text:
Motion psychophysics: 1985–2010
This review traces progress made in the field of visual motion research from 1985 through to 2010. While it is certainly not exhaustive, it attempts to cover most of the major achievements during that period, and speculate on where the field is heading.
Motion psychophysics: 1985–2010
David Burr
, Peter Thompson
Department of Psychology, University of Florence, Via S. Salvi 12, Florence, Italy
CNR Institute of Neuroscience, Via Moruzzi 1, Pisa, Italy
Department of Psychology, University of York, York, England, United Kingdom
article info
Article history:
Available online xxxx
Visual motion
Speed perception
Visual illusions
This review traces progress made in the field of visual motion research from 1985 through to 2010. While
it is certainly not exhaustive, it attempts to cover most of the major achievements during that period, and
speculate on where the field is heading.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Pre-history
This review of motion psychophysics picks up the story from
where Ken Nakayama (1985) left off. Those with an interest in an-
cient history are recommended to go there for an excellent review
of work in the 60s and 70s.
Our review starts at a fortunate time, when many seminal mod-
els of motion perception hit the scene, several in a single volume of
the Journal of the Optical Society. These models changed the way
people thought about motion perception, and set solid ground for
the development of more complete models in the following years,
as well as providing the impetus for further research.
The momentum for this new approach had been building for
some time: our understanding of the underlying physiology of mo-
tion processing had been boosted by studies by Zeki (1980) and
Albright (1984, 1984) who demonstrated the importance of area
and showed an elegant columnar organisation of directionally
selective cells there. This work in the monkey was supported by
the intriguing report by Zihl and colleagues (1983) of a 'motion
blind' patient who, it was suggested, might have bilateral damage
to the human analogues of MT.
If the early years of the 1980s were a golden age of motion pro-
cessing then it was because of groundwork laid down in the years
before. The 1960s and 70s were a time when our understanding of
spatial vision leapt forward. Seminal papers by Robson (1966),
Campbell and Robson (1968), Blakemore and Campbell (1969),
Graham and Nachmias (1971) and many others had established
the sine-wave grating as the stimulus of choice for research in spa-
tial vision. Tuned 'spatial frequency channels' seemed to be a real-
ity (Braddick, Campbell, & Atkinson, 1978), established by a raft of
psychophysical procedures and by single unit recording as well.
The systems-theory approach had also been most successful in
studies of the temporal sensitivity, primarily to flicker (DeLange,
1958; Robson, 1966; Roufs, 1972). Pioneering work by Tolhurst
and others (Kulikowski & Tolhurst, 1973; Tolhurst, 1973, 1975)
did much to promote the idea that perhaps human vision involved
separate 'pattern' and 'motion' pathways, an idea that persists to
this day, albeit under different guises, such as the parvocellular–
magnocellar distinction, and dorsal and ventral streams. By the
early 80s we had good psychophysical support for direction selec-
tive channels and even an idea of the temporal tuning of channels
as well (Anderson & Burr, 1985; Thompson, 1983, 1984; Watson &
Robson, 1981) though the speed tuning of these channels remained
largely mysterious. David Marr, who had died tragically at the age
of 35 in 1980 had left a rich legacy for our understanding of vision
and for computational models of motion processing in his book
Vision, published posthumously in 1982 (Marr, 1982) and in a
wonderful paper with Shimon Ullman (Marr & Ullman, 1981).
Another force that drove the massive rise in research in motion
perception was technology. Computers revolutionized the study of
motion, allowing for dynamic and continual updating of frames, an
enormous advance on pre-computer technology like the tachisto-
scope. In the early years, computer-generated motion stimuli were
also somewhat limited, essentially one-dimensional patterns such
as sine-wave gratings (generated by purpose-built machinery un-
der computer control), or random-dot stimuli (usually only two-
frame). Other possibilities did exist, using, for example, dynamic
frame-free point-plotting techniques (Ross & Hogben, 1974), but
these did not prevail. Two-dimensional stimuli, even plaids, were
0042-6989/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
Corresponding author at: CNR Institute of Neuroscience, Via Moruzzi 1, Pisa,
E-mail address: firstname.lastname@example.com (D. Burr).
Throughout this review we have used MT rather than V5. This is merely for
convenience and in no way should be taken as an indication of the authors' loyalties
on this matter.
Vision Research xxx (2011) xxx–xxx
Contents lists available at ScienceDirect
Vision Research
journal homepage: www.elsevier.com/locate/visres
Please cite this article in press as: Burr, D., & Thompson, P. Motion psychophysics: 1985–2010. Vision Research (2011), doi:10.1016/j.visres.2011.02.008
beyond the scope of most labs. Purpose-built framestores, notably
from Cambridge Research Systems, who have specialized in vision
research equipment, made life much easier for all. In addition to
advances in hardware, many software packages were developed
by community-minded colleagues. An early one was Landy, Cohen
and Sperling's (1984) comprehensive ''HIPS'' package under Unix.
But for motion perception, Dennis Pelli's (1997) and David Brai-
nard's (1997) Psychotoolbox package proved invaluable, both for
the technically challenged and technically competent researchers,
allowing them to create rapidly and at little expense interesting
stimuli and run experiments on their Mac or PC. This package is
continually being developed and improved, and is to this day one
of the major tools for motion research.
So at the start of 1985 the big issues were: how is direction
selectivity achieved in the visual system? What is the spatial tun-
ing of direction selective channels? How do we encode speed?
Where are these computations carried out in the visual system?
Is second order motion really coded differently from first order mo-
tion? How are local-motion signals integrated into the coherent
motion of objects (solving, amongst other things, the aperture
problem)? How and why do we segregate different motion signals?
How does motion interact with other attributes, such as perceived
position and form?
In this review we shall trace the progress in our understanding
of some of these key questions. There are thousands of papers that
have made a contribution to progress (and a few that have made a
contribution to our lack of progress) so this review will necessarily
be very selective. There are some areas that, for space constraints,
we have decided to omit completely, such as the perception of
''biological motion'', a fundamental motion task for social crea-
tures: we refer the interested reader to an excellent recent review
by Blake and Shiffrar (2007), and invite them to play with Nikolaus
Troje's amusing demo. We note also the fundamental contributions
of researchers such as Tony Movshon and Bill Newsome to under-
standing the physiological circuitry of motion pathways, but this
was to be covered by separate review. And within the areas we
have chosen to review, we will undoubtedly omit to mention some
seminal papers and will mention others of only modest value
(probably our own and those of close friends). We apologise for
this, but this review would have fallen foul of just the same preju-
dices if you had written it, dear reader.
2. Motion detectors as spatio-temporal filters
1985 was a landmark year for research on motion perception.
That year the Journal of the Optical Society published a special edi-
tion on motion perception, which included the influential contri-
butions of Adelson and Bergen (1985), van Santen and Sperling
(1985), Watson and Ahumada (1985) and others. These important
papers (and another published in the Proceedings of the Royal
Society: Burr, Ross, & Morrone, 1986), shared a common theme.
Following the zeitgeist of the successful application of Fourier
analysis to visual perception, they define motion in frequency
space, and show how suitably tuned spatio-temporal filters can
model well human motion perception (see Burr (1991, chap. 15),
for a review of this approach). The details of the various models
are probably less important than the general message: that many
aspects of motion, thought to be mysterious, are well explained
in the frequency domain.
The contributions are all subtly different, but perhaps Adelson
and Bergen (1985) explain most clearly how motion can be repre-
sented as an orientation in x–y–t space, and readily extracted as
spatio-temporal energy by suitable filters. Fig. 1 illustrates the
main aspects of this model. There are three important parts to their
model: non-directionally tuned spatial and temporal filters (A and
B), that smooth the motion input in space and in time; the ''quad-
rature pairing'' of the filters (complementary phase-tuning), that
gives direction selectivity (C); and the squaring of the responses
before summing (C), that smoothes out the ripples and gives a con-
stant response to a drifting sinusoid. Perhaps the most important
aspect is the quadrature phase arrangement of the filters, that
gives the unit directional selectivity and, to a lesser extent (as we
will discuss later) a certain degree of speed selectively.
Adelson and Bergen show that their model is not only capable of
analysing real motion but explains many other phenomena as well,
including apparent, or sampled motion, previously thought to re-
flect separate processes (e.g. Kolers, 1972
). They also explain some
motion illusions that were popular at the time, including the ''flu-
ted square wave'' illusion (Adelson, 1982), and the reverse-phi illu-
sion of Stuart Anstis (1970). In both cases the explanation of the
illusions is that the stimuli actually contain motion energy in the
direction in which they are perceived, even though this is not obvi-
ous without analysing the spatio-temporal frequency spectrum.
Interestingly, the reversed phi illusion has recently been extended
to demonstrate different transmission times of on- and off-
luminance channels (Del Viva, Gori, & Burr, 2006), again taking
advantage of the fact that this illusion has spatio-temporal energy
corresponding to the perceived direction of motion. These fre-
quency-based models also provide the basis for the explanation
of many illusions discovered more recently, such as Pinna and
Brelstaff's (2000) powerful illusion, discussed in detail in a later
The other papers in the series attacked the problem from differ-
ent viewpoints. Watson and Ahumada (1985) give an excellent
summary of the known properties of motion perception, and rigor-
ously develop their model of motion perception, constrained by
this knowledge. The model differs subtly from Adelson and Bergen,
in that their filters are assembled in series, and the output not
squared, but the basic message is selectivity in space–time. van
Santen and Sperling (1985) again come up with a very similar
model, and analyse in detail the differences between the models.
Importantly, they point out how all models build on the pioneering
work of Reichardt (1957), Reichardt (1961), that compares the out-
put from one part of space with the delayed output of another (see
Fig. 2). Two such units operate together, mutually inhibiting each
other to eliminate a response to flashes. The original Reichardt
detector had no filters, just sampling two points of the retina and
a simple delay line (although later adaptations recognized the need
from filtering: Egelhaaf, Hausen, Reichardt, & Wehrhahn, 1988).
Van Santen and Sperling (1985) show the utility of spatial and tem-
poral filters in producing the spatial and temporal offsets, and how
this eliminates potential problems in point-sampling, like aliasing.
They (and also Adelson & Bergen, 1985) show formally the
mathematical similarities of the Reichardt models, and the new
filter-based models. More recently, Morgan (1992b) varied the
contrast in a two-frame motion sequence to demonstrate that
the spatial filtering operation precedes the directional motion
Burr and colleagues (Burr, 1983; Burr & Ross, 1986; Burr et al.,
1986) took a slightly different approach. They were less interested
in developing a model of velocity perception as in explaining how
the visual system manages to perceive veridically the form of ob-
jects in motion. Again their model was based on the spatio-
temporal filter approach, but rather than assume the existence of
separable filters, they measured them, using the psychophysical
technique of masking. The resultant hypothetical spatio-temporal
filter was not spatio-temporally separable, as others had assumed,
but this probably made very little difference to the thrust of the
idea. What was perhaps more useful was the transform of the filter
from its representation in frequency space to the more intuitive
representation in space–time: the spatio-temporal receptive field,
2 D. Burr, P. Thompson / Vision Research xxx (2011) xxx–xxx
Please cite this article in press as: Burr, D., & Thompson, P. Motion psychophysics: 1985–2010. Vision Research (2011), doi:10.1016/j.visres.2011.02.008
oriented in space–time (see Fig. 3 and Burr & Ross, 1986). This rep-
resentation makes immediately obvious many of the phenomena
that seemed mysterious, such as motion smear (Burr, 1980, see
also Section 6.1), ''spatio-temporal interpolation'' (URL: see movie
1)(Burr, 1979) and even point to explanations of seemingly unre-
lated phenomena, like metacontrast (Burr, 1984). Interestingly,
many similar issues are re-emerging as ''problems'' in recent times
(e.g. Boi, Ogmen, Krummenacher, Otto, & Herzog, 2009). Prelimin-
ary work has suggested that these illusions can be explained, both
qualitatively and quantitatively, by spatio-temporal filters oriented
in space–time (Pooresmaeili, Cicchini, Morrone, & Burr, 2010).
Perception of sampled motion as continuous can be envisaged
as an integration within homogenous regions of the receptive field.
This was not the first time that sampled motion had been ex-
plained in terms of the frequencies generated by sampling, but it
is possibly more intuitive to some than the more rigorous and
quantitative explanations in frequency space (Burr, Morrone, &
Ross, 1985; Watson, Ahumada, & Farrell, 1983).
3. Second-order, higher-order and feature-tracking motion
Since the beginning of the formal study of motion perception,
researchers have classified motion into a variety of types. The Ges-
taltists (e.g. Wertheimer, 1912) used letters of the alphabet to de-
fine the various motion phenomena they devised. In more recent
times, it has long been though that ''apparent'' motion was distinct
from ''real'' motion (e.g. Kolers, 1972). And in a very influential
paper, Oliver Braddick (1980) introduced the distinction between
what he termed ''short range'' and ''long range'' motion.
We now know that many motion phenomena, from simple mo-
tion of real objects through to apparent motion and a range of clas-
sical illusions are readily explicable in terms of the motion energy
in the stimulus, rendering many of the classical distinctions of the
Gestaltists less useful. However, some phenomena are clearly not
immediately accountable for by the energy of the stimulus. These
include bi-stable motion displays like the Ternus Effect (Pantle &
Picciano, 1976; Ternus, 1950), and also the ''short range'' and
''long-range'' division of Braddick (1980). But more challenging
were the effects that came to be called second-order motion, fol-
lowed by third-order and many other more subtle types of motion.
Fig. 1. Constructing a spatio-temporally tuned motion detector. (A and B) The
models of Adelson and Bergen (1985), Watson and Ahumada (1985) and van Santen
and Sperling (1985) all start with separable operators (or impulse response
functions) tuned in space (A) and in time (B), each both in sine and in cosine phase.
Each spatial operator is multiplied with each temporal operator to yield four
separate spatio-temporal impulse response functions of different phases. (C)
Appropriate subtractive combination of these separable spatio-temporal impulse
response functions yields two ''quadrature pairs'' of linear filters (Watson &
Ahumada, 1985), oriented in space–time (hence selective to motion direction). In
Adelson and Bergen's model, these are combined after squaring to yield a phase
independent measure what is known as ''motion energy''. The full detector has
another quadrature pair tuned to the opposite direction, which combines subtrac-
tively to enhance direction selectivity (and inhibition responsiveness to non-
directed flashes). (D) The spatio-temporal energy spectrum of the motion detector
in C. Responding only to one quadrant of spatio-temporal frequency gives the
direction selectivity, and a broad selectivity to speed. Reproduced with permission
from Adelson and Bergen (1985).
εεεε εεεεεε
Fig. 2. The ''Reichardt detector'' in its simplest form. This schema effectively
constitutes the backbone to any motion detector. The key is that it samples from
two points in space connected by a delay line (indicated by
). In this version, there
are two opposed detectors that mutually inhibit each other, preventing a response
to non-directed flashes. Adelson and Bergen (1985) demonstrate that this version of
the Reichardt detector is formally equivalent to their model.
D. Burr, P. Thompson / Vision Research xxx (2011) xxx–xxx
Please cite this article in press as: Burr, D., & Thompson, P. Motion psychophysics: 1985–2010. Vision Research (2011), doi:10.1016/j.visres.2011.02.008
3.1. Second-order motion
Second-order motion was first demonstrated by Andrew Der-
rington and colleagues (Badcock & Derrington, 1985; Derrington
& Badcock, 1985; Derrington & Henning, 1987). Derrington's exam-
ples were complex gratings, comprising two drifting harmonics
that caused ''beats'', as they come in and out of phase. The apparent
direction of motion of these patterns could vary, either in the phys-
ical direction of motion, as predicted by energy models, or in the
direction of the beats (that contain no energy in Fourier space that
would excite the energy models). The phenomenon could not be
explained by trivial non-linearities, such as distortion products
(Badcock & Derrington, 1989).
This class of motion stimulus, which contains no energy in the
Fourier plane describing the direction of perceived motion, has var-
iously been called ''non-Fourier motion'', second-order motion (a
more correct term that has prevailed), higher-order motion and
sometimes ''feature motion''. Zanker (1990), Zanker (1993) devised
another motion stimulus that he coined ''theta motion'' (see demo:
URL, movie 6), motion of motion-defined forms: for example left-
ward drifting dots confined to a rectangular region that was itself
drifting rightwards. Zanker proposed a ''two-layer'' model to ac-
count for ''theta motion'', where the second layer took the output
of a motion energy operator (first layer) as input, and extracted
the motion of the motion-defined object.
The phenomenon of second-order motion was brought force-
fully to the attention of the vision community by Chubb and
Sperling (1988), who devised a clever series of ''drift-balanced''
stimuli, which even on a fine scale, have no directed motion en-
ergy. Yet these stimuli are perceived clearly to move in one
direction or another (see demo: URL, movies 4 and 5). In this paper,
Chubb and Sperling provide a recipe for generating second-order
motion stimuli, prove rigorously that standard Reichardt-like mod-
els will not detect these stimuli, and go onto develop a model that
will detect them. The major feature in the model is the non-linear
rectifying stage after the linear filters, which renders the output
visible to an energy-extraction stage.
Chubb and Sperling (1988, p. 2004) point out that although ''the
existence non-Fourier mechanisms is hardly surprising, such
mechanisms have, however, received no thorough investigation''.
Not then they hadn't! But their publication initiated a cottage
industry of second-order motion research, dominating the vision
sessions at ARVO and ECVP, and generating some hundreds of pa-
pers (well beyond the scope of this brief review). The debate re-
volved principally around whether the two forms of motion
really comprised functionally distinct systems, or whether both
could be subserved by the same system. For example, Taub, Victor,
and Conte (1997) claim, with supporting evidence, that the most
parsimonious explanation is that both types of motion are detected
by a common mechanism, with a simple rectifying non-linearity at
the front end to convert the ''non-Fourier'' into ''Fourier'' motion
energy. Cavanagh and Mather (1989) also make a strong case for
a single motion system, with different styles of front-end detectors.
Ample evidence also exists for the opposing thesis. Animation
sequences that require integration of first-order and second-order
frames do not give rise to unambiguous motion (Ledgeway &
Smith, 1994; Mather & West, 1993). And there are qualitative dif-
ferences between the two types of motion: for second-order mo-
tion, thresholds for identifying motion direction are higher
(relative to detection threshold) than for first-order motion (Smith,
Snowden, & Milne, 1994), and the temporal acuity for second-order
motion is lower than for first-order (Derrington, Badcock, &
Henning, 1993; Smith & Ledgeway, 1998). While first-order motion
seems to show a lower limit for speed, the limit for second-order
motion seems to be defined by a minimal displacement rather than
a minimum speed (Seiffert & Cavanagh, 1998). Perhaps the stron-
gest evidence is neuropsychological, as several patients have been
described with selective impairment of either first or second-order
motion (Greenlee & Smith, 1997; Vaina & Cowey, 1996; Vaina,
Cowey, & Kennedy, 1999; Vaina, Makris, Kennedy, & Cowey,
1998; Vaina & Soloviev, 2004).
The evidence from imaging is less clear. Smith, Greenlee, Singh,
Kraemer, and Hennig (1998) report that the various motion areas re-
spond to the two types of motion differentially, with area V3 and its
ventral counterpart VP responding more strongly to second-order
than to first-order motion, raising the possibility that these areas
represent explicitly second-order motion. However, the difference
in responsiveness was not large, showing considerable overlap
Fig. 3. (A) Spatio-temporal tuning of a hypothetical unit of the human motion system, measured by the technique of ''masking'' (Burr et al., 1986). The function is tuned to
1 c/deg, 8 Hz, and falls off steadily away from the peak (contour lines represent 0.5 log-unit attentions). (B) Spatio-temporal receptive field derived from the filter (assuming,
somewhat unrealistically, linear phase). Forward cross-hatching represents excitatory regions, back cross-hatching inhibitory regions. The orientation in space–time means it
has a preferred velocity, both direction and speed. Spatio-temporal operators of this sort (inferred from all the filter-based motion models of the mid '80s) go a long way
towards explaining many phenomena, such as integrating to path of sampled motion (indicated by the series of dots) so it is perceived as smooth, and ''spatio-temporal
interpolation'' (see Burr & Ross, 1986). They also help to explain why we do not see the world to be as smeared as may be expected from a ''camera'' analogy. The field extends
for over 100 ms in time (indicated by symbol T
) and may be expected to smear targets by this amount. However, the analysis is not in this direction, but orthogonal to the
long axis of the receptive field, where the spread in space–time is considerably less.
4 D. Burr, P. Thompson / Vision Research xxx (2011) xxx–xxx
Please cite this article in press as: Burr, D., & Thompson, P. Motion psychophysics: 1985–2010. Vision Research (2011), doi:10.1016/j.visres.2011.02.008
across areas. TMS studies failed to disrupt selectively first- and
second-order motion (Cowey, Campana, Walsh, & Vaina, 2006).
There are also several psychophysical studies less consistent with
the existence of two separate systems, such as cross adaptation be-
tween first- and second-order stimuli (Ledgeway, 1994; Turano,
1991), although later studies suggested that the cross-system adap-
tation was weaker and less specific (Nishida, Ledgeway, & Edwards,
Of course evidence for interactions and cross-talk between the
two putative systems cannot be taken as evidence that all motion
is subserved by a single system. Even if functionally distinct sys-
tems do exist, one would expect that their output would be com-
bined at some stage to yield a common motion signal. At present
the bulk of evidence points to independent mechanisms at low lev-
els, combining to contribute to the sense of motion. Whether the
mechanisms are anatomically distinct remains a moot point.
3.2. Third-order or attentional motion
As the battle raged between adherents of the single and dual
systems, the issue became further complicated by the introduction
of yet another class of motion, variously termed ''third-order'' (Lu
& Sperling, 1995a, 1995b, 2001) or ''attentional'' motion
(Cavanagh, 1992; Verstraten, Cavanagh, & Labianca, 2000). While
first- and second-order motion were distinguished on strictly de-
fined physical characteristics – the absence of modulation of aver-
age luminance over time – third-order motion results from
psychological attributes of the stimuli, such as ''salience'' or ''atten-
tion'', neither particularly amenable to tight definition. Lu and
Sperling (2001) operationally defined salience as the probability
that a part of the image will be perceived as ''figure'' rather than
''ground''. The motion is therefore that of the perceptually salient
figure, over a background. Examples can be constructed to which
both the first- and second-order systems are blind, such as a
moving stimulus that continually changes in its defining quality,
say between orientation, contrast and chromaticity. Many other
examples exist, such as equiluminant gratings, where one colour
is more salient than the other.
has also been implicated in describing higher-order mo-
tion. Attention was first linked to motion perception by Wertheimer
(1912) some 100 years ago, particularly in disambiguating ambiguous
motion. More recently it has been shown that attention affects consid-
erably adaptation of motion mechanisms (Alais & Blake, 1999;
Chaudhuri, 1990, see also Section 9), and disambiguating cleverly de-
signed stimuli (Lu & Sperling, 1995a). Patrick Cavanagh went further
and suggested that a whole class of motion stimuli, not altogether
dissimilar from the third order motion stimuli of Lu and Sperling,
can be defined as attentional motion stimuli. A typical example of such
a stimulus could be a luminance-modulated grating drifting in one
direction with a superimposed chromatic-modulated grating drifting
in the opposite direction: attending to one or the other determines
the direction of drift. Whether motion of this type is functionally
distinct from third order motion, or indeed whether either type really
defines a unique class of motion is, of course, subject to debate. For fur-
ther elucidation, the interested reader is referred to Cavanagh's (2011)
review in this issue.
3.3. Feature tracking
One question that many perplexed readers may wish to ask at
this stage is ''what purpose does this second- and higher-order mo-
tion serve?'' When, during our normal dealings with the world,
may we expect to encounter a second-order motion stimulus,
modulated, say, in contrast but not luminance or anything else?
The whole field may seem somewhat academic, remote from real
world situations. One approach has been to suggest that the high-
er-order motions represent a form of feature tracking, a system spe-
cialized to monitor the motion of salient features. This of course is
the stated aim of Lu and Sperling's third-order motion, but may in
fact be a more general goal of some motion mechanisms.
The early motion models of the Marr group were designed to
track edges in two-dimensional motion (Hildreth, 1984; Marr &
Ullman, 1981). Although much experimental evidence is consistent
with edge-tracking, or more generally, feature-tracking (Cavanagh
& Mather, 1989; Derrington & Ukkonen, 1999; Morgan, 1992a;
Morgan & Mather, 1994; Seiffert & Cavanagh, 1998), this approach
has not dominated in recent years. One possible exception is Del
Viva and Morrone (1998, 2006) who developed a feature-tracking
algorithm, based on the highly successful ''local energy'' feature
detection algorithm (Morrone & Burr, 1988; see also in this issue
Morgan, in press). They first apply the energy model to reveal sali-
ent features in scenes, then search for peaks in space–time corre-
sponding to the motion of these features. In some respects the
model resembles Chubb and Sperling's (1988), in that the early
non-linearity converts the contrast features into energy detectable
by basic Reichardt-type models. They show that their algorithm
can predict qualitatively and quantitatively human perceptual per-
formance on many interesting examples of motion stimuli that
defy most other motion models. In particular, they show the
importance of ''phase congruence'' between harmonics of com-
pound gratings in determining whether the harmonics will move
as a block, or be seen in transparency. Phase, also important for
Fleet and Langley's (1994) model, has little effect on Fourier power
(and hence Reichardt detectors), but is fundamental in the forma-
tion of visually salient features. The feature-tracking algorithm
provides a good account of the phase dependence.
The field of first- and higher-order motion systems is not for the
faint-hearted, as it is easy to lose one's way in the maze of confus-
ing terminology, fine distinctions and even technical imperfections
(such as failure to drift-balance stimuli). Lu and Sperling (2001)
made a sterling effort to homogenize the field with a lengthy re-
view, complete with axioms, definitions and mathematical proofs.
But not all accept their demarcation zones or explanations, so it is
fair to say that there is no consensus in this sub-field of motion
perception, whose popularity rose so rapidly in the 1990s, and fell
with almost equal rapidity a few years ago.
3.4. Low- and high-level motion
As mentioned earlier, since the formal study of motion percep-
tion began, many different criteria have been used to classify mo-
tion stimuli. Besides the ith order type of motion, another useful
criterion to survive is the distinction between low- and high-level
motion. This is, of course, a somewhat imprecise and ambivalent
distinction: whereas the second and third order stimuli are defined
by their physical properties (in relation to the precise energy mod-
els of motion detection), low- and high-level stimuli refer to the
presumed site of analysis in the vision system of those particular
system. But despite this caveat, the distinction has proven to be
useful. As will be discussed in the following two sections,
measuring contrast thresholds of motion stimuli (often, but not
necessarily, of sine-wave gratings) seems to tap early neural levels
like V1. The assumption is that contrast-thresholding occurs lar-
gely in V1, as the physiology suggests (Boynton, Demb, Glover, &
Heeger, 1999; Sclar, Maunsell, & Lennie, 1990). Coherence thresh-
olds for random-dot kinematograms, on the other hand, seem to
tap higher-order processes, with much greater spatial and tempo-
ral integration (Burr, Morrone, & Vaina, 1998; Santoro & Burr,
Aptly termed by Vincent Walsh (2003) ''the psychologist's weapon of mass
D. Burr, P. Thompson / Vision Research xxx (2011) xxx–xxx
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1999). Motion aftereffects measured by motion coherence show
complete interocular transfer (suggesting higher-level analysis)
whereas tests with static stimuli showed very little transfer (Ray-
mond, 1993, see Section 9).
Although the theoretical basis of low- and high-level motion
stimuli is certainly questionable, the distinction has proven to be
useful, in the most unlikely circumstances. For example, schizo-
phrenic patients show impairment of motion coherence but not
contrast sensitivity thresholds (Chen, Nakayama, Levy, Matthysse,
& Holzman, 1999), implying compromise in higher level but not
low-level motion mechanisms. A similar result has been demon-
strated with infusion of the serotonergic hallucinogen psilocybin
(Carter et al., 2004), suggesting that, like schizophrenia, psilocybin
affects high-level motion processes. Interestingly, schizophrenic
patients also show weakened centre-surround processing of mo-
tion mechanisms (Tadin et al., 2006), presumably a higher-level
property (see further discussion of this technique in following
4. Segmentation and integration of motion signals
Reliable motion perception requires integration of signals over
large regions – to improve signal-to-noise levels – but also, in some
circumstances, not to integrate, but to segregate (see Braddick,
1993, for an excellent discussion of this issue). One obvious exam-
ple of this is the well known ''aperture problem'', discussed below.
An analogous problem occurs over time, in what is called the ''cor-
respondence problem'' (Julesz, 1971; Ullman, 1979): in a moving
random-noise kinematogram, which dots go with which? Locally
there exist many solutions while globally the problem becomes
much more constrained.
There is a good deal of evidence for integration of motion mech-
anisms. One clear example is what has been termed as ''motion
capture'', first described by Donald MacKay (1961), and further
studied by Ramachandran and Inada (1984, 1985): a field of dy-
namic random dots with no clear direction of motion can be ''cap-
tured'' by a moving frame, or low-frequency grating or even a
subjective contour. Other clear examples for segregation exist,
such as the fact that shapes can be defined by motion alone (Julesz,
1971), and ''pop-out'' of motion against stationary backgrounds
(Dick, Ullman, & Sagi, 1987).
As this review goes to press, a dramatic new demonstration of
the power of motion integration has been published. Suchow and
Alvarez (2011) show that objects changing in colour, luminance,
size or shape appear to stop changing when they are rotated alto-
gether (see demo on http://www.cell.com/current-biology/ab-
stract/S0960-9822(10)01650-7#suppinfo). The explanation for
this impressive demonstration is far from clear, but it seems It
seems plausible that this integration process subsumes all the
dynamic signals within the area, not only directional motion sig-
nals but also dynamic signals associated with changes in colour,
size or shape. Thus the individual colour changes of each dot are
not registered, but consumed within the global motion of the dots.
This demonstration points to the limits in our capacity to keep
dynamic change signals segregated while global motion mecha-
nisms are integrating over space and time (see also Burr, 2011).
4.1. The aperture problem – and plaids
Nowhere is the conflicting requirement for segregation and
integration more apparent than in the 'aperture problem'. Fig. 4A
redrawn from Hildreth (1983) illustrates the point. As a circle
moves horizontally to the right, the local changes in the image
can be in a very wide range of directions. Local measurements of
motion, such as must be taken by neurons with small receptive
fields can only indicate the motion perpendicular to the orientation
of the edge passing through its field. To determine the true global
motion of the object, local motions must be combined in some
way. The real problem here is for the system to know when to
combine motions so a global percept of a moving object emerges
and when to segregate these motions so we can resolve a moving
pattern from its background. Adelson and Movshon (1982)
this problem with a seemingly simple stimulus – two sinusoidal
gratings of different orientations moving therefore in different
directions. The question they asked was, under what conditions
will the two gratings slide one over the other transparently and
when will they cohere into a single 'plaid' pattern. Adelson and
Movshon's conclusions were really rather simple: seen in vector
space, each grating's motion is consistent with a family of motions
that lie along a line. Each motion has such a constraint line and
these two lines cross one another at 'the intersection of constraints'
(Fig. 4B). This point determines the single direction and speed of
motion that can satisfy both components of the plaid. And this
intersection of constraints appeared to predict rather well the
behaviour of the plaids, even in the case where the intersection
Fig. 4. (A) Illustration of the aperture problem (redrawn from Hildreth (1983)).
When a circle moves horizontally, the local movement of the contours may be in a
wide range of directions. If only the vector of motion perpendicular to the local edge
orientation is seen, the range of motions of the circle will extend from vertically
downwards through rightwards movement to vertically upwards. This gamut of
motion directions must be integrated to give the global movement. (B) The
intersection of constraints model of plaid motion (from Adelson & Movshon 1982).
Upper: A 45 degree grating with a motion vector perpendicular to its orientation is
ambiguous in that the size of the vector of motion parallel to its orientation is not
knowable. The dotted constraint line provides the locus of all the motion vectors.
Middle: When added to a second grating, orthogonal to the first and moving
upwards to the right, a single point marks the intersection of the two constraint
lines, which predicts correctly the perceived horizontal movement of the plaid.
Lower: A so-called 'type 2' plaid in which the intersection of constraints prediction
of motion lies outside the component vectors. This prediction is therefore, very
different from a vector sum or vector average model of plaid motion.
6 D. Burr, P. Thompson / Vision Research xxx (2011) xxx–xxx
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of constraints prediction is at odds with the vector sums of the
The question of where in the visual system these computations
are carried out has been examined at length. It might have been
thought that Adelson and Movshon's paper demonstrated every-
thing we needed to know about plaids, but not so. In the 1980s
and 1990s research on plaids reached epidemic proportions (rival-
ling that of second-order motion!); some have questioned the
intersection of constraints model suggesting that, when Fourier
and non-Fourier components are combined the vector sum or vec-
tor average of the components gives a more accurate estimation of
the direction of movement of the resulting plaid (Ferrera & Wilson,
1990; Wilson & Kim, 1994; Yo & Wilson, 1992), while others have
suggested a role for local features 'blobs' in the plaid patterns (e.g.
Alais, Wenderoth, & Burke, 1994; Bowns & Alais, 2006). Work from
Derrington has supported at least two of these models; Derrington
and Suero (1991) showed that reducing the perceived speed of one
of the components of a plaid by adaptation (Thompson, 1982)
shifts the direction of the plaid as a real reduction in the compo-
nent's speed would have. This finding and others (e.g. Welch,
1989) support the notion that the plaid velocity is based on the
computation of the component speeds. Derrington, Badcock, and
Holroyd (1992) came to a somewhat different conclusion when
they demonstrated that subjects were able to make direction dis-
criminations on plaids even when such discriminations could not
be made on the components.
Whether or not research on plaids has resolved how they are
processed in the visual system, one thing is clear: plaids exemplify
some of the real problems that we face in motion perception –
when should we integrate components into a single motion and
when should we segregate motions.
4.2. Integration and segregation mechanisms
One mechanism for integration over space is the simple linear
filtering incorporated into most modern models of motion energy
detection (see first section). These filters naturally blur together
all signals falling within their receptive fields. Psychophysical stud-
ies suggest that the size of the receptive fields of motion detectors
increase with velocity preference, and can be quite large, up to 8°
for low-frequency, fast-moving gratings (Anderson & Burr, 1987,
1991). The receptive fields also extend over time, for around
100 ms (Burr, 1981). But the situation is more complex than pre-
dicted by the spatial and temporal extent of the front-end filters.
There is also good evidence that motion signals from these front-
end Reichardt-like detectors are combined at a later, intermediate
stage of motion processing. For example, Yang and Blake (1994)
used a masking paradigm to show that low and high spatial fre-
quency information combine to mediate perception of coherent
motion of random-dot patterns. Using a different paradigm, Bex
and colleagues (2002) similarly showed that local-motion detec-
tors have narrow-band spatial frequency tuning while global-
motion detectors integrate across spatial frequency.
Indeed, it seems that in general, coherence thresholds for ran-
dom-dot patterns tap into a higher level of processing. For exam-
ple, detection thresholds for discriminating motion coherence
improve with exposure duration up to 3 s, compared with 100–
300 ms for contrast detection thresholds. The limit suggested by
temporal summation of contrast agrees well with the temporal
properties of neurones in primary visual cortex (Duysons, Orban,
Cremieux, & Maes, 1985; Tolhurst & Movshon, 1975). However,
integration times beyond 1 s are quite beyond what would be ex-
pected in primary cortex, implying the action of higher mecha-
nisms, such as prefrontal cortex, and the functional link with
area MT (Zaksas & Pasternak, 2006). Random-dot patterns also re-
veal spatial summation fields much larger than that revealed by
contrast sensitivity measurements, up to 70° (Burr et al., 1998),
particularly for flow motion (see next section).
It is important to note that although the motion system can
summate over large regions, the summation is not obligatory,
but under clear attentional control (Burr, Baldassi, Morrone, &
Verghese, 2009). When regions of moving stimuli are cued, the
non cued regions can be ignored, even when the cued regions are
not contiguous in space. This shows that the summation does not
reflect a large, inflexible receptive field of a high-level mechanism,
but flexible summation under attentional control. Indeed there is
evidence that summation between patches of motion stimuli is
more effective than within a single contiguous patch of compara-
ble area (Verghese & Stone, 1995; Verghese & Stone, 1996).
Not only is motion integration under voluntary control, but it is
strongly subject to contextual influences. One of the clearest dem-
onstrations of this is Lorenceau and Alais's (2001) diamond figure
orbiting behind an occluding surface (see Fig. 5 and demo: URL,
movie 9). Although the local signals within the separate apertures
have completely ambiguous direction, and in isolation will be seen
as motion following the aperture outline, the global impression is
of an orbiting diamond outline. However, when the stimuli within
the local windows are swapped, leaving the local stimulation pat-
terns unaltered but affecting the global solution, the pattern is per-
ceived as sliding motion rather a rotating diamond. In general, the
local motion components were perceived to move coherently
when they define a closed configuration, but not when they define
an open configuration. This demonstration provides yet another
example of the resourcefulness of the system in integrating motion
signals appropriately, depending on context. It also demonstrates
the tight links between form and motion perception (often consid-
ered to be independent ''modules''), where form provides a clear
veto for motion integration in the absence of closure.
It has long been known that motion summation, at least at
intermediate and higher levels, cannot be obligatory, as motion
can itself be a cue for scene segregation. For example, if within a
given region (such as a square) all dots move in a given direction,
whereas those outside the region are stationary, or oppositely
drifting, the square will clearly stand out (e.g. Julesz, 1971). The
resolution of motion as a cue to segregation is less than that of
luminance, but is nevertheless quite fine, in the order of 2
(Loomis & Nakayama, 1973; Nakayama, Silverman, MacLeod, &
Mulligan, 1985; Regan & Hong, 1990). Watson and Eckert (1994)
measured a ''motion-contrast sensitivity function'' by modulating
spatial bandpass noise with sinusoidally varying motion, both in
the direction of the edge (shear) and orthogonal to it, and deter-
mined the amplitude of the modulation that could be discrimi-
nated from dynamic noise as a function of modulation frequency.
For the highest spatial frequency bandwidth, the cut-off modula-
tion frequency was 4–6 c/deg, suggesting that, for the slow speed
(1 deg/s) studied, the smallest receptive field for a motion detector
was about 10
, or a half-period resolution of 5
: coarser than for
luminance modulation, but nevertheless very fine, highlighting
the capacity of the visual system to segment on the basis of veloc-
ity. Burr, McKee, and Morrone (2006) showed that motion-defined
resolution varied with both filter frequency and image speed, best
performance for unfiltered patterns moving at 1–4 deg/s, yielding a
stripe resolution of about 3
, corresponding well to estimates of
smallest receptive size of motion units under these conditions,
suggesting that opposing signals from units with small receptive
fields (probably located in V1) are contrasted efficiently to define
Tadin, Lappin, Gilroy, and Blake (2003) have described a clever
technique for investigating the neural mechanisms underlying the
segregation of motion signals. They use a variant of the summation
technique, varying the size of visual stimuli and measuring direc-
tion discrimination thresholds (by varying exposure duration).
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Their counterintuitive result is that for high-contrast stimuli,
increasing the size of the stimulus (over about 3°) decreases sensi-
tivity for direction discrimination. Large stimuli are also less effec-
tive for inducing the motion-after effect (see also Section 9). They
suggest that these results reflect the action of centre-surround
neural mechanisms, like those that have been described for area
MT (Born, Groh, Zhao, & Lukasewycz, 2000; Born & Tootell, 1992)
and MSTl (Eifuku & Wurtz, 1998): large stimuli activate the inhib-
itory surround, weakening the response of these units. Further
studies using the reversed correlation technique reveal more about
the spatial and temporal properties of these suppression mecha-
nisms (Tadin et al., 2006).
4.3. Motion transparency
An important practical example of where motion segregation is
essential is motion transparency, the capacity to see a foreground
field slide over a stationary or differently moving background. This
requires the visual system to represent multiple motions in the
same part of the visual field. A trilogy of papers in 1994 made an
important contribution to our understanding of the psychophysics,
physiology and computational modelling of transparency (Qian &
Andersen, 1994; Qian, Andersen, & Adelson, 1994a, 1994b). The
first paper studied the psychophysics of transparency. They de-
vised a clever but simple stimulus in which two patterns of pseu-
do-randomly positioned dots moved in opposite directions over
the same region. When the patterns were constrained so the
motion signals were locally opposed (paired), there was no percep-
tual impression of transparency (URL: movies 7 and 8). To produce
transparency, it was necessary for the displays to have locally
unbalanced motion signals, with some micro-regions containing
motion in one direction, others in the other direction. This, more
than any other example, demonstrates the incredible flexibility of
the motion system to integrate or segregate. Provided there are
some regions with net motion in a given direction, the system
can segregate these from those moving in the other direction,
and then integrate these disparate regions to yield one or more
coherent surfaces moving in particular directions.
In the second paper, Qian and Andersen (1994) studied how
cells in V1 and MT respond to these types of patterns. In general,
V1 cells do not distinguish between the stimulus conditions where
the dots of opposite motion direction were constrained to fall
within a local region (paired), and where the patterns contained lo-
cally unbalanced signals (unpaired). MT cells, on the other hand,
reliably distinguished between the two conditions, responding
well only to the non-paired stimuli. They suggest that this is
consistent with a two-stage model. The first stage, like a simple
Reichardt detector responding only to motion energy, corresponds
well to the behaviour of V1 cells. The second stage, like the combi-
nation of Reichardt detectors illustrated in Fig. 2, introduces local
inhibition between opposing directions of motion within a local re-
gion. This stage presumably has a function of noise suppression,
and preventing flicker producing a sense of motion. fMRI studies
have revealed similar differences in humans: V1 responds more
strongly to counterphase flicker (the sum of two opposed drifting
gratings) than to a single drifting grating, but for MT the reverse
is true (Heeger, Boynton, Demb, Seidemann, & Newsome, 1999).
What remains to be explained, of course, is how the signals of
directed motion – some leftward others rightward – combine
appropriately with each other to yield the impression of a surface
in motion. This clearly recalls the idea of ''common fate'' of Wert-
heimer (1912). What it points to, however, is a very clear example
of how the visual system needs to segregate stimuli on the basis of
their direction of motion, and then to integrate these same signals.
No linear system can fulfil both requirements at the same time.
Some intermediate non-linearity – which we can describe as a fea-
ture extraction – is necessary.
There is also evidence (Del Viva & Morrone, 2006; Meso &
Zanker, 2009) that transparency is determined by ''phase congru-
ency'' (which to a large extent govern visually salient features: Mor-
rone & Burr, 1988). When two extended patterns with clear features
drift in opposite directions (for example two square waves), those
Fourier components in the composite, bidirectional stimulus that
are not coherent in phase are seen to drift in transparency (demo).
To model the effect it is necessary to introduce an oriented spatio-
temporal filter that operates on the output of a feature-extraction
model selective to phase congruency. With this scheme, pooling
of motion signals occurs between components that give rise to fea-
tures, while segregation for the transparency is achieved by analys-
ing the trajectories of the features along fixed directions.
Fig. 5. Integration of local-motion signals depends on spatial form. This demonstration (that can be seen on www.xxxxxxx) is a simulation of a diamond pattern (left) or cross
(right) orbiting behind two vertical apertures (illustrated by the dark stripes). At left, global motion is seen, of a diamond pattern coherently orbiting behind the apertures. At
right observers perceive local vertical motion within the stripes. The only physical difference between the two stimuli is that the two stripes have been swapped. Lorenceau
and Alais (2001) suggest that the diamond is perceived coherently because it is a closed, convex shape whereas the cross is not and triggers a form-based veto of global
motion integration.
8 D. Burr, P. Thompson / Vision Research xxx (2011) xxx–xxx
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5. Optic flow and complex motion
The flow of optical images on our retinae produced by motion
through the environment provides a rich source of visual informa-
tion, fundamental for many functions such as ''heading'' and naviga-
tion through complex visual environments. Optic flow can be
decomposed into several bases functions, including radial, circular,
translation and sheer (Helmholtz, 1858; Koenderink, 1986). In the
early 1990s, several different groups described neurones in the dor-
sal portion of the medial superior temporal cortex (MSTd) of maca-
que monkeys that respond selectively to individual flow
components (such as circular or radial motion), or combinations
of them (Duffy & Wurtz, 1991; Graziano, Andersen, & Snowden,
1994; Orban et al., 1992; Tanaka, Fukada, & Saito, 1989; Tanaka &
Saito, 1989). In the adjacent area MT neurones are also selective
to motion, but respond well only to simple translational motion of
appropriate velocity, not to circular or radial motion. The functional
importance of MST to heading is underlined by the demonstration
that micro-stimulation of MST neurones influences the direction
of heading of a behaving monkey (Britten & van Wezel, 1998; see
also Wurtz, 1998). Area MST is not the only area that responds to op-
tic flow: other areas in the parietal lobe, such as the ventral intrapa-
rietal cortex (VIP) and area 7a are both sensitive to flow stimuli
(Read & Siegel, 1997; Schaafsma, Duysens, & Gielen, 1997).
The single-cell physiological studies outlined above provide
very clear evidence for the existence in non-human primates of
specific neural mechanisms tuned to optic flow motion. These
studies are reinforced by many psychophysical studies pointing
to the existence of analogous neural units in humans. In the late
'70s, Regan and Beverley (eg 1978, 1979) conducted a series of
important studies, suggesting the existence of specialized detec-
tors for motion in depth, or ''looming detectors'' as they became
termed (see also Freeman & Harris, 1992). However, it is not clear
that the adaptation and masking techniques that they adopted
necessarily probe the higher level areas like MST, as they will also
affect earlier areas like V1 and MT, which can complicate the inter-
pretation of results.
More recently Morrone, Burr, and Vaina (1995) provided more
direct evidence for mechanisms in humans that integrate local-
motion signals along complex, optic-flow trajectories. They
measured coherence thresholds for discriminating the direction of
radial, circular and translational motion in a limited lifetime, ran-
dom-dot stimulus. The stimulus dots were curtailed to a variable
number of symmetrically-opposed sectors: increasing the number
of exposed sectors increased the area of the motion stimulus.
Thresholds increased with stimulus area, by the amount expected
from ideal summation of the motion signals within the sectors.
Importantly, for radial and circular motion, the local direction in
the displayed sectors was maximally different, either opposite or
orthogonal. Nonetheless, the system integrated optimally the lo-
cal-motion signals of different directions, pointing to mechanisms
– like the cells of area MSTd – that integrate local-motion signals
along complex optic-flow trajectories. The integration under these
conditions was obligatory, as adding noise to the non-signal sectors
reduced sensitivity predictably. Interestingly, contrast sensitivity
measures did not reveal the same sort of summation trends. The
results were interpreted as implying two levels of analysis, a lo-
cal-motion analysis limited by contrast thresholds (probably V1),
followed by a system that integrates flow information (similar to
MSTd). Note that although the integration in these conditions was
obligatory, later studies showed that the integration was under
attentional control (Burr et al., 2009), pointing to very flexible
integration mechanisms.
Snowden and Milne (1996, 1997) provided further evidence for
optic-flow mechanisms, showing that adapting to, say, radial mo-
tion vignetted behind a radial mask, causes a strong aftereffect
when the adjacent regions (that had previously been masked) are
viewed. No local detectors visible on viewing the aftereffect had
been adapted, so the adaptation must be at the level of a global,
integrating unit. Other evidence for a hierarchical processing of
motion, from local signals to flow motion, is that radial and circular
motion appears faster than translational motion (Bex, Metha, &
Makous, 1998), and the aftereffects for this type of motion are
stronger and longer lasting than for translation (Bex, Metha, &
Makous, 1999).
In agreement with the neurophysiological studies, psychophys-
ical summation studies suggest that these units have very large
receptive fields (Burr et al., 1998), and summate information over
lengthy periods, 1 or 2 s (
Santoro & Burr, 1999). There is also some
evidence in humans for selectivity along ''cardinal directions'' of
optic flow – radial and circular motion – (Burr, Badcock, & Ross,
2001; Morrone, Burr, Di Pietro, & Stefanelli, 1999) although not
all results point in this direction (Snowden & Milne, 1996). Imagin-
ing studies in humans also suggest that flow motion is analysed by
a specialized region within the human MT complex (Huk,
Dougherty, & Heeger, 2002; Morrone et al., 2000).
Finally, neuropsychological observations seem to confirm the
evidence for the existence of specialized flow detectors in humans,
and suggest that they are anatomically distinct from other motion
areas. Lucia Vaina and colleagues (Vaina & Cowey, 1996; Vaina & Sol-
oviev, 2004) have reported two cases with bilateral occipital-parie-
tal lesions who present with clear deficits in optic flow perception,
including heading and radial motion. Both patients performed well
on other visual tasks, such as direction discrimination and percep-
tion of two-dimensional form from direction or speed differences.
During the period of this review there has accumulated a vast
body of evidence from electrophysiology, psychophysics, imaging
and neuropsychology studies pointing to the existence in primates
of motion detectors specialized for the analysis of optic flow. This
information is used by the visual system for a variety of functions,
most importantly in helping us navigate through complex visual
environments. How optic flow information is used for heading,
and how it combines with other non-visual information is an
important topic, but one that goes beyond the scope of this review.
The interested reader is referred to Warren's (2004) excellent
6. Appearance of objects in motion: motion blur and speedlines
One of the more important consequences of the filter motion-
models discussed in Section 2 was to provide a basis for an expla-
nation of the appearance of objects in motion, not merely the fact
that they move in a certain direction and speed. Many of the mod-
ular models of vision assume that form and motion are processed
separately, by different brain areas (e.g. Marr, 1982; Mishkin,
Ungerleider, & Macko, 1983; Zeki, 1993). While this may or may
not be to some extent true (see for example Burr, 1999; Lennie,
1998), motion and form are clearly interconnected. The most obvi-
ous example is ''biological motion'' (see Blake & Shiffrar, 2007),
where it is the motion that defines the form. But even for simple
objects in motion, the mechanisms that analyse their form must
be capable of taking into account the motion.
6.1. Motion blur
One very basic aspect of form analysis of moving objects is that
they do not seem to be as smeared as would be expected on a sim-
ple ''camera analogy'' (Burr, 1980). Early visual mechanisms inte-
grate information for around 100 ms (Barlow, 1958), even for
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objects in motion (Burr, 1981). This integration may be expected to
smear the images over time, like opening the shutter of a still cam-
era for this period. The trick is, however, that motion mechanisms
are tuned to the motion and hence oriented in space–time (Fig. 3).
This means that they do not simply integrate over time, but they
integrate in the direction of the receptive field in space–time.
The spatial structure of the image in motion is analysed not normal
to the space axis (as static objects would be) but normal to the axis
of slant of the spatio-temporal receptive field (see also Burr & Ross,
1986, and Fig. 3). That is, they effectively rotate space–time, effec-
tively annulling the smearing effects of the motion. The relevant
smear is not given by the duration over which these detectors
spread, but by the width normal to their axis. Detectors not tuned
to the motion cannot do this, and will cause smear much the same
as a still camera will. Since these initial experiments, a great deal of
work has been done on motion smear, largely by Beddel and his
group, showing that many factors contribute to smear, such as
the presence of multiple rather than single targets (Chen, Bedell,
& Ogmen, 1995), and pursuit eye movements (Bedell, Chung, &
Patel, 2004; Tong, Stevenson, & Bedell, 2008).
6.2. Motion streaks
It turns out that there another side to the motion-smear coin,
one that has come to be known as ''motion streaks'', or ''speed-
lines''. About 12 years ago Wilson Geisler (1999) pointed out that
the motion streaks left behind by moving stimuli provide poten-
tially important information about the direction of motion, partic-
ularly in conditions where direction can be ambiguous as a result
of the aperture problem. He pointed out that moving objects of fi-
nite size will stimulate two classes of cell: those tuned to the direc-
tion of motion, but also cells without motion tuning, oriented
orthogonally (in space–space) to the direction of motion (see
Fig. 6). He proposed a simple model where the broad-motion and
stationary direction-selective units could be multiplied together.
Around this time, Ross and colleagues (2000) reported a new
motion illusion in which random sequences of glass patterns (pairs
of dots all aligned in a coherent fashion, to form global patterns)
appear to move in coherent directions, following the direction of
the dot pairs (URL: see movies 2 and 3). There is no actual motion
energy in this direction and it is easy to show that the motion en-
ergy is completely random. Indeed, if the motion detectors have an
orientation preference orthogonal to their preferred direction of
motion, then the motion should be orthogonal to the pattern, yet
it is seen clearly to follow in the same direction as the spatial form,
parallel, not orthogonal to the dot pairing. Ross et al. (2000) ini-
tially explained the illusion in terms of a high level interaction be-
tween form and motion channels. While this is possible, they also
considered the possibility that the illusion results from the dot
pairs stimulating the Geisler motion streak, or ''speed-line'' mech-
anisms. The randomly positioned dot pairs should generate a
strong, but non-coherent sense of motion, equally strong in all
directions, exciting many broadly tuned motion detectors of the
type shown in Fig. 6. However, only very limited classes of static,
orientation-selective neurons will be stimulated, those parallel to
the dot-pair alignment. This mechanism will signal local motion
parallel to the direction of dot alignment (in both directions),
which will lead to global coherent motion that follows the coher-
ent glass pattern. Interestingly, the apparent direction of motion
of these glass patterns is not fixed, but alternates, as would be ex-
pected by the random changes in average motion energy.
Much evidence, both psychophysical and neurophysiological,
has accumulated in favour of motion streaks. Burr and Ross
(2002) showed that noise or Glass patterns oriented near the direc-
tion of motion strongly degrade motion discrimination thresholds.
Furthermore, motion induced by glass patterns adds vectorially
with real motion, suggesting that common mechanisms are being
stimulated (Krekelberg, Dannenberg, Hoffmann, Bremmer, & Ross,
2003). The streaks left by fast motion interact with stationary ori-
ented patterns in interesting ways, causing motion aftereffects and
tilt illusions (Apthorp & Alais, 2009), raising contrast thresholds in
an orientation-specific manner (Apthorp, Cass, & Alais, 2010) and
even causing orientation-selective suppression in rivalry (Apthorp,
Wenderoth, & Alais, 2009).
There is also good electrophysiological evidence that motion
streaks activate neurons in early visual cortex. Geisler and col-
leagues (2001) reported that cells in V1 of cat and monkey respond
to dot motion orthogonal to their preferred direction (producing
''motion streaks'' parallel to their preferred orientation), and that
the relative strength of the response to this direction increases
Fig. 6. ''Speedlines'' in human vision. (A) Cartoonists have long used the device of ''speedlines'' to indicate motion (introduced by Rudolph Dirks in his Katzenjammer kids'').
More recently, Greek artist Kostas Varotsos has produced three-dimensional motion streaks in this famous statue ''the runner'' (1988). The impression of fast motion is
unmistakeable. (B) Stylized illustration of Geisler's (1999) ''motion streak'' model. The output of a neuron, or population of neurons, with spatially oriented receptive fields
but no direction tuning (above) is combined with broadly directionally selective cells of orthogonal tuning. The spatially oriented, ''non-motion'' unit greatly enhances the
direction selectivity of the motion detection unit. It has been suggested that mechanisms of this type lead to the sense of coherent motion from randomly draws of glass
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with stimulus speed. Just as dynamic glass patterns (that contain
no coherent motion energy) are seen by humans to move coher-
ently (Ross et al., 2000), they also stimulate cells in the superior
temporal sulcus (STS) of monkey (Krekelberg et al., 2003). The
direction preference of these STS cells was tuned for both real
and ''implied'' motion, and to combinations of them, suggesting
that these cells did not distinguish between them. Taken together
these results suggest that the implied motion streaks of dynamic
glass patterns generate motion signals in early visual cortex, to
which the cells in STS respond, in the same way that they do to real
motion signals.
Evidence from imaging studies suggests that implied motion
from dynamic random glass patterns stimulates human motion
areas (Krekelberg, Vatakis, & Kourtzi, 2005). Furthermore, adapta-
tion to implied motion transferred to real motion in dorsal motion
areas, suggesting that the same sub-population of neurons is selec-
tive to both real and implied motion. Other areas, such as the lat-
eral occipital complex, did distinguish between real and implied
motion. Apthorp and colleagues (Apthorp et al., 2010) have re-
ported direct imaging evidence for encoding of motion streaks in
human visual cortex. They trained a multivariate classifier on sta-
tionary oriented stimuli. This classifier was then able to detect reli-
ably the direction of fast (''streaky'') motion, but not slow motion,
in many early visual areas, including V1. All the evidence suggests
that the streaks are real, and aid in encoding motion direction.
If nothing else, the studies on motion streaks have illustrated
the resourcefulness of the visual motion system, to use all available
information – even a cue that might normally be thought of as a
hindrance to motion perception rather than a feature – to help it
uncover the direction of moving objects and solve the aperture
7. Influence of motion on position and space
The previous sections show strong interactions between motion
and form processing in human vision. This section explores studies
showing how motion also has a profound influence on perceived
position of objects.
7.1. The ''flash-lag'' illusion
Perhaps the clearest and best known example of motion influ-
encing the perceived position of a target is the ''flash-lag'' illusion:
a stimulus moving continuously seems to be advanced compared
with the position of a briefly flashed light. It is one of the more ro-
bust visual illusions, easily demonstrated in the classroom under
almost any lighting conditions (demo). For example, you can
mount a translucent card in front of a photographic flash and move
it around in normal lighting, periodically setting off the flash: the
flash seems to lag behind the moving card.
The illusion dates back at least to the 1930s, when Metzger
(1931) reported that rotating stimuli seemed to move ahead of
brief flashes of the stimulus moving behind adjacent slits. Donald
Mackay rediscovered the effect by observing that under strobe-
lighting, the glowing head of a moving cigarette moved ahead of
the base (Mackay, 1958). But Nijhawan's (1994) recent rediscovery
and new interpretation of the illusion has spurred a surge of inter-
est, largely because the neural mechanisms of motion perception
are now much better understood, and we have more robust basic
models to build on. Nijhawan's original explanation was interest-
ing, couched in terms of a solution to an inherent problem of using
dynamic perception to guide action. Given the various delays in
processing visual stimuli, from photo-transduction onwards, the
system is always working with information that is at least
100 ms old. Therefore, in order to judge the position at the present
time it is necessary to extrapolate the motion trajectory and this,
he claimed, was why a moving target seems to lead a flashed sta-
tionary one. Certainly a good idea, but it has not stood up to rigor-
ous testing. Perhaps the most direct test of extrapolation was to
measure the effect when the moving stimulus stopped abruptly
or changed direction or speed: an extrapolated trajectory goes be-
yond the reversal point, but this was not observed experimentally
(Brenner & Smeets, 2000; Whitney, Cavanagh, & Murakami, 2000;
Whitney & Murakami, 1998; Whitney, Murakami, & Cavanagh,
2000). Further evidence against the extrapolation hypothesis is
that in order to compensate for neural latencies, the magnitude
of the effect should scale with latency. For example, at low lumi-
nance (which increases latency), the effect should increase, but
in practice it diminishes (Krekelberg & Lappe, 1999) or even re-
verses (Purushothaman, Patel, Bedell, & Ogmen, 1998).
The failure of the extrapolation hypothesis led Whitney and
coworkers to suggest another simpler explanation, the ''differential
latency hypothesis''. Put simply, they claim that the lag of the flash
occurs because the visual system responds with shorter latency to
moving than to flashed stimuli, providing good evidence that the
magnitude of the effect was determined by time, rather than dis-
tance. While this explanation has the appeal of simplicity, it again
fails to account for many of the complexities of the flash-lag phe-
nomenology. For example, increasing the number of flashes (in a
repetitive sequence), or the duration of the flash leads to a
reduction in the magnitude of flash-lag (difficult to reconcile with
a simple latency). Furthermore, the flash-lag effect is far more gen-
eral than was originally thought. Indeed, it does not require that
objects actually move in space, but can change in other dimen-
sions, such as colour or luminance (Sheth, Nijhawan, & Shimojo,
2000), and even works for streams of changing letters (Bachmann,
Luiga, Poder, & Kalev, 2003; Bachmann & Poder, 2001).
Murakami (2001) devised a particularly clever adaptation of the
flash-lag effect. Rather than using continuous motion, bars were
presented in random positions over time, and subjects judged
whether they appeared to the left or right of a marker; again, this
produced a robust flash-lag effect, with the additional advantage of
being an objective technique, not possible to predict by cognitive
reasoning. These results were difficult to reconcile with theories
such as interpolation or spatial averaging, but did seem reasonably
consistent with differential latencies. Whatever the explanation
the flash-lag effect may be, it appears to have one crucial conse-
quence in everyday life; Baldo, Ranvaud, and Morya (2002) pro-
vided convincing evidence that soccer assistant referees' errors in
flagging offsides are consistent with the flash-lag effect influencing
their decisions.
The flash-lag illusion is not restricted to vision. Analogous phe-
nomena occur in audition, both for moving sound sources and
''chirps'', sounds that increase or decrease in pitch over time (Alais
& Burr, 2003). Indeed the magnitude of the effect is much greater
than in vision, up to 200 ms compared with the far more modest
20 ms in vision. Flash-lag phenomena also occur cross-modally:
probing auditory motion with a visual flash and vice versa. For
these effects differential latencies seem particularly implausible.
Indeed Arrighi, Alais, and Burr (2005) tested the latency hypothesis
directly and showed not only that the latencies are insufficient to
explain the measured flash-lag results, but actually go in the wrong
Despite the enormous research effort expended on the flash-lag
effect, no single clear explanation has emerged. Most agree that
neural latencies per se are not the explanation, but it is still far
from clear what mechanisms lead to the perceived delay. The de-
bate about whether the flash-lag illusion is one of space or time
is probably misconceived. When objects are in motion, space and
time become inseparable (see Fig. 3). The complete explanation
of the flash-lag effect almost certainly needs to be couched in
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terms of space–time, rather than trying to treat the two dimen-
sions separately.
In the end the flash-lag effect has probably opened more prob-
lems than it has solved. In particular it has raised the general ques-
tion of how time and temporal order is encoded in the brain, which
has proven to be an extremely profitable line of research: but
unfortunately well outside of the scope of this review.
7.2. Effect of motion on perceived position
Observe a grating drift behind a stationary window, and the
window appears to be displaced in the direction of the motion.
The effect, described by De Valois and De Valois (1991), is extre-
mely compelling, with shifts up to 15 min for low-frequency grat-
ings drifting at 4–8 Hz (URL: movie 10). A similar effect had been
described by Matin, Boff, and Pola (1976), who showed that two
opposed line segments rotating around a common point appear
to be offset in the direction of rotation. Ramachandran and Anstis
(1990) also reported that random dots moving within a stationary
window displace the position of the window, and that the effect is
strongest when the patterns are equiluminant. All these demon-
strations go to show that motion affects space perception: position
and motion are not completely independent for the brain. It is still
not exactly clear how this occurs, but presumably it is related to
the signal that spatio-temporal receptive fields of the type shown
in Fig. 3 give about the location in space of objects stimulating
About the same time, Snowden (1998) and Nishida and
Johnston (1999) went onto show that motion can distort posi-
tion indirectly, via the motion aftereffect. After viewing a drift-
ing grating (or rotating windmill) for some seconds, a grating
patch displayed to the adapted region seems to be displaced
in the direction of the motion aftereffect. Interestingly, the spa-
tial distortions caused by motion extend beyond the range of
the moving stimulus. Whitney and Cavanagh (2000, 2002)
showed that moving stimuli affect the perceived position of
stimuli briefly flashed to positions quite remote from the mo-
tion; they also influence fast reaching movements to stationary
objects (Goodale, in press; Whitney, 2002; Whitney, Westwood,
& Goodale, 2003; Yamagishi, Anderson, & Ashida, 2001). Very
brief motion displays are sufficient to create large spatial dis-
tortions, maximum at motion onset, suggesting very rapidly
adapting mechanisms (Roach & McGraw, 2009). Interestingly,
the spatial distortions produced by motion and by adapting to
motion are clearly distinguishable from the classical motion
aftereffects. Whitney and Cavanagh (2003) have demonstrated
clear shifts in spatial position, with no corresponding afteref-
fect. McKeefry, Laviers, and McGraw (2006) have more convinc-
ing evidence: while the motion aftereffect is chromatically
selective, not transferring from one colour to another, or from
colour to luminance, motion-induced spatial distortions were
completely insensitive to chromatic composition. The dissocia-
tion between chromatic selectivity of aftereffects suggested that
chromatic inputs are segregated during initial analysis, but are
later integrated, before the site where motion affects spatial
The studies reviewed in this section show that form, motion and
position cannot be thought of in isolation. Form can influence mo-
tion – most clearly shown in the ''motion streak'' studies – and mo-
tion can influence form, in reducing blur in moving objects and in
strongly affecting the perceived position of objects in motion and
objects flashed near moving stimuli. Although the debate often
stagnates on issues like whether the effects result from distortions
to space or to time, it should be now clear that space and time are
not neatly separable for motion, so the distinction is moot.
8. Perception of speed
8.1. Models of speed perception
This review started by discussing several models of motion per-
ception that heralded the era we are reviewing. These models
proved very successful in detecting the direction of motion, with
much more limited success in judging speed. A key element of
these models is a low-level motion filter, selective for spatial fre-
quency, orientation and direction of motion could be construction
from non-selective components. As discussed earlier these models
were basically very similar, but subtly different, particularly in
how they might encode speed information. Watson and Ahumada
showed that a collection of their linear filters might be combined
into a 'vector motion sensor' that can estimate speed and direction
while Adelson and Bergen combined the linear filters to compute
motion energy.
The Adelson and Bergen spatio-temporal energy model, in its
simplest incarnation, suffers from the fact that changes in velocity
cannot be discriminated from changes in contrast. This issue was
addressed directly by them in a following paper where they noted
that ''at a given spatial frequency, the value of an energy measure
is a function of both the velocity and the contrast of the stimulus
pattern'' (Adelson & Bergen, 1986). They proposed that one solu-
tion to this problem might be to compare the relative outputs of
a set of spatio-temporal energy detectors with different broad tem-
poral frequency tuning. Specifically a group of three detectors, one
tuned to leftward (L), one to rightward (R) and one for static (S) en-
ergy might be compared as (R L)/S to give a monotonic change in
response with velocity. This normalisation scheme has many
attractions, not least that the opponent energy measure (R L)
has a long history of being a convenient mechanism to explain
the movement aftereffect, stretching back to Sutherland (1961) if
not Exner (1888). And, as noted by Adelson and Bergen (1986) such
an opponent energy measure can be extracted by Reichardt detec-
tors (Fig. 2).
The Watson and Ahumada (1985) model achieves a contrast
invariant measure of velocity in a somewhat different way; their
scalar sensors are combined into groups that share location and
spatial frequency, but which differ in preferred direction. By reading
out the temporal frequency response of these vector motion sensors,
an unambiguous measure of velocity may be derived, as velocity is
merely temporal frequency divided by spatial frequency.
8.2. Effect of contrast on perceived speed
It is now known that the perception of velocity is not entirely
independent of contrast; this was reported by Thompson (1976,
1982) and has been confirmed on many occasions since (Blake-
more & Snowden, 1999; Brooks, 2001; Hurlimann, Kiper, & Caran-
dini, 2002; Muller & Greenlee, 1994; Stocker & Simoncelli, 2006;
Stone & Thompson, 1992). Even reaction times to motion onset,
long known to depend on stimulus speed (Tynan & Sekuler,
1982), are influenced by stimulus contrast so they depend on per-
ceived, not physical speed (Burr, Fiorentini, & Morrone, 1998).
Any model of motion perception must make a comparison be-
tween elements tuned to different aspect of the stimulus, to
generate motion invariance. The earliest models, now termed 'ratio
models' were originally invoked to explain the motion aftereffect
(Barlow & Hill, 1963; Exner, 1894; Sutherland, 1961) but ratio
models have also been suggested in a slightly different form as a
model of speed coding. Tolhurst, Sharpe, and Hart (1973) sug-
gested that speed might be determined by taking the ratio of the
movement-analysing and pattern-analysing channels and this idea
was echoed by Thompson (1982) to account for the dependence of
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speed on contrast. A more rigorously defined version of a ratio
model was outlined by Harris (1986) who refined the motion
detector proposed by Marr and Ullman (1981). Essentially Harris
takes the ratio of putative pattern and flicker channels to derive
a signal that varies linearly with speed.
More recently Heeger (1987) developed the models based on
spatio-temporal filtering to tackle the problem of extracting veloc-
ity information in a range of moving stimuli from sine-grating
plaids (Adelson & Movshon, 1982), moving random dot fields to
a computer-generated flight through Yosemite valley. Heeger
exploited the fact that in the spatio-temporal frequency domain
the power spectrum of a one-dimensional signal velocity is repre-
sented a straight line whose slope corresponds to velocity. Extend-
ing this to two dimensions the velocity of a 2-D texture will be
represented by a tilted plane. Heeger's model uses a 'family' of mo-
tion-energy filters; in the particular implementation in the 1987
paper he envisages twelve energy filters, eight of which are most
sensitive to a particular direction of motion and four of which
are most sensitive to stationary patterns of different spatial
Heeger's model performs impressively in extracting image
velocity as well simulating some well-established psychophysical
findings, and has physiological plausibility with velocity-tuned
units envisaged at the level of MT. A slightly different approach
was taken by Grzywacz and Yuille (1990) in their computational
model of velocity coding in the visual cortex. Like Heeger (1987)
they took as their starting point the computation of motion ener-
gies. However they identified a number of weaknesses in Heeger's
model including the assumption of a flat power spectrum which
limits the range of stimuli for which the Heeger model estimates
velocity correctly, and the biological plausibility of Heeger's com-
putational requirements. Grzywacz and Yuille show that a popula-
tion of spatio-temporal filters needs to be decoded simultaneously
to measure local velocity and that 'pattern' cells in MT are suitable
candidates for this task. Thus, they argue, the role of MT is more
likely to be velocity estimation with motion coherence taking place
later in the visual pathway.
The models of Heeger (1987) and Grzywacz and Yuille (1990)
were further developed by Simoncelli and Heeger (1998). Again
this is a two-stage model with V1 seen as the site of direction tun-
ing while MT extracts velocity information. A further refinement of
this model is described in Rust, Mante, Simoncelli, and Movshon
(2006). These computational models appeal to existing neuro-
physiological and psychophysical findings and a full description
of them is beyond the scope of this review. An excellent summary
of velocity computation in the primate visual system is to be found
in Bradley and Goyal (2008).
8.3. The Bayesian approach
Any model of speed processing uses departures from veridical
perception to inform the model. A very different approach to inter-
pret these departures has emerged that appeals to Bayesian statis-
tics. Ascher and Grzywacz (2000) proposed one such model that
the authors felt was more realistic than the motion-energy models
that used non-causal temporal filters and flat spatial spectra – both
properties that Ascher and Grzywacz felt were 'unrealistic'. Key to
this model and others developed around the same time was the be-
lief that the prior distribution of velocities in the natural world is
not flat, but biased towards slow speeds (Ullman & Yuille, 1989).
Weiss and Adelson (1998) and Weiss, Simoncelli, and Adelson
(2002) extended the Bayesian model to provide a more rigorous
instantiation of Helmholtz's dictum that given the inherent ambi-
guity of visual information, it is the job of our perceptual system to
make the best guess about the visual world (see also Stocker &
Simoncelli, 2006). Thus if objects are more likely to be moving
slowly rather than fast, then a 'slow prior' should apply. And the
noisier the signal the more influence the prior should have. Indeed
the authors propose that ''in the absence of any image data the
most probable velocity is zero'' (Weiss et al., 2002, p. 599). Intrigu-
ingly there is good evidence that increasing noise in the visual sys-
tem by means of repetitive transcranial magnetic stimulation
(rTMS) of areas V3A and MT+ has the effect of decreasing perceived
speed (McKeefry, Burton, Vakrou, Barrett, & Morland, 2008).
One persuasive aspect of this Bayesian model is that the appar-
ent decrease in speed of low contrast stimuli (Thompson 1982)is
entirely to be expected. Furthermore the influence of contrast on
perceived direction of moving plaids (especially type 2 – Fig. 4B)
and lines can be accounted for. Weiss et al. (2002) conclude:
''...we believe the underlying principle will continue to hold: that
many motion 'illusions' are not the result of sloppy computation
but rather the result of a coherent computational strategy that is
optimal under reasonable assumptions''. No one has given better
advice to anyone studying visual 'illusions'. One note of caution
might be that there are counter examples that the Bayesian model
is less able to accommodate: reducing contrast does not always
lead to a reduction in perceived speed. Gegenfurtner and Hawken
have ample evidence that at higher rates of motion reducing con-
trast has little effect on perceived velocity, while Thompson,
Brooks, and Hammett (2006) believe it can actually result in an in-
crease in speed. Furthermore reducing luminance, which must
surely reduce image data, can also increase perceived speed (Ham-
mett, Champion, Thompson, & Morland, 2007).
An example of where the Bayesian approach has been applied
with great success is in predicting the perceived speed from a mix-
ture of retinal and extra-retinal movement, during pursuit eye
movements. Freeman, Champion, and Warren (2010) show that
combining two separate Bayes estimates at relatively early stages
of visual processing, one for retinal motion and one for the pursu-
ing speed, predicts well the perceived speed of pursued targets.
8.4. The contribution of colour to speed
During the 1980s there was increasing evidence for separate
sub-systems in the primate visual pathway. The X and Y cell divi-
sion in the cat (Enroth-Cugell & Robson, 1966), which became
associated with the 'pattern' and 'flicker' channels in humans
(1973), now became a division between the parvocellular and
magno-cellular pathways. Drawing on the neuro-physiological
observations of Zeki (1978), Zeki (1980) and others, Livingstone
and Hubel (1987) drew clear distinctions between the properties
and roles for these two visual streams. The magno-cellular path-
way was identified as a colour-blind motion pathway. This conclu-
sion was in part based on the finding that at equiluminance (also
more clumsily known as iso-luminance), when the response of
the magno-cellular pathway would be minimal, perceived velocity
is very much reduced (Cavanagh, Tyler, & Favreau, 1984a;
Ramachandran & Gregory, 1978). However, there is also evidence
that motion perception is not always colour-blind. This has been
demonstrated in a series of papers by Cavanagh and colleagues
(e.g. Cavanagh et al., 1984a; e.g. Cavanagh, Boeglin, & Favreau,
1985) In one of these, Cavanagh and Anstis (1991) opposed a drift-
ing luminance grating and a colour grating and, by adjusting the
luminance contrast found the null point where the resulting count-
erphase grating appear to drift in neither direction – giving them
the equivalent luminance contrast of the colour grating. Their re-
sults suggested that there was an important contribution of colour
to the perception of motion.
Further evidence has come from Hawken, Gegenfurtner, and
Tang (1994) who argued that if there is a single motion pathway
that receives both luminance and chromatic information then the
dependence of relative perceived speed on relative contrast
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(Thompson, 1982) should be the same for both types of stimuli.
However their results show a very different relationship, with
equiluminant stimuli having a much steeper contrast dependence
than the luminance stimuli. These results held only for slowly
moving stimuli; at high speeds the contrast dependence was low
for both stimuli suggesting the possibility of a single fast motion
pathway that is not colour-blind but is largely contrast invariant.
Again, reaction times to moving chromatic gratings are determined
by perceived – not physical – speed, even though there is an enor-
mous discrepancy between the two for slowly moving chromatic
gratings (Burr et al., 1998).
The idea that we have more than one motion pathway was pur-
sued further by Gegenfurtner and Hawken (1996) who measured
perceived velocity as a function of contrast not just for luminance
and equiluminant gratings but also for plaids, second-order, ampli-
tude-modulated, drift-balanced stimuli. Below about 4 deg/s they
again found that reducing contrast reduces perceived velocity
and the dependence on contrast is greater for equiluminant grat-
ings than for luminance gratings. This result is in line with the find-
ings of Thompson (1982) and Stone and Thompson (1992).
Interestingly the greatest effects were found with non-Fourier
drift-balanced stimuli (Chubb & Sperling, 1988), but again the
effects were limited to low rates of motion.
If there exist more than one motion pathway at slow speeds it is
of interest to know over what range they operate. Thompson
(1982) believed the upper limit for a reduction in contrast leading
to a reduction in speed was about 4 Hz, that is it was a temporal
frequency rather than a velocity limit. Gegenfurtner and Hawken
(1996) came to a somewhat different conclusion believing that
the limit was determined by a combination of both spatial and
temporal frequencies. However their results were sufficiently lim-
ited to prevent them from reaching any firm conclusions.
At low velocities at least it appears that both the parvocellular
and the magno-cellular pathway are involved in the computation
of velocity. The obvious approach is to take some ratio of magno
to parvo response to compute velocity. However some authors
are rather coy about this. Hammett, Champion, Morland, and
Thompson (2005) refer to the ratio of two temporal channels,
one low-pass and one band pass. Clearly they have in mind magno-
cells and parvocells and even label them 'm' and 'p', after Perrone
(2005), but without explicitly wishing to involve both pathways
in speed perception. A somewhat updated version of this ratio
model by Hammett et al. (2007) again employed the low- and
band-pass temporal filters proposed by Perrone (2005), this model
can accommodate several findings in the literature: some velocity
aftereffects (Hammett et al., 2005), decreases and increases in per-
ceived speed at low contrast (Thompson et al., 2006) and increases
in perceived speed at low luminance (Hammett et al., 2007).
8.5. Speed-tuned neural units?
Both for technical and theoretic reasons (particularly the simple
Fourier description), much research into speed perception has used
moving sine-wave gratings, defined by their spatial and temporal
frequencies. Clearly if we have true 'speed-tuned' cells in the visual
pathway then the temporal frequency tuning of cells would have to
vary with the stimulus spatial frequency. Physiological reports of
the tuning of cells in cat and monkey Area 17 (e.g. Foster, Gaska,
Nagler, & Pollen, 1985; Tolhurst & Movshon, 1975) suggested that
this was not the case and that there was separable tuning for
spatial and temporal frequency. Clearly if we were to find 'veloc-
ity-tuned' units we should have to look elsewhere. The obvious
candidate site was area MT.
Since 1983 it has been suspected that MT contained some real
velocity-tuned cells (Newsome, Gizzi, & Movshon, 1983). The same
group later reported that 'for some neurons in MT, the spatio-
temporal tuning is distinctly non-separable, with the optimal spa-
tial frequency varying with the optimal temporal frequency to
maintain a constant optimal speed for all stimulus configurations.'
Movshon, Newsome, Gizzi, & Levitt, 1988). More recent work by
Perrone and Thiele (2001) has confirmed that many cells in MT
can be regarded as truly velocity-tuned, although this conclusion
was challenged, in part, by Priebe, Cassanello, and Lisberger
(2003), who estimated that perhaps only 25% of MT cells were
speed-tuned when tested with sine-wave gratings. Strikingly there
appeared to be a unimodal continuum of cells from speed-tuned to
spatio-temporally separable, with most cells falling somewhere
between the extremes. Furthermore when stimuli comprising
two sine-wave gratings were used then the tuning of cells moved
towards the speed-tuned end of the continuum. In other words it
may be that sine-wave gratings, for all their popularity in motion
research are precisely the stimuli that the system finds it hardest
to deal with. Later work by Perrone (perrone & Thiele, 2002; Perro-
ne, 2004) developed a plausible account of how speed-tuned MT
units could be constructed from their V1 input. Meanwhile Priebe,
Lisberger, and Movshon (2006) have re-examined speed tuning in
V1 cells and have found that, while nearly all direction-selective
simple cells have responses separable for spatial and temporal fre-
quency, the complex cells were somewhat similar to the MT cells
reported by Priebe et al. (2003). Thus over the past twenty years
we have seen a shift in our understanding of speed tuning in the
visual system; in the 1980s most cells seemed to have tuning
separable for spatial and temporal frequencies whilst now non-
separable speed tuned units seem to be ubiquitous.
The belated but nonetheless comforting finding that there ex-
ist speed tuned neurones in the visual pathway has also received
support from fMRI studies. Lingnau, Ashida, Wall, and Smith
(2009) have used an adaptation paradigm introduced by
Grill-Spector and Malach (2001) to investigate this; following
adaptation to a high contrast drifting grating, the fMRI signal
change was recorded when a probe stimulus was either of the
same speed or the same temporal frequency. Using the logic that
if the same neuronal populations encode both the adaptation and
probe stimuli the response to the latter will be attenuated,
Lingnau et al. found good evidence for speed-tuning in areas
MT and MST.
Evidence for the involvement of V3A as well as MT+ in motion
processing in general and speed processing in particular has come
from studies employing repetitive transcranial magnetic stimula-
tion (rTMS). McKeefry et al. (2008) reported that rTMS applied to
these areas reduced the perceived speed of stimuli and often im-
paired speed discrimination but had no effect on spatial frequency
discrimination. Unfortunately the exact effect of rTMS on brain
processing is unknown. It might increase neural noise (Walsh &
Cowey, 2000) in which case the decrease in perceived speed would
sit well with Bayesian models of speed processing (Stocker &
Simoncelli, 2006) but there are also other possibilities; the effects
of TMS have been shown to be state dependent: rTMS will on some
occasions facilitate and on some occasions suppress activity,
depending on the baseline activity of the targeted area of the brain
(Silvanto, Cattaneo, Battelli, & Pascual-Leone, 2008). More specifi-
cally Cattaneo and Silvanto (2008) showed that following adapta-
tion to motion in one direction, the application of TMS can
enhance the detection of motion direction in the adapted direction
relative to the unadapted direction. Thus it would appear that TMS
has a similar effect as micro-stimulation of the adapted population.
Burton, McKeefry, Barrett, Vakrou, and Morland (2009) have built
on this finding to investigate the effects of TMS on speed percep-
tion. The most accepted model of speed encoding would propose
that we take the ratio of two speed tuned channels, one low-pass,
tuned to slow speeds, the other band pass and tuned to higher
speeds (e.g. Hammett et al., 2005). Following adaptation to a fast
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speed, the band-pass channel is adapted, the ratio drops and
perceived speed is reduced. Adaptation to the slow speed should
adapt the low-pass channel more and perceived speed increases.
This is what Burton et al. found. But they also found that TMS com-
bined with this adaptation reduced the perceived speed after
either adaptation, a result not expected if TMS boosts the adapted
neurons. Burton et al. interpret their findings as showing that TMS
suppresses the most responsive neurons to a stimulus, rather than
boosting the most adapted.
8.6. Speed perception during pursuit eye movements
Much research on our perception of speed has sought to sim-
plify the problem by carrying out observations with the head in a
fixed position and with the subject fixating a stationary point. Fur-
thermore stimuli are often of short duration to restrict eye move-
ments. The goal in most experiments here is to examine motion
across the retina. However, when faced with motion in the real
world we generally track the stimulus with our eyes, so in order
to compute speed we must combine both eye movement and ret-
inal movement. (We shall leave aside the problem of head move-
ment in the perception of speed as relatively little research has
looked at it). There has been a general assumption that two motion
illusions arise because of errors associated with estimating eye
velocity from extra-retinal signals; the Filehne illusion and the Au-
bert–Fleischl phenomenon. By ascribing these illusions to the gain
of the eye-velocity signal being less than unity, the tacit assump-
tion is that the retinal motion signal is error free. However, as
pointed out by Freeman and colleagues (Freeman, 2001; Freeman
& Banks, 1998; Sumnall, Freeman, & Snowden, 2003), this seems
an unlikely state of affairs as it is well known that retinal speed
is affected by contrast (Thompson, 1982), spatial frequency
(Diener, Wist, Dichgans, & Brandt, 1976) and colour (Cavanagh, Ty-
ler, & Favreau, 1984b). Freeman and Banks (1998) proposed that
estimates of 'head-centric' velocity errors arise both from our
estimates of eye velocity and in retinal motion, and this model
accurately predicted the magnitude of the Filehne and Aubert–
Fleischl illusions.
In the Filehne illusion (Filehne, 1922) a smooth pursuit eye
movement made across a stationary background will result in
the background appearing to move in a direction opposite to the
eye movement. In the related Aubert–Fleischl effect (Aubert,
1886; Fleischl, 1882) the perceived speed of a tracked moving tar-
get is lower than a target that moves across the stationary retina. In
both these cases, changes in spatial frequency and/or contrast af-
fect the size of the illusions but it is only the perceived retinal
speed and not the extra-retinal signal that is spatial frequency
and contrast dependent (Freeman & Banks, 1998; Sumnall et al.,
2003). This convincingly suggests that both extra-retinal errors
and retinal speed estimate errors are responsible for mispercep-
tions of speed when eye movements are involved. Murakami
(2007) has provided some support for this approach by showing
that the Filehne illusion at equiluminance can be reduced or re-
versed as the input gain of retinal velocity is lowered under these
conditions. See Freeman et al. (2010) for a discussion of how these
errors come about.
Smooth pursuits are not the only class of eye movement to af-
fect motion perception. Saccades also impact heavily on motion
perception, principally in reducing sensitivity to fast motion of
low spatial frequencies (Burr, Holt, Johnstone, & Ross, 1982; Burr,
Morgan, & Morrone, 1999; Burr, Morrone, & Ross, 1994; Shiori &
Cavanagh, 1989), but also by affecting the motion selectivity of
MT neurons in interesting and unexpected ways. Unfortunately,
we cannot extend our review to cover this interesting line of re-
search, but the interested reader is referred to Kowler's (in press)
review in this series.
If the problems involved in computing head-centric speed have
been taxing, then matters can only get worse if the observer moves
through the world. The field of optic flow has a long history
stretching back to Gibson and beyond (see Mollon, 1997) and a full
discussion of it is outside the scope of this review. However recent
developments which address the knotty problem of how we assess
the motion of objects during our self-motion are particularly excit-
ing. Work by Warren and Rushton (e.g. Rushton & Warren, 2005;
Warren & Rushton, 2009) has spawned the 'flow parsing hypothe-
sis'. In essence this proposes that there is a global subtraction pro-
cess that cancels the overall expanding radial flow that results
from our movement forward in the world. The key is the global
nature of the mechanism that discounts the retinal motion that
may be attributed to the observer's motion. It would appear that
local motion mechanisms make very little contribution to the pro-
cess. For more discussion on these issues, the reader is referred to
specific reviews, such as Warren (2004).
9. Adaptation to movement and the motion aftereffect (MAE)
A question that has occupied almost more attention than how
do we encode motion in the visual pathway is where we do so.
The motion aftereffect (MAE) has played a key role in this line of
inquiry. At one time it appeared that the partial interocular trans-
fer of the MAE and its immunity from the effects of attention lo-
cated much motion processing around primary visual cortex and,
a little later, in MT, but certainly before higher levels of processing
where attention might be expected to have an effect. However re-
search in the past 25 years has radically altered our views of the
MAE or perhaps MAEs and of the influence of attention on early
motion processing.
9.1. The effect of attention of the motion aftereffect
Wohlgemuth (1911), whose review of the MAE remains the sin-
gle most important work on the subject, asked, in one of his exper-
iments, the question of whether or not the size of the aftereffect
was affected by the attentional state of the subject. His experiment
suggested that the MAE was unaffected by attention and that posi-
tion was not challenged for many years. Indeed, Blake and Fox
(1974) and He, Cavanagh, and Intriligator (1996) seemed to sup-
port the low level nature of adaptation in that rendering an adapt-
ing stimulus 'invisible' by binocular rivalry or crowding did not
affect its efficacy in inducing an aftereffect. These conclusions sup-
port the idea that sensory adaptation is a low-level process that
precedes conscious perception and the effects of attention. The sin-
gle contrary voice was Chaudhuri (1990) who claimed that the
MAE was indeed modulated by attention. Clearly Chaudhuri was
unaware of Wohlgemuth's findings – which goes to show that
sometimes one is better off not knowing the literature. When
Gandhi, Heeger, and Boynton (1999) reported that spatial attention
did affect the fMRI response in V1 they listed no fewer than nine
previous studies using functional neuroimaging and ERPs that
had found no effect of selective spatial attention in human V1.
Chaudhuri, once a lone voice crying in the wilderness, soon at-
tracted many converts and disciples. Shulman (1993) confirmed
Chaudhuri's results and Lankheet and Verstraten (1995) demon-
strated that attention could modulate the strength of the motion
signals that gave rise to the MAE. Alais and Blake (1999), in an ele-
gant experiment, showed how a 'bivectorial' motion stimulus –
comprising two sets of dots moving is different directions – would
produce an MAE whose direction depends on the attention devoted
to one of the component motions. This result clearly sits uncom-
fortably with Blake's earlier work and he has since recanted his for-
mer position. He now has evidence that the MAE is substantially
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reduced during binocular rivalry and crowding (Blake, Tadin, Sobel,
Raissian, & Chong, 2006). The seeming contradiction between these
findings and his previous position was reconciled by considering
the contrast of the adapting pattern. It is widely believed that as
adaptation contrast increases, so does the strength of the afteref-
fect, but that there is a compressive non-linearity in the aftereffect
such that when the adaptation contrast exceeds about 2–3% con-
trast, the aftereffect strength remains nearly constant (Keck,
Palella, & Pantle, 1976). Blake et al. (2006) note that previous
reports that show no effect of suppression on aftereffect strength
have all used high adaptation contrasts, contrasts that might pro-
duce saturated aftereffects. Therefore it could be the case that
the effects of suppression by rivalry or crowding could be masked
by this saturation. By adapting to lower contrasts on the rising part
of the contrast-response curve Blake et al. were able to show that
binocular rivalry and crowding can indeed affect the strength of
the aftereffect.
9.2. Neuroimaging the motion aftereffect
Since the early 1990s much evidence from neuro-imaging has
supported this general premise that attention can influence visual
processing, even at early stages (as early as the LGN: O'Connor,
Fukui, Pinsk & Kastner, 2002). An early study by Corbetta, Miezin,
Dobmeyer, Shulman, and Peterson (1991) obtained psychophysical
evidence that speed discrimination was better when subjects at-
tended to one attribute of the stimulus rather than dividing their
attention and that PET measurements of extra-striate visual areas
during these tasks were modulated by selective attention. Further
support for the effects of attention has come from Rees, Frith, and
Lavie (1997) who demonstrated that both activity in MT and the
duration of the MAE were reduced when a high-load irrelevant lin-
guistic task was carried out simultaneously. This finding was taken
to support Lavie's theory (Lavie & Tsal, 1994) that, given finite
attentional resources, we will be less able to attend to the motion
stimulus when more attentional demands are made by the
high-load task.
The past ten to fifteen years have seen many imaging studies
that have confirmed the involvement of human MT+ in motion
adaptation (e.g. Corbetta, Miezin, Dobmeyer, Shulman, & Petersen,
1990; Corbetta et al., 1991; e.g. Beauchamp, Cox, & DeYoe, 1997;
Buchel et al., 1998; Chawla et al., 1999; Huk & Heeger, 2000; O'Cra-
ven, Rosen, Kwong, Treisman & Savoy, 1997; Treue & Martinez
Trujilo, 1999). One note of caution was sounded by Huk, Ress,
and Heeger (2001) who pointed out that because the MAE was
such an 'engaging' illusion, subjects might attend more to the illu-
sory motion than to a control stimulus. Thus studies which com-
pared the BOLD response in MT+ while experiencing an MAE
compared to a stationary pattern might be confounding the effects
of attention with the illusory motion. Huk et al's suspicions were
well-founded; their results showed that the effects of attention
on MT+ activity can be large, comparable in size with the activity
produced by the MAE. However, when controlling for the effects
of attention they did confirm that direction-selective adaptation
does produce direction-selective imbalances in MT+ responses.
The floodgates were now open for anyone with access to fMRI to
investigate in humans what had only been demonstrated previ-
ously in the macaque monkey. Huk and Heeger (2001) saw the
opportunity to see if the human visual system had the same 'com-
ponent-motion' and 'pattern-motion' cells reported in MT
(Movshon, Adelson, Gizzi, & Newsome, 1985). Area V1 appeared
to have only component-motion cells – cells that respond to mo-
tion orthogonal to local contour orientation – while MT appear to
have both component-motion and pattern-motion cells; the latter
responding to the direction of motion of whole patterns irrespec-
tive of the orientation of their components. The distinction in these
two cell types had been revealed in experiments using plaid stim-
uli and Huk and Heeger (2000) too used adaptation to plaids to
separate pattern from component motions. In a cunning design,
they combined pairs of component gratings into plaids that either
all moved in the same direction or different directions. Thus an
area of the brain that only responded to component motion would
see no difference between the two sets of stimuli but an area with
pattern-component cells would treat the two sets differently. In
line with previous expectations area MT+ showed much greater
adaptation to the coherent pattern motion. The authors also re-
ported pattern-motion adaptation to a lesser degree in areas V2,
V3, V3A and V4v.
9.3. Multiple sites for the motion aftereffect?
If it now seems well-established that motion is processed in
multiple sites along the visual pathway and now it appears that
we can reveal different stages of this processing with suitable psy-
chophysical tasks. If motion is processed in many parts of the vi-
sual system (V1, V3, and MT+ for example), and if there is good
evidence that these areas appear to be susceptible to adaptation,
shouldn't we be able to discriminate between adaptation at one
site rather than the other? There is increasing evidence that the an-
swer to this question is 'yes'.
In 1986 von Grunau demonstrated that long range apparent
motion was capable of generating an aftereffect on a flickering test
pattern but not on a static one. At the time this seemed to suggest
that the dynamic test was just a more sensitive way of measuring
the effect. However Hiris and Blake (1992) reported that following
adaptation to motion the aftereffect seen is markedly different
depending upon whether the test pattern is a static or dynamic dis-
play. Hiris & Blake reasoned that testing on a stationary pattern
would not optimally test those motion mechanisms involved in
the adaptation, whereas a test pattern of dynamic visual noise
might. They found that the MAE on the dynamic display could be
confused for real motion, but the MAE on the static display never
was. Raymond (1993), noting that it is generally assumed that
the degree of interocular transfer of an aftereffect is an index of
the proportion of binocularly driven cells involved with the effect
(Moulden, 1980; Movshon, Chambers, & Blakemore, 1972), re-
ported that when tested with a dynamic test pattern the MAE
showed nearly 100% interocular transfer. This, she suggested, arose
because of the total binocularity of cells in MT (Zeki, 1978), an area
that does not respond to stationary stimuli (Albright, Desimone, &
Gross, 1984) but does to dynamic stimuli. Nishida, Ashida, and Sato
(1994) showed further differences between the two types of MAE,
the static aftereffect showed partial interocular transfer following
adaptation to first-order motion whereas what they called the
'flicker MAE' (tested on a counterphase modulated grating) showed
complete interocular transfer with adaptation to either first- or
second-order motion. Nishida and Sato (1995) went onto pit the
two aftereffects against each other; adapting to first-order motion
in one direction and second-order motion in the opposite direction.
This led to a static MAE predominantly induced by the first-order
motion and a flicker MAE in the opposite direction produced by
the second-order motion. This gave further support to the idea that
the static MAE reflects activity in lower-level motion mechanisms,
perhaps in V1, while the flicker MAE reveals higher-level motion
processing, perhaps in MT. Intriguingly Ashida and Osaka (1995)
found that the flicker MAE seemed to depend on the adaptation
velocity and not, as is the case with the static MAE (Pantle,
1974), on the adaptation temporal frequency. A dependence on
adaptation velocity was exactly what was reported for the velocity
aftereffect by Thompson (1981).
Further evidence for two aftereffects, one in originating in V1
and the other in MT has come from Aghdaee and Zandvakili
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(2005) who used a logarithmic spiral as the adaptation stimulus.
They tested the MAE with both the stationary adapt stimulus
and with its mirror image. One property of the mirror-image test
stimulus is that all contours in the pattern lie orthogon