The reference frame of the tilt aftereffect
CNRS Laboratoire Psychologie de la Perception,
Université Paris Descartes, Paris, FranceTomas Knapen
CNRS Laboratoire Psychologie de la Perception,
Université Paris Descartes, Paris, FranceMartin Rolfs
CNRS Laboratoire Psychologie de la Perception,
Université Paris Descartes, Paris, FranceMark Wexler
CNRS Laboratoire Psychologie de la Perception,
Université Paris Descartes, Paris, FrancePatrick Cavanagh
Perceptual aftereffects provide a sensitive tool to investigate the influence of eye and head position on visual processing.
There have been recent indications that the TAE is remapped around the time of a saccade to remain aligned to the
adapting location in the world. Here, we investigate the spatial frame of reference of the TAE by independently manipulating
retinal position, gaze orientation, and head orientation between adaptation and test. The results show that the critical factor
in the TAE is the correspondence between the adaptation and test locations in a retinotopic frame of reference, whereas
world- and head-centric frames of reference do not play a significant role. Our results confirm that adaptation to orientation
takes place at retinotopic levels of visual processing. We suggest that the remapping process that plays a role in visual
stability does not transfer feature gain information around the time of eye (or head) movements.
Keywords: active vision, eye movements, receptive fields, spatial version, visual cortex
Citation: Knapen, T., Rolfs, M., Wexler, M., & Cavanagh, P. (2010). The reference frame of the tilt aftereffect. Journal of
Vision, 10(1):8, 1–13, http://journalofvision.org/10/1/8/, doi:10.1167/10.1.8.
Introduction
We have the impression of stable visual perception of
the world around us despite our eye, head, and body
movements that drastically change the images landing on
our retinas. For perception of the world to be stable,
movements of eyes and head have to be taken into account
and recent neurophysiology has provided several indica-
tions of possible mechanisms. Visual perception takes as
its initial input the signals from the retina, so the original
visual signals are based in retinotopic coordinates. This
frame of reference rotates and translates relative to world
and head coordinates whenever the eyes rotate in their
sockets and it rotates and translates relative to the world
whenever the eyes or head rotate or translate. This leads to
the interdependence of several different reference frames,
namely those based on retinal, head (also called cranio-
topic), and body (or world) coordinates. These three
reference frames are the principal coordinate systems that,
when the appropriate extra-retinal signals are taken into
account, could support behavior and representations in
world-centric coordinates.
There is evidence at various levels of the visual system
for signals selective to gaze and head orientation. For
example, the visual sensitivity of many retinotopic neurons
in parietal cortex is modulated by gaze direction and head
orientation relative to body and world (Andersen, Essick, &
Siegel, 1985; Andersen, Snyder, Li, & Stricanne, 1993),
enabling at least theoretically, a recovery of locations in
world coordinates (Snyder, Grieve, Brotchie, & Andersen,
1998). There is also an influence of gaze direction on
single cell responses in areas V1, V2, V3A, and V4
(Galletti & Battaglini, 1989; Rosenbluth & Allman, 2002;
Trotter & Celebrini, 1999). In line with these physiolog-
ical reports, the strength of visual aftereffects, such as
those for motion and tilt, decreases by about 10% if gaze
shifts by more than 60 degrees between adaptation and
test even when the test stimulus is at the same retinal
location as the adaptation stimulus (Nishida, Motoyoshi,
Andersen, & Shimojo, 2003).
Although cells modulated by eye, head, and body
positions could underlie a recovery of world coordinates,
the findings of Duhamel, Colby, and Goldberg (1992) and
others (Batista, Buneo, Snyder, & Andersen, 1999; Colby,
Duhamel, & Goldberg, 1996; Heiser & Colby, 2006)in
parietal areas have offered an alternative mechanism.
Specifically, these authors report cells that become active
before a saccade brings a stimulus into their receptive
field (remapping). Thus, prior to an eye movement these
cells are activated by stimuli presented in two regions:
locations in their classical receptive field and locations in
the world that will fall inside their receptive field only
after the saccade. This means that these neurons have
Journal of Vision (2010) 10(1):8, 1–13 http://journalofvision.org/10/1/8/ 1
doi: 10.1167/10.1.8 ISSN 1534-7362 * ARVOReceived August 24, 2009; published January 19, 2010

Figure 1. Design of experiments. (A) Experiment 1. The time course of trials in the different conditions of Experiment 1. Three seconds of
adaptation were followed by 1 s for eye movements, after which a test stimulus of 50 ms was presented. Changes: With the head
remaining in the same orientation one can change gaze and retinal position between adaptation and test, in a 2 by 2 design. Between
adaptation and test there were always two saccades to equate the number of eye movements across trials. Reference frames: Using
these different conditions, we can differentiate between head/world reference frames on the one hand, and the retinal reference frame
on the other, but this design conflates head and world reference frames. To differentiate between the two, we need head movements.
(B) Experiment 2. The design with changes of head orientation between adaptation and test and the trial time course. Again, in two
conditions gaze is changed and in two conditions retinal position is changed, but now these changes are combined with the changes in
head orientation. (C) Effector changes: Design matrix for the changes using different effectors, i.e., world, head, and gaze. (D) Reference
frames: Design matrix that shows the factors of the different reference frames. Vectors from this matrix were used for the generation of
refactored data in Figures 3C and 3D. For example, the factor of the head-centric reference frame is (1 + 3 j 2 j 4) / 2 in Experiment 1
and (5 + 7 j 6 j 8) / 2 in Experiment 2, whereas the factor of the world-centric frame of reference is (1 + 3j 2j 4) / 2 in Experiment 1 and
(6 + 8 j 5 j 7) / 2 in Experiment 2.
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 2

access to the amplitude and direction of the impending
saccade and can use this information to pre-activate even
before visual information reaches their classical receptive
field. The same process has also been found in the frontal
eye fields (Sommer & Wurtz, 2006; Umeno & Goldberg,
1997, 2001) and visual cortex (Nakamura & Colby, 2002)
using single-cell physiology, and similar responses have
been demonstrated in humans in both parietal (Medendorp,
Goltz, Vilis, & Crawford, 2003; Merriam, Genovese, &
Colby, 2003) and visual cortices (Merriam, Genovese, &
Colby, 2007) using functional imaging. Remapping has
been suggested as a solution to visual stability (Melcher
& Colby, 2008; Wurtz, 2008) because it could be used
to keep track of where targets are in the world as the
eyes move even though it is based on a retinotopic
representation.
Psychophysical investigation of the feature content of
remapping activity is possible using negative aftereffects,
a prominent example of which is the tilt aftereffect (TAE).
In this illusion, prolonged exposure to a tilted stimulus
causes changes in the sensitivity of the visual system such
that a subsequently presented vertical pattern will appear
to be tilted in the direction opposite to the adapting
pattern. This illusion lasts several seconds, so that the
subject may make a saccade between adaptation and test.
This allows researchers to investigate whether feature-
specific information embodied as adaptation is remapped.
If adaptation is remapped when we make a saccade, we
should be able to find a TAE by testing in retinal locations
that have not been stimulated but correspond to the world-
or head-centric location of the adapting stimulus.
There have been reports that form and motion after-
effects may also be remapped around the time of a saccade
(Ezzati, Golzar, & Afraz, 2008; Melcher, 2007) in order to
be aligned in a spatiotopic frame of reference (Melcher,
2005). The results for motion adaptation are controversial,
however, as other studies find no evidence of spatiotopy, but
report instead that the reference frame of motion adaptation
is robustly retinotopic (Knapen, Rolfs, & Cavanagh, 2009;
Wenderoth & Wiese, 2008).
In order to investigate the different reference frames
involved in vision, it is necessary to separate the
presentation of adaptation and test stimuli with an effector
movement, such as a change in position of the stimulus on
the screen (change in world location), or movement of the
observer’s gaze or head orientation. In our study here,
changes in world position, gaze direction, and head
orientation combine to provide coincidence, or lack
thereof, between adaptation and test stimulus presentation
in three different reference frames. This adaptation-test
coincidence in different reference frames allows us to
dissociate the importance of neural processing in retina-,
head- and world-centric coordinate systems. Because the
inclusion of head rotations requires special precautions,
we separated our study into two experiments, one in
which the head was held fixed and one in which the head
was rotated between adaptation and test on every trial.
The conditions in this experimental design are depicted in
Figure 1. This design allows us to compare all relevant
reference frames and the additional and independent effect
of gaze direction (but not head direction) of the retino-
topic TAE within experiments.
As we see from left to right in Figure 1A,inExperiment1
there are conditions with correspondence of stimulus
position between adaptation and test in (1) all three,
(2) none, (3) head and world, and (4) retinal reference
frames, respectively. In Experiment 2 (Figure 1B), head
orientation is always changed between adaptation and test.
This allows us to examine the difference between world-
and head-centric reference frames. In the conditions of
Experiment 2, there is correspondence between adaptation
and test in (5) head and retinal, (6) world, (7) head, and
(8) world and retinal, when seen from left to right. So, in
total, all 8 possible combinations of the three reference
frames are investigated.
In previous research that used only an eye movement to
dissociate retinal and spatial positions (Ezzati et al., 2008;
Knapen et al., 2009; Melcher, 2005, 2007, 2008a, 2008b;
Wenderoth & Wiese, 2008), spatiotopic tests are at the
same location in space but also at the same location in
head-centered and body-centered coordinates. In these
experiments, the eyes move to a new fixation spot
following adaptation and the test is presented at the same
spatial location as the adapting stimulus. Since the eyes
have moved but the head has not, the locations that are
considered spatiotopic (same in world coordinates) are
also the same in head-based coordinates. Our present
design enables us to disentangle eye, head, and world-
spatial coordinates by separating the adapting and test
stimulus by a change in world position, a change in gaze,
and/or a change in head orientation.
Materials and methods
Experiments 1 and 2
Six participants (3 naive) took part in Experiment 1 and
6 in Experiment 2 (4 naive), age 20–42. Observers were
seated in a silent and dimly lit room with the head
positioned on a chin rest, 63 cm (Experiment 1) or 57 cm
(Experiment 2) in front of a computer screen.
Experiment 1
Stimuli were presented on a gamma-linearized 22W
Formac ProNitron 22800 screen with a spatial resolution
of 1440 by 1050 pixels and a vertical refresh rate of 100 Hz.
Gaze position of the right eye was measured using an
EyeLink 1000 Desktop Mount (SR Research, Osgoode,
Ontario, Canada) with an average spatial resolution of
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 3

0.25 to 0.5 degrees of visual angle, sampling at 1 kHz.
Saccades were detected using a two-dimensional velocity
space algorithm (Engbert & Mergenthaler, 2006). The
experiment was controlled by an Apple MacPro Xeon
computer running custom software. Manual responses were
recorded via a standard keyboard.
Stimulus presentation
The location of the fixation mark was 5 degrees left or
right of the center of the screen. Stimuli were presented at
j10, 0, or 10 degrees eccentricity on the horizontal
midline of the screen. Thus, the distance from fixation to
the adaptation or test stimulus was always 5 degrees, and
the distance between adaptation and test stimuli was either
0 or 10 degrees in retinal or spatial coordinates. This
stimulus layout is shown in Figure 2. Between adaptation
and fixation, observers were required to make 2 saccades,
one to an intermediate position above or below the center
of the screen. The location (above, below) of this
intermediate fixation mark alternated from trial to trial.
This dual saccade approach serves to equate the number of
saccadic transients (Nishida et al., 2003)thatmay
influence perceptual adaptation (Ross & Ma-Wyatt, 2004).
Stimulus properties
Both adapting and test stimuli were Gabor patterns,
with an envelope A of 1.3 degrees of visual angle and a
spatial frequency of 1.44 cycles per degree. Adaptation
contrast was 100% to maximize the magnitude of the TAE
(Parker, 1972), and the grating was cycled for one full
period during the adaptation presentation. The direction of
this cycling motion was drawn randomly for each trial.
Test contrast was 50% in Experiment 1, to increase the
magnitude of the TAE (Parker, 1972). Adaptation tilt in
both experiments was T15 degrees. The fixation stimulus
consisted of a black circle, 14Vacross, within which a 6V
colored disk was drawn. The color of the fixation mark
indicated the phase of the trial to the observer. The
fixation mark was red during adaptation and refixation
phases, green during and before test stimulus presentation,
and blue when the observers was to answer.
Adaptation duration was 3000 ms, observers were given
500 ms to fixate at the eccentric intermediate fixation
position (see Figure 1), and 750 ms for reaching the
fixation mark used during test stimulus presentation. Test
presentation duration was 50 ms. After test stimulus
presentation, observers responded using the arrow keys
on the keyboard, indicating the perceived orientation of
the test stimulus (tilted to the left or to the right).
Test stimulus orientation ranged from j4 to 4 degrees
with 1-degree steps. Adaptation tilt, experimental con-
ditions, test stimulus orientation, fixation position, and
head orientation (in Experiment 2) were interleaved
randomly. In Experiment 1, five sessions in which each
condition was sampled 4 times were run for each
observer, leading to a maximal total of 20 judgments per
data point. Gaze position was recorded in all trials, and
trials in which gaze position was outside a 2.5-degree
radius around the intended fixation position at any single
time point during the trial’s adaptation or fixation phases,
the trial was excluded from further analysis. This strict
exclusion rule resulted in the deletion of 4.5 T 1.5% of the
trials. Saccade latencies for the first saccade were 123.3 T
5.7 ms, and for the second saccade to the fixation location
for testing it was 98.9 T 7.6 ms.
The remaining data were combined across adaptation
tilt and fixation position for fitting of two parameters,
standard deviation and mean (A and 2) of a single
cumulative Gaussian function, of which the mean repre-
sents the TAE. As expected, this resulted in almost
identical results when compared to the difference between
2 parameters of fits to data for both adaptation orientations
separately. We chose to fit one function instead of two to
improve fit reliability. This also enables bootstrapping of
single fit results in order to calculate standard errors.
Experiment 2
All experimental parameters were identical to Experi-
ment 1, except the following. Stimuli were presented
on a 20W Dell screen with a spatial resolution of 1024 by
768 pixels and a vertical refresh rate of 120 Hz. Gaze
position of both eyes was measured using an EyeLink2
Head-mounted system (SR Research, Osgoode, Ontario,
Canada). Three-dimensional head orientation was
recorded using an optical motion tracker (LaserBird,
Ascension), with the lightweight sensor worn on the
EyeLink2 helmet that held it fixed to the head. The
experiment was controlled by a Dell computer running
custom software. Manual responses were recorded via a
standard keyboard.
Figure 2. Stimulus image and fixation locations layout for Experi-
ment 1. Intermediate fixation stimulus locations and possible test
fixation location are shown using diminished opacity.
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 4

Stimulus presentation
Gaze angle and head angle were varied according to the
design depicted in Figure 1. Head orientations were
measured with respect to a near-vertical axis of rotation,
calculated in a preliminary calibration procedure in which
the subjects performed natural sideways head rotations.
Orientation 0 corresponds to the subject directly facing the
monitor, and positive orientations correspond to head
turns to the right. Head orientations during adaptation and
test were T7 and T7, or T14 and 0 degrees, depending on
conditions (see Figure 1). Thus, the change in head
orientation was equal across conditions in this second
experiment. Gaze orientation and retinal stimulus eccen-
tricity was always T7 degrees. During the 1-s interval
between adaptation and test, observers were required to
rotate their head to a designated angle. They were guided
in their head rotation by a tone, whose frequency and
spatial origin indicated the desired direction of head
rotation, and which would attenuate as the observer’s
head approached the desired orientation, and which would
stop altogether when the observer’s head orientation was
within 1 degree of the desired head orientation, indicating
that the desired head orientation had been reached.
Test stimulus contrast was 100% and the adapting
grating was not cycled in this second experiment. The
fixation mark was a 6V colored disk. The color of the
fixation mark indicated, conjointly with the auditory
signals provided, whether the observer’s head orientation
was within set limits (green when in range, red when
further head rotation was required).
Adaptation duration was 3000 ms, 1 s was allotted to
reach the desired head orientation for test stimulus
presentation. Test presentation duration was 100 ms.
Both gaze and head orientations were recorded at the
screen refresh rate for offline analysis. In conditions 5 and 6,
observers made saccades to the second fixation point
(latency 182 T 2.4ms),followedbyaslowerhead
movement; in the two other conditions, observers main-
tained fixation and moved their heads. Trials in which the
observer failed to rotate the head into the desired range
within the 1-s interval appropriated for the head rotation or
in which gaze and head orientation deviation during
adaptation and test was greater than the 95% confidence
interval across all trials in that session were discarded from
further data analysis.
Results
Experiment 1: Head fixed
Adaptation to tilt causes a subsequent vertical test
pattern to appear to be tilted in the opposite direction: the
TAE. Figure 3A shows the data for the first experiment, in
which the head was fixed in all conditions. Clearly, strong
TAEs occur only when the adapting and test stimuli
coincide on the retina. This is confirmed by the signifi-
cance of the retina effect in a repeated measures ANOVA
(F(1, 5) = 23.8, p G 0.01). Although the difference
between first and fourth bars could be interpreted as a
replication of previous results (Nishida et al., 2003), in our
model the factor of gaze does not reach significance
(F(1, 5) = 5.2, p = 0.07), nor is there a significant
interaction (F(1, 5) = 1.4, p = 0.29). After statistical
analysis, these results can be further visualized by plotting
the factors of the different reference frames and the effect
of gaze by multiplying the data for each subject with the
design vector of that factor as given in Figure 1D. For
instance, to generate the value for the head-centric frame
of reference this becomes the multiplication of data in
conditions (1 + 3 j 2 j 4) / 2 and for retinal it is (1 + 4 j
2 j 3) / 2. The gaze dependency effect is recovered from
the retinotopic TAEs, that is, from conditions 1 and 4.
Replotting the data in this manner emphasizes visually
what was clear from the statistics: the TAEs found in
Experiment 1 are solely retinotopic.
Experiment 2: Head shifted
The data for the second, head-moving experiment is
depicted in Figure 3B. Again, by far the largest values for
the TAE occur in situations where the adapting and testing
stimulus coincide in terms of retinal position (5 and 8).
There is a slight difference between conditions 6 (corre-
spondence in world coordinates) and 7 (correspondence in
head coordinates), which differ in terms of the factor of
gaze, albeit in conditions where there is no retinal overlap
between adaptation and test. This factor of gaze does not
reach significance in a repeated measures ANOVA (F(1, 5) =
1.4, p = 0.28). As in Experiment 1, the retinal factor is
significant (F(1, 5) = 13.6, p = 0.01) and the interaction
between factors is not (F(1, 5) = 1.7, p = 0.25). As in
Figure 3C,inFigure 3D we replot the data by multiplying
the vector of the design for all head-shifted conditions for
visual emphasis. The gaze dependency factor is computed
from conditions 5 and 8, and by means of example, the
world reference frame factor is computed as follows:
(6 + 8 j 5 j 7) / 2, as can be gleaned from Figure 1D.
Again, the results of this computation show that the
retinotopic frame of reference is the only significant factor.
Discussion
We have conducted two experiments that determine
the coordinate frame of the tilt aftereffect. Specifically,
we differentiate between the retinotopic and head- and
world-centric frames of reference. The data from our
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 5

two experiments show unequivocally that the coordinate
frame for the tilt aftereffect is principally retinotopic. We
find no evidence of adaptation in the reference frames of
head or world. Thus, our results point strongly to a
dominant role of mechanisms in lower, retinotopically
organized visual areas as the neural substrate for
adaptation to orientation.
Our experimental design was intended to investigate the
role of different reference frames in the generation of the
TAE. Independently of the question of reference frame, a
related question is whether a change using an effector
such as the eye, the head, or the world has an impact on
the TAE. Full investigation of the effect of effector
changes would require a different set of experiments that
would be outside the scope of the present paper. However,
in our experimental design, we can investigate the effect
of gaze on the retinotopic TAE. In both our experiments,
there is a trend toward larger TAE when gaze direction
remains the same in both adaptation and test. This effect
could be mediated by the known dependence of neural
activity on gaze direction even in the lowest levels of
visual cortex (Galletti & Battaglini, 1989; Rosenbluth &
Allman, 2002; Trotter & Celebrini, 1999). This trend is in
accordance with previous psychophysical results showing
gaze dependence of the TAE (Nishida et al., 2003). This
effect of gaze difference on the magnitude of the TAE
reaches borderline significance at the gaze difference used
in our main experiment. To more directly compare
Nishida et al.’s (2003) study with our own present study,
we conducted a control experiment to investigate the
influence of gaze difference between adaptation and test
(details of the experiment are described in Appendix A).
Figure 3. (A) Results of Experiment 1. TAE magnitude in the four different conditions depicted in Figure 1A. TAE magnitude is greatest in
the conditions in which the test stimulus coincided with the adapting stimulus on the retina. There is hardly any TAE when the test stimulus
and adapting stimulus do not coincide on the retina (second and third bars). (B) Results of Experiment 2. TAE magnitude in the four
different conditions depicted in Figure 1B. As in Experiment 1, TAE magnitude is greatest in those conditions in which test and adapting
stimuli coincided on the retina (first and fourth bars). Black error bars indicate the standard error across subjects. The light gray error bars
indicate the mean and the standard error on the fitted mean (1000-fold bootstrap) for each subject separately. (C, D) Refactored TAEs for
Experiments 1 and 2, respectively. We multiply the design vector for each of the reference frames of interest (see Figure 1D), including the
gaze correspondence, with the data on a per-subject bases. This distilled data we plot with error bars that signify 95% confidence
intervals, allowing direct visual assessment of the different reference frames’ roles. Clearly, only the retinal frame of reference is of
importance.
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 6

In our control experiment, we increase the gaze angle
difference parametrically and replicate Nishida et al.’s
results by finding a significant dependence of TAE on
gaze difference between adapt and test.
Rieser and Banks (1981) found that the TAE occurs in a
retinal frame of reference under conditions of head
rotations about the line of sight. In their study, the TAE
was fully retinotopic, and any world-referenced results
were due to extravisual head orientation adaptation. The
threshold elevation aftereffect also occurs in a retinal
frame of reference when rotations of the head about the
line of sight are used to distinguish reference frames
(Findlay & Parker, 1972; Mitchell & Blakemore, 1972).
We investigate the importance of the separate frames of
reference that play a role in our TAE experiments. In our
results, there is a very dominant influence of the retinal
reference frame in the TAE (see Figure 3). Using head
movements, we can distinguish whether the computations
underlying the tilt aftereffect extend beyond retinotopic
processing in a head-centered or a body- or world-
centered (spatiotopic) frame of reference, if any.
These results are most readily understood from the
visualization shown in Figures 3C and 3D. This figure
shows the weights of the factors for the three reference
frames in question and indicates that there is no role for
head-centric nor world-centric processing in the gener-
ation of the TAE: only the retinal frame of reference is of
importance.
The absence of a spatiotopic effect in both our experi-
ments differs from previous results (Melcher, 2005, 2007,
2008a, 2008b). Based on these earlier results, Melcher
(2005, 2007, 2008a, 2008b) and his colleagues proposed
that information regarding visual features, such as the gain
control settings for those features (their adaptation), is
remapped on retinotopic representations around the time
of each saccade to remain aligned with their locations in
space (Melcher, 2007; Melcher & Colby, 2008). We
explored these empirical claims and the possible sources
of differences between the earlier results and our own by
replicating the experimental conditions of Melcher’s
experiments. Using code and details of experimental
procedures provided by Dr. Melcher, in several experi-
ments we were unable to replicate the reported pattern of
results. We are therefore at a loss concerning the source of
the difference between Melcher’s results and our own.
Detailed methods and results for this set of experiments
are presented in Appendix A.
Information intimately linked to navigation and percep-
tion of space for motor behaviors is known to be analyzed
in higher level areas (Colby & Goldberg, 1999; Snyder
et al., 1998), and it is thus not surprising that these areas
take into account not only visual information but also
different forms of proprioceptive information to create a
role for other than retinal reference frames (Bradley,
Maxwell, Andersen, Banks, & Shenoy, 1996; Crowell,
Banks, Shenoy, & Andersen, 1998). For visual feature
information, which is analyzed in a frame of reference
bound to the retina, the situation is likely very different.
For instance, eye movements can be made to any target in
the visual field, and it is known that adaptation to
orientation takes place in primary visual cortex (Dragoi,
Rivadulla, & Sur, 2001; Dragoi, Sharma, & Sur, 2000; Jin,
Dragoi, Sur, & Seung, 2005). This means that remapping
of adaptation would require that the modified, adapted
state of neurons that is thought to be the substrate of
perceptual aftereffects (Clifford et al., 2007; Jin et al.,
2005; Kohn & Movshon, 2003, 2004; Schwartz, Hsu, &
Dayan, 2007) be transmitted horizontally through the
brain in any direction and amplitude depending on the
impending eye movement, necessitating a very dense
connectivity in lower level visual cortex for which there
seems to be no neurophysiological evidence.
Our results indicate that adaptation to stimulus features
occurs only at the retinotopic levels of the visual hierarchy
that are known to be involved in analysis of features such
as orientation (Hubel & Wiesel, 1959). In this regard, our
results dovetail very well with other recent results in face
adaptation (Afraz & Cavanagh, 2008, 2009) and motion
adaptation (Knapen et al., 2009; Wenderoth & Wiese, 2008).
Lastly, our results suggest that the remapping process that
plays a role in visual stability (Duhamel et al., 1992)is
unlikely to involve a remapping of feature gain control
settings that underlie the perceptual effects of adaptation.
Appendix A
Additional experiments
Spatiotopicity of the TAE?
We also performed several additional experiments to
investigate the origin of the difference between our results
and those reported previously (Melcher, 2005, 2007,
2008a, 2008b).
Additional conditions
Figure A1 shows the design we used based as closely as
possible on Melcher’s original experiment (Melcher,
2005), and the resulting data after 5 s of adaptation in
4 subjects. Stimulus parameters were identical to our
Experiment 1. These results fail to show any significant
spatiotopic TAE. Dr. Melcher kindly showed us a new
procedure that he felt was even more successful and sent
us experimental code as well. Using this second design,
observers adapted in the periphery and then saccaded to
the adapting stimulus’ location on the screen, where they
judged the tilt of the test, now presented at the fovea
(rather than the original adaptation at the fovea with test
in the periphery; Melcher, 2005). We randomly interleaved
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 7

these conditions, the original and this new procedure
as depicted in the top row of Figure A2A. That is, in
half of the trials, adaptation was peripheral (left column)
and test foveal, whereas in the other half of the trials,
adaptation was foveal and test peripheral (right column,
original design; Melcher, 2005).
Whereas strong retinotopic TAEs were found using both
paradigms, neither experimental paradigm yielded signifi-
cant spatiotopic TAEs. For adaptation in the periphery and
test at the spatiotopic location (the new design), there is a
significant TAE, but when corrected for the non-specific
TAE this result disappears (t-test left column, p = 0.08),
indicating that, as in the second experiment, the effect can
be accounted for by spatially general non-specific adapta-
tion. The original design (Melcher, 2005)yieldsa
spatiotopic TAE in neither corrected nor uncorrected form
(shaded right column, Figure A2A). The bottom row
shows the true spatiotopic TAE, corrected by subtracting
the non-specific TAE for each observer, identified by their
initials, separately.
Presentation sequence
Another difference between our experimental approach
and that of Melcher is that in our experiments all
conditions were interleaved, whereas in his they were
blocked per session. We therefore repeated our experi-
ment blocking conditions in a single session. A finding of
a spatiotopic TAE in the blocked design, but not in the
interleaved design, would indicate that expectancy regard-
ing the location of stimulus reappearance plays a role in
the spatiotopic TAE. Figure A2B shows that there is no
spatiotopic TAE when employing the blocked presentation
sequence, either. This indicates that differences in results
are not due to a difference in presentation sequence. Again,
the spatiotopic TAE corrected for the non-specific TAE is
shown in the bottom row for individual subjects.
Figure A1. Spatiotopic TAE experiment following Melcher’s original design: Conditions and results. (A) Experimental design as used by
Melcher and duplicated here. (B) As in our Experiment 1, the retinotopic condition produces a strong TAE. None of the baseline,
spatiotopic, and opposite conditions show any TAE. Black error bars indicate the standard error across subjects. The light gray error bars
indicate the mean and the standard error on the fitted mean (1000-fold bootstrap) for each subject separately.
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 8

Attentional control
As suggested by Melcher (2008b), the spatiotopic TAE
may rely on remapping processes that are known to be
specific to task-relevant (attended) targets (Goldberg,
Bisley, Powell, & Gottlieb, 2006; Gottlieb, Kusunoki, &
Goldberg, 1998). To investigate whether we can find a
spatiotopic TAE when attention is explicitly directed to
a stimulus, we conducted the experiment depicted in
Figure A2C (top row). With two adapting stimuli at equal
distance from fixation, a central cue indicated to the
observer to which of the two stimuli should be attended.
During the adaptation interval 4 or 5 Gaussian-enveloped
contrast decrements (A = 100 ms, contrast decrement =
0.75) occurred in this stimulus, which the observer had to
count. After adaptation, the observer made a saccade to
either the screen location where the attended stimulus had
been, or the opposite side, where an opposite-orientation
Figure A2. Extra experiments: Conditions and results. (A) Original and inverted experimental design of the spatiotopic TAE experiment.
Adaptations in the periphery (left column) and in the fovea (right column, original design) yield similar results. The “spatiotopic” TAE does
not reach significance in either case, when corrected for the non-specific TAE. Corrected spatiotopic TAEs are shown on a per-subject
basis in the bottom row. (B) When using a blocked design, presenting only stimuli from a single condition in one session, the results are
similar to those found when using a randomized presentation sequence (A, left column, and Figure 1, top row). (C) Control experiment:
attention. Attention was directed at one of two oppositely tilted gratings at either side of fixation, as indicated by two arrow signs above and
below fixation. Observers were instructed to count the number of contrast decrements (4 or 5) in the attended stimulus. After this peripheral
adaptation, a saccade was made to either the attended or non-attended stimulus, and a test stimulus would be presented at either a
spatiotopically or retinotopically corresponding location. Again, a strong retinotopic TAE is evident, and its magnitude is not greatly dependent
on attention. In addition, whether or not attention was directed to the adapting stimulus location, no significant spatiotopic TAE is found.
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 9

adaptation stimulus had been presented. After this saccade,
a test was presented either at the spatiotopically corre-
sponding location of the attended or non-attended stimulus,
or at a retinotopically corresponding location. An addi-
tional condition tested, as in the other experiments, the non-
specific TAE. The fixation mark changed position to a
location on the screen with the same distance to the initial
fixation position, but above or below the center of the
screen. The observer saccaded to that location and the test
stimulus was presented there, as was the case in the
spatiotopic conditions. Results are shown in the middle
row of Figure A2C. In the retinotopically corresponding
locations, there are strong TAEs in both the attended and
non-attended conditions. In the spatiotopically corre-
sponding locations, there was no TAE, whether attention
had been explicitly directed to the adapting stimulus or
not: in both cases the TAE was not significantly different
from that found using the non-specific test. In all these
additional experiments, parameters were identical to those
stated for the main Experiments 1 and 2 with the exception
of two parameters that were changed to match exactly those
in the experimental code furnished by Dr. Melcher. Size of
the stimuli was changed to A = 0.8 degrees of visual angle
and spatial frequency was changed to 2.16 cycles per
degree. Adaptation duration was 4 s in all additional
experiments. In all experiments, eye movements were
recorded and analyzed. As in the first experiment, gaze
position was recorded in all trials, and trials in which
gaze position was outside a 2.5-degree radius around the
intended fixation position at any single time point during
the trial’s adaptation or fixation phases, the trial was
excluded from further analysis. Note that subjects showing
a spatiotopic TAE in the experiment in Figure A2A in
the peripheral-adaptation, changed experimental paradigm
fail to show the same pattern of results upon retesting
(Figures A2B and A2C). This variability was typical for
spatiotopic TAEs indicating that the results that did
reach significance for some subjects in some sessions
were due to chance variations. In contrast, retinotopic
TAEs were all significant, all the time, showing that the tilt
aftereffect is robustly retinotopic and shows no evidence of
spatiotopy.
Gaze dependency of the TAE
We performed two control experiments to investigate
whether the difference in gaze angle between adaptation
and test influences the size of the retinotopic TAE in a
parametric way. We used a pair of oppositely oriented
stimuli, above and below fixation, as both adapting and
test stimuli replicating the stimulus arrangement by
Nishida et al. (2003). We used custom software on a
Figure A3. Gaze dependency of the TAE in our experiment. As difference in gaze angle between adaptation and test increases, the
strength of the TAE decreases. Dashed lines result from the statistics as described in the text, for both experiments separately. Note that
both slope and offset were fitted in both experiments: there is highly similar change with gaze angle difference both with and without the
addition of a surrounding frame. The blue vertical arrow at 10 degrees difference indicates the gaze difference used in our Experiment 1,
the gaze difference value used by Nishida et al. (2003) is depicted by the red arrow.
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 10

Macbook Pro displaying stimuli on a single Dell 20W LCD
screen running at a resolution of 1600
1200 and a
refresh rate of 60 Hz, placed at 31-cm distance, sub-
tending 62 degrees in width. This allowed us to para-
metrically increase the gaze difference between adaptation
and test over a range large enough to investigate the
difference between our main results and the results by
Nishida et al. (2003), who used a difference in gaze of
62 degrees. We ran two experiments; one in which the full
screen was of mean luminance as in all our experiments,
the other in which the two stimuli were surrounded by a
frame of mean luminance, with the screen at the lowest
luminance setting (black), as in Nishida et al. (2003). In
both control experiments, adaptation and test were
separated by two saccades, as in our Experiment 1. The
adaptation stimulus was presented on one side of the
screen and the test stimulus was presented at distances of
0, 12, 24, 36, or 47 degrees away (no frame experiment),
or 0, 10, 20, or 40 degrees away (frame experiment).
Stimulus size, spatial frequency, contrast, adaptation tilt,
test stimulus tilt range, and distance between fixation and
stimuli were identical to our previous experiments. Adap-
tation duration was 5 s. The width of the surrounding frame
was 4.5 times the standard deviation of the Gabors, and the
height was 9 times the standard deviation. Four subjects
ran in both experiments; 3 were naive in each (Figure A3).
Both with and without a frame around the stimulus, our
data show that the retinotopic TAE decreases with the
increase in gaze away from the direction held during
adaptation (without frame linear regression slope =
j0.0086 deg TAE per deg gaze difference, t = j2.94,
p = 0.03 with frame slope = j0.0092 deg TAE per deg
gaze difference, t = j2.90, p = 0.03). This set of
experiments replicates the gaze dependency of the TAE
found by Nishida et al. (2003) and supports our claim that
our gaze contingent TAE was smaller because the gaze
change in our experiment was smaller.
Additional information
The authors declare no conflict of interest. Observers
gave informed consent for their participation.
Acknowledgments
PC is supported by a Chaire d’Excellence.
Author contributions: Tomas Knapen and Martin Rolfs
contributed equally to this work.
Commercial relationships: none.
Corresponding author: Dr. Tomas Knapen.
Email: tknapen@gmail.com.
Address: 45 Rue des Saints Pe`res, 75006 Paris, Ile-de-
France, France.
References
Afraz, S.-R., & Cavanagh, P. (2008). Retinotopy of the face
aftereffect. Vision Research, 48, 42–54. [PubMed]
[Article]
Afraz, A., & Cavanagh, P. (2009). The gender-specific
face aftereffect is based in retinotopic not spatiotopic
coordinates across several natural image transforma-
tions. Journal of Vision, 9(10):10, 1–17, http://
journalofvision.org/9/10/10/, doi:10.1167/9.10.10.
[PubMed][Article]
Andersen, R. A., Essick, G. K., & Siegel, R. M. (1985).
Encoding of spatial location by posterior parietal
neurons. Science, 230, 456–458. [PubMed]
Andersen, R. A., Snyder, L. H., Li, C. S., & Stricanne, B.
(1993). Coordinate transformations in the representa-
tion of spatial information. Current Opinion in
Neurobiology, 3, 171–176. [PubMed]
Batista, A. P., Buneo, C. A., Snyder, L. H., & Andersen,
R. A. (1999). Reach plans in eye-centered coordinates.
Science, 285, 257–260. [PubMed]
Bradley, D. C., Maxwell, M., Andersen, R. A., Banks,
M. S., & Shenoy, K. V. (1996). Mechanisms of
heading perception in primate visual cortex. Science,
273, 1544–1547. [PubMed]
Clifford, C. W., Webster, M. A., Stanley, G. B., Stocker,
A. A., Kohn, A., Sharpee, T. O., et al. (2007). Visual
adaptation: Neural, psychological and computational
aspects. Vision Research, 47, 3125–3131. [PubMed]
[Article]
Colby, C. L., Duhamel, J. R., & Goldberg, M. E. (1996).
Visual, presaccadic, and cognitive activation of single
neurons in monkey lateral intraparietal area. Journal
of Neurophysiology, 76, 2841–2852. [PubMed]
Colby, C. L., & Goldberg, M. E. (1999). Space and
attention in parietal cortex. Annual Review of Neuro-
science, 22, 319–349. [PubMed]
Crowell, J. A., Banks, M. S., Shenoy, K. V., & Andersen,
R. A. (1998). Visual self-motion perception during head
turns. Nature Neuroscience, 1, 732–737. [PubMed]
Dragoi, V., Rivadulla, C., & Sur, M. (2001). Foci of
orientation plasticity in visual cortex. Nature, 411,
80–86. [PubMed]
Dragoi, V., Sharma, J., & Sur, M. (2000). Adaptation-
induced plasticity of orientation tuning in adult visual
cortex. Neuron, 28, 287–298. [PubMed][Article]
Duhamel, J.-R., Colby, C. L., & Goldberg, M. E. (1992).
The updating of the representation of visual space in
parietal cortex by intended eye movements. Science,
255, 90–92. [PubMed]
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 11

Engbert, R., & Mergenthaler, K. (2006). Microsaccades
are triggered by low retinal image slip. Proceedings
of the National Academy of Sciences of the United
States of America, 103, 7192–7197. [PubMed]
[Article]
Ezzati, A., Golzar, A., & Afraz, A. S. (2008). Topography
of the motion aftereffect with and without eye
movements. JournalofVision,8(14):23, 1–16,
http://journalofvision.org/8/14/23/, doi:10.1167/
8.14.23. [PubMed][Article]
Findlay, J. M., & Parker, D. M. (1972). An investigation of
visual orientation constancy using orientation-specific
properties of acuity and adaptation. Perception, 1,
305–313. [PubMed]
Galletti, C., & Battaglini, P. P. (1989). Gaze-dependent
visual neurons in area v3a of monkey prestriate
cortex. Journal of Neuroscience, 9, 1112–1125.
[PubMed]
Goldberg, M. E., Bisley, J. W., Powell, K. D., &
Gottlieb, J. (2006). Saccades, salience and attention:
The role of the lateral intraparietal area in visual
behavior. Progress in Brain Research, 155, 157–175.
[PubMed]
Gottlieb, J. P., Kusunoki, M., & Goldberg, M. E. (1998).
The representation of visual salience in monkey
parietal cortex. Nature, 391, 481–484. [PubMed]
Heiser, L. M., & Colby, C. L. (2006). Spatial updating in
area lip is independent of saccade direction. Journal
of Neurophysiology, 95, 2751–2767. [PubMed]
[Article]
Hubel, D. H., & Wiesel, T. N. (1959). Receptive fields of
single neurones in the cat’s striate cortex. Journal of
Physiology, 148, 574–591. [PubMed][Article]
Jin, D. Z., Dragoi, V., Sur, M., & Seung, H. S. (2005). Tilt
aftereffect and adaptation-induced changes in orien-
tation tuning in visual cortex. Journal of Neuro-
physiology, 94, 4038–4050. [PubMed][Article]
Knapen, T., Rolfs,M., & Cavanagh, P. (2009). The reference
frame of the motion aftereffect is retinotopic. Journal of
Vision, 9(5):16, 1–7, http://journalofvision.org/9/5/16/,
doi:10.1167/9.5.16. [PubMed][Article]
Kohn, A., & Movshon, J. A. (2003). Neuronal adaptation
to visual motion in area mt of the macaque. Neuron,
39, 681–691. [PubMed][Article]
Kohn, A., & Movshon, J. A. (2004). Adaptation changes
the direction tuning of macaque mt neurons. Nature
Neuroscience, 7, 764–772. [PubMed]
Medendorp, W. P., Goltz, H. C., Vilis, T., & Crawford,
J. D. (2003). Gaze-centered updating of visual space
in human parietal cortex. Journal of Neuroscience,
23, 6209–6214. [PubMed][Article]
Melcher, D. (2005). Spatiotopic transfer of visual-form
adaptation across saccadic eye movements. Current
Biology, 15, 1745–1748. [PubMed][Article]
Melcher, D. (2007). Predictive remapping of visual
features precedes saccadic eye movements. Nature
Neuroscience, 10, 903–907. [PubMed]
Melcher, D. (2008a). Dynamic, object-based remapping of
visual features in trans-saccadic perception. Journal
of Vision, 8(14):2, 1–17, http://journalofvision.org/8/
14/2/, doi:10.1167/8.14.2. [PubMed][Article]
Melcher, D. (2008b). Selective attention and the active
remapping of object features in trans-saccadic per-
ception. Vision Research, 49, 1249–1255. [PubMed]
[Article]
Melcher, D., & Colby, C. L. (2008). Trans-saccadic
perception. Trends in Cognitive Sciences, 12, 466–473.
[PubMed][Article]
Merriam, E. P., Genovese, C. R., & Colby, C. L. (2003).
Spatial updating in human parietal cortex. Neuron,
39, 361–373. [PubMed][Article]
Merriam, E. P., Genovese, C. R., & Colby, C. L. (2007).
Remapping in human visual cortex. Journal of
Neurophysiology, 97, 1738–1755. [PubMed][Article]
Mitchell, D. E., & Blakemore, C. (1972). The site of
orientational constancy. Perception, 1, 315–320.
[PubMed]
Nakamura, K., & Colby, C. L. (2002). Updating of the
visual representation in monkey striate and extras-
triate cortex during saccades. Proceedings of the
National Academy of Sciences of the United States
of America, 99, 4026–4031. [PubMed][Article]
Nishida, S., Motoyoshi, I., Andersen, R. A., & Shimojo, S.
(2003). Gaze modulation of visual aftereffects. Vision
Research, 43, 639–649. [PubMed][Article]
Parker, D. M. (1972). Contrast and size variables and the tilt
after-effect. The Quarterly Journal of Experimental
Psychology, 24, 1–7. [PubMed]
Rieser, J. J., & Banks, M. S. (1981). The perception of
verticality and the frame of reference of the visual tilt
aftereffect. Perception & Psychophysics, 29, 113–120.
[PubMed]
Rosenbluth, D., & Allman, J. M. (2002). The effect of
gaze angle and fixation distance on the responses of
neurons in V1, V2, and V4. Neuron, 33, 143–149.
[PubMed][Article]
Ross, J., & Ma-Wyatt, A. (2004). Saccades actively
maintain perceptual continuity. Nature Neuroscience,
7, 65–69. [PubMed]
Schwartz, O., Hsu, A., & Dayan, P. (2007). Space and
time in visual context. Nature Review Neuroscience,
8, 522–535. [PubMed]
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 12

Snyder, L. H., Grieve, K. L., Brotchie, P., & Andersen,
R. A. (1998). Separate body- and world-referenced
representations of visual space in parietal cortex.
Nature, 394, 887–891. [PubMed]
Sommer, M. A., & Wurtz, R. H. (2006). Influence of the
thalamus on spatial visual processing in frontal
cortex. Nature, 444, 374–377. [PubMed]
Trotter, Y., & Celebrini, S. (1999). Gaze direction
controls response gain in primary visual-cortex
neurons. Nature, 398, 239–242. [PubMed]
Umeno, M. M., & Goldberg, M. E. (1997). Spatial
processing in the monkey frontal eye field: I.
Predictive visual responses. Journal of Neurophysiol-
ogy, 78, 1373–1383. [PubMed][Article]
Umeno, M. M., & Goldberg, M. E. (2001). Spatial
processing in the monkey frontal eye field: II.
Memory responses. Journal of Neurophysiology, 86,
2344–2352. [PubMed][Article]
Wenderoth, P., & Wiese, M. (2008). Retinotopic encoding
of the direction aftereffect. Vision Research, 48,
1949–1954. [PubMed][Article]
Wurtz, R. H. (2008). Neuronal mechanisms of visual
stability. Vision Research, 48, 2070–2089. [PubMed]
[Article]
Journal of Vision (2010) 10(1):8, 1–13 Knapen, Rolfs, Wexler, & Cavanagh 13