PNAS | April 24, 2001 | vol. 98 | no. 9 | 5252-5257
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Neurobiology
A wholly empirical explanation of perceived motion
Zhiyong
Yang,
Amita
Shimpi, and
Dale
Purves*
Department of Neurobiology, Box 3209, Duke University Medical
Center, Durham, NC 27710
Contributed by Dale Purves, February 23, 2001
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Abstract |
Because the retinal activity generated by a moving object cannot
specify which of an infinite number of possible physical displacements
underlies the stimulus, its real-world cause is necessarily uncertain.
How, then, do observers respond successfully to sequences of images
whose provenance is ambiguous? Here we explore the hypothesis that the
visual system solves this problem by a probabilistic strategy in which
perceived motion is generated entirely according to the relative
frequency of occurrence of the physical sources of the stimulus. The
merits of this concept were tested by comparing the directions and
speeds of moving lines reported by subjects to the values determined by
the probability distribution of all the possible physical displacements
underlying the stimulus. The velocities reported by observers in a
variety of stimulus contexts can be accounted for in this way.
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Introduction |
Physical motion is the
continuous displacement of an object within a frame of reference; as
such, motion is fully described by measurements of translocation.
Perceived motion, however, is not so easily defined. Because the
real-world displacement of an object is conveyed to an observer only
indirectly by a changing pattern of light projected onto the retinal
surface, the translocation that uniquely defines motion in physical
terms is always ambiguous with respect to the possible causes of the
changing retinal image (1-3). This ambiguity presents a fundamental
problem in vision: how, in the face of such uncertainty, does the
visual system generate definite percepts and visually guided behaviors
that usually (but not always) accord with the real-world causes of
retinal stimuli?
In the present article, we examine the hypothesis that the visual
system solves this dilemma by a strategy in which the retinal image
generates the probability distributions of the possible sources of the stimulus.
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Methods |
The stimuli we used consisted of a line translating from left to
right in the frontal parallel plane behind an aperture. The line was
presented at orientations of 20-60° in 10° increments relative to
the horizontal axis (except for the inverted V aperture, in which case
the moving line was presented at 10-50°). All stimuli subtended
4 × 4° and were shown on a 19-inch monitor at a frame rate
of 25, 30, or 35 frames per second; the viewing distance was 150 cm.
The luminance of stimulus line and aperture boundaries was 119 cd/m2 (white), and background 0.7 cd/m2 (black). The stimuli used in the control
experiments mentioned at the end of Results were the same,
except that the aperture boundaries were invisible, and the background
was a uniform texture of intermediate luminance (46 cd/m2).
Subjects (the authors and three naïve subjects, all of whom had
normal or corrected-to-normal vision) identified the direction and
speed of the line by adjusting a dot that was initially moving in a
random direction and speed, presented within a separate but otherwise
similar aperture (Fig. 1). The observers
were instructed to regard the stimuli as they would any other scene,
and no feedback about performance was given. The perceived direction
and speed of the moving line were indicated by clicking on a position
in the matrix, the axes of which represented horizontal and vertical speed. When a judgment was made, the dot returned to the starting position, and the movie was shown again. This procedure was repeated until the subject judged that the velocities of the line and the dot
were the same (usually within three to five presentations of the
movie).
One run containing the five different line orientations for each
aperture constituted a block, which took 8-10 min to complete. For
each aperture type studied, the subjects performed the task for 10 blocks. To avoid adaptation, the time between blocks was at least 10 min; the interval between experiments for different stimulus parameters
was at least a day. The total time for each subject to complete the
full battery of tests (two apertures and the corresponding controls)
was about 10-12 h, a workload distributed over several weeks. The test
platform used was MATLAB Psychophysical toolbox (4).
A square-root-error criterion was used to compare subject performance
and predicted percepts. The parameters that produced the
least-square-root error were chosen as the most appropriate values for
a particular experimental condition and are given in the relevant
figure legends.
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Results |
If this concept of how we see motion is correct, then the
perception of a sequence of retinal images will always be determined by
the probability distribution of the set of all the possible physical
sources underlying a sequence of projected retinal images: the speed
and direction seen will simply reflect the shape of this distribution.
Accordingly, the initial challenge in assessing this hypothesis about
motion perception was to determine the probability distribution of the
possible physical displacements underlying any given visual stimulus.
Theoretical Framework.
The physical motion underlying a sequence of images projected onto a
plane is necessarily related to the set of all possible correspondences
and differences between any two images in the series. Consider, for
example, the stimulus sequences generated by the uniform translocation
of a straight line (e.g., a rod at a given orientation moving steadily
in the frame of reference; Fig. 2). With
respect to any two lines projected onto a plane by such a source at
different times, the logically complete set of correspondences and
differences between any two sequential projections is given by:
(i) the identity of line elements (i.e., points or line
segments) in the two images; (ii) the appearance of new
elements in the second image compared with the first from portions of
the object previously hidden; (iii) the disappearance of
elements in the second image compared with the first as a result of
portions of the object that become hidden; and (iv)
deformation of the projected line in the image sequence arising from
movement of the object closer to or further from the image plane,
rotation of the object, or its physical deformation. This definition of the correspondences and differences in any two sequential images is
valid, in principle, for any type of image feature and any number of
images in a sequence.
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Fig. 2.
The complete set of correspondences and differences between sequential
images of a line moving uniformly is defined by four factors.
(A) Identity. A line point or segment at time
t that occupies any position on the visible line at time
t + 1 defines identical elements in the two images (in
this and subsequent figures, identity is indicated by a black line
segment). (B) Appearance. The elements of the line
indicated in blue at time t + 1 do not correspond to any
of the elements visible at time t and have thus appeared
in the interval between the generation of the two images.
(C) Disappearance. The elements of the line indicated in
red at time t do not correspond to any visible elements
at time t + 1 and have thus disappeared in the interval.
(D) Deformation. The projected line images can also
differ as a result of movement of the source toward (or away) from the
observer, by rotation, or by physical deformation (here indicated by a
uniform extension of the line segment during the interval; deformation
in subsequent figures is also indicated in green). Because the
contributions of identity, appearance, disappearance, and deformation
of the line elements are conflated in any two sequential images, the
physical displacement underlying the stimulus generated by a moving
line is profoundly ambiguous. Any account of the possible sources of
the stimulus must therefore take into account the contributions of
these four factors.
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Constructing the probability distribution of the possible sources of a
stimulus on this basis requires: (i) formally stating all
the possible correspondences and differences in the sequence of images
underlying a motion stimulus; (ii) describing quantitatively how these correspondences and differences in the image plane are generated; (iii) using this information to calculate how the
contributions of identity, appearance, disappearance, and deformation
are combined in a set of probability distributions that includes all of
the possible real-world displacements underlying the stimulus;
(iv) deriving a principle for combining the relevant
probability distributions; and (v) devising a procedure to
determine the expected perception on the basis of this combined
probability distribution.
A first step in our approach was thus to provide a quantitative
description of all the correspondences and differences in the image
plane between two sequential projections in the image sequence. To this
end, consider a linear object steadily translating in a given direction
whose movement is limited to a frontal plane (Fig.
3). The example in Fig. 3A
illustrates the relationship in the projected sequence of identity,
appearance, disappearance, and deformation. In Fig. 3A1, the
segment AE at time t is identical to segment A'E' at time
t + 1, defining identity. Appearance is defined by segment
CA' at t + 1 and disappearance by segment E'B'. Deformation
is illustrated in Fig. 3A2 by extending segment A'B' at
t + 1 to segment A''B''. Note that when translation is in a frontal plane, all possible correspondences and differences in the
projected line other than those generated by identity, appearance, or
disappearance are limited to physical deformation (i.e., a stretching
or contracting of the line along its axis rather than rotation or
movement nearer to or further from the observer).
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Fig. 3.
Any projection sequence generated by the translation of a line in a
frontal parallel plane can be decomposed into the contributions of
identity, appearance, disappearance and deformation, as defined in Fig.
2. (A) Relationship of identity, appearance,
disappearance and deformation. (1) Line AB at time
t moves to A'B' at time t + 1 at speed
V and in a direction  . In this example, AE and A'E'
are identical; segment CA' appears in the interval, and segment EB
disappears. (2) Line A'B' is further deformed such that this segment is
extended along its axis to A''B''. The positions of the points on
A''B'' on CD can be calculated on the basis of the supposition of
linear deformation and an anchor point  , whose position is not
changed by deformation. U1 = CA'', and
U2 = DB'' are the two unmatched line segments
resulting from line translation and deformation that are not visible at
both t and t + 1. (B)
Determination of the anchoring point. The mean position
of the anchoring point (0) in the probability
distribution P() in Eq. 5 can be
determined by the relation (1  0):0 = DQ:CP. That
is, (1 0):0 = tan( 1):tan(2);
0 = 0.5, (1 = 2 = 90°); 1 and
2 are the angles between line CD and lines
connecting A and C and B and D, respectively.
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A mathematical statement of the relationships between identity,
appearance, disappearance, and deformation illustrated in Fig. 3 is as
follows. Let V and represent the translation speed and
direction, respectively, of the source giving rise to the projected
line in the image plane in Fig. 3A1( being the direction relative to the line). Further, let be the line orientation relative to the horizontal axis of the reference frame. The two unmatched parts of the lines in Fig. 3A2 (i.e., the parts of
the lines not visible in the projections at both t and
t + 1) can then be determined as functions of the underlying
physical displacements. Thus, the unmatched segments CA'' (denoted as
U1) and DB'' (denoted as
U2) in Fig. 3A2 are given by
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[ 1 ]
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In these equations, 1 and
2 are the angles between the line at
t + 1 and lines connecting A,C and B,D in Fig.
3A2, respectively. U1 > 0 if it
lies to the right of the line connecting A and C; otherwise,
U1 < 0. U2 > 0 if it lies to the left of the line connecting B and D; otherwise,
U2 < 0.
Eq. 1 introduces two variables that describe the physical
deformation of the line in Fig. 3A2: 
, which signifies
the extent of deformation, and , the coordinate of an anchoring
point (defined as the position along the projected line that is not
changed by deformation). The reason for introducing these variables is
that the vectors at the aperture boundary cannot be taken simply as object velocities measured locally. The local configuration of the
vectors of AC or BD along the aperture boundary in Fig. 3 could have
been generated in an infinite number of ways; furthermore, the velocity
vectors AC and BD cannot both belong to the motion field of a rigid
object at the same time.
The next step was to determine the properties of the variables
pertinent to deformation and anchoring. If L(t + 1) is the length of A''B'' at time t + 1 in Fig.
3A2, L(t) the length of AB at time
t, and La the distance of
the anchoring point from one of the end points of the line, then line
length change caused by deformation is given by = A''B'' A'B' = A''B'' AB = L (t + 1) L(t), and the anchoring point coordinate = La/L(t). To
calculate the positions of A''B'' on CD, for example, it is necessary
to determine (i) how much of the total line length change arises from deformation and (ii) the anchoring point. If the
deformation is less than the total difference in the length of the
projected line, then
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[ 2 ]
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where Lv(t) and
Lv(t + 1) are the lengths
of line at time t and t + 1, respectively. They
are modeled probabilistically because, given any two images, neither
the amount of deformation nor the anchoring point is known.
The next requirement was to compute the probability distributions of
the possible physical displacements underlying the stimulus. For the
visible portion of the stimulus line in Fig. 3A, the
probability Pr of any particular speed
and direction (V, ) is
![P<SUB><UP>r</UP></SUB>=N<SUB><UP>r</UP></SUB><UP>exp</UP>[<UP>−</UP>K<SUB><UP>r</UP></SUB>(V<UP>sin</UP>&thgr;−V<SUB>⊥</SUB>)<SUP>2</SUP>],](/content/vol98/issue9/fulltext/5252/img004.gif)
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[ 3 ]
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where V
is the velocity
measured normal to the orientation of the stimulus line, and
Kr is the level of noise in the generative process and/or the relevant measurements. This equation is
obtained under the assumption that for the visible portion of the
stimulus line, only the velocity perpendicular to the line is
measurable, and that the noise in this velocity caused by the generative process and/or the relevant measurements is additive Gaussian. This is a form of the so-called motion constraint equation (5).
Probability distributions P1 and
P2 could likewise be computed for the
two unmatched elements of the stimulus line, U1
and U2. For this purpose, we also used Gaussians,
such that
![P<SUB>2</SUB>=P(<UP>U</UP><SUB>2</SUB>)=N<SUB>2</SUB><UP>exp</UP>[<UP>−</UP>K<SUB>2</SUB>(<UP>U</UP><SUB>2</SUB>−<UP>U</UP><SUB>0</SUB>)<SUP>2</SUP>].](/content/vol98/issue9/fulltext/5252/img006.gif)
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[ 4 ]
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In these expressions, U0 is the mean of
these Gaussian distributions and depends on the geometrical
relationship between the line and an explicit occluder or the occluder
implied by the geometry of the line at subsequent positions. These
distributions are obtained under the assumption that whether or not the
line segments at the aperture boundary at t and t + 1 are related by identity depends on how much the line moves
outside/inside the aperture between t to t + 1. Given additive Gaussian noise in the image formation process, Eq. 4 follows.
We also used Gaussians to specify the distributions of and ,
such that
![P<SUB>&dgr;</SUB>=P(&dgr;)=N<SUB>&dgr;</SUB><UP>exp</UP>[<UP>−</UP>K<SUB>&dgr;</SUB>(&dgr;−&dgr;<SUB>0</SUB>)<SUP>2</SUP>],](/content/vol98/issue9/fulltext/5252/img008.gif)
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[ 5 ]
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where 0, 0 are
the means of the Gaussians. The mean position
(0) of the anchoring point () was
determined in the following way. Suppose that the change of the line
length from t to t + 1 is entirely because of
deformation, as in Fig. 3B. If the stimulus line is deformed
linearly, which is the only form of deformation that can occur under
the conditions considered in Fig. 3, then the coordinate of the mean
position (0) of the anchoring point on the
line is proportional to the displacement of the line AB along its
terminator (i.e., AC and BD) projected onto the moving line (i.e., CP
and DQ; see Fig. 2B). Thus,
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[ 6 ]
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In this expression, 0 = 0.5 if
1 = 2 = 90°;
0 is measured from the line ending on the line
connecting A and C. If 0 = 0 or
0 = 1, then one end of the line is the
anchoring point itself. If 1 < 0 < = +
or < = 0 < 1, then the
anchoring point lies outside of the line segment. Thus,
0 is uniquely determined by the relationship
between the line and its visible ends as the orientation of the
stimulus line changes. These several equations define, in probabilistic
terms, the interplay of translation, deformation, and the geometrical
configuration generated by the moving line and the aperture boundary,
thus incorporating all of the physical degrees of freedom pertinent to
motion stimuli of the sort considered in Fig. 3.
The three probability distributions directly relevant to the possible
source of the stimulus (Pr,
P1, and
P2) must then be combined to provide
the joint probability distribution needed to predict the perceived
movement that the observer would be expected to see. If
P(V, , , ) denotes this joint
probability, then
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[ 7 ]
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where P0 is the distribution of
linear objects previously experienced by human beings, and the terms
designated by w are the weights given to the relevant
probability distribution Pr, Pr
P1,
PrP2 and
PrP1P2
that could have generated any given stimulus. Note that 0 
wr,w1,w2,w1,2 1; wr + w1 + w2 + w1,2 = 1, and that the bracketed term
on the right side of Eq. 7 includes competitive and
cooperative combinations of probabilities.
For the stimuli used in the psychophysical tests below, there are only
four conditional relationships of P1,
P2, and
Pr.
(i) Both U1 and U2 are
determined by the same points on the line at the two subsequent
positions. In this case, the product of
P1,
P2, and
Pr is relevant to the joint
probability distribution (6).
(ii) The visible endpoints at time t and
t + 1 are not the same. In this case,
U1 and U2 are not defined.
Because there is no additional information available from the endpoints
(6), the sources of the stimulus will be determined by the probability function Pr of the possible sources of
the visible line.
(iii) Only the unmatched portion designated
U1 is determined by the same point on the line at
the two subsequent positions. In this case, only
P1 multiplied by
Pr is relevant to the joint probability distribution.
(iv) Only the unmatched portion designated
U2 is determined by the same point on the line at
the two subsequent positions. In this case, only
P2 multiplied by
Pr is relevant to the joint probability distribution.
These four cases exclude each other; more importantly, there is no way
to be sure which of them underlies the stimulus. Thus they correspond
to the four terms in the bracket in Eq. 7, each with a
finite "weight" relevant to the likelihood of having caused the
stimulus (i.e., the terms wr,
w1,
w2,
w1,2). Because there is no basis for
determining values of these weights from the first principles, they
were assigned on the basis of psychophysical performance (see below)
(see also ref. 7). Other possible principles for combining the relevant
probability distributions (e.g., random combination of
P1,
P2, and
Pr, winner-take-all competition
between P1,
P2, and
Pr, or simple multiplication of
P1,
P2, and
Pr) do not fully incorporate these
four conditions or their exclusivity.
As a last step, a procedure is needed to draw conclusions from the
joint probability distribution P(V, , ,
). Here, speed (V) and direction () are the primary
variables, because observers sense (and report) the velocity of the
stimulus line. Accordingly, we integrated out and in
P(V, , , ) such that
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[ 8 ]
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Note that integrating out and (8, 9) is not equivalent to
dismissing the effects of and .
To make specific behavioral predictions, we used the local mass mean.
Thus,
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[ 9 ]
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where (V*, *) are the predicted speed and direction,
respectively, exp(qv(V V*)2 q
( *)2) is a local loss function, and
qv,
q are positive constants. Because
the local topography of the probability distribution is taken into
account by this technique, it is more appropriate than mean, median or
local maximum (10, 11).
Applying Eq. 9 (and making use of Eqs.
1-8) thus allows prediction of the direction and
speed of a moving line stimulus that should be seen if motion
perception were based solely on the probability distributions of the
possible sources of the image sequence.
Perceptual Tests.
It has long been known that both the perceived direction and speed of a
moving line are markedly affected by the context in which the source of
the stimulus is viewed (3). When, for example, an obliquely oriented
line moves horizontally from left to right, observers perceive the
velocity of the object to be approximately that of the physical motion
of the source. When, however, the same moving line source is occluded
by a right angle aperture, the perceived direction of motion is
downward and to the right at a slower speed (3). We therefore tested
how well the probabilistic model described in the previous section
accounts for these psychophysical observations.
Fig. 4A illustrates an example
of a stimulus of this type, and Fig. 4B the probability
distribution of the possible velocities that underlie the stimulus in
this context. As indicated in Fig. 4C, the directions of
movement (and consequent speeds) reported by subjects are predicted
remarkably well by the local mass mean of the possible sources of the
stimuli. When the source line is set at an orientation of less than
45° with respect to the horizontal, the perceived direction of motion
is biased away from the perpendicular toward the horizontal axis.
Conversely, when the orientation of the moving line is greater than
45°, the perceived direction is biased to a lesser degree away from
the perpendicular toward the vertical axis. In either case, the
perceived speed of the line is systematically underestimated with
respect to the speed associated with horizontal motion of the source
(see also Fig. 7).
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Fig. 4.
Comparison of the perceived motion of a line moving across a right
angle aperture and the perceptions predicted by the distribution of the
possible sources of the stimulus. (A) A representative
stimulus (line orientation = 40°). (B)
Probability distribution of possible translations underlying the
stimulus in A. (C) The directions
(Left) and speeds (Right) of the motion
perceived. Different colors represent data for each different subject
(vertical bars are standard deviations). The black lines with circles
are the predictions of the theory. In this and subsequent figures,
directions are indicated in degrees relative to the moving line (90°
being perpendicular to the line) and speeds as the distances in visual
angle between two subsequent line positions in that direction. For all
of the conditions, U0 in Eq. 4 and
0 in Eq. 5 were set to 0. K1,
K2 in Eq. 4 were set to be
equal. P0 in Eq. 7 was set
to be a constant. wr in Eq. 7 was also set to 0. K = 0.5 × 0.15 2 = 22, K = 0.5 [Lv(t + 1) Lv(t)]2,
qv = 200, q = 1,640. In this experimental
condition, w1= 0.01, w2 = 0.18, w1,2 = 0.81, Kr = 0.48;
Kr = 10.20.
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The empirical reason for these biases in the perceived velocity of the
moving line is illustrated in Fig. 5. The
stimulus in Fig. 4A could be generated by only four
conditionally independent situations: (i) a linear object,
both ends of which are fully in view (indicated by circles in Fig.
5A1; in this case, the difference in the stimulus line
between t and t + 1 would arise entirely from
deformation); (ii) a longer object seen through an aperture (Fig. 5A2); (iii) a longer object with only the
right end actually occluded (Fig. 5A3); or (iv) a
longer object with only the left end occluded (Fig. 5A4).
Each of these conditions is associated with a different probability
distribution of possible underlying sources; indeed, these are the four
conditional relationships referred to in more general terms in the
theoretical framework section (see above). For the stimulus in Fig.
4A, without other cues, the situation in Fig.
5A1 is the most probable. Furthermore, Fig. 5A4
is a little more likely than the situations shown in Fig.
5A2 and A3. The reason is indicated in Fig.
5B: for a line at this orientation translating in a frontal
plane, there are more possible translational velocities (vectors in the
area shaded blue) that could move the line to the right than downward
(vectors in the area shaded yellow). Thus when the line orientation is less than 45° (i.e., toward the horizontal), the perceived direction will be biased away from the direction perpendicular to the line toward
the horizontal axis. Conversely, when the line orientation is greater
than 45°, the perceived direction will be biased toward the vertical
axis.
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Fig. 5.
Empirical explanation of the biases in the perceived direction of
motion of a line translating in the frontal parallel plane.
(A) The four possible conditional relationships (1-4)
pertinent to the projection lines in Fig. 4; see text for detailed
explanation. (B) The two diagrams on the
Left show that for a line oriented at an angle less than
45° with respect to the horizontal axis, there are more possible
translational velocities whose direction of movement is to the right
(vectors in the area shaded blue) than downward (vectors in the areas
shaded yellow). The histogram on the Right shows this
difference in terms of the number of vectors illustrated in
Left. (Note that this preponderance of possible sources
of translation will always bias perception toward the longer distance
traveled along the side of the aperture; conversely, sources arising
from deformation will bias perception toward the shorter distance
traveled along side of the aperture.)
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This same general argument should apply to the biases observed in any
aperture. As a further challenge, therefore, we examined the perceived
direction and speed elicited by a line moving across an aperture in the
shape of an inverted V, with a vertex angle of 60° (Fig.
6A). Fig. 6B shows
the probability distribution of the velocities that could underlie the
stimulus in Fig. 6A and Fig. 6C the
subjects' responses to a range of such stimuli. In this case, the
perceived direction of motion lay between the perpendicular and the
right side of aperture. More generally, when the line was oriented at a
relatively small angle, the perceived direction was to the right of the
perpendicular; when, however, the line was at a relatively large angle,
the perceived direction was to the left side of the perpendicular. In
both cases, the speed was systematically underestimated with respect to
horizontal translation of the line. When the angle of orientation was
very large, the perceived direction actually lay outside the boundaries
of the aperture. As indicated in Fig. 6C, the performance of
the subjects is remarkably well predicted by the probability
distribution of the possible sources of the stimulus series (see also
Fig. 7).
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Fig. 6.
Comparison of the perceived motion of a line moving across an inverted
V aperture with a vertex angle of 60° and the values predicted.
(A) A representative stimulus (line orientation = 20°). (B) Probability distribution of possible
translations underlying the stimulus in A.
(C) The directions (Left) and speeds
(Right) of the motion perceived. Different colors
represent data for each different subject. The black lines with circles
are the predictions of the theory. In this experimental condition,
w1 = 0, w2 = 0.18, w1,2 = 0.82, K1 = 2.80, Kr = 9.80.
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Fig. 7.
Comparison of the present predictions of the perceived directions with
the predictions made by other models for a right angle aperture
(Top) and an inverted V aperture
(Bottom). Triangles indicate the directions of the left
terminator and upside-down triangles the directions of the right
terminator. Diamonds show the averages of terminator directions, and
stars the average of the terminator directions and the
direction perpendicular to the line. Red circles are the average
response of six subjects studied here, and blue squares the predictions
of the present theory. It is difficult to explain what subjects
actually see without considering the complete set of possible stimulus
sources.
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Results similar to those illustrated in Figs. 4 and 6 were also
obtained for circular and vertical apertures and in control experiments where the aperture boundaries were invisible.
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Discussion |
The fundamental problem in motion perception is the inevitable
ambiguity of any sequence of images projected from a source onto a
plane, such as the central retina: the observer must respond appropriately to the stimulus, but the sequence of retinal images does
not allow a definite determination of its source. There is no
analytical way to resolve this dilemma, because the requisite information is not present in the sequence of retinal images. This
problem could be solved, however, if the perceived motion were
determined by accumulated experience, such that the percept elicited
would always be isomorphic with the probability distribution of the
source of the stimulus. In this conception of motion perception (and
vision more generally), the neuronal activity elicited by any
particular stimulus would, over the course of both phylogeny and
ontogeny, come to match ever more closely the probability distribution
of the same or similar stimulus sequences (12). The aim of the
experiments reported here was to test this hypothesis by establishing
the probability distributions of the physical displacements underlying
simple linear motion stimuli and then comparing the percepts predicted
on this basis to the percepts reported by subjects.
To construct probability distributions that reasonably represent past
experience with a simple source, such as a uniformly translating rod
[the stimulus source studied by Wallach 65 years ago (3)], we
considered the complete set of all of the correspondences and
differences between any two projections in the image sequence and then
used this conceptual framework to compute the probability distributions
of the possible sources of the stimulus. In each of the cases we
examined, the percepts reported could be accounted for in this way. In
contrast, any theory of motion perception that fails to take into
account: (i) the probabilistic nature of the geometrical
configurations near where the moving line intersects the aperture
boundary; (ii) the conceptual inconsistency between terminator velocities and rigid object movements (the fact, for instance, that terminator velocities are inconsistent with rigid motion); (iii) the interplay of all of the physical degrees
of freedom underlying the stimuli; and/or (iv) the
conditional probabilistic relationships between the events in space and
time will have difficulty rationalizing these phenomena. For example,
studies of the aperture problem (6, 13-18) have generally focused on
an analysis of points along the aperture boundary, where the line
terminators are taken to convey information about the underlying
conditions (e.g., occlusion, transparency, or stereo disparity). The
assumption in such studies is that motion perception can be determined
by a visual evaluation of unique velocities at these points. However, explanations based on line terminators (6, 14, 16, 18), or even a
quasiprobabilistic version of this concept (16, 18), do not accord with
what subjects actually see (Figs. 4, 6, and 7).
Finally, we note that the wholly empirical strategy for responding
successfully to inherently ambiguous motion stimuli is much the same as
the strategy used to perceive other visual qualities. Evidently the
visual system generates the perception of luminance, spectral
differences, and orientation in the same general way (12).
| |
Acknowledgements |
We especially thank S. Nundy, J. Voyvodic, and B. Lotto for much
advice and criticism. We are also grateful to T. J. Andrews, A. Basole, M. Changizi, D. Fitzpatrick, S. M. Williams, and L. White
for useful comments. This work was supported by National Institutes of
Health Grant NS29187.
| |
Footnotes |
*
To whom reprint requests should be addressed. E-mail:
purves{at}neuro.duke.edu.
| |
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www.pnas.org/cgi/doi/10.1073/pnas.091095298
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