). According to this guided
search model, stimulus-driven (bottom-up) and task-
driven (top-down) stimulus processing interact to create
an activation map of attentional priority. VS is more effi-
cient the higher the attentional priority of the target item,
as compared with the attentional priorities of the distrac-
tor items. However, there is again no obvious rationale for
why a sole perpendicular stimulus rotation should change
the attentional priorities of targets and distractors.
Students of orientation anisotropy in these shape-from-
shading VS studies sought to explain the empirically de-
rived horizontal efficiency disadvantage by assuming that
a priori knowledge influences visual perception. Specifi-
Figure 1. Four exemplary visual search displays, each with four items containing one
target stimulus (i.e., the stimulus in the lower left corner). Left panels: Vertical orienta-
tion. Right panels: Horizontal orientation. Upper panels: Shape-from-shading stimuli.
Lower panels: Bipartitioned stimuli. Upper left panel: Vertical shape-from-shading
condition. Upper right panel: Horizontal shape-from-shading condition. Lower left
panel: Vertical bipartitioned condition. Lower right panel: Horizontal bipartitioned
condition.
Vi s u a l se a r c h , or i e n ta t i o n an i s o t r o p y , a n d erps 525
studies, reported, as the main f inding emerging from P3
studies in VS tasks, that display size affects P3 amplitude
(the more items in a display, the smaller the P3 amplitude;
but see Luck & Hillyard, 1990, for divergent findings).
We also recorded visual evoked potentials (VEPs; see
Hillyard, Teder-Sälejärvi, & Münte, 1998, for a review).
The f irst VEP component that we measured was a posi-
tivity termed P1. The P1 is usually measured at parieto-
occipital electrodes, and it reflects activity of extrastri-
ate areas in the 85- to 130-msec range (Di Russo, Aprile,
Spitoni, & Spinelli, 2007; Di Russo, Martínez, Sereno,
Pitzalis, & Hillyard, 2002). The second VEP component
that we measured was the posterior N1 (140–200 msec
at parieto-occipital electrodes) component (cf. Di Russo
et al., 2007).
Here, we conducted two VS experiments in order to
challenge the replicability (Experiment 1) and the speci-
ficity (Experiment 2) of behavioral orientation anisotropy.
Furthermore, both of these experiments were designed to
investigate whether or not behavioral anisotropy is accom-
panied by cortical orientation anisotropy at various levels
of processing by measuring VEPs and the P3 component
of the ERP in shape-from-shading VS studies for the first
time ever.
EXPERIMENT 1
Method
Participants
Sixteen healthy undergraduate students at the University of Tech-
nology Braunschweig participated in the experiment (two male; age,
20– 44 years; M 5 24.4 years). They volunteered to participate in
return for course credit. Fifteen of them were right-handed. All the
participants had normal or corrected-to-normal visual acuity. They
were naive with regard to the issues in the study.
Stimuli, Display, and Apparatus
We used stimulus materials identical to those in Thornton and
Gilden (2007). Circular disks, illustrated in the upper panels of Fig-
ure 1, subtended 1.5º of visual angle. Some of these shaded disks
convey an impression of depth based exclusively on subtle variations
(gradients) in luminance. Small reverse-shaded inducer elements
were included so as to increase the percept of shape—in particular,
in singleton (set size 5 1) displays. The orientation of the gradient
was either vertical or horizontal. The shading gradient either ran
from top to bottom (white to black), perceived as surface bumps,
or had the opposite polarity (white to black from bottom to top),
perceived as surface dimples, when the orientation of the gradient
was vertical. The shading gradient either ran from left to right (white
to black) or had opposite polarity (white to black from right to left),
when the orientation of the gradient was horizontal. This orientation
of the gradient is thought to reduce distinctions in surface curvature
and converts the task mainly to a judgment of shading polarity.
The shaded disks were configured about a central fixation point
along a virtual circle with a radius that subtended 2º of visual angle.
Disks were drawn at canonical locations along the virtual circle (45º,
245º, 135º, 2135º). Items were distributed randomly to one of these
four positions in cases in which fewer than four items were presented
within a display. The entire display was rotated about fixation to re-
move configural effects by choosing a uniform deviate from the in-
terval 625º. Disks were presented against a gray background (RGB
color code: 178, 178, 178). The contrast relation between disks and
background was such that some regions of the disks were brighter
than the background and others were darker than the background
(Aks & Enns, 1992).
on general principles of lateral inhibition in visual process-
ing (see the Discussion section in Experiment 2 and also
Z. Li, 1999, 2002, and Nothdurft, 1991, for related models
of VS). The logic behind the test of these two competing
accounts was that the light-from-above account predicts
that anisotropy occurs only if shape-from-shading stimuli
are presented in this kind of VS studies. In sharp contrast,
the context model predicts that the anisotropy that has
repeatedly been demonstrated with shape-from-shading
stimuli should also appear, with similar strength, with all
sorts of other vertically and horizontally oriented stimuli.
The first experiment employed a VS paradigm in which
circular disks with shading gradients running either from
top to bottom (vertical-shading gradient) or from left
to right (horizontal-shading gradient) served as stimuli
(Thornton & Gilden, 2007). These stimuli were shaded
from white to black. In the vertical-shading task, they
were perceived as surface bumps (white above stimu-
lus) or as surface dimples (white below stimulus). The
horizontal- shading task was based on the same stimulus
set as that used in the vertical-shading task, except that the
target and distractor elements were rotated 90º counter-
clockwise. The RT data in an earlier study in which these
stimuli were used (Thornton & Gilden, 2007) showed that
VS was more efficient in the vertical-shading task than in
the horizontal-shading task—that is, a behavioral orienta-
tion anisotropy effect. In line with the light-from-above
account, Thornton and Gilden argued that while a bias
for overhead lighting might induce shape-from-shading
(experience of concavity or convexity, respectively) in
the vertical-shading task, the light-from-above assump-
tion might not influence perceptual experience in the
horizontal- shading task, thereby removing distinctions in
surface curvature and reducing the task to a strict judg-
ment of shading polarity.
We adopted Thornton and Gilden’s (2007) vertical- and
horizontal-shading tasks in our study. We assessed ERPs in
addition to behavioral performance measures, in an effort
to examine the cortical mechanisms of visual processing
in these shape-from-shading VS tasks. The ERP technique
allows one to measure cortical activity with excellent tem-
poral resolution (Luck, 2005). The P3 (or P300) is per-
haps the most-studied ERP component (for reviews, see
Kok, 2001; Kopp, 2008). It is generally accepted that a
distinction can be made between two subcomponents—
namely, the novelty P3 (P3a) and the target P3 (P3b, or
“classical” P3; Spencer, Dien, & Donchin, 2001). The P3b
(the component focused on in the present study, further
referred to as P3) has a posterior-parietal scalp distribu-
tion. There is, as of yet, no consensus about what cog-
nitive or cortical process the P3 reflects (Luck, 2005).
The hallmark of the P3 amplitude is that it is sensitive
to target probability: The P3 amplitude gets larger as the
target probability gets smaller (Kopp, 2008). Moreover,
it has been repeatedly shown that it is the probability of
the task-defined stimulus class that matters, not the prob-
ability of the physical stimulus (Kopp, 2008). Therefore,
the P3 component of the ERP must be generated after the
stimulus has been categorized, according to the rules of
the task (Luck, 2005). Kok, in his extensive review of P3
526 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
ucts, Gilching, Germany) from frontal (F7, F3, Fz, F4, F8), central
(T7, C3, Cz, C4, T8), parietal (P7, P3, Pz, P4, P8), occipital (O1,
O2), and mastoid (M1, M2) sites. Ag–AgCl EEG electrodes were
used. They were mounted on an EasyCap (EasyCap, Herrsching-
Breitbrunn, Germany). Electrode impedance was kept below 10 kΩ
(mean impedance: 4 kΩ). All EEG electrodes were referenced to
average reference. Participants were informed about the problem
of noncerebral artifacts, and they were encouraged to reduce them
(Picton et al., 2000). Ocular artifacts were monitored by means of
bipolar pairs of electrodes positioned at the sub- and supraorbital
ridges (vertical electrooculogram, vEOG) and at the external ocular
canthi (horizontal electrooculogram, hEOG). The EEG and EOG
channels were amplified with a band-pass of 0.01–30 Hz and were
digitized at 250 Hz.
Offline analysis was performed by means of the BrainVision Ana-
lyzer Version 1.05 software (Brain Products, Gilching, Germany).
Manual artifact rejection was performed before averaging in order to
discard trials during which an eye movement or any other noncerebral
artifact occurred. Semiautomatic blink detection and the application
of an established method for ocular artifact removal were employed
for ocular correction (Gratton, Coles, & Donchin, 1983). A digital
high-pass filter was applied to the data (0.75 Hz, 48 dB/oct) in order
to eliminate low-frequency variations in the EEG signal that were
associated with the occasional occurrence of electrodermal artifacts.
The EEG was then divided into epochs of 1,000-msec duration, start-
ing 100 msec before the display onset. The prestimulus baseline of
100 msec was subtracted from the sampling points. The EEG was
averaged offline. Error trials (misses, false alarms) were excluded
from averaging. Deflections in the averaged EOG waveforms were
small, indicating that fixation was well maintained.
Data Analysis
Behavioral performance
. Behavioral task performance was
quantified in two ways. First, the median of the response speed for
each table cell of the design matrix (Table 1) was computed for each
individual participant, and these median individual RTs were sub-
jected to statistical analysis.1 Second, the accuracy of the behavioral
responses was computed for each table cell of the design matrix
(Table 1) for each individual participant. Percentage of misses was
computed for pure and mixed target-present trials. Percentage of
false alarms was computed for target-absent trials. All these percent-
ages were transferred into the arcsin transformation prior to statisti-
cal analysis.
ERPs
. The amplitude and latency of the P1 and N1 peaks were
measured at the amplitude peak in the intervals from 80 to 200 msec
(P1) and from 140 to 240 msec (N1) at two parietal (P7, P8) and two
occipital (O1, O2) electrodes. Individual amplitudes and latencies
were determined for each electrode. These measures were derived
from stimulus-locked averages. Amplitude was measured as the
difference between peak amplitude and the mean voltage during
100-msec prestimulus baseline; latency was measured relative to
stimulus onset.
Since the time elapsing between stimulus onset and the partici-
pant’s final decision is highly variable in VS, the ERP components
related to search-terminating decisions, such as the P3, were ex-
pected to be poorly time-locked to stimulus onset. However, much
less variance was expected in the time-locking between these ERP
waves and the behavioral response. Therefore, two types of P3 aver-
ages were calculated (Luck, 2005), one in which stimulus onset was
the time-locking event (stimulus-locked averages) and one in which
the behavioral response was the time-locking event (response-locked
averages).
Amplitudes and latencies of the P3 were measured at Pz. Latencies
were measured as the time between stimulus onset and the maximum
positive peak occurring between 270 and 680 msec poststimulus,
and amplitudes were measured as the area under the curve in this la-
tency range in stimulus-locked averages. An area, rather than a peak
measure, was used for the P3 because the greater latency variation
expected for larger set sizes and for the horizontal-shading condi-
There were nine basic types of stimulus displays. Each display
contained either one, two, or four disks (set size; displays contain-
ing three disks were excluded from this design). Displays consisted
exclusively of distractors (target-absent trials), of targets (pure
target- present trials), or of some combination of a variable number
of targets and distractors (mixed target-present trials). Table 1 shows
the frequencies of encountering each type of stimulus display. This
particular design matrix was necessary to ensure that the probability
of target-present and target-absent displays was balanced across the
three set size conditions.
The stimuli were displayed on a 19-in. CRT monitor with a high
refresh rate (100 Hz at a resolution of 1,280 3 1,024 pixels). The
experimental protocol was carried out by a Presentation (Neurobe-
havioral Systems, Albany, CA) program written on a personal com-
puter (PC). Manual responses were executed on both Ctrl buttons of
a wireless keyboard (Logitech, Romanel-sur-Morges, Switzerland)
and were recorded by the Presentation program. The left Ctrl key was
pressed by the index finger of the left hand, whereas the index finger
of the right hand was used to press the right Ctrl button. Stimulus
displays were preceded by a fixation stimulus (250-msec duration of
presentation; 1,000-msec stimulus onset asynchrony). The stimulus
displays remained present until response. Response–stimulus inter-
vals were fixed at 1,000 msec.
Task and Procedure
In the most common version of VS task, observers conduct
speeded searches to determine whether a single target element is
or is not present in a display of distractor elements. Multiple target
search augments the standard design by including trials with more
than one target (Table 1). The participant’s task remains the same
as in single-target search—that is, to indicate whether any targets
are present.
The assignment of targets and distractors was counterbalanced
across participants. Eight participants searched white above and
white left disks for targets, whereas the remaining 8 participants
searched white below and white right disks for targets. The assign-
ment of response buttons to target and distractor decisions was like-
wise counterbalanced across participants.
Each participant completed four blocks of trials (432 trials each).
The spatial orientation of the shading gradients was manipulated
blockwise: Two of the blocks made use of vertically shaded disks,
and the other two blocks made use of horizontally shaded disks.
The sequence of shading orientations was counterbalanced across
participants in such a way that 8 participants performed the two ver-
tical blocks before the two horizontal blocks, whereas the remaining
8 participants started with the horizontal blocks and finished the
experiment with the vertical blocks. The performance of a block of
trials lasted about 15 min. Short breaks of about 5 min separated the
blocks. The experiment was carried out in a dimly lit room in which
the participants sat 1 m away from the CRT. In order to familiarize
the participants with the demands of the task, a few practice trials
were administered for each shading orientation condition before the
experiment actually began.
Electrophysiology
Continuous EEG was recorded by means of another PC, a
QuickAmps-72 amplifier (Brain Products, Gilching, Germany)
and the BrainVision Recorder Version 1.02 software (Brain Prod-
Table 1
Number of Trials, Separately for Set Size and Number of Targets
Set Number of Targets
Size 0 1 2 4 Total
1 144 144 – – 288
2 144 72 72 288
4 144 48 48 48 288
Total 432 264 120 48 864
Vi s u a l se a r c h , or i e n ta t i o n an i s o t r o p y , a n d erps 527
than in the horizontal-shading task; the difference was
5 msec in the set size one condition, 65 msec in the set
size two condition, and 91 msec in the set size four condi-
tion. The RT results led to a significant shading orienta-
tion 3 set size interaction effect [F(2,30) 5 8.89, p ,
.003, η2
p 5 .37, ε 5 .88; see Figure 2, upper left panel].
Response accuracy was also higher in the vertical-shading
task than in the horizontal-shading task, especially in the
set size four condition, resulting in a significant shading
orientation 3 set size interaction [F(2,30) 5 10.67, p ,
.002, η2
p 5 .42, ε 5 .82; see Figure 2, lower left panel].
These data show a behavioral orientation anisotropy effect
that gradually evolves as the VS displays contain more and
more stimuli.
Target-absent trials and pure target-present tri-
als
. Next, we consider the results from those trials on
which all the stimuli were distractors (target-absent tri-
als) or targets (pure target-present trials), respectively (see
Table 1). RTs and error rates are summarized in Figure 2
(right panels). RTs were generally shorter for pure target-
present trials than for target-absent trials. This difference
was more pronounced in the horizontal-shading task than
in the vertical-shading task, particularly at the largest set
size. The results led to a significant shading orientation 3
set size 3 target interaction [F(2,30) 5 9.85, p , .003,
η2
p 5 .40, ε 5 .77; see Figure 2, upper right panel]. Re-
sponse accuracy was higher in pure target-present trials
than in target- absent trials, especially in nonsingleton (set
tion can distort peak amplitude measures (Luck, 2005). In response-
locked averages, P3 latencies were measured as the time between
the motor response and the maximum positive peak occurring in the
window between 200 msec preresponse and 200 msec postresponse;
P3 amplitudes were measured as the area under the curve within this
latency range.
Statistical analyses
. Behavioral and electrophysiological mea-
sures were analyzed with repeated measures ANOVAs, carried out
at the .01 significance level and adjusted for nonsphericity with the
Hyunh–Feldt epsilon coefficient. The results of the univariate tests
are provided, using a format that gives the uncorrected degrees of
freedom (Picton et al., 2000). A measure of effect size, η2
p (partial
eta squared), is also provided.
Behavioral measures (RTs, response accuracy) in one-target-
present trials (see Table 1) were analyzed with two within-subjects
factors: shading orientation (vertical, horizontal) and set size
(one, two, or four items). The analyses of target-absent trials and
pure target-present trials comprised an additional within-subjects
factor—namely, target (target absent, pure target present).
P3 measures were analyzed with three within-subjects factors:
shading orientation (vertical, horizontal), set size (one, two, or four
items), and target (target absent, target present). The analysis of P1
and N1 measures comprised two additional within-subjects factors—
namely, location (occipital, parietal) and hemisphere (left, right).
Results
Behavioral Performance
One-target-present trials
. First, we consider the re-
sults from the one-target-present trials (see Table 1). RTs
and error rates are summarized in Figure 2 (left panels).
RTs were shorter for targets in the vertical-shading task
Set Size
RT (msec)
800
750
700
650
600
550
500
450
RT (msec)
800
750
700
650
600
550
500
450
p(e)
0.15
0.10
0.05
0
p(e)
0.15
0.10
0.05
0
12 4
Set Size
12 4
A
B
Vertical gradient
Horizontal gradient
Pure target-present, vertical
Target-absent, vertical
Pure target-present, horizontal
Target-absent, horizontal
Figure 2. Behavioral results (M 6 SE) obtained in Experiment 1: response times (RTs) and
proportions of errors [p(e) s]. Left panels: RTs (upper panel) and p(e)s (lower panel) from one-
target-present trials, in the vertical- and the horizontal-shading conditions and as a function
of set size (one, two, and four items). Right panels: RTs (upper panel) and p(e)s (lower panel)
on pure target-present and target-absent trials, in the vertical- and horizontal- shading condi-
tions and as a function of set size (one, two, and four items).
528 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
of varying set size (one, four), collapsed over the two ori-
entation conditions (vertical, horizontal), are displayed in
Figure 3 (upper panels). The P1 and N1 peaks tended to
decrease in amplitude and latency as set size increased,
probably because of changes in stimulus parameters, rather
than changes in decision processes. The set size main effect
was significant for P1 latencies [F(2,30) 5 63.71, p , .001
(four shorter than one), η2
p 5 .81, ε 5 .69], N1 amplitudes
[F(2,30) 5 51.56, p , .001 (four more negative than one),
η2
p 5 .78, ε 5 .71], and N1 latencies [F(2,30) 5 44.81, p ,
.001, η2
p 5 .75, ε 5 1.0 (four shorter than one)].
size . 1) VS displays, resulting in a significant set size 3
target interaction [F(2,30) 5 8.09, p , .003, η2
p 5 .35,
ε 5 1.0; see Figure 2, lower left panel]. The RT data again
show a behavioral orientation anisotropy effect that gradu-
ally evolves as the VS displays contain more and more
stimuli and that is much more distinct on target-absent
trials than it is on pure target-present trials.
ERPs
P1/N1 amplitude and latency measures
. The ERPs
elicited at parieto-occipital electrodes by stimulus displays
Experiment 1
Experiment 2
P7 P8
O1 O2
P7 P8
O1 O2
3
1
1
3
5
100 0 100 200 300
µV
3
1
1
3
5
100 0 100 200 300
µV
Time (msec)
3
1
1
3
5
100 0 100 200 300
µV
3
1
1
3
5
100 0 100 200 300
µV
Time (msec)
Set size 1
Set size 2
Set size 4
Figure 3. Grand average visual evoked potentials at parieto-occipital
electrodes as a function of set size, obtained in Experiment 1 (upper
panels) and in Experiment 2 (lower panels).
Vi s u a l se a r c h , or i e n ta t i o n an i s o t r o p y , a n d erps 529
amplitudes (horizontal P1 more positive than vertical
P1).2
P3 amplitude and latency measures
. Stimulus dis-
plays also elicited a large P3 wave with parietal maximum
(see Figures 5 and 6, upper panels). Stimulus-locked av-
erages (see Figure 5, upper left panel) showed that the
target-present stimulus displays elicited more positive P3
mean amplitudes than did the target-absent stimulus dis-
plays [F(1,15) 5 60.53, p , .001, η2
p 5 .80]. P3 mean
amplitudes in the response-locked averages were also en-
hanced in target-present trials, as compared with target-
P1 amplitudes were slightly more positive and N1
amplitudes were slightly less negative in the horizontal-
shading task than they were in the vertical-shading
task (see Figure 4, upper panels). Both peak amplitude
measures showed significant orientation effects [P1
amplitudes, F(1,15) 5 11.04, p , .006, η2
p 5 .42; N1
amplitudes, F(1,15) 5 16.02, p , .002, η2
p 5 .52]. These
P1 and N1 amplitude findings demonstrate that behav-
ioral orientation anisotropy is accompanied by cortical
orientation anisotropy. Specif ically, the earliest sign
of cortical orientation anisotropy was observed in P1
Experiment 1
Experiment 2
P7 P8
O1 O2
P7 P8
O1 O2
3
1
1
3
100 0 100 200 300
µV
3
1
1
3
100 0 100 200 300
µV
Time (msec)
3
1
1
3
100 0 100 200 300
µV
3
1
1
3
100 0 100 200 300
µV
Time (msec)
Vertical
Horizontal
Figure 4. Grand average visual evoked potentials at parieto-occipital
electrodes for vertically and horizontally oriented stimuli obtained in
Experiment 1 (upper panels) and in Experiment 2 (lower panels).
530 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
(set size one), 223 msec (set size two), and 228 msec (set
size four), a difference that failed to reach statistical sig-
nificance [F(2,30) 5 5.27, p 5 .02, η2
p 5 .26, ε 5 .82].
Discussion
Our behavioral results replicate the behavioral orienta-
tion anisotropy that has been reported in earlier shape-from-
shading VS studies (Adams, 2007; Kleffner & Ramachan-
dran, 1992; Sun & Perona, 1998; Thornton & Gilden, 2007;
Wolfe et al., 1999). Specif ically, RTs and error measures
revealed that VS for vertically shaded stimuli was more ef-
ficient than VS for horizontally shaded stimuli under non-
singleton display conditions. We found orientation 3 set
size interaction RT effects in one-target-present trials, and
this two-way interaction was also much stronger in target-
absent trials than it was in pure target-present trials.
This is the first study that we are aware of to report ERP
measures from a shape-from-shading VS experiment.
We basically found two cortical correlates of behavioral
anisotropy. First, VEP amplitudes showed evidence of ori-
entation anisotropy. Specifically, peak amplitudes in the
P1 latency range were slightly, but reliably, more positive
in the horizontal-shading condition than in the vertical-
shading condition. It is not possible at the moment to de-
termine whether the P1 or the N1 component of the ERP,
or both, or another ERP component has changed. Yet the
absent trials [F(1,15) 5 21.9, p , .001, η2
p 5 .59; see
Figure 5, upper right panel].
Stimulus-locked P3 mean amplitudes decreased as set
size increased [F(2,30) 5 14.16, p , .002, η2
p 5 .49, ε 5
.68]. Importantly, the set size effect on P3 amplitudes was
orientation specific, because the amplitude decrement with
increasing set size was much stronger in the horizontal-
shading task than it was in the vertical-shading task
[F(2,30) 5 13.09, p , .002, η2
p 5 .47, ε 5 .61; see Figure 6,
upper left panel]. This finding constitutes evidence for an-
other cortical orientation anisotropy effect that is expressed
in stimulus-locked P3 mean amplitudes (vertical P3 .
horizontal P3) and that is specifically induced by nonsin-
gleton VS displays. Response-locked P3 mean amplitudes
decreased as set size increased [F(2,30) 5 7.21, p , .005,
η2
p 5 .33, ε 5 .88; see Figure 6, upper right panel], without
a statistically reliable modulation by shading orientation
[F(2,30) 5 1.38, p 5 .27, η2
p 5 .08, ε 5 .81].
Set size strongly affected stimulus-locked P3 peak la-
tencies, with a mean latency of 431 msec in the set size
one condition, 459 msec in the set size two condition, and
484 msec in the set size four condition. This observation
was corroborated by a significant set size main effect
[F(2,30) 5 12.23, p , .002, η2
p 5 .45, ε 5 .71]. P3 peak
latencies in the response-locked averages were somewhat
less sensitive to the manipulation of set size: 239 msec
Experiment 1
Pz
3
1
1
0 200 400 600 900 300 3000
µV
Time (msec)
5
800 600
S-Locked R-Locked
Experiment 2
3
1
1
0 200 400 600 900 300 3000
µV
5
800 600
Time (msec)
Absent
Present
Figure 5. Grand average stimulus-locked (left panels) and response-locked (right
panels) event-related brain potentials at electrode Pz for target-absent and target-
present displays obtained in Experiment 1 (upper panels) and in Experiment 2
(lower panels).
Vi s u a l se a r c h , or i e n ta t i o n an i s o t r o p y , a n d erps 531
modulation of the P3 amplitude set size effect by the ori-
entation of the shading gradient could not be observed
in response-locked averages. The reasons for this effect
being absent in response-locked averages are not entirely
clear. According to one view, the processing difference
that is reflected in the shading orientation 3 set size in-
teraction in the stimulus- locked averages is time-locked
to stimulus-oriented processes, rather than to response-
related processes.
Taken together, we found evidence of cortical anisot-
ropy at multiple levels of the cortical hierarchy, and these
anisotropies pointed in opposite directions. Specifically,
whereas amplitudes in the P1 latency range were slightly
more positive under horizontal-shading conditions, P3 am-
plitudes were more positive under nonsingleton, vertical-
shading conditions. To our knowledge, no earlier study has
examined ERP measures from comparable shape-from-
shading VS studies. There are only two ERP studies that
have reported relevant data. Mamassian, Jentzsch, Bacon,
and Schweinberger (2003) presented ambiguously shaded
patterns and examined VEPs. They found correlations be-
change in voltage in the P1 latency range reflects an orien-
tation effect over the occipital cortex in the latency range
between 80 and 200 msec. Second, mean amplitudes of
the P3 component of the ERP showed evidence of cortical
anisotropy, since P3 amplitudes, but not latencies, were
differentially affected by set size in the vertical- and the
horizontal-shading conditions. Specifically, P3 amplitude
decrement that is usually associated with an increase in
the number of items in VS displays (Kok, 2001) was more
pronounced under horizontal-shading conditions than it
was under vertical-shading conditions.
A notoriously difficult issue in ERP research is whether
or to what degree apparent condition or group differences
in average amplitudes are due to differences in trial-to-
trial latency variability. With regard to this question, it
is important to note that we used area-based P3 ampli-
tude measures that are useful for mitigating the effects
of trial-to-trial latency variability under most conditions,
particularly when the waveforms are not multiphasic
and when overlapping components do not preclude the
use of a wide measurement window (Luck, 2005). The
Experiment 1
Pz
3
1
1
0 200 400 600 900 300 3000
µV
Time (msec)
5
800 600
S-Locked R-Locked
Experiment 2
3
1
1
0 200 400 600 900 300 3000
µV
5
800 600
Time (msec)
Horizontal, 1
Horizontal, 2
Horizontal, 4
Vertical, 1
Vertical, 2
Vertical, 4
Figure 6. Grand average stimulus-locked (left panel) and response-locked (right
panel) event-related brain potentials at electrode Pz in the vertical- (blue lines) and
horizontal- (red lines) shading conditions and as a function of set size (one, two, and
four items in Experiment 1 [upper panels]; one and four items in Experiment 2
[lower panels]).
532 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
ported behavioral anisotropy needs to be assessed further.
One caveat to this model is that it does not provide a com-
prehensive rationale toward understanding the observed
ERP amplitude anisotropies.
An important caveat to the light-from-above account for
the reported behavioral anisotropy has been provided by
van Zoest, Giesbrecht, Enns, and Kingstone (2006). The
authors of this study demonstrated orientation anisotropy
in the absence of shape-from-shading stimuli. In three of
their experiments, anisotropy was observed on vertical and
horizontal displays in which the stimuli were clearly not
interpretable as 3-D surfaces. The sole exception to that
rule occurred in their Experiment 4, in which the elimina-
tion of interitem symmetry resulted in equal search effi-
ciency for vertical and horizontal displays. These findings
were interpreted in terms of item similarity. Specifically, it
was conjectured that targets and distractors are perceived
as being more similar on horizontal (as compared with
vertical) displays—thereby decreasing search efficiency
(Duncan & Humphreys, 1989) and breaking ground for
orientation anisotropy, except under conditions in which
interitem symmetry is eliminated.
On the basis of these earlier findings, Experiment 2
served to examine whether or not behavioral and/or corti-
cal orientation anisotropy occurs specifically in response
to shape-from-shading stimuli. In order to examine the
specificity of these phenomena, we employed two differ-
ent types of stimuli: the smoothly and continuously graded
shape-from-shading stimuli of Experiment 1 and newly
constructed, discontinuous stimuli (see the lower panels
of Figure 1). These bipartitioned disks contain a step dif-
ference in luminance in the vertical (cf. lower left panel
of Figure 1) or in the horizontal (cf. upper right panel of
Figure 1) direction. They were originally introduced by
Kleffner and Ramachandran (1992) as stimuli in control
VS displays that do not convey depth information, as
confirmed by Aks and Enns (1992). Nevertheless, it was
never examined before whether orientation anisotropy oc-
curs when tested with this kind of bipartitioned stimuli.
This was the purpose of Experiment 2.
According to the light-from-above account for orien-
tation anisotropy in VS tasks, the 3-D interpretation of
the visual stimuli presupposes vertical-shading gradients
such that the bias for overhead lighting is able to sup-
port perception of concavity or convexity, respectively.
In contrast, the bias for overhead lighting should be able
to support the 3-D perception of stimuli neither in cases
of horizontal-shading gradients—thereby giving rise to
orientation anisotropy—nor in cases in which stimuli do
not convey depth information (as in the case of vertical
and horizontal bipartitioned stimuli). Thus, the light-
from-above model predicts the occurrence of orientation
anisotropy solely when tested with shape-from-shading
stimuli, but not when tested with bipartitioned stimuli.
Method
Participants
Twenty-four healthy undergraduate students at the University
of Technology Braunschweig who had not participated in Experi-
tween P1 amplitudes and observer biases for particular spa-
tial positions of the assumed light source. These data were
interpreted as ERP evidence that a priori knowledge about
the source of light is represented early in the visual system.
Hou, Pettet, Vildavski, and Norcia (2006) updated visual
stimuli, thereby alternating their perceptual interpretations
systematically. When stimuli were updated in asymmet-
ric conditions, the perceptual interpretation changed from
two-dimensional to three-dimensional. Symmetric updat-
ing conditions were characterized by two corrugated sur-
faces that looked laterally translated, without any change
in depth interpretation. VEPs in response to asymmetric
shifts were characterized by enhanced, sustained negative
waveforms in the latency range between 150 and 300 msec
poststimulus over the posterior scalp, as compared with
VEPs in response to symmetric shifts, possibly reflecting a
cortical correlate of depth perception. Taken together, these
studies showed that a priori knowledge about the source of
light and depth perception modulate VEP amplitudes in the
P1 and N1 latency range.
There is only one published study that examined neu-
rophysiological correlates of shape-from-shading in VS.
Lee, Yang, Romero, and Mumford (2002) recorded spik-
ing responses of V1 and V2 neurons of macaque mon-
keys. Their task was to fixate a target during VS for shape-
from-shading stimuli that were similar to those used by
Ramachandran (1988) and by us. V2, but not V1, neurons
responded highly sensitively to the shape-from-shading
stimuli, possibly indicating that V2 may be the f irst cor-
tical area that is sensitive to 3-D surface shape. These
neurophysiological data are in general accord with our
P1 data, if one considers the extrastriate sources of the P1
component (Di Russo et al., 2007; Di Russo et al., 2002).
EXPERIMENT 2
The results of Experiment 1 showed that behavioral
anisotropy is a replicable phenomenon in shape-from-
shading VS studies. Specifically, VS under nonsingleton
conditions is more efficient for vertically shaded stimuli
than it is for horizontally shaded stimuli. Furthermore, this
behavioral anisotropy may result from anisotropic corti-
cal processing of vertical and horizontal visual stimuli,
respectively, because amplitudes in the P1 latency range
were more positive under horizontal shading conditions,
whereas P3 amplitudes were more positive under non-
singleton vertical shading conditions.
We outlined in the introduction to this article that be-
havioral anisotropy is usually interpreted as resulting
from perceptual pop-out effects that are putatively sup-
ported by the light-from-above assumption (Kersten et al.,
2004; Ramachandran, 1988; Ramachandran & Rogers-
Ramachandran, 2008). According to this model, the bias
for overhead lighting enables the perception of vertically,
but not horizontally, shaded stimuli three-dimensionally,
and the availability of 3-D cues (i.e., concavity, convex-
ity) aids efficient VS (Adams, 2007; Adams et al., 2004;
Kleffner & Ramachandran, 1992; Sun & Perona, 1998;
Thornton & Gilden, 2007; Wolfe et al., 1999). However,
the validity of the light-from-above account for the re-
Vi s u a l se a r c h , or i e n ta t i o n an i s o t r o p y , a n d erps 533
factors: type of gradient (shape-from-shading, bipartitioned), spa-
tial orientation (vertical, horizontal), polarity of the target-defining
feature (white above, white below, white left, white right), set size
(one or four items), and target (presence, absence). P3 measures
were analyzed with four within-subjects factors: type of gradient
(shape-from-shading, bipartitioned), spatial orientation (vertical,
horizontal), set size (one or four items), and target (presence, ab-
sence). The analysis of P1 and N1 measures comprised an additional
within-subjects factor—namely, location (occipital, parietal) and
hemisphere (left, right).
Results
Behavioral Performance
RTs were shorter in the set size one condition than they
were in the set size four condition [F(1,23) 5 114.92, p ,
.001, η2
p 5 .83]. RTs were also shorter for target-present
trials than they were for target-absent trials [F(1,23) 5
64.32, p , .001, η2
p 5 .74]. This target effect on RTs
was more pronounced for 3-D stimuli than it was for
2-D stimuli [F(1,23) 5 9.66, p , .006, η2
p 5 .30]. The
target effect on RTs was also modulated by the interac-
tion of orientation condition (vertical, horizontal) and set
size (one, four) [F(1,23) 5 13.38, p , .002, η2
p 5 .37].
Separate ANOVAs were performed within each orienta-
tion condition to parse the three-way interaction. A sig-
nificant two-way interaction of target (present, absent)
and set size (one, four) emerged for horizontal conditions
[F(1,23) 5 10.04, p , .005, η2
p 5 .30]. In contrast, set size
and target exerted main effects only for vertical conditions
[F(1,23) 5 132.62, p , .001, η2
p 5 .85, and F(1,23) 5
56.81, p , .001, η2
p 5 .71, respectively]. Thus, the target
effect on RTs showed an increment across set size condi-
tions in the horizontal, but not in the vertical, orientation
condition, leading to particularly long RTs in nonsingle-
ton horizontal target-absent trials.
RTs were generally shorter for vertically than for
horizontally oriented stimuli [F(1,23) 5 35.91, p ,
.001, η2
p 5 .61]. As in Experiment 1, this anisotropy ef-
fect was more pronounced when nonsingleton displays
(set size four), as compared with singleton displays (set
size one), were presented [F(1,23) 5 29.95, p , .001,
η2
p 5 .57]. Importantly, set-size-dependent orientation
anisotropy was clearly not modulated by type of gradi-
ent [F(1,23) 5 1.79, p 5 .19, η2
p 5 .07]. When separate
ANOVAs were performed on each stimulus type (3-D,
2-D), a significant two-way interaction of orientation
ment 1 volunteered in the experiment (six male; age, 20–36 years;
M 5 22.8 years). Twenty-two of them were right-handed. All the
participants had normal or corrected-to-normal visual acuity. They
were naive with regard to the issues in the study.
Stimuli, Display, and Apparatus
The stimuli, display, and apparatus were the same as those in Ex-
periment 1, except for the following modif ications. Bipartitioned
disks that comprised a step difference in luminance in the verti-
cal (cf. lower left panel of Figure 1) or in the horizontal (cf. lower
right panel of Figure 1) direction were introduced, in addition to the
shape-from-shading stimuli. Shape-from-shading and bipartitioned
disks possessed identical diameters. We made an attempt to hold
mean luminance contrast across the two types of gradients constant
by subjectively adjusting them.
Task and Procedure
The task and procedure were the same as those in Experiment 1,
except for the following modifications. There were four basic types
of stimulus displays. Each display contained either one or four
disks (set size). Displays either consisted exclusively of distrac-
tors (target-absent trials) or contained one target (target-present
trials). Thus, multiple-target trials were not applied in this experi-
ment. Table 2 shows the frequencies of encountering each type of
stimulus display. Each participant completed eight blocks of trials
(208 trials each). Each block of trials comprised equal numbers of
target-present and target-absent trials, as well as equal numbers of
singleton and nonsingleton trials (see Table 2). The type of gradi-
ent (shape-from- shading, bipartitioned) and their spatial orientation
(vertical, horizontal), as well as the polarity of the target-defining
feature (white above, white below, white left, white right), were ma-
nipulated blockwise, in a counterbalanced manner. The assignment
of response buttons to target and distractor decisions was likewise
counterbalanced across participants. The performance of one block
of trials lasted about 10 min.
Electrophysiology
Electrophysiology was the same as in Experiment 1.
Data Analysis
Behavioral performance
. Measurement of behavioral perfor-
mance was the same as in Experiment 1.
ERPs
. Measurement of ERPs was the same as in Experiment 1,
except for the following modif ications. Stimulus-locked P3 ampli-
tudes and latencies were measured in the time window between 270
and 850 msec poststimulus. Response-locked P3 amplitudes and
latencies were measured in the time window between 200 msec pre-
response and 100 msec postresponse.
Statistical analyses
. The statistical analyses were the same as in
Experiment 1, except for the following modif ications. Behavioral
measures (RTs, response accuracy) on target-present and target-
absent trials (see Table 2) were analyzed with five within-subjects
Table 2
Number of Trials, Separately for Set Size, Target Presence Versus Absence,
and Stimulus Conditions (Type of Gradient, Orientation, Polarity)
Stimulus Condition
Shape-From-Shading (3-D) Bipartitioned (2-D)
Vertical Horizontal Vertical Horizontal
Above Below Left Right Above Below Left Right Total
Set Size 1
Present 52 52 52 52 52 52 52 52 416
Absent 52 52 52 52 52 52 52 52 416
Set Size 4
Present 52 52 52 52 52 52 52 52 416
Absent 52 52 52 52 52 52 52 52 416
Total 208 208 208 208 208 208 208 208 1,664
534 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
This observation on error rates parallels the observation
on RTs, providing convergent evidence that nonsingleton
horizontal target-absent displays posed specific difficul-
ties to the perceivers.
ERPs
P1/N1 amplitude and latency measures
. The ERPs
elicited at parieto-occipital electrodes by stimulus dis-
plays of varying size (one, four) are displayed in Figure 3
(lower panels). P1 and N1 peak amplitudes and laten-
cies decreased as set size increased, probably because of
changes in stimulus parameters, rather than changes in
decision processes. The set size main effect reached statis-
tical significance for P1 latencies [F(1,23) 5 204.87, p ,
.001, η2
p 5 .90], N1 amplitudes [F(1,23) 5 112.31, p ,
.001, η2
p 5 .83], and N1 latencies [F(1,23) 5 197.04,
p , .001, η2
p 5 .90]. P1 amplitudes were affected by the
two-way set size 3 location of electrode (occipital, pari-
etal) interaction [F(1,23) 5 8.90, p , .008, η2
p 5 .28].
P1 peak amplitudes were also affected by orientation
[F(1,23) 5 11.77, p , .003, η2
p 5 .34 (horizontal P1 more
positive than vertical P1)], thereby replicating the finding
that we had obtained in Experiment 1. Importantly, the type
of gradient 3 orientation interaction was not statistically
significant [F(1,23) , 1]. When separate ANOVAs were
performed on each stimulus type (3-D, 2-D), a significant
orientation effect emerged for the 2-D stimuli [F(1,23) 5
8.02, p , .01, η2
p 5 .26], whereas the orientation effect
for the 3-D stimuli merely emerged as a statistical trend
(vertical, horizontal) and set size (one, four) emerged
for the 3-D stimuli [F(1,23) 5 25.76, p , .001, η2
p 5
.53], reflecting orientation anisotropy. Most important,
this interaction was also signif icant for the 2-D stimuli
[F(1,23) 5 25.89, p , .001, η2
p 5 .53]. The upper panels
of Figure 7 depict the relevant mean RTs. A look at these
mean RTs reveals that orientation anisotropy appeared,
in similar strength, with both sorts (3-D, 2-D) of verti-
cally and horizontally oriented stimuli. The nonspecific-
ity of orientation anisotropy is a finding that is clearly
incompatible with the light-from-above account for ori-
entation anisotropy.
The analysis of error rates confirmed this conclusion.
Error rates were influenced by set size [F(1,23) 5 24.44,
p , .001, η2
p 5 .52] and by target [F(1,23) 5 35.91, p ,
.001, η2
p 5 .61]. Type of stimuli exerted neither a main
effect [F(1,23) 5 1.10, p 5 .31, η2
p 5 .05], nor any sig-
nificant interaction effect [all Fs(1,23) # 5.83, ps $ .02,
η2
ps # .20], on error rates. Specifically, the three-way type
of gradient 3 orientation 3 set size interaction clearly
failed to reach statistical signif icance [F(1,23) , 1]. In
contrast, orientation (vertical, horizontal) influenced
error rates [F(1,23) 5 12.92, p , .003, η2
p 5 .36 (hori-
zontal . vertical)] in interaction with the set size condi-
tion [F(1,23) 5 37.68, p , .001, η2
p 5 .62 (four . one; see
Figure 7, lower panels)]. Error rates in horizontal displays
of the set size four condition were particularly high when
targets were absent [F(1,23) 5 10.79, p , .004, η2
p 5 .32
(three-way interaction of orientation, target, and set size)].
Set Size
RT (msec)
800
750
700
650
600
550
500
450
RT (msec)
800
750
700
650
600
550
500
450
p(e)
0.10
0.05
0
p(e)
0.10
0.05
0
14
Set Size
14
A
B
Vertical gradient
Horizontal gradient
3-D2-D
Figure 7. Behavioral results (M 6 SE) obtained in Experiment 2: response times (RTs)
and proportions of errors [p(e) s]. Left panels: RTs (upper panel) and p(e)s (lower panel)
for shape-from-shading (3-D) conditions. Right panels: RTs (upper panel) and p(e)s (lower
panel) for bipartitioned (2-D) conditions.
Vi s u a l se a r c h , or i e n ta t i o n an i s o t r o p y , a n d erps 535
type of gradient nor orientation nor any interaction involv-
ing these factors yielded statistically significant effects
[all Fs(1,23) # 5.63, ps $ .03, η2
ps # .19]. P3 peak laten-
cies in the response-locked averages were influenced by
set size [F(1,23) 5 9.92, p , .005, η2
p 5 .30 (one earlier
than four)], by the interaction between set size and target
effects [F(1,23) 5 8.46, p , .009, η2
p 5 .27], and by ori-
entation conditions [F(1,23) 5 17.96, p , .001, η2
p 5 .44
(vertical earlier than horizontal)].
Discussion
The present data are not consistent with the light-from-
above account for orientation anisotropy in VS tasks. On
the one hand, we replicated behavioral (Experiment 1;
Adams, 2007; Kleffner & Ramachandran, 1992; Sun & Pe-
rona, 1998; Thornton & Gilden, 2007; Wolfe et al., 1999)
as well as cortical (Experiment 1) orientation anisotropy
under shape-from-shading conditions. On the other hand,
neither behavioral nor cortical orientation anisotropy oc-
curred exclusively under shape-from-shading conditions.
In contrast, behavioral and cortical anisotropy occurred
under bipartitioned conditions, in a manner that was com-
pletely indistinguishable from the shape-from-shading
conditions.
Behavioral orientation anisotropy is therefore a very
robust (see also Adams, 2007; Kleffner & Ramachan-
dran, 1992; Sun & Perona, 1998; Thornton & Gilden,
2007; Wolfe et al., 1999), yet nonspecific (see also van
Zoest et al., 2006), phenomenon of VS. Furthermore,
anisotrop ic cortical processing of vertical and horizontal
visual stimuli seems to be a robust phenomenon as well,
since both amplitude changes in the P1 and P3 latency
range that were reported from Experiment 1 could be
replicated in Experiment 2. Again, we found evidence of
cortical anisotropy at multiple levels of the cortical hierar-
chy, and these anisotropies pointed in opposite directions.
Specifically, whereas amplitudes in the P1 latency range
were slightly more positive under horizontal orientations,
P3 amplitudes were more positive under nonsingleton ver-
tical orientations. Both ERP amplitude effects occurred in
equal measure under shape-from-shading conditions, as
well as under bipartitioned conditions.
The nonspecif icity of behavioral and cortical orienta-
tion anisotropy is inconsistent with the light-from-above
account for orientation anisotropy in VS tasks. According
to this model of orientation anisotropy, to interpret visual
stimuli three-dimensionally presupposes vertical-shading
gradients such that the bias for overhead lighting is able to
support perception of concavity or convexity, respectively.
A 3-D interpretation of stimuli is not expected to occur in
any of the remaining conditions of our VS task (Aks &
Enns, 1992). Therefore, behavioral and cortical anisot-
ropy that we observed under bipartitioned conditions are
clearly inconsistent with the light-from-above account for
orientation anisotropy in VS tasks.
The item similarity model of orientation anisotropy
(van Zoest et al., 2006) can explain the nonspecificity of
behavioral anisotropy, yet the model does not provide a
rationale for understanding the observed cortical anisotro-
pies. Furthermore, its essential conjecture—namely, that
[F(1,23) 5 6.51, p 5 .02, η2
p 5 .22]. P1 peak latencies
were also affected by orientation [F(1,23) 5 9.34, p ,
.007, η2
p 5 .29 (horizontal longer than vertical)], but again
this influence of orientation was clearly not modulated by
type of gradient [F(1,23) , 1]. In separate ANOVAs on
each stimulus type (3-D, 2-D), the orientation effect failed
to reach statistical significance [for 2-D stimuli, F(1,23) 5
5.05, p 5 .04, η2
p 5 .18; for 3-D stimuli, F(1,23) 5 2.64,
p 5 .12, η2
p 5 .10]. The ANOVA on N1 amplitudes yielded
a significant three-way orientation 3target 3 set size in-
teraction [F(1,23) 5 23.16, p , .001, η2
p 5 .50]. Type of
gradient or interactions between this factor and any other
factor did not reach statistical significance [all Fs(1,23) #
6.84, ps $ .02, η2
ps # .23]. Finally, N1 latencies were un-
affected by orientation, type of gradient, their interaction,
and interactions between these factors and any other fac-
tors [all Fs(1,23) # 6.42, ps $ .02, η2
p # .22].
P3 amplitude and latency measures
. The stimulus
displays also elicited large P3 waves with parietal maxi-
mum (see Figures 5 and 6, lower panels). Stimulus-locked
averages showed that target-present displays elicited more
positive P3 mean amplitudes than did target-absent dis-
plays [F(1,23) 5 22.65, p , .001, η2
p 5 .50; see Figure 5,
lower left panel]. Response-locked P3 mean amplitudes
also showed a target effect [F(1,23) 5 27.22, p , .001,
η2
p 5 .54], modulated by type of stimuli (3-D, 2-D)
[F(1,23) 5 14.75, p , .002, η2
p 5 .39; see Figure 5, lower
right panel].
Stimulus-locked P3 mean amplitudes decreased as set
size increased [F(1,23) 5 20.32, p , .001, η2
p 5 .47; see
Figure 6, lower left panel]. Importantly, the set size effect
on P3 mean amplitudes was orientation specific, because
the amplitudes decreased much more with increasing set
size in horizontal than in vertical conditions [F(1,23) 5
17.44, p , .001, η2
p 5 .43]. The orientation 3 set size in-
teraction effect on P3 mean amplitude was independent of
type of stimuli [F(1,23) 5 3.66, p 5 .07, η2
p 5 .14]. This
finding replicates the orientation anisotropy of stimulus-
locked P3 mean amplitudes (nonsingleton vertical P3 .
nonsingleton horizontal P3) that we had observed in Ex-
periment 1. Furthermore, it shows that the orientation
anisotropy of stimulus-locked P3 mean amplitudes does
not occur specifically in response to shape-from-shading
stimuli. This conclusion was further corroborated by two
separate ANOVAs that revealed a significant two-way ori-
entation 3 set size interaction for 3-D stimuli [F(1,23) 5
13.46, p , .001, η2
p 5 .37 (nonsingleton vertical P3 .
nonsingleton horizontal P3)], as well as for 2-D stimuli
[F(1,23) 5 14.94, p , .001, η2
p 5 .39 (nonsingleton verti-
cal P3 . nonsingleton horizontal P3)]. Response-locked
P3 mean amplitudes also decreased as set size increased
[F(1,23) 5 9.44, p , .006, η2
p 5 .29; see Figure 6, lower
right panel], without a statistically reliable modulation by
type of stimuli, orientation conditions, or their interaction.
In particular, the orientation 3 set size interaction failed
to reach statistical signif icance [F(1,23) 5 5.52, p 5 .03,
η2
p 5 .19].
Set size also affected stimulus-locked P3 peak latencies
(four later than one), as evidenced by a significant set size
main effect [F(1,23) 5 13.66, p , .002, η2
p 5 .37]. Neither
536 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
Figure 8 describes how signal processing within a local
network modulates signals in a particular perceptive field,
here termed “PF0,” at a particular point in discrete time, t.
Specifically, f(∙), the contextual filtering function, con-
tributes to convert the input to PF0, x0,t (x0,t $ 0), to its
output y0,t (y0,t $ 0). Two general assumptions about the
architecture of this locally interconnected system of per-
ceptive fields form the basis of our model of orientation
anisotropy in VS. First, at time instant t21, corollaries of
output signals from each perceptive field are sent to cor-
tical interneurons, exemplified by y0,t21 and yn,t21, with
y0,t21 $ 0 and yn,t21 $ 0. Second, if two corollaries ex-
cite the interneurons concurrently, suppression at time in-
stant t is exhibited to the perceptive fields that have been
the origin of the corollaries, exemplified by f(∙) $ 0. Sub-
stantial suppression of the input signal to PF0 will result
in case of simultaneous isomorphic input signals to the
interneuron of comparable strength, thereby providing a
mechanism for powerful contextual f iltering suppress-
ing locally homogeneous information represented in the
perceptive fields.4
Our specific model comes next. We first suppose that
the computational implementation of contextual filter-
ing within this system of locally interconnected percep-
tive fields consists of divisive normalization (Albrecht &
Geis ler, 1991; Heeger, 1992; Wainwright, Schwartz, &
Simoncelli, 2002). That is, if y0,t describes the output of
PF0 at time t, it can be computed as
yx
fy y
n
t
t
tnt
n
N
0, =
+⋅
(
)
=
−−
=
0
01 1
1
1
12
,
,,
,
,,,..
β
.. ,,N
(1)
targets and distractors are perceived as being more similar
on horizontal than on vertical displays—needs to be tested
empirically.
An alternative account for the observed orientation
anisotropy in VS tasks may originate from some of the
emergent properties of cortical visual neurons (for reviews,
see Angelucci & Bressloff, 2006; Carandini et al., 2005;
Seriès, Lorenceau, & Frégnac, 2003). Orientation tuning—
that is, responding optimally to a certain orientation and
less to others—is among the most prominent properties
of neurons in the striate cortex (Hubel & Wiesel, 1962).
Orientation selectivity is also the preferred property exam-
ined in neurophysiological studies of cortical visual neu-
rons when contextual influences on spiking responses of
visual neurons are under scrutiny. Specif ically, presenting
two stimuli concurrently, one in the receptive field of visual
neurons and another in the spatial surround of the recep-
tive field, usually results in a massive suppression of the
spiking response. This surround suppression is maximal
under iso-oriented surround conditions (i.e., when the re-
ceptive field and surround stimuli are identically oriented),
whereas surround suppression is negligible under ortho-
oriented surround conditions (i.e., when the receptive field
and surround stimuli are perpendicular to each other).
Our model of orientation anisotropy in VS conveys the
mechanisms of surround suppression to mid-level (extra-
striate) vision, as illustrated in Figure 8. Both panels of
Figure 8 show a system of neighboring perceptive fields
(Jung & Spillmann, 1970; Spillmann, 1994),3 exemplified
by two perceptive fields, that are selectively responsive
either to vertical (left panel) or to horizontal (right panel)
input signals from low-level vision.
Vertical Input Signals
From Low-Level Vision
Horizontal Input Signals
From Low-Level Vision
To High-Level Vision To High-Level Vision
X0,tXn,tX0,t
Y0,tY0,t
Xn,t
Y0,t1Yn,t1
Y0,t1Yn,t1
PF0PFnPF0PFn
f()f()
Figure 8. A sketch of our model of contextual filtering in mid-level vision. Each panel
shows a system of neighboring perceptive f ields, exemplified by two perceptive fields (PF
0
,
PF
n
) that are selectively responsive either to vertical (left panel) or to horizontal (right panel)
input signals from low-level vision. Note the anisotropy of the vertical and horizontal input
signals from low-level vision (x
0,t
, x
n,t
, vertical , horizontal). The loops between perceptive
fields give rise to contextual filtering by divisive normalization, leading to surround suppres-
sion in cases of isomorphic input signals to neighboring perceptive fields (i.e., when x
0,t
and
x
n,t
excite PF
0
and PF
n
simultaneously). Multiplicative filtering functions are required to
model an anisotropic response (y
0,t
, vertical . horizontal). Triangles represent interneurons.
Triangle-shaped arrowheads signify excitatory connections; diamond-shaped arrowheads
represent inhibitory connections. Dashed lines indicate the conditionality of multiplicative
contextual filtering. See the text for details.
Vi s u a l se a r c h , or i e n ta t i o n an i s o t r o p y , a n d erps 537
PFn does not impose an inhibitory effect on PF0. Contex-
tual filtering therefore seems to possess at least two major
characteristics. First, the strength of the inhibitory effect
on a perceptive field depends in a multiplicative manner
on the outputs of the field itself and of each of its con-
nected neighbors. In essence, then, this locally intercon-
nected system of perceptive fields can be identified as a
nonlinear system (Wu, David, & Gallant, 2006). Second,
in cases in which there are no output signals of neigh-
boring perceptive fields, the inhibitory influence features
conditionality, because its minimum is simply zero ac-
cording to f(y0,t21, yn,t21 5 0) 5 0.
In a general sense, the mechanism of contextual filtering
may provide crucial modulatory functions for visual pro-
cessing. First, the primary function of contextual filtering
is redundancy reduction (Barlow, 2001). Specif ically, the
saliency (Itti & Koch, 2001) of large regions of isomorphic
input signals will be greatly attenuated, whereas the saliency
of nonisomorphic input signals, such as edges, boundaries,
and contours, will be much less modified by contextual fil-
tering. The accentuation of discontinuous regions of input
signals may facilitate the segmentation of visual scenes and
figure–ground separation. This analysis ultimately leads
to a center–surround hypothesis for visual saliency (Gao,
Mahadevan, & Vasconcelos, 2008) that enables efficient
coding at higher levels of visual analysis (Barlow, 2001).
Second, the reciprocity of contextual filtering, as defined
above, may be comparably important for visual processing:
Salient low-level features will be integrated to nonsalient
high-level bundles of features (and finally objects), and
vice versa. The reciprocity of contextual filtering suggests
that infrequently processed low-level visual features (origi-
nating from unpredictable, surprising, or even novel events
and objects) gain a saliency advantage at higher levels of
visual processing. This analysis ultimately leads to proba-
bilistic models of visual saliency (Itti & Baldi, 2009) if one
considers that low-level visual processing reflects the sta-
tistical properties of natural scenes in an adaptive manner
(Geisler, 2008; Simoncelli & Olshausen, 2001).
The proposed contextual-filtering model explains the
behavioral orientation anisotropy observed in our VS
studies via its supposed modulatory influences on visual
saliency. Specifically, the initial processing advantage of
horizontal content at low levels of visual analysis is as-
sumed to become reversed at those levels of visual pro-
cessing that follow contextual filtering, thereby slowing
VS for horizontal content. In this regard, it is worth men-
tioning that a distinct behavioral orientation anisotropy
effect occurred exclusively in nonsingleton conditions of
our VS tasks, as if its occurrence depends considerably on
contextual filtering. Z. Li (1999, 2002) argued that many
basic phenomena of VS (Wolfe, 2007) could be traced
back to receptive field–surround interactions of visual
cortical neurons (see also Nothdurft, 1991, for another
contextual model of VS). The details and the persuasive-
ness of these two models of VS are beyond the scope of
this article and will not be portrayed here.
The proposed contextual-filtering model also explains
why the two observed cortical anisotropy effects pointed
in opposite directions. We conjectured above that the
with x0,t representing the input signal at time t, f(y0,t21,
yn,t21) $ 0 being the inhibitory influence of PFn on PF0 at
time t, parameter β $ 0 to be determined empirically, and
N denoting the number of connected perceptive fields that
may impose a suppressive effect on PF0. Equation 1 can
be interpreted as a contextual filtering function, param-
eterized via f() by corollaries of the time-lagged outputs,
y0,t21 and yn,t21, respectively. A formal approach for de-
riving Equation 1 can be found in the Appendix.
Second, we suppose that the magnitude of the horizon-
tal input from low-level vision surpasses the magnitude of
the vertical input from low-level vision (see Figure 8). Our
supposition that horizontal and vertical inputs are pro-
cessed anisotropically at low-level vision can be defended
on empirical grounds. B. Li, Peterson, and Freeman (2003)
reported an orientation anisotropy with regard to the num-
ber of visual neurons that prefer certain orientations: There
are more neurons (in the cat’s striate cortex) with horizon-
tal preference than there are neurons with preference for
vertical or oblique orientations. The authors interpreted
this orientation anisotropy as reflecting the fact that neu-
ral representations correlate with statistical properties of
natural scenes (Geisler, 2008) at low-level vision in an
adaptive manner (Simoncelli & Olshausen, 2001). Thus,
our observation of ERP amplitude anisotropies in the P1
latency range seems to reflect the anisotropic processing
of vertical and horizontal content in low-level vision (ver-
tical , horizontal; B. Li et al., 2003).
Third, we suggest a specific contextual filter function.
Applying simple algebraic rules reveals that linear filter
functions, f() 5 a * x, are incapable of accounting for
an anisotropic output of the system of perceptive f ields
that we specified above. The reason for this incapability
of linear filter functions is that x/Σna * x is equivalent
to x/n * a * x, which is equivalent to 1 / n * a—that is, a
quantity that is independent of x. Therefore, anisotropic
input signals from low-level vision to perceptive fields
(see above) will not be conserved in the output of these
perceptive fields; their output will be constant when x
changes, because it will depend only on n and a. To simu-
late an anisotropic output of the system of perceptive fields
is possible if one considers quadratic filter functions,
f() 5 x2. In this case, simplification of x/Σn x2 yields
x/n * x2, which is equivalent to 1 / n * x. Here, anisotropic
input signals to perceptive fields will be conserved in the
output of these perceptive fields, but in a reciprocal man-
ner: The responses to larger input signals will be smaller,
and vice versa (see Figure 8).
We therefore suggest a specif ic parameterization f()
and, thereby, a specific contextual filtering function. The
inhibitory loop between neighboring perceptive fields can
be described as multiplicative:
f(y0,t21, yn,t21) 5 y0,t21 yn,t21, n 5 1, 2, . . . , N. (2)
If y0,t21 5 yn,t21 5 y, we simply have f(y0,t21,
yn,t21) 5 y2. Interestingly, quadratic contextual filtering
by divisive normalization has been advocated earlier in an
attempt to account for nonlinear properties of visual neu-
rons (Schwartz & Simoncelli, 2001). On the other hand,
if yn,t21 5 0, then f(y0,t21, yn,t21) 5 0, which means that
538 Ko p p , Kiz i l i r m a K , li e b s c h e r , ru n g e , a n d We s s e l
context model. Additional evidence that visual informa-
tion processing is strongly modulated by contextual inter-
action comes from psychophysical studies in which ob-
servers had to discriminate the orientation of lines. When
tested with simple stimuli, these studies showed that per-
formance is best for horizontal and vertical orientations
and worst for oblique orientations (the oblique effect; Es-
sock, DeFord, Hansen, & Sinai, 2003; Hansen & Essock,
2004). However, these authors showed that, when tested
with more complex images consisting of naturalistic con-
tent, performance is best for oblique and vertical orienta-
tions and worst for horizontal orientations (the horizontal
effect). They interpreted this horizontal effect as being the
consequence of minimizing the visual saliency of the hori-
zontal content under more naturalistic conditions.
The context model of VS is similar to earlier models of
VS (Z. Li, 1999, 2002; Nothdurft, 1991), and it is consis-
tent with some of the most important VS phenomena (see
Wolfe, 2007, for a review of these phenomena), such as the
set size effect (by increasing n in Equation 1), the target
absence effect (target-absent displays are necessarily more
homogeneous than target-present displays), and the target–
distractor similarity effect (by increasing the sum over the
y y products in the denominator of Equation 1 after in-
sertion of Equation 2). It rests on a simple mechanism of
lateral inhibition that is supposed to occur ubiquitously in
the whole brain and that has been studied most elegantly in
the visual system (for reviews, see Angelucci & Bressloff,
2006; Carandini et al., 2005; Seriès et al., 2003).
We proposed here a simple, yet highly integrative, model
of behavioral and electrophysiological properties of ori-
entation anisotropy in VS. Our context model highlights
local suppressive interactions as a cortical mechanism of
information processing, putatively achieved through lat-
eral inhibition. The pursuance of appropriate research on
orientation anisotropy may well help to decide between
two fundamentally contrasting views of visual perception.
The light-from-above model of orientation anisotropy is
explicitly a model of indirect perception (Kersten et al.,
2004; Ramachandran, 1988; Ramachandran & Rogers-
Ramachandran, 2008). In these models, visual perception
is thought to involve the activation of nonsensory knowl-
edge, such as beliefs, memories, and inferences. Accord-
ing to direct models of visual perception, optical stimu-
lation is extraordinarily rich and provides such a precise
specification of the environment that perceivers need only
detect the appropriate information without nonsensory
contributions (see Michaels & Carello, 1981, for a com-
prehensive review of the distinctions between indirect and
direct models of visual perception). The context model of
orientation anisotropy is consistent with the direct view of
visual perception, since it attributes anisotropy to lateral
processes within the visual system itself.
AUTHOR NOTE
J.K. is now at the Department of Psychology, Philipps University
Marburg. Thanks are due David Gilden, University of Texas at Austin,
for providing his stimulus materials. Steve Luck, University of Califor-
nia, Davis, and three anonymous reviewers offered many valuable com-
ments and suggestions for improving earlier drafts of the manuscript. We
also thank Wolfgang Skrandies, Justus Liebig University, Giessen, and
anisotropic ERP amplitudes in the P1 latency range reflect
vertical and horizontal content being processed aniso-
tropically in low-level vision (vertical , horizontal; B. Li
et al., 2003). In agreement with this claim, the horizontal
enhancement of ERP amplitudes in the P1 latency range
was observed independently of set size conditions and,
thus, independently of the conditionality of contextual fil-
tering. Furthermore, the anisotropic P1 and P3 amplitude
changes pointed in opposite directions, because we mea-
sured a horizontal enhancement of ERP amplitudes in the
P1 latency range but a vertical enhancement of P3 ampli-
tudes. This pattern of ERP amplitude effects is compatible
with the reciprocity of the contextual-filtering model if one
assumes that whereas ERP amplitudes in the P1 latency
range reflect input to the proposed system of neighbor-
ing perceptive fields, P3 amplitudes reflect their output. In
line with this conjecture, recall that whereas the horizontal
enhancement of ERP amplitudes in the P1 latency range
occurred independently of set size conditions, we observed
that the vertical enhancement of P3 amplitudes depended
on set size conditions: It occurred exclusively in response
to four-item displays, as if its occurrence is considerably
dependent on the effects of contextual filtering. Finally,
the mere existence of a set size main effect on P3, but not
P1, amplitudes (P3 set size four , P3 set size one; see
also Kok, 2001) is compatible with assuming that P3, but
not P1, amplitudes are massively influenced by contextual
filtering. Overall, the proposed model is remarkably suc-
cessful in accounting not only for behavioral orientation
anisotropy, but also for the fact that the two observed cor-
tical anisotropy effects pointed in opposite directions and
that they were differentially affected by set size.
The context model accounted for the behavioral and
cortical anisotropies that we observed in our own experi-
ments. It can also account for the body of work on anisot-
ropies in shape-from-shading VS studies (Adams, 2007;
Kleffner & Ramachandran, 1992; Sun & Perona, 1998;
Thornton & Gilden, 2007; Wolfe et al., 1999) and in van
Zoest et al.’s (2006) study (Experiments 1–3). Its explan-
atory power is limited only by the data from van Zoest
et al.’s Experiment 4, in which no orientation anisotropy
was found under conditions of interitem asymmetry. How-
ever, these findings might be compatible with our context
model if perceptive fields do not exhibit only orientation
specificity, but are also specif ic with regard to other (yet
to be determined) features of the visual input. Given this
to be true, the context model of anisotropy predicts less
pronounced anisotropy when dissimilar, as compared with
when similar, stimuli occur in the search displays. For ex-
ample, if perceptive fields are tuned for a combination
of orientation and spatial frequency, the context model
predicts stronger orientation anisotropy when stimuli have
the same spatial frequency, as compared with when spatial
frequency differs between stimuli.
We found only one study that directly examined the ef-
fects of manipulating target–distractor orientation (Wolfe
et al., 1999, Experiments 1 and 4). Here, search for targets
rotated 90º from the distractors was more efficient than
search for targets rotated 180º from the distractors. These
findings are clearly compatible with predictions of our
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NOTES
1. Medians are used in the RT calculations, which has the advantage
of minimizing the effects of extreme data points. However, Miller (1988)
APPENDIX
In its most general form, the model can be written as
yAx
BC fy y
n
t
t
tnt
n
N
0
0
01 1
1
12
,
,
,,
,
,,=
+⋅
(
)
=
−−
=
,, ..., .N
(A1)
Without loss of generality, the number of free parameters can be reduced as follows:
yx
B
A
C
Afy y
n
t
t
tnt
n
N
0
0
01 1
1
12
,
,
,,
,
,,=
+⋅
(
)
=
−−
=
,, ..., .N
(A2)
In the complete absence of contextual filtering—that is, when all f(y0,t21, yn,t21) 5 0—Equation A2 is then
transparent—that is, y0,t 5 x0,t, if B/A 5 1. This analysis leads to our specific formulation of the contextual
filtering function,
yx
fy y
n
t
t
tnt
n
N
0
0
01 1
1
1
12
,
,
,,
,
,,,.=
+⋅
(
)
=
−−
=
β
..., ,N
(A3)
with β 5 C/A. Equation A3 equals Equation 1.
This approach to deriving the contextual filtering function was brought to our attention by Tim Fingscheidt,
who argued, and we agree, that the function needs a more comprehensive formulation. We honestly thank him
for his valuable suggestion.
(Manuscript received September 18, 2009;
revision accepted for publication August 20, 2010.)
... Specifically, they conjectured that targets and distractors are perceived as being more similar to each other when objects are horizontally oriented as compared to when they are vertically oriented, thereby decreasing search efficiency (Duncan & Humphreys, 1989). Second, we proposed a context model of orientation asymmetry in VS which has its roots in normalization theories of cortical neuronal computation (Kopp et al., 2010;Kopp et al., 2011;Carandini & Heeger, 2012). Basically, normalization equations compute ratios between the response of individual neurons and the summed activity of neuron pools. ...
... Each participant completed eight blocks of trials (see Table 1 Pz. An area rather than a peak measure was used for P3 amplitudes because the latency variation that was expected for multiple object conditions could greatly distort peak amplitude measures (Kopp et al., 2010). When single objects were presented, peak latencies in the grand-average waveforms differed between vertical (364 ms latency) and horizontal (392 ms latency) target orientation conditions (cf. Figure 5). ...
... Hence, P3 amplitudes were measured as the area under the curve within the latency range ±50 ms around these condition-specific peak latencies. When four objects were presented, grand-average waveforms showed the expected multiple peak structure (cf. Figure 5; see also Kopp et al., 2010). We chose the latency of the central peak in the grand-average waveforms (436 ms latency), and we analyzed P3 amplitudes in those conditions in which four objects had been presented as the area under the curve within the latency range 436 ±50 ms. ...
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... It remains to be delineated how our findings can be reconciled with this more traditional view. P300 amplitude variation is known to be related to many other variables, such as the difficulty of a task (Kopp, Kizilirmak, Liebscher, Runge, & Wessel, 2010) or the specific temporal regimes on a task (Gonsalvez, Barry, Rushby, & Polich, 2007). A comprehensive theory of P300 amplitude variation still needs to be developed (see Johnson, 1986;Polich, 2007, for corresponding attempts). ...
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