Neural mechanisms of speed perception: transparent motion
Bart Krekelberg1and Richard J. A. van Wezel2,3
1Center for Molecular and Behavioral Neuroscience, Rutgers University, Newark, New Jersey;2Biomedical Signals and
Systems, MIRA, Twente University, Enschede, The Netherlands; and3Department of Biophysics, Donders Institute for Brain,
Cognition and Behaviour, Radboud University, Nijmegen, The Netherlands
Submitted 8 May 2013; accepted in final form 1 August 2013
Krekelberg B, van Wezel RJ. Neural mechanisms of speed
perception: transparent motion. J Neurophysiol 110: 2007–2018,
2013. First published August 7, 2013; doi:10.1152/jn.00333.2013.—
Visual motion on the macaque retina is processed by direction- and
speed-selective neurons in extrastriate middle temporal cortex (MT).
There is strong evidence for a link between the activity of these
neurons and direction perception. However, there is conflicting evi-
dence for a link between speed selectivity of MT neurons and speed
perception. Here we study this relationship by using a strong percep-
tual illusion in speed perception: when two transparently superim-
posed dot patterns move in opposite directions, their apparent speed is
much larger than the perceived speed of a single pattern moving at
that physical speed. Moreover, the sensitivity for speed discrimination
is reduced for such bidirectional patterns. We first confirmed these
behavioral findings in human subjects and extended them to a monkey
subject. Second, we determined speed tuning curves of MT neurons to
bidirectional motion and compared these to speed tuning curves for
unidirectional motion. Consistent with previous reports, the response
to bidirectional motion was often reduced compared with unidirec-
tional motion at the preferred speed. In addition, we found that tuning
curves for bidirectional motion were shifted to lower preferred speeds.
As a consequence, bidirectional motion of some speeds typically
evoked larger responses than unidirectional motion. Third, we showed
that these changes in neural responses could explain changes in speed
perception with a simple labeled line decoder. These data provide new
insight into the encoding of transparent motion patterns and provide
support for the hypothesis that MT activity can be decoded for speed
perception with a labeled line model.
motion perception; speed coding; macaque monkey; middle temporal
area; labeled line
VISUAL MOTION PATTERNS strongly activate neurons in striate and
extrastriate cortex both in macaques and humans. Single-cell
recordings in macaques have shown that neurons in the middle
temporal cortex (MT) are not only highly responsive to motion
but also strongly tuned for motion direction and speed, and
there is compelling evidence that perceived direction can be
decoded from neural activity in MT based on a labeled line
model (for review, see Born and Bradley 2005; Parker and
Newsome 1998). In this decoding model each neuron repre-
sents a certain direction of motion (its label, identified by its
preferred direction) and spikes from the neuron represent
evidence in favor of that direction of motion.
There is direct evidence that area MT is also involved in
speed perception. Lesions in area MT lead to impairments in
speed perception (Orban et al. 1995; Pasternak and Merigan
1994), trial-to-trial variations in MT responses are related to
speed perception (Liu and Newsome 2005), and microstimu-
lation of groups of neurons that prefer high speeds changes
speed perception (Liu and Newsome 2005). Further evidence
comes from the use of visual illusions that decrease or increase
the perceived speed of moving patterns. The behavioral effect
on perceived speed of the step size in apparent motion
(Churchland and Lisberger 2001), the contrast of moving
sinusoidal gratings (Priebe 2004), motion adaptation (Krekel-
berg et al. 2006a), acceleration (Schlack et al. 2007, 2008), as
well as stimulus size (Boyraz and Treue 2011) can all be linked
to firing rate changes in area MT via labeled line models.
Nevertheless, the link between speed-related firing rate
changes in area MT and perceived speed is not as clear-cut as
for perceived direction. The sensitivity of MT neurons for
speed is typically less than the sensitivity of the whole animal,
and microstimulation effects on speed judgments are not as
prominent as in direction discrimination tasks (Liu and New-
some 2005). In addition, there appears to be an asymmetry in
the relationship between neural and behavioral responses that
depends on the relationship between the stimulus and the speed
preference of the (group of) cells under study. Whereas stimuli
with speeds on the ascending flank of the tuning curve show
the expected influence of trial-to-trial variability and micro-
stimulation, this association is much weaker (and statistically
nonsignificant) for stimuli on the descending flank (Liu and
Newsome 2005). Such an asymmetry would not be expected in
a labeled line model. Moreover, earlier studies have shown an
unexpected monotonic relationship between microstimulation
current and perceived speed as measured by oculomotor re-
sponse (Groh et al. 1997). Finally, we have previously reported
evidence against the labeled line model based on a visual
illusion that leads to misperceptions in speed (Krekelberg et al.
2006b). Notably, when the luminance contrast of moving
random dot patterns is reduced, the subjective speed percept
decreases dramatically, but the speed tuning of MT neurons
shifts in a direction that is opposite to that predicted by the
labeled line model.
While there can be little doubt that area MT plays some role
in speed perception, we believe that a better understanding of
these discrepancies between changes in MT activity, the la-
beled line model, and speed perception can provide important
insight into the relation between neural activity and behavior.
To further constrain this relationship, we investigated the
representation of the speed of transparent motion in area MT.
When two patterns move transparently in opposite directions,
perceived visual speed increases dramatically (up to 50%)
compared with the perceived speed of the individual compo-
nents (De Bruyn and Orban 1999). Such a large perceptual
effect should have a clear neural signature.
Address for reprint requests and other correspondence: B. Krekelberg,
CMBN, Rutgers Univ., 197 University Ave., Newark, NJ 07102 (e-mail: bart
J Neurophysiol 110: 2007–2018, 2013.
First published August 7, 2013; doi:10.1152/jn.00333.2013.
20070022-3077/13 Copyright © 2013 the American Physiological Society www.jn.org
In our study we first confirmed the behavioral findings by
showing a large overestimation of the speed of bidirectional
motion patterns in both humans and the macaque monkey.
Subsequently, we recorded neural responses to bidirectional
patterns and their unidirectional components at different
speeds. Finally, we performed a quantitative analysis of the
relationship between these responses and behavioral measures
of sensitivity and bias in speed perception. Our findings pro-
vide clear support for the hypothesis that speed perception is
linked to neural activity in area MT via a labeled line decoder
MATERIALS AND METHODS
Two adult male rhesus monkeys (Macaca mulatta; monkeys M and
S) were used in the electrophysiological experiments. Monkey M
performed the behavioral experiments. Experimental and surgical
protocols were in accordance with the National Institutes of Health
(NIH)’s guidelines for humane care and use of laboratory animals and
were approved by the local animal use committee.
Five naive human subjects and one author participated in the
human psychophysical experiments. All human subject procedures
were in accordance with international standards (Declaration of Hel-
sinki) and NIH guidelines and were approved by the institutional
review board, and participants gave their informed, written consent.
All subjects had normal or corrected-to-normal visual acuity.
All visual stimuli were generated with in-house OpenGL software
using a high-resolution graphics display controller (Quadro Pro
Graphics card, 1,024 ? 768 pixels, 8 bits/pixel). In the experiments
with monkey subjects, stimuli were displayed on a 21-in. monitor
(Sony GDM-2000TC; 75 Hz, noninterlaced; 1,024 ? 768 pixels); in
the experiments with human subjects we used a 19-in. Sony Trinitron
E500 monitor (75 Hz, noninterlaced, 1,024 ? 768 pixels). The output
of the video monitor was measured with a PR650 photometer (Photo
Research, Chatsworth, CA), and the voltage/luminance relationship
was linearized independently for each of the three guns in the CRT.
Stimuli were viewed from a distance of 57 cm in a dark room (?0.5
Monkeys were seated in a standard primate chair (Crist Instru-
ments, Germantown, MD) with the head post rigidly supported by the
chair frame. Eye position was sampled at 60 Hz with an infrared
video-based system (IScan, Burlington, MA), and the eye position
data were monitored and recorded with the CORTEX program (Lab-
oratory of Neuropsychology, National Institute of Mental Health;
http://dally.nimh.nih.gov/), which was also used to implement the
behavioral paradigm and to control stimulus presentation.
Stimuli and Experimental Paradigms
We used random dot patterns consisting of 100 dots moving within
a 10°-diameter circular aperture. The lifetime of the dots was infinite,
and they were randomly repositioned after leaving the aperture. Dots
were 0.15° in diameter and had a luminance of 30 cd/m2. The gray
background was 5 cd/m2. In the physiological experiments, the
direction of motion was adjusted to match the axis of neuronal
preferred direction rounded to the nearest multiple of 45°.
Psychophysical paradigm. Figure 1A shows the paradigm we used
to investigate how transparent, bidirectional motion affected per-
ceived speed in humans. Subjects fixated a small red dot at the center
of the screen. Two patches of dots appeared 10° left and right of
fixation. The subject’s task was to determine which of the two patches
contained the dots with the fastest speed.
In one patch (the reference), either all the dots moved rightward
[“unidirectional condition” (uni)] or half of the dots moved rightward
and the other half moved leftward (bi). The speed of all dots in the
reference was the same but varied across conditions (1, 2, 5, 10, 20,
Fig. 1. Experimental paradigms. A: sequence of events in the paradigm used for the behavioral experiments. Subjects fixated a red dot, and 2 patterns appeared
for 500 ms. In the human behavioral experiments there were 2 conditions. In the first condition a bidirectional motion pattern (2 dot patterns transparently moving
in opposite directions) and a unidirectional motion pattern were shown (bi-uni). In the second condition 2 unidirectional motion patterns were shown (uni-uni).
In the monkey experiments there was a third condition in which 2 bidirectional motion patterns were shown (bi-bi). In the monkey experiments the bi-uni
condition was only shown for a small subset of trials and rewarded randomly. Subjects were instructed to indicate the pattern that moved fastest by a key press
(human) or an eye movement to 1 of 2 targets (monkey). B: in the physiological experiments 1 pattern was presented in the receptive field (indicated by dashed
line). The only behavioral requirement for the monkey was to fixate the red spot for the duration of the trial.
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40°/s). In the other patch (the test), all dots moved rightward and their
speed was slower or faster than the reference speed by 0%, 10%, 40%,
or 80%. Human subjects performed the speed discrimination task
comparing unidirectional tests and reference (uni-uni) or a bidirec-
tional reference and a unidirectional test (bi-uni). The 84 test condi-
tions (uni-uni/bi-uni ? 6 reference speeds ? 7 test speeds) were
After the 500-ms stimulus presentation, the dot patterns were
extinguished and subjects answered the question “Which pattern
moved faster?” by pressing one of two keys on the keyboard. The
human subjects received no feedback on their performance, and the
next trial started immediately after the subjects’ response. The posi-
tions of test and reference stimuli were varied randomly across trials.
Each comparison of reference speed and test speed was repeated 20
For monkey M we maintained the identical layout and stimuli, but
the animal reported which patch moved faster by making an eye
movement toward one of two small green dots that appeared 10° left
or right of fixation once the moving stimuli were extinguished.
In most trials, the monkey compared a unidirectional reference to
a unidirectional test (uni-uni) or a bidirectional reference to a bidi-
rectional test (bi-bi). Because any illusory speed percept would affect
both test and reference equally, we rewarded the animal for veridical
performance on these trials. On a small subset of trials, the animal
compared a bidirectional reference with a unidirectional test of the
same physical speed (bi-uni). We expected a potentially large illusory
change in perceived speed; hence on these trials we rewarded the
animal on 60% of trials, independent of the animal’s response on that
trial. In our experience, including a large number of randomly re-
warded conditions typically leads to random behavior; hence we
limited the uni-bi conditions to the comparison of two physically
equal speeds (and therefore did not measure the full psychometric
curve in this condition). The data reported here (?16,000 trials) were
recorded across 13 days immediately after training on uni-uni and
bi-bi comparisons for several weeks.
Electrophysiological paradigm. We recorded the activity of single
units in area MT with tungsten microelectrodes (FHC, 3–5 M?) in
two monkeys. Neurophysiological signals were filtered, sorted, and
stored with the Plexon system (Plexon). We identified area MT
physiologically by its characteristically high proportion of cells with
directionally selective responses, receptive fields (RFs) that were
small relative to those of neighboring area MST, and its location on
the posterior bank of the superior temporal sulcus. The typical
recording depth agreed well with the expected anatomical location of
MT determined from structural MR scans. For more details, see
Hartmann et al. (2011) and Richert et al. (2013).
We used automated methods to determine cells’ directional selec-
tivity and RF location (Krekelberg and Albright 2005). The approx-
imate RF center and the preferred direction of motion revealed by
these methods were used to optimize stimuli for subsequent neuronal
response measurements (i.e., we used the preferred direction as
estimated by this method rounded to the nearest 45° to align the
direction of dot motion with the preferred-antipreferred axis and the
location of the coarsely mapped RF to place the dot pattern on its
In the main paradigm, we measured speed tuning curves of MT
cells, using random dot patterns that appeared 250 ms after the
monkey started fixating a central red dot and were extinguished 500
ms later. The range of speeds was 1, 2, 4, 8, 16, 32, and 64°/s, and for
each cell we measured the speed tuning curve with unidirectional
patterns moving in the preferred direction (uni-pref), unidirectional
patterns moving in the antipreferred direction (uni-anti), and bidirec-
tional patterns in which half of the dots moved in the preferred and
half of the dots moved in the antipreferred direction (bi). In the
bidirectional condition the speed of all dots was always equal.
All conditions were randomly interleaved. Trials in which eye
position deviated from a 2°-wide square window centered on the
fixation spot were aborted and excluded from analysis. Unless cell
isolation was lost prematurely, each condition was repeated 15 times.
Psychophysical data. Separately for each combination of reference
and test stimulus, we calculated the percentage of trials in which
subjects responded that the test stimulus was faster. Using the psignifit
MATLAB toolbox (Wichmann and Hill 2001a), we fit these data with
cumulative Gaussians and obtained an estimate of the point of sub-
jective equality (PSE), defined as the speed where the fitted curve
crossed 50% “test faster,” as well as the sensitivity, defined as the
slope of the psychometric curve at the PSE. The Monte Carlo
simulations of the pfcmp function in the psignifit toolbox were used to
determine whether two psychometric functions (e.g., corresponding to
different motion patterns) were significantly different (Wichmann and
To estimate the monkey’s PSE for uni-bi comparisons based only
on the comparison of physically matched uni- and bidirectional
speeds, we determined his psychometric curve based jointly on the
trials of the uni-uni and bi-bi comparisons and then determined by
how much this curve would have to be shifted to explain the perfor-
mance on the single uni-bi comparison. In other words, for this
ballpark estimate we assumed that the animal’s psychometric curve in
the uni-bi trials was shifted but that its slope was the same as the
average slope on the uni-uni and bi-bi comparisons.
Physiological data. Our primary measure of the neural response
was the spike count in the 500 ms following stimulus onset. This
window was corrected for each neuron’s response latency, which was
determined by using a maximum likelihood estimator that assumes
Poisson spiking statistics (Friedman and Priebe 1998). (We also
performed all analyses with a window starting 200 ms after stimulus
onset and ending with stimulus offset; excluding onset transients in
this manner led to highly similar effects and did not change any of our
As has been shown before, speed tuning curves in MT are well-fit
by log-Gaussians (Nover et al. 2005). We parameterized the tuning
curves separately for the uni-pref, uni-anti, and bi conditions as r ?
? ? ??exp??
determine the posterior probability distribution of all such log-Gauss-
ian tuning functions based on the spike count data of all trials and the
assumption of Poisson variability (Cronin et al. 2010). In this equa-
tion, the parameter ? is referred to as the offset (it reflects the part of
the response that is not speed tuned), ? is the amplitude (it reflects the
strength of the speed tuning), ? is a unitless parameter that reflects
the (scale invariant) tuning width, and ? is the preferred speed. The
Bayesian fitting procedure calculates the posterior probability distri-
bution of all four parameters, which is useful to show the range of
tuning curves that are compatible with the data (and the log-Gaussian
model) (e.g., Fig. 3). For cell-by-cell comparisons (Fig. 4) and the
simulations of Fig. 8, we obtained a point estimate for each of the
parameters by taking the median across each of the posterior distri-
butions. We refer to this point estimate as the “best fit.”
We compared the log-Gaussian fits with a model in which the spike
count was independent of the speed (i.e., untuned) and denoted a cell
as speed tuned if the Bayes factor comparing these two models was at
least 10 for both the uni-pref and bi conditions (i.e., the log-Gaussian
model was at least 10 times more likely to explain the data than the
In the nonparametric analyses we determined the median firing rate
across trials per cell for each condition. We calculated the direction
selectivity index (DSI) on the basis of the median firing rates for the
preferred (P) and antipreferred (A) directions per speed as (P ? A)/
(P ? A). The preferred speed was defined as the unidirectional motion
pattern that generated the largest median response. To generate
population responses, we normalized the firing rate of each cell by its
2??2?log2?s⁄???2?and used a Bayesian method to
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peak response and then determined the median across neurons. To
generate a preferred-speed aligned population response, we binned the
observed median response across trials as a function of the difference
(in octaves) between stimulus speed and preferred speed. In other
words, we described the median response as a function of ?speed ?
log2(speed) ? log2(?) for each cell, binned this in octaves, and then
determined the median across all neurons for every ?speed bin where
we had at least 25 observations (i.e., neurons).
Power-law summation. In the power-law summation model (Brit-
ten and Heuer 1999), the response to a compound stimulus (the
bidirectional pattern, rbi) is determined by a nonlinear summation of
the response to the two components (runi-pref, the unidirectional
preferred and runi-anti, the unidirectional antipreferred response):
rbi? a ???runi-pref?g??runi-anti?g?
The gain (a), power (g), and offset (b) are free parameters, which were
determined (per neuron) with least-squares optimization.
Decoding. We investigated the extent to which a simple labeled
line decoding model could relate the neural responses with the
behavioral data. In this model a spike from a neuron is interpreted as
a vote in favor of the base-2 logarithm of that neuron’s preferred
We used the parametric fits of each neuron together with the
assumption of Poisson variability to generate simulated population
responses for each of the displays that occurred in the behavioral
paradigm. In other words, for each (simulated) behavioral trial we
generated the response of the 103 speed-tuned neurons to the test
stimulus and the response of the same 103 neurons to the reference
Note that this relies on the common assumption that for each
speed-tuned neuron that we recorded in one hemisphere there exists a
neuron with identical properties in the opposite hemisphere (the
anti-neuron) and that a perceptual decision is made by comparing the
activity in these two groups of neurons. Note also that, because we
mapped speed tuning for each neuron in its preferred and antipreferred
directions only, our sample contained only neurons that responded
maximally to at least one of the directions of motion in the bidirec-
tional pattern. In other words, our decoder used only a slice through
the two-dimensional space of neurons with all possible preferred
directions and speeds. An optimal decoder, and quite likely the brain,
could also use the information provided by neurons whose preferred
direction is not matched to any of the directions in the bidirectional
stimulus, as well as knowledge about the variability and tuning width
of the neurons (Krekelberg et al. 2003; Morris et al. 2013). Given how
well the simple decoder worked (see Fig. 8), and because we recorded
speed tuning only in two directions, we did not pursue such ap-
For each neuron, the response was normalized to its peak response
(i.e., divided by the response to the neurons’ preferred speed). This
resulted in two population vectors: t
the response to the reference. Each neuron was assigned a label
defined by the 2-base log of its preferred speed (l
then calculated the decoded speed as the inner product of the popu-
lation activity vector and the label vector, normalized by the sum (|t
→, the response to the test, and r
→; see below). We
→|) of the population activity:
→?, sreference? r
We used this procedure to generate 1,000 synthetic trials for each
of the test speeds, and for each motion type, and then compared the
decoded test and reference speed to answer the same question that the
subjects answered: Was the test faster than the reference (stest?
sreference)? For each simulated trial this resulted in a binary decision,
just like the outcome of a real behavioral trial. To generate psycho-
metric functions we analyzed those binary decisions with procedures
identical to those used for the actual behavioral data (see above).
In the first decoder, the population vector of speed labels (l
defined as the base-2 log of each neuron’s preferred speed for
unidirectional motion. For the second decoder we first used the same
Bayesian fitting procedure as described above but now without taking
stimulus type (uni- or bidirectional) into account. The label (l
then defined by the preferred speed that resulted from this procedure.
Loosely speaking, one can view this as an average preferred speed
across the uni- and bidirectional patterns. For the third decoder, we
used the preferred speed for bidirectional motion as the label.
The results are divided into three parts. First, we document
how transparent motion affected perceived speed in humans
and monkeys. Second, we describe how bidirectional, trans-
parent motion influenced responsivity and speed tuning of MT
neurons. Third, we present a decoding analysis that links the
neural and behavioral data via a labeled line model.
Previously, De Bruyn and Orban (1999) have shown that the
speed of two transparently moving dot patterns is overesti-
mated. To allow a direct comparison of behavioral with phys-
iological data, we replicated their findings using the stimuli we
used in the physiological recordings, investigated a wider
range of speeds, and obtained behavioral data in healthy human
volunteers as well as a monkey. The details of the paradigm are
described in MATERIALS AND METHODS. Briefly, both the human
and monkey subjects viewed two patches of moving random
dots and reported which of the two moved faster (Fig. 1A).
Figure 2 shows the results. The blue psychometric curves in
Fig. 2A demonstrate that the five subjects correctly compared
the speed of two unidirectional patches while overestimating
the speed of bidirectional patches (red curves), compared with
unidirectional patches. The shallow slopes of the red curves in
Fig. 2A show that sensitivity was reduced for the bidirectional
patches compared with the unidirectional patches. Both the
increase in PSE (P ? 0.001) and the decrease in slope (P ?
0.005) were consistent across subjects and reference speeds
(Fig. 2, B and C).
The monkey (Fig. 2D) compared two unidirectional patches
(uni-uni; blue curve), two bidirectional patches (bi-bi; green
curve), or a unidirectional test with a bidirectional reference
whose physical speed was identical (uni-bi; red asterisk). The
monkey’s sensitivity for bidirectional patches was reduced
compared with unidirectional patches (P ? 0.001), and, just
like the human subjects, he significantly overestimated the
speed of the bidirectional reference patch compared with a
unidirectional test patch (red asterisk; the unidirectional test
was reported as faster in 39% of trials; P ? 0.001, binomial
test). The red dotted curve in Fig. 2D shows a psychometric
curve with a slope determined from the pooled uni-uni and
bi-bi comparison trials, while the PSE (20%) was chosen to fit
the performance on the uni-bi comparisons (see MATERIALS AND
METHODS). Hence, a ballpark estimate for the magnitude of
speed overestimation by monkey M is 20%.
To summarize, the behavioral data were qualitatively con-
sistent across subjects, species, reference speeds, and repli-
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cated previous studies: subjects were less sensitive to bidirec-
tional speed (Verstraten et al. 1996), and they overestimated its
speed (De Bruyn and Orban 1999). Next, we describe the
neural representation of these motion patterns in macaque MT.
Neural Representation of Speed
We recorded from 126 neurons in area MT of two monkeys
(monkey S: 46 cells, monkey M: 80 cells). Their RF eccentricity
ranged from 3° to 15°, which was well matched to the position
of the stimuli used in the behavioral experiments (10°). Even
though the stimuli were not optimized (in size or dot density)
per neuron, the responses were clearly direction selective.
Direction selectivity depended on the speed of the stimuli.
Across all neurons and speeds, the DSI (see MATERIALS AND
METHODS) had a median of 0.32, while the peak DSI across
speeds had a median across the sample of 0.49. (Note that our
definition of DSI does not remove the spontaneous firing rate;
doing so increases this median peak DSI to 0.86).
In agreement with earlier findings (Lagae et al. 1993; Rod-
man and Albright 1987), most cells (122/126, 97%) were
significantly speed tuned (as defined in MATERIALS AND METH-
ODS) for unidirectional patterns. Most of these (103/122, 84%)
were also significantly speed tuned for bidirectional patterns.
The log-Gaussian was a close fit to the speed tuning curves for
unidirectional (R2? 0.9; compatible with earlier reports by
Nover et al. 2005) and bidirectional (R2? 0.9) patterns. The
distribution of preferred speeds (for unidirectional motion in
the preferred direction) was broad; the quartile range extended
from 9°/s to 42°/s with a median of 25°/s. These properties are
in general agreement with other studies (Churchland and Lis-
berger 2001; DeAngelis and Uka 2003; Duijnhouwer et al.
2013; Liu and Newsome 2005).
Illustrative example cells. In each cell, we mapped the speed
tuning curve, using unidirectional motion of 100 randomly
positioned dots moving in the preferred direction (uni-pref),
unidirectional motion in the antipreferred direction (uni-anti),
and bidirectional motion with 50 dots moving in the preferred
and 50 dots moving in the antipreferred direction (bi). Figure 3
shows these tuning curves for nine example cells that illustrate
the range of effects we found in our MT sample.
6 9 10 11
Uni Test Speed (deg/s)
Uni Test Faster (%)
50 100150 200250
PSE Uni−Uni (% of Ref)
PSE Uni−Bi (% of Ref)
Test Speed (% of Ref)
Test Faster (%)
Fig. 2. Perceptual effects of transparency. A: psychometric curves for 5 human subjects. In the uni-uni condition, the subjects compared 2 patches of unidirectional
motion, one with a fixed (reference) speed of 10°/s and the other with the variable speed shown on x-axis. In the uni-bi condition, the subjects compared a
unidirectional test speed (x-axis) to a bidirectional reference moving at 10°/s. The clear rightward shift of the point of subjective equivalence (PSE) in the uni-bi
conditions represents a strong overestimation of the perceived speed of the bidirectional reference. The intersection of the dotted black lines indicates the PSE
for veridical speed perception. B: comparison of PSE in the uni-uni and uni-bi conditions for a range of reference speeds. Each data point represents data from
a single subject for a single reference speed. Reference speeds (°/s) are color coded according to the key. This plot confirms that the effect shown in A
(overestimation of bidirectional speed) was found consistently, and across the range of reference speeds. C: comparison of the sensitivity (the slope of the
psychometric function in A at the PSE) in the uni-uni and uni-bi conditions for a range of reference speeds. Sensitivity was consistently higher in the uni-uni
condition. D: behavioral data from 1 monkey subject (monkey M). The uni-uni and uni-bi conditions were identical to those of the human subjects. In the bi-bi
condition monkey M compared the speed of a bidirectional test stimulus with the speed of a bidirectional reference. The data were averaged over reference speeds,
and therefore the test speed on the x-axis is expressed as % of the reference speed. The data show that monkey M was less sensitive for the bi-bi comparison
than the uni-uni comparison. Just like the human subjects, monkey M overestimated the speed of bidirectional stimuli compared with unidirectional reference
patterns (uni-bi, red asterisk; error bars representing the 95% confidence limits have a length of 4%, which is smaller than the marker). The red dotted line is
a psychometric function whose PSE was chosen to match with the uni-bi performance, while the slope was estimated jointly from the uni-uni and bi-bi trials.
The intersection of the dotted black lines indicates the PSE for veridical speed perception.
2011 SPEED PERCEPTION IN MT
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Figure 3, A and B, show examples that match previous
reports on transparent motion (Snowden et al. 1991; van Wezel
et al. 1996); bidirectional motion evokes a response in between
the response evoked by the preferred and the antipreferred
direction of motion. A model in which the bidirectional re-
sponse is the (weighted) average of the preferred and anti-
preferred response would fit such cells well (see below for a
quantitative treatment). Averaging, however, does not ade-
quately describe the response pattern seen in the remaining
panels of Fig. 3. The neurons in Fig. 3, C–E, for instance,
reduced their preferred speed when exposed to bidirectional
motion. The neurons in Fig. 3, F and G, responded to all speeds
of bidirectional patterns and lost their speed tuning. The neuron
in Fig. 3H responded to antipreferred motion at high speeds
when presented in isolation but responded to the bidirectional
stimulus as if it was identical to the preferred stimulus and did
not contain any motion in the antipreferred direction (winner-
take-all behavior; see below). Finally, the neuron in Fig. 3I was
not direction sensitive (red and blue curves overlap), but at low
speeds it responded better to bidirectional than unidirectional
Cell-by-cell analysis. For each cell, we fit a log-Gaussian
tuning curve to the responses to motion in the preferred di-
rection and, separately, for bidirectional motion. Figure 4
compares the four parameters of these fits on a cell-by-cell
basis for the 103 neurons with significant speed tuning for both
uni- and bidirectional patterns. Figure 4A shows that the offset
of the tuning curve, which represents the part of the response
that is independent of the speed of the stimulus, generally
increased for bidirectional motion. This effect was highly sig-
nificant (sign test; P ? 0.01). We used an orthogonal regres-
sion to quantify the effect as a 60% increase in the untuned
response. Figure 4B compares the amplitude of the speed
tuning curves for uni- and bidirectional motion. The amplitude
was significantly reduced (sign test; P ? 0.01), and, on aver-
age, the amplitude of the bidirectional response was 71% of the
amplitude of the unidirectional response. Figure 4C shows that
the preferred speed for bidirectional stimuli was typically
lower than the preferred speed of unidirectional stimuli (sign
test; P ? 0.01).
Bi − Offset (spk/s)
Firing Rate (spk/s)
Fig. 3. Speed tuning curves of 9 example neurons from
area MT. In all conditions the dot patterns (in both
preferred and antipreferred directions) were moving at
the speed indicated on the x-axis. A–I: 9 cells that span
the range of effects we found. Error bars on the data
points indicate SE. The solid curves represent the best
fit; the colored areas around the curves represent the
family of tuning curves consistent with the data (see
MATERIALS AND METHODS). Consistent with previous
reports (Snowden et al. 1991), many cells responded
less to bidirectional motion than to unidirectional
motion. This suppression, however, was not constant
across speeds, and most cells also showed enhanced
responses to bidirectional motion of certain speeds.
Bi − Amplitude (spk/s)
Bi − Preferred Speed (deg/s)
0.11 10 100
Uni − Offset (spk/s)
1 10 100
Uni − Amplitude (spk/s)
Uni − Preferred Speed (deg/s)
Uni − Tuning Width (deg/s)
Bi − Tuning Width (deg/s)
Fig. 4. Cell-by-cell comparison of tuning parameters. This plot contains only
significantly tuned cells (n ? 103). A: comparison of the speed-independent
(i.e., untuned) response for bidirectional stimuli vs. unidirectional stimuli
moving in the preferred direction (offset parameter: ? in Eq. 1). B: comparison
of the tuning amplitude (?). C: comparison of the preferred speed (?).
D: comparison of the speed tuning width (?). This figure shows that when a
bidirectional stimulus was shown MT neurons typically responded more to all
speeds (A) but with a reduced amplitude (B). In addition, most cells preferred
lower speeds in bidirectional motion patterns (C).
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These changes in the parameters of the log-Gaussian tuning
function go a long way to describe the response changes of the
example cells in Fig. 3. For instance, the offset increase can be
seen in Fig. 3, D, F, G, and I. A decrease in amplitude is seen
in all example cells except Fig. 3, C and H, and a reduced
preferred speed is clearly noticeable in Fig. 3, C–E.
The tuning width was characterized by the unitless param-
eter ?. In our sample ? ranged from 0 to 3 with a median of 1.5
for unidirectional patterns, similar to the values reported by
Nover et al. (2005). The scatterplot in Fig. 4D shows that even
though bidirectional patterns often induced relatively large
changes in tuning width, there was no consistent pattern (sign
test; P ? 0.8) across the sample. We investigated whether a
pattern could be discerned when taking preferred speed into
account. For neurons with low preferred speeds tuning was
typically broader for bidirectional motion (i.e., ? was reduced),
while neurons with high preferred speeds often had narrower
tuning for bidirectional motion (i.e., ? was increased). How-
ever, this correlation between the change in ? and the preferred
speed of the neuron was weak (r ? 0.23, P ? 0.05); hence
most of the variance in tuning width changes induced by
bidirectional patterns remains unexplained.
Normalization. We investigated whether a simple normal-
ization model could describe the relation between the response
to the two unidirectional patterns and the response to the
bidirectional pattern. Specifically, we used least-squares opti-
mization to fit a power law model to the responses to the
bidirectional patterns (see MATERIALS AND METHODS). Across our
sample of 126 cells this power law model explained little of the
variance in the response to bidirectional motion (median ex-
plained variance 46%). The model failed entirely (explained
variance ?10%) for 49 of the neurons (? 39%). Figure 3, A
and E–G, show example neurons from this category. For the
subset of 37 neurons (? 29%) where the model worked
reasonably well (explained variance ? 75%), the power pa-
rameter (g) was typically above 20, which means that the
power-law summation was essentially winner-take-all. Figure
3H shows the speed tuning curves for one of these neurons.
This fitting exercise shows that the interaction between the
components of bidirectional patterns could in general not be
captured by power-law summation. To understand why, we
investigated how this interaction was affected by firing rate,
direction selectivity, and speed tuning.
Suppression and facilitation. The first study to investigate
bidirectional transparent motion in the macaque brain reported
mainly suppressive effects (Snowden et al. 1991), which those
authors defined as a response to bidirectional motion that was
reduced compared with unidirectional preferred motion. We
followed their convention and defined an index [suppression
index (SI)] as 1 ? B/P, where B corresponds to the bidirec-
tional response and P to the unidirectional preferred direction
response. We calculated SI for each ?speed as well as the DSI
for each ?speed. Figure 5 represents the median SI across
neurons as a function of DSI (x-axis), while maintaining the
dependence on ?speed (shown as a label near the data point).
Clearly, SI typically increased with DSI. (Note that DSI ap-
pears relatively low due to the fact that it is an average over the
variability induced by different test speeds and because spon-
taneous firing rate is included in our definition of DSI. The first
paragraph of RESULTS documents the direction selectivity of
these cells.) The fact that the SI depended on DSI is not
surprising, as motion opponency increases direction selectivity
(Adelson and Bergen 1985; Krekelberg 2008; Krekelberg and
Albright 2005) and should increase suppression for bidirec-
tional motion stimuli.
However, the mapping from DSI to SI is not one-to-one,
which implies that stimulus speed also affected the SI. For
example, given approximately equal DSI (e.g., 0.2), responses
to bidirectional patterns with speeds below the preferred speed
(?speed ? ?2) were facilitated (SI ? 0), while responses to
bidirectional patterns above the preferred speed (?speed ? 2)
were suppressed (SI ? 0). This effect is partially captured by
the statement that suppression is larger near the preferred speed
(?speed ?0) and drops off for speeds above (?speed ? 0) or
below (?speed ? 0) the preferred speed. For speeds well
below the preferred speed the suppression turns into facilita-
tion. A third effect can be inferred from Fig. 5 and Fig. 6:
suppression was weaker when firing rates for the preferred and
antipreferred motions were lower.
To quantify these three relationships we determined the
linear partial correlation between SI, DSI, ?speed, and the sum
of the response to the preferred and antipreferred stimulus.
Suppression was primarily determined by DSI (r ? 0.47, P ?
0.001), next by the summed firing rate (r ? 0.36, P ? 0.001),
and to a lesser, but statistically significant extent by the
difference between the test speed and the preferred speed (r ?
0.11, P ? 0.005). In words, the data show that the response to
bidirectional patterns was suppressed more when they moved
at speeds for which the neuron had high direction selectivity,
more for speeds that evoked a high firing rate, and more for
speeds near the preferred speed. These effects can also be seen
in the averaged responses, which we present next.
Average responses. Figure 6A shows the median normalized
response of our sample of MT neurons (all neurons; n ? 126)
for each speed and in the three motion conditions (uni-pref,
uni-anti, bi). This confirms that for some speeds the response to
0 0.10.20.3 0.4
Direction Selectivity Index
Fig. 5. Suppression and enhancement. Data points show the median suppres-
sion index (SI; y-axis) as a function of the median direction selectivity index
(DSI; x-axis). These averages were determined after aligning the tuning curves
to the preferred speed (i.e., based on the data shown in Fig. 6B); this allows us
to label each data point with the difference between stimulus speed and
preferred speed (?speed). Error bars show SE across the population. This
figure shows that SI depends both on DSI and on ?speed: suppression
increased with direction selectivity but, in addition, decreased for speeds
further from the preferred speed.
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bidirectional patterns is suppressed compared with unidirec-
tional motion in the preferred direction. At low speeds, how-
ever, the population response was enhanced in the bidirectional
The speed dependence of suppression is seen more clearly in
Fig. 6B, which shows the sample average after aligning the
preferred speeds of all cells. Note that, to use the entire
population, we defined preferred speed here nonparametrically
as the speed that induced the largest response. Using the
parametric definition (i.e., Fig. 4C) on the subset of cells that
were significantly tuned resulted in a qualitatively similar
graph (not shown). Here, we clearly see an enhanced response
at low speeds and a suppressed response near the preferred
speeds. However, it is also clear from these figures that DSI
varied considerably across speeds. Typically DSI was small at
low speeds and peaked near the preferred speed. Hence another
valid description of the responses to bidirectional patterns is
that they are suppressed when neurons are strongly direction
selective and enhanced when they are weakly direction selec-
tive. The cell-by-cell analysis above quantifies the relative
strength of speed tuning, direction selectivity, and the strength
of the response on suppression.
Linking Neural and Behavioral Data
Qualitatively, the reduced dynamic range for bidirectional
stimuli (Fig. 4B) should result in a loss of sensitivity, and the
labeled line decoder predicts that a reduction of the preferred
speed for bidirectional stimuli (Fig. 4C) results in an increase
of perceived speed. The goal of this section is to make these
links quantitative by using a labeled line population decoding
algorithm in which each neuron votes for its preferred speed
with a weight proportional to its firing rate (see MATERIALS AND
Figure 7 shows the population activity that the decoder used
to determine stimulus speed. Specifically, Fig. 7 shows the
response of our MT sample to uni- and bidirectional stimuli at
seven different speeds. In terms of the decoder, the number
along the x-axis corresponds to the label and the length of the
vertical lines represents the vote for that label. Clearly, at slow
stimulus speeds there were many votes for slow labels (Fig. 7,
bottom left), while at high stimulus speeds the votes were
predominantly for fast labels (Fig. 7, top right). The circles in
Fig. 7 represent the decoded speed for each stimulus speed for
unidirectional (black) and bidirectional (red) patterns. The
decoder generally overestimated the speed of slow stimuli,
while it underestimated the speed of fast stimuli. This is a
consequence of the boundaries (e.g., none of our neurons had
a preferred speed above 64°/s or below 1°/s; hence our decoder
could never decode a speed above 64°/s or below 1°/s) and the
fact that more neurons in our sample preferred fast speeds than
slow speeds. These decoding biases are well known (Krekel-
berg et al. 2006b; Priebe and Lisberger 2004); we ignore them
here by focusing on decoding relative speeds mainly from the
center of the speed range (see DISCUSSION).
In our first decoder, we equated a neuron’s label with its
preferred speed for unidirectional motion, generated popula-
tion responses like those shown in Fig. 7, decoded the speed for
a test and a 10°/s reference stimulus, and compared those two
decoded speeds to answer the question “Which was faster, the
test or the reference?” In terms of Fig. 7 this corresponds to a
comparison of two of the circles at different speeds (y-axis),
e.g., a black and a red circle for a comparison of uni- and
bidirectional motion and two black circles for a uni-uni com-
parison. Repeating this procedure in 1,000 simulated trials with
independent Poisson noise for each neuron resulted in the data
points shown as solid circles in Fig. 8. The solid curves show
the neurometric curves fitted to these data points. The neuro-
metric curve for bi-bi comparisons (green) was shallower than
the curve for uni-uni comparisons (blue). This demonstrates a
lower sensitivity for bidirectional than unidirectional motion.
1 2 4 8 16 32 64
-4 -2 0 2
Speed (octaves from ps)
Normalized Response Normalized Response
Fig. 6. Population average speed tuning. A: normalized
firing rate averaged over all cells (n ? 126). Consistent
with the cell-by-cell comparison, bidirectional patches
sometimes evoke reduced responses (especially near
the preferred speed) but sometimes enhanced re-
sponses (at low speeds). B: normalized firing rate after
aligning the preferred speeds of each cell. The response
to bidirectional patterns was suppressed near the pre-
ferred speed and enhanced at lower speeds and showed
a reduction in preferred speed.
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Numerically, the slope at the PSE was 0.007 for uni-uni and
0.005 for bi-bi, a 29% loss in sensitivity.
Next, we compared the PSEs. For uni-uni comparisons the
PSE was at 101% and for bi-bi comparisons 102%, indicating
that the decoder had no bias for such comparisons. For the
uni-bi comparisons, however, (red solid line in Fig. 8), the PSE
was 189%, showing a large overestimation of the speed of
bidirectional motion. (A unidirectional pattern would have to
move 89% faster to be decoded as the same speed as a bidi-
The choice of each neuron’s label in this labeled line
decoder is somewhat arbitrary. For instance, one could argue
that in a visual system exposed to natural motion, which
includes bidirectional motion, the labels should not only be
determined by unidirectional motion. As a simple exploration
of this possibility, we investigated what would happen if the
labels were instead determined by the average of the two
motion types (see MATERIALS AND METHODS). This decoder still
had less sensitivity for bi-bi comparisons than for uni-uni
comparisons (10% loss in sensitivity; not shown), and the
decoder’s PSE for the uni-bi comparison was 163% (dashed-
dotted red line in Fig. 8). Finally a decoder based on labels
defined by the preferred speed to bidirectional patterns had a
slightly increased sensitivity for bi-bi comparisons (5%; not
shown) but nevertheless overestimated the speed of bi- com-
pared with unidirectional patterns (PSE 132%; dotted red line
in Fig. 8).
Taken together, these decoder simulation results show that
reasonable assumptions about the labels used to decode MT are
compatible with a loss of sensitivity for bidirectional motion on
the order of 25% and an overestimation of the speed of
bidirectional patterns on the order of 50%. These estimates are
compatible with the measured perceptual effects in Fig. 2. The
monkey’s sensitivity loss was 23%, and we estimated his
overestimation of bidirectional speeds to be 20%. For the
human subjects, the sensitivity loss varied between 18% and
50% (quartile range across all data in Fig. 2C) and the over-
estimation of the speed of bidirectional motion varied between
43% and 76% (quartile range across all data in Fig. 2B). As can
be inferred from Fig. 7, however, the decoder predicted that the
perceived speed difference between uni- and bidirectional
1248 16 32 64
Preferred Speed (deg/s)
Stimulus Speed (deg/s)
Fig. 7. MT population activity in response to uni- and
bidirectional motion patterns. Each vertical line repre-
sents the activity of a single neuron in our sample.
Black lines represent the response to unidirectional
motion and red lines the response to bidirectional
motion. Neurons are sorted by their preferred speed
along the x-axis, and stimulus speed is represented
along the y-axis. As an example, the arrowhead high-
lights the response of a neuron with a preferred speed
just above 2°/s to stimuli moving at 64°/s. Its response
to unidirectional motion (black vertical line) is much
less than its maximum response (indicated by horizon-
tal dashed lines). The vertical red line shows that this
neuron responds more strongly to bidirectional motion
(at 64°/s). (Black lines are thick only to allow us to
overlay the response to bidirectional motion with the
thin red lines). The circles indicate the decoded speed
for each stimulus as determined by the labeled line
model (black, unidirectional motion; red, bidirectional
motion). This graph shows how increasing the stimulus
speed (bottom to top along y-axis) shifts the population
activity from low-speed-preferring neurons to high-
speed-preferring neurons (left to right along x-axis).
This underlies the model’s ability to decode speed from
50100 150 200250
Test Speed (% of Ref)
Test Faster (%)
Fig. 8. Speed discrimination based on a labeled line model and MT responses.
The model used only the responses of 126 MT neurons to determine whether
the test patch (moving at speed represented on x-axis) moved faster than the
reference patch (moving at a fixed speed of 10°/s). These simulated behavioral
experiments match the behavioral experiments shown in Fig. 2. The figure
shows that the decoder performed the uni-uni task at a high level of perfor-
mance. The same decoder, however, had reduced sensitivity for bidirectional
stimuli and overestimated the speed of bidirectional patterns compared with
unidirectional patterns (red solid line). The dotted and dashed red lines show
the results of the bi-uni task when the label of the neurons was based on the
preferred speed for bidirectional patterns or the average of the 2 motion types,
respectively. These results are in good qualitative agreement with the human
and monkey behavioral data of Fig. 2 and support the view that MT responses,
decoded with a labeled line decoder, could indeed underlie the perception of
speed in uni- and bidirectional patterns.
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patterns diminishes with increases in the test speed. The
behavioral data did not show this effect (Fig. 2B). We return to
this issue in DISCUSSION.
Our behavioral data confirm earlier findings that the speed of
bidirectional motion is more difficult to discriminate (Ver-
straten et al. 1996) and perceived to be faster (De Bruyn and
Orban 1999) than unidirectional motion. The speed tuning of
neurons in macaque area MT also differed greatly when mea-
sured with unidirectional motion or bidirectional motion. No-
tably, the neurons had a reduced dynamic range and generally
preferred lower speeds in the bidirectional motion patterns.
Unlike previous reports, we found that the response to bidirec-
tional patterns could be suppressed or enhanced compared with
the unidirectional preferred pattern and that this depended on
the neurons’ direction selectivity, speed preference, and overall
firing rate. We were able to link these complex neural re-
sponses to our behavioral characterization of perceived speed
by a simple labeled line decoder. Just like the human and
monkey observers, the decoder performed with high sensitivity
for unidirectional patterns, was less sensitive for bidirectional
motion, and overestimated the speed of bidirectional motion.
After discussing low-level confounds and alternative inter-
pretations, we discuss the novel insights that our data provide
into the processing of transparent motion per se, as well as the
relationship between neural activity in MT and the perception
Under some conditions—for instance, to make sense of the
optic flow created by self-motion—relative motion is more
informative than absolute motion. If a neuron encoded relative
speed, then the response to a 2°/s bidirectional stimulus should
correspond to a 4°/s unidirectional stimulus. In other words,
the relative speed assumption predicts a leftward shift of the
speed tuning curve by precisely 1 octave. Figure 3C is an
example of a neuron that matches this prediction. The over-
view in Fig. 4C, however, shows that while shifts in preferred
speed are predominantly leftward their magnitude is quite
variable across the population and the 1-octave shift predicted
by the relative speed model does not appear to be particularly
common. Hence, our data do not support the idea that MT cells
generally respond to relative speed. Determining whether a subset
of cells (such as the example cell in Fig. 3C) do represent relative
motion would require a more extensive sampling of different
combinations of stimulus speeds and directions.
In principle, the substantial inhomogeneities in directional
preference across the RF we recently reported (Richert et al.
2013) could contribute to differences in the response to unidi-
rectional and bidirectional stimuli. However, because we re-
peated each condition on average 12 times, and each repeat
consisted of a new set of dots whose starting positions were
randomized within the 10° aperture, such variability should
average out across multiple trials.
Competitive Interactions in Transparent Motion
Previous work has shown that the percept of transparent
motion does not require multiple activity peaks (corresponding
to the directions of motion) in the MT population. Instead, the
percept of transparent motion can be extracted from the overall
pattern of population activity without the need for distinct
peaks (Treue et al. 2000). Generation of such patterns of
activity can be achieved in models that rely on a local compe-
tition between the neurons representing multiple directions of
motion (Qian and Andersen 1994; Qian et al. 1994). Neural
signatures of competition have been described as a suppression
of the neural response to bidirectional motion patterns com-
pared with unidirectional motion in the preferred direction
(Snowden et al. 1991; van Wezel et al. 1996). Our examination
of bidirectional motion across a range of speeds, however,
revealed a much richer repertoire of interactions between
opposing directions of motion. These could be understood as
the competitive interaction among multiple components that
presumably arises as an emergent property of the recurrently
connected neural network for motion detection (Grossberg
1973; Krekelberg and Albright 2005).
Our finding that suppression was mainly found near the
preferred speed, while enhancement dominated for suboptimal
speeds, is reminiscent of the contrast dependence of normal-
ization (Heuer and Britten 2002): two stimuli that each provide
weak drive to a neuron sum supralinearly, while stimuli that
provide strong drive interact sublinearly. Our analysis of power-
law summation, however, shows that a model based solely on
untuned normalization cannot capture the complexity found here.
The partial correlation analysis clarifies that the response to
bidirectional motion of a given speed is determined by the direc-
tion selectivity, the total response to each of the unidirectional
components, as well as the speed tuning. Hence, a model to
capture this complexity would have to be tightly linked with a
model for direction selectivity (to explain the dependence on
DSI), normalization (to explain the dependence on the total firing
rate), and speed tuning (to explain the explicit dependence on the
Linking with Perception
Our findings add support to the claim that speed perception
and neural activity in area MT are causally related via a labeled
line decoder. This decoder, however, is far from perfect.
Notably, taken at face value, the decoder incorrectly predicted
biases in decoding absolute speed (none of the circles in Fig. 7
matches the stimulus speed) and a decrease of the perceived
relative speed of uni- and bidirectional patterns with stimulus
speed (black and red circles in Fig. 7 move closer together with
increasing stimulus speed). At least in part, these decoding
errors are due to the overabundance of neurons with high
preferred speeds and the absence (in our sample) of neurons
with preferred speeds above 64°/s. Such unequal distributions
of the label necessarily introduce biases in labeled line decod-
ing (Krekelberg et al. 2006b; Priebe and Lisberger 2004),
although they can be reduced by using a weighted and/or
nonlinear average across the population (Salinas and Abbott
1994). By focusing our decoding analysis on the center of the
range of preferred speeds in our sample, we minimized the
influence of these effects and found a good match with
the behavioral data in that same range. The visual system,
however, has to cope with the full range of speeds in the
environment, and it is not clear how it avoids boundary effects
(if it uses labeled line decoding). This highlights a conceptual
difference between labeled line decoding of a sensory variable
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that has no boundaries (e.g., direction) and one that has
boundaries (e.g., speed has boundaries at zero and at the
highest preferred speed in the population). Labeled line aver-
aging works well in the former but can be problematic in the
latter sensory domain.
In previous work we have shown that the change in per-
ceived speed induced by manipulating stimulus contrast of
random dot patterns is not captured by a labeled line model in
area MT (Krekelberg et al. 2006b). Although it is far from the
only argument against a labeled line for speed (see introduc-
tion), it is clearly the odd one out of studies based on visual
illusions. The present study does not resolve this discrepancy,
but it does suggest that the influence of stimulus contrast on
speed perception may be a special case.
In this context, we note that a striking effect of luminance
contrast on neural responses in the visual system is the increase
in response latency at low contrasts. Such response latency
differences are typically not found in the other manipulations
that lead to speed misperceptions (e.g., adaptation, stimulus
size, or bidirectional motion). Hence it seems possible that an
extension of the labeled line model that takes the latency of the
response into account could be fruitful (Chase and Young
2007; Gawne et al. 1996). We note, however, that response
latency depends not only on contrast but also on speed and
direction tuning, surround interactions, and the magnitude of
the response (Raiguel et al. 1989, 1999). Experimentally it is
not feasible to control each of these variables independently,
which hampers the isolation of a single underlying quantity
that identifies perceived speed. Of course, this raises the
question of how the brain manages to do so, given that these
same confounds exist in everyday life as well. Our findings
show that the labeled line model fares well under very con-
strained conditions (the comparison of bi- and unidirectional
patterns of moving dots). Similarly, variants of the labeled line
model have been shown to explain the influence of other
isolated stimulus manipulations
(Churchland and Lisberger 2001), adapted motion (Krekelberg
et al. 2006a), accelerated motion (Schlack et al. 2007), stimulus
size (Boyraz and Treue 2011)]. Even though each of these
studies used a labeled line model, they are subtly different in
the definition of the label, as well as the measure of neural
activity that is used in the decoder. Hence it is not clear that a
single model could explain all of these data sets in a quantita-
tive manner. The true challenge remains to develop a single
model that relates neural activity (in MT or elsewhere) to the
perceived speed of natural stimuli in a manner that explains
how nuisance features such as luminance, contrast, size, mo-
tion direction, and transparency affect the percept of speed.
We thank Tom Albright for his early support of this project, Jennifer
Costanza, Dinh Diep, and Doug Woods for technical assistance, and Roger
Bours for his help with data analysis.
This research was supported by the National Eye Institute under award
number R01 EY-017605.
No conflicts of interest, financial or otherwise, are declared by the author(s).
Author contributions: B.K. and R.J.A.v.W. conception and design of
research; B.K. and R.J.A.v.W. performed experiments; B.K. and R.J.A.v.W.
analyzed data; B.K. and R.J.A.v.W. interpreted results of experiments; B.K.
and R.J.A.v.W. prepared figures; B.K. drafted manuscript; B.K. and
R.J.A.v.W. edited and revised manuscript; B.K. and R.J.A.v.W. approved final
version of manuscript.
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