Journal of Experimental Psychology:
Human Perception and Performance
2006, Vol. 32, No. 2, 300 –313
Copyright 2006 by the American Psychological Association
0096-1523/06/$12.00 DOI: 10.1037/0096-1523.32.2.300
Learning to Control Collisions: The Role of Perceptual Attunement and
Action Boundaries
Brett R. Fajen and Michael C. Devaney
Rensselaer Polytechnic Institute
The authors investigated the role of perceptual attunement in an emergency braking task in which
participants waited until the last possible moment to slam on the brakes. Effects of the size of the
approached object and initial speed on the initiation of braking were used to identify the optical variables
on which participants relied at various stages of practice. In Experiments 1A and 1B, size and speed
effects that were present early in practice diminished but were not eliminated as participants learned to
initiate braking at a rate of optical expansion that varied with optical angle. When size and speed were
manipulated together in Experiment 2, the size effect was quickly eliminated, and participants learned to
use a 3rd optical variable (global optic flow rate) to nearly eliminate the speed effect. The authors
conclude that perceptual attunement depends on the range of practice conditions, the availability of
information, and the criteria for success.
Keywords: visually guided action, perceptual learning, optic flow, collision avoidance, time-to-contact
as participants learned to rely on a higher order optical variable
defined by a combination of optical angle and expansion rate.
The present study was motivated by considering the role of
perceptual attunement in the context of continuously controlled
visually guided actions, such as braking, steering, and fly ball
catching. Up until this point, the role of perceptual attunement in
such tasks has not been seriously considered because the assumption has been that all observers, regardless of level of experience,
regulate their actions around the critical value of a single optical
invariant (see Fajen, 2005b, for a more in-depth discussion).1 For
example, according to the most widely accepted theory of visually
guided braking, deceleration is regulated around a critical value of
⫺0.5 of the optical variable ␶˙ (Lee, 1976; Yilmaz & Warren,
1995). But despite its widespread acceptance, there is little empirical evidence to support the single optical invariant assumption for
visually guided action. Furthermore, this assumption has prevented
researchers from considering the possibility that the poorer performance of novices reflects the use of noninvariants and that
improvement with practice on a visually guided action reflects the
ability to become attuned to more reliable optical variables.
To understand how attunement might play a role in improving
performance on a visually guided action such as braking, imagine
a driver moving on the highway at a constant speed toward a
distant toll booth. When should the driver start braking? How
much brake pressure should be applied? The answers depend on
several factors, such as the distance to the toll booth, the speed of
approach, the strength of the brake, and the driver’s tolerance for
risk. The driver could initiate braking early and slow down grad-
What distinguishes experts from novices performing the same
perceptual or perceptual-motor skill? Some researchers believe
that the superior performance of experts can be attributed, in part,
to the ability to become attuned to more effective optical variables
with practice (E. J. Gibson, 1969; J. J. Gibson, 1966, 1986). This
form of learning, which has been called perceptual attunement,
was demonstrated by Michaels and de Vries (1998) and Jacobs,
Runeson, and Michaels (2001) using perceptual judgment tasks.
Michaels and de Vries instructed participants to judge the relative
force exerted by a videotaped or computer-generated figure pulling
on a bar. Jacobs et al. used the classic task in which participants are
asked to judge the relative mass of two colliding balls. Both studies
showed that perceptual judgments before practice were based on
optical variables that weakly correlated with the relevant property
(i.e., relative force or relative mass). After practice with feedback,
observers learned to use optical variables that more closely correlated with the relevant property. Perceptual attunement has also
been demonstrated using a perceptual-motor task in which observers were instructed to time the release of a pendulum to strike an
approaching ball (Smith, Flach, Dittman, & Stanard, 2001). During
the early stages of practice, most participants released the pendulum when the rate of optical expansion of the approaching ball
reached a critical value, resulting in systematic biases in performance when ball size and speed were manipulated. After several
sessions of practice, the effects of ball size and speed diminished
Brett R. Fajen and Michael C. Devaney, Department of Cognitive
Science, Rensselaer Polytechnic Institute.
This research was supported by Grant BCS 0236734 from the National
Science Foundation. We thank Andy Peruggi and Parthipan Pathmanapan
for creating the computer-generated displays for these experiments.
Correspondence concerning this article should be addressed to Brett R.
Fajen, Department of Cognitive Science, Carnegie Building 305, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180. E-mail:
[email protected]
1
Some readers may question the claim that noninvariants have been
ignored in studies of visually guided action. Indeed, it is not uncommon for
noninvariants to be considered in investigations of tasks such as catching,
hitting, and avoiding collisions. Our claim regarding the tendency to focus
exclusively on optical invariants concerns investigations of continuously
controlled visually guided action, such as those mentioned in the text.
300
LEARNING TO CONTROL COLLISIONS
301
ually, or wait until the toll booth is closer and slam on the brakes.
However, if the driver waits too long before starting to brake or
increases deceleration too gradually, then at some point the deceleration required to stop will exceed the maximum deceleration of
the brake and it will no longer be possible to stop within the limits
of the brake.
To control deceleration so that it is always still possible to stop,
one must be able to detect information about the deceleration
required to stop relative to the brake’s maximum possible deceleration (Fajen, 2005a, 2005c). In terms of spatial variables, the
constant rate of deceleration that would bring the driver to a stop
at the toll booth without making any further adjustments is equal
to
dideal ⫽ v 2/2z,
(1)
2
where v is speed, z is target distance, and v /2z is the “ideal
deceleration” (abbreviated dideal) in the sense that no further adjustments are necessary as long as current deceleration is equal to
v 2/2z. Further, v/z is equal to the inverse of the amount of time
remaining until the driver reaches the toll booth assuming constant
velocity (which Lee, 1976, called time-to-contact) and is specified
by the ratio of the rate of optical expansion ␪˙ to the optical angle
␪ (or 1/␶, where ␶ ⫽ ␪˙ /␪). Speed (v) is also optically specified.
When an observer translates over a textured ground surface at a
fixed eyeheight, the optical velocity of each point on the ground
surface depends on the point’s azimuth and declination. In addition, the optical velocity of each point is proportional to the ratio
of observer speed (v) to eyeheight (e). Thus, v/e is a global
multiplier that affects the optical motion of all points on the ground
surface in the same way. This ratio (v/e) is referred to as global
optic flow rate (GOFR; Larish & Flach, 1990; Warren, 1982). As
long as eyeheight is fixed, which it typically is for the kinds of
activities that involve visually guided braking (e.g., driving, cycling, playing sports), GOFR specifies speed.2
Substituting ␪˙ /␪ (or 1/␶) for v/z and GOFR for v, Equation 1 can
be expressed in terms of optical variables as
dideal ␣ GOFR ⫻ ␪˙ /␪ ⫽ GOFR/␶.
(2)
(Note that the “2” in the denominator of Equation 1 may be
dropped in Equation 2 because GOFR ⫻ ␪˙ /␪ is proportional to, not
equal to, dideal.) Thus, to avoid a collision, one could adjust brake
pressure to keep the perceived ideal deceleration, based on
GOFR ⫻ ␪˙ /␪, below a critical value that is calibrated to maximum
deceleration (see Fajen, 2005c, for more on the role of calibration
in visually guided braking).
GOFR ⫻ ␪˙ /␪ is an example of an optical invariant because it
uniquely specifies ideal deceleration across variations in observer
speed and object size. This is illustrated in Figure 1A, which shows
the value of GOFR ⫻ ␪˙ /␪ as a function of time for 25 simulated
approaches to an object in which speed is constant within each
approach but varies randomly between 3.6585 and 15.0 m/s between approaches.3 The size (i.e., the radius) of the approached
object also varies randomly between 0.15 and 0.615 m between
approaches. The black dots correspond to the point at which the
ideal deceleration was equal to 10 m/s2 (the maximum rate of
deceleration used in the experiments) for each simulated approach.
Because GOFR ⫻ ␪˙ /␪ is invariant across changes in speed and
size, its value at this boundary is the same for each trial.
Figure 1. Global optic flow rate (GOFR) ⫻ ␪˙ /␪ (A) and ␪˙ (B) as a
function of time for 25 simulated approaches. Object size (i.e., radius)
varied randomly between 0.15 and 0.615 m, and initial speed varied
randomly between 3.6585 and 15.0 m/s. The black dots indicate the point
on each trial at which ideal deceleration was equal to maximum
deceleration.
2
Speed is also specified by edge rate (ER), which is defined as the
number of texture elements that pass by a fixed point of reference in the
visual field per unit of time (Warren, 1982). Unlike GOFR, ER is invariant
over changes in eyeheight but not over changes in texture density. In
principle, observers could rely on ER rather than, or in addition to, GOFR.
However, Dyre (1997) found that perceptual judgments of self-motion
were affected more by GOFR than ER, and Fajen (2005a) found that
GOFR dominated ER in a visually guided braking task. Thus, we mainly
refer to GOFR in this article but note here that observers could also rely on
ER.
3
The ranges of initial speeds and object sizes correspond to those used
in the experiments.
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FAJEN AND DEVANEY
Although information that specifies ideal deceleration is available
in the optic array, this does not necessarily mean that it is actually
used. There are also many noninvariants whose value when ideal
deceleration is equal to maximum deceleration is affected to at least
some degree by size and speed. Figure 1B shows the value of one
noninvariant, expansion rate (␪˙ ), as a function of time for the same 25
simulated approaches in Figure 1A. Unlike the invariant, the value of
␪˙ at the moment that the ideal deceleration is equal to the maximum
deceleration (indicated by the black dots in Figure 1B) varies between
approaches. Thus, perceiving ideal deceleration on the basis of ␪˙
would result in systematic overestimation or underestimation of ideal
deceleration as speed and size vary. However, the reliability of ␪˙
depends on the range of object sizes and initial speeds, and there are
other noninvariants that vary less than ␪˙ . So depending on tolerance
for error, performance based on a noninvariant may still be “good
enough.”4
Do observers rely on the invariant or a noninvariant to keep
ideal deceleration within the limits of the brake? Can improvement
in performance be attributed to attunement to more reliable optical
variables with practice? The research by Michaels and de Vries
(1998), Jacobs et al. (2001), and Smith et al. (2001) that was
summarized at the beginning of this article suggests that people do
rely on noninvariants at least some of the time, and that they
converge on more reliable variables with practice under certain
conditions. However, the tasks used in those studies were unrelated to the kinds of visually guided actions that are under continuous control, such as braking, steering, and fly ball catching.
Demonstrating perceptual attunement in the context of such visually guided actions is a challenge because when actions are continuously regulated, it is usually possible to correct for errors that
arise from systematic overestimations or underestimations resulting from the use of a noninvariant. Attempting to infer the optical
variable on which participants relied by looking at the effects of
various manipulations (e.g., object size and speed) would not be as
effective for continuously regulated actions as it is for precisely
timed ballistic actions, such as releasing a pendulum to hit an
approaching ball (e.g., Smith et al., 2001).
To investigate the role of perceptual attunement in the context of
braking, we developed an “emergency braking” task in which
participants were instructed to wait until the last possible moment
to stop at an object (a stop sign) in the path of motion by initiating
maximum brake pressure. To perform the task successfully, participants must “slam on the brakes” at the moment that ideal
deceleration is equal to maximum deceleration.5 If participants
rely on the optical invariant (i.e., GOFR ⫻ ␪˙ /␪) to perceive ideal
deceleration, then the ideal deceleration at which braking is initiated should be unaffected by the size of the stop sign and the initial
approach speed. On the other hand, if the initiation of braking is
affected by these factors, then participants must be using a noninvariant, and the pattern of errors can be used to make inferences
about which noninvariant is being used. To compare performance
at different stages of learning, we adopted a design similar to that
used by Smith et al. (2001). The experiments consisted of blocks
of trials, and analyses were conducted for each block to determine
the optical variables on which participants relied at each stage of
practice.
One might wonder whether anything can be learned about
normal, regulated braking by studying how people perform an
emergency braking task, which is not a visually guided action. If
normal, regulated braking is controlled by keeping the perceived
ideal deceleration within the limits of the brake as suggested by
Fajen (2005a, 2005c), then participants must be able to reliably
perceive ideal deceleration relative to maximum deceleration
across changes in speed and size. Because the emergency braking
task requires participants to slam on the brakes at the moment that
perceived ideal deceleration equals maximum deceleration, this
task provides a useful way to measure the reliability with which
participants perceive ideal deceleration across variations in size
and speed. Thus, by studying emergency braking, we may be able
to learn something about how normal braking is controlled and
whether improvement with practice is due to perceptual
attunement.
Now that we have explained how perceptual attunement might
play a role in improving performance in a visually guided action
such as braking, let us show how data from the emergency braking
task can be represented in ways that allow us to make simple
comparisons with the predictions of different optical variables.
Figure 2 shows ideal deceleration at the onset of braking (based on
vonset2/2zonset) as a function of stop sign radius (Figure 2A) and
initial speed (Figure 2B). If participants rely on the optical invariant, then the data should fall along a line with zero slope.6 If
participants initiate deceleration at a fixed rate of optical expansion, then the data should fall along a curve that slopes downward
in the sign radius plot and upward in the initial speed plot. That is,
braking should be initiated earlier when radius is large and speed
is slow. Lastly, if the rate of optical expansion at which braking is
initiated is proportional to optical angle (i.e., if braking is initiated
at a fixed value of ␪˙ or 1/␶), then the data should fall along a flat
line in the sign radius plot and an upwardly sloping curve in the
initial speed plot.7
Another useful way to represent the data is to plot expansion
rate at onset as a function of optical angle at onset (see Figure 3),
which Smith et al. (2001) referred to as optical state space. One
advantage of an optical state space representation is that expansion
rate and ␪˙ strategies are easier to visualize. Regardless of whether
sign radius (Figure 3A) or initial speed (Figure 3B) is varied, the
expansion rate strategy corresponds to a line in optical state space
with a zero slope and a positive intercept (dotted line), and the ␪˙ /␪
strategy corresponds to a line with a positive slope and a zero
intercept (dashed line). Visualizing the predictions of the optical
invariant can be more difficult because optical state space does not
4
For example, ␪˙ /␪ varies across changes in initial speed but not across
changes in object size. If conditions are encountered in which the range of
initial speeds is narrow, then performance based on ␪˙ /␪ may be indistinguishable from performance based on the optical invariant.
5
In practice, observers may initiate emergency braking a split second
before ideal deceleration reaches maximum deceleration to compensate for
perceptual-motor time delays.
6
The location of the y-intercept relative to the brake’s maximum deceleration indicates whether there was an overall bias to initiate deceleration
too early or too late. Thus, if participants are calibrated to the strength of
the brake and do not exhibit any biases, then the y-intercept should
correspond to the brake’s maximum deceleration.
7
The particular critical value of the corresponding optical variable will
affect the height but not the shape of the curve. The critical values used in
Figure 2 would result in an overall bias to stop at or before reaching the
stop sign across the range of sign radii and initial speeds.
LEARNING TO CONTROL COLLISIONS
Figure 2. Predicted ideal deceleration at onset as a function of sign radius
(A) and initial speed (B) based on global optic flow rate (GOFR) ⫻ ␪˙ /␪
(solid line), ␪˙ /␪ (long dashed line), and ␪˙ (short dashed curve).
include a dimension for GOFR. Rather than adding a third dimension, the predictions for different initial speed conditions (i.e.,
different values of GOFR) can be represented as different lines in
optical state space (Figure 3C). If participants rely on the optical
invariant, then the data for a given initial speed should fall along
a line with a zero intercept and a positive slope inversely proportional to GOFR. As initial speed varies, the line’s slope changes,
but it always intercepts the y-axis at zero. The solid lines in Figures
3A–3B show the predictions of the optical invariant when sign
radius and initial speed are varied separately. Even though the
optical invariant is composed of three component optical variables,
the predictions can be represented by a single line in optical state
space when initial speed is fixed because the value of GOFR is
always the same (Figure 3A). When initial speed varies and sign
radius is fixed, the predictions can be represented by a curve rather
than a straight line in optical state space (Figure 3B).
303
Although these plots are useful for making comparisons between the data and predictions of each model, we did not expect
that the data would necessarily align with the predictions of any
one of these variables. ␪˙ , ␪˙ /␪, and GOFR ⫻ ␪˙ /␪ are simply three
out of an infinite number of ways of defining boundaries in optical
state space. The fact that these three variables can be expressed as
simple combinations of component optical variables does not
necessarily mean that actual performance is any more likely to
correspond to the predictions of one of these models. For example,
the data might fall along a line in optical state space that lies
between the predictions of the ␪˙ and ␪˙ /␪ models, or even fall along
a curve. It is just as important to be able to describe and interpret
these possible outcomes.
Smith et al. (2001) recognized this problem and pointed out that
any linear margin (i.e., boundary) in optical state space can be
expressed by the equation ␪˙ ⫽ a␪ ⫹ b, where a is the slope and b
is the intercept. This equation provides a convenient way to describe data that do not necessarily conform to the predictions of
any of the idealized models. For example, a line in optical state
space that lies between the predictions of the ␪˙ and ␪˙ /␪ models
would have a positive slope and intercept. ␪˙ , ␪˙ /␪, and GOFR ⫻ ␪˙ /␪
are simply special cases in which a ⫽ 0 and b ⬎ 0 (for a ␪˙
strategy), a ⬎ 0 and b ⫽ 0 (for a ␪˙ /␪ strategy), and a ⬀ GOFR⫺1
and b ⫽ 0 (for a GOFR ⫻ ␪˙ strategy).8 In the data analyses
reported below, we fit a line to the data from each block to obtain
an estimate of slope and intercept so that actual performance could
be compared with each of the idealized models.
The other aim of this study was to better understand some of the
factors that influence the optical variables to which one becomes
attuned. Previous research has shown that observers who practice
the same task under a different range of conditions can become
attuned to different optical variables (Jacobs et al., 2001; Smith et
al., 2001). Such range effects most likely occur because the reliability of any given noninvariant depends on the range of conditions encountered by the observer. To illustrate this point in the
context of the emergency braking task, recall that ␪˙ /␪ is equivalent
to an optical invariant when sign radius varies and initial speed is
fixed (see Figure 2A) but not when initial speed varies and sign
radius is fixed (see Figure 2B). If perceptual attunement depends
on the reliability of an optical variable, and reliability is affected
by the range of conditions, then observers who practice under
different conditions may learn to rely on different optical variables.
This prediction was tested by comparing situations in which sign
radius varies and initial speed is fixed (Experiment 1A) with
situations in which sign radius is fixed and initial speed varies
(Experiment 1B).
Finally, the influence of available information on attunement
was tested by manipulating the presence of the ground plane.
When the ground plane was absent, participants could not use any
optical variable whose components include GOFR, including the
optical invariant (GOFR ⫻ ␪˙ /␪). The question was whether par8
Smith et al. (2001) took this equation a step further and suggested that
perceptual attunement itself was a process in which the parameters a and
b were adjusted so as to improve performance. We prefer not to make any
commitments at this point to the mechanisms involved in perceptual
attunement, but we use this equation as a convenient way to describe data
and compare it with the predictions of the three idealized models.
304
FAJEN AND DEVANEY
ticipants in the ground condition would always use GOFR when
GOFR was available and could be used to improve performance.
Recall that ␪˙ /␪ is effectively an optical invariant in Experiment 1A
because initial speed is fixed. Thus, optimal performance could be
achieved in Experiment 1A without using GOFR. In contrast,
GOFR is useful in Experiment 1B because initial speed varied.
Hence, if participants always use available information when such
information can be used to improve performance, then performance in the ground and air conditions should be similar in
Experiment 1A and different in Experiment 1B.
Experiments 1A and 1B
The primary goal of Experiment 1 was to demonstrate that
improvement in performance on a perceptual-motor task can be
attributed (at least, in part) to perceptual attunement. Participants
completed 10 blocks of 30 trials of the emergency braking task,
and analyses were conducted on the data from each block to
identify the optical variable on which observers relied at each stage
of practice. Range effects on attunement were also tested by
comparing conditions in which sign radius varied and initial speed
was fixed (Experiment 1A) with conditions in which sign radius
was fixed and initial speed varied (Experiment 1B). Lastly, the
influence of available information was tested by manipulating the
visibility of the textured ground plane.
Method
Figure 3. Predictions based on global optic flow rate (GOFR) ⫻ ␪˙ /␪
(solid line), ␪˙ /␪ (long dashed line), and ␪˙ (short dashed line) represented in
optical state space (␪˙ vs. ␪). A: Variable sign radius/fixed initial speed. B:
Variable initial speed/fixed sign radius. C: Variable sign radius/variable
initial speed. Thin lines in A and B show trajectories through optical state
space for different values of sign radius or initial speed.
Participants. Twenty students participated in Experiment 1A, and 16
different students participated in Experiment 1B. Students were recruited
from psychology courses and received extra credit for participating. In both
experiments, half of the students were randomly assigned to the ground
condition and the other half to the air condition.
Displays and apparatus. Displays were generated using OpenGL running on a Dell Precision 530 Workstation and were rear-projected by a
Barco Cine 8 CRT projector onto a large (1.8 m ⫻ 1.2 m) screen at a frame
rate of 60 Hz. The displays, which were similar to those used by Yilmaz
and Warren (1995), simulated observer movement along a linear path
toward three red and white octagonal stop signs (see Figure 4, top). The sky
was light blue, and a gray cement-textured ground surface 1.1 m below the
observer’s viewpoint was present in the ground condition but not in the air
condition. One stop sign was positioned on the observer’s simulated path
of motion and the other two were positioned on the right and left. The
distance between stop signs was always four times the radius of the signs.
The center of each sign was at the same height as the simulated viewpoint,
and there were no posts anchoring the bottom of the signs to the ground
surface. Floating stop signs were used to provide a stronger test of the
effects of size. Had the stop signs been anchored to the ground with a post,
then the distance from the center of the sign to the base of the post would
have been constant across changes in size, potentially affecting the size
manipulation.
In Experiment 1A, initial speed was fixed at 10 m/s, and sign radius
varied between 0.15, 0.165, 0.195, 0.255, 0.375, and 0.615 m. In Experiment 1B, sign radius was fixed at 0.225 m, and initial speed varied between
3.6585, 6.0, 8.8235, 11.5385, 13.6364, and 15.0 m/s. The sign radii and
initial speeds were chosen so that the radial travel time (i.e., the time it
takes the observer to travel the distance of one sign radius) were identical
in both experiments (Smith et al., 2001). The advantage of using the same
radial travel times is that the set of trajectories through optical state space
(depicted by the thin solid lines in Figures 3A–3B) were the same for both
experiments. In other words, the pattern of optic flow that was generated by
the stop sign prior to the onset of braking was identical. However, the
LEARNING TO CONTROL COLLISIONS
305
location of the stop sign. Mean stopping location for each block was
indicated by the short gray line (red in the actual display), and the standard
deviation of stopping distance was indicated by the gray bar (blue in the
actual display). Participants were encouraged to monitor their performance
at the end of each block and to keep trying to improve performance
throughout the entire experiment. There were no practice trials prior to the
first block, and the entire experiment lasted approximately 45 min.
Results and Discussion
Figure 4. Top: Screen shot of sample trial from the ground condition.
Bottom: Screen shot of summary screen shown to participants between
blocks to indicate mean and standard deviation of final stopping distance.
consequences of variations in sign radius on final stopping distance are
different from the consequences of variations in initial speed. Radial travel
times for the six conditions were 0.015, 0.0165, 0.0195, 0.0255, 0.0375,
and 0.0615 s. Initial distance was determined by sign radius in both
experiments so that the center stop sign always occupied the same visual
angle (1.2°) at the beginning of the trial.
Procedure. Trials were initiated by moving the joystick to the neutral,
zero-deceleration position and pressing the trigger button. The scene appeared, and simulated motion toward the stop signs began immediately.
Participants were told that the brake was not like a normal brake in that
deceleration could not be adjusted once braking was initiated. Hence their
task was to figure out when to start braking so that they would stop as
closely as possible to the stop signs. At the moment that the joystick was
displaced from the center neutral position, a fixed deceleration of 10 m/s2
was initiated. Displays ended when participants came to a stop, even if they
collided with the stop sign. The final frame was displayed for 1 s before the
intertrial screen appeared.
There were five repetitions per condition in each block, and 10 blocks
per session. At the end of each block, a screen summarizing the participant’s performance on each completed block was presented (see Figure 4,
bottom). The white vertical line under the stop sign corresponds to the
Final stopping distance. Mean final stopping distance is
plotted as a function of block for Experiments 1A and 1B in
Figures 5A and 5B, respectively. A positive final stopping
distance indicates that the observer stopped before reaching the
stop sign. These figures show that there was an overall collision
avoidance bias. That is, despite the instructions to stop as
closely as possible regardless of collision, participants tended to
err on the side of braking too early rather than too late. A
significant effect of block in both experiments, F(9, 162) ⫽
22.15, p ⬍ .001, in Experiment 1A and F(9, 126) ⫽ 10.54, p ⬍
.001, in Experiment 1B indicated that the collision avoidance
bias diminished with practice. However, it was present through
all 10 blocks in both conditions of both experiments. Neither
the main effect of environment nor the Block ⫻ Environment
interaction was significant. Mean standard deviation of final
stopping distance, shown in Figures 5C–5D, also decreased in
both conditions, indicating that participants became more consistent with practice, F(9, 162) ⫽ 20.04, p ⬍ .001, in Experiment 1A and F(9, 126) ⫽ 11.50, p ⬍ .001, in Experiment 1B.
Again, neither the main effect of environment nor the Block ⫻
Environment interaction was significant.
Effects of sign radius in Experiment 1A. Mean ideal decel2
eration at the onset of braking was calculated using v onset
/(2 ⫻
zonset), where vonset and zonset are the speed and distance at brake
onset. Figures 6A and 6C show mean ideal deceleration at onset
as a function of sign radius in the ground and air conditions,
respectively. Data from Blocks 1 and 10 are shown, along with
the predictions of the ␪˙ , ␪˙ /␪, and GOFR ⫻ ␪˙ /␪ models. A 6 (sign
radius) ⫻ 10 (block) ⫻ 2 (environment) mixed analysis of
variance (ANOVA) revealed significant main effects of sign
radius, F(5, 90) ⫽ 88.71, p ⬍ .001, and block, F(9, 162) ⫽
10.88, p ⬍ .001, as well as a significant Sign Radius ⫻ Block
interaction, F(45, 810) ⫽ 3.48, p ⬍ .001. Neither the main
effect of environment nor any of the interactions involving
environment were significant. The main effect of sign radius
indicates that participants tended to initiate deceleration earlier
(i.e., at lower values of dideal) when sign radius was larger.
Hereafter, this tendency is referred to as the size effect. The
significant Sign Radius ⫻ Block interaction indicates that the
strength of the size effect diminished with practice, but the
simple main effect of sign radius in Block 10 was significant in
both the ground, F(5, 45) ⫽ 8.56, p ⬍ .001, and air, F(5, 45) ⫽
9.56, p ⬍ .001, conditions, confirming that participants failed to
completely eliminate the size effect within 10 blocks of
practice.
Optical state space analysis provides a tool for visualizing such
changes in performance in terms of optical variables. Data from
each block were plotted in optical state space, and ␪˙ was regressed
against ␪. Figures 7A, 7C, and 7E show the mean slope, intercept,
and r2 values, respectively, of the line in optical state space that
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FAJEN AND DEVANEY
Figure 5. Mean final stopping distance (A and B) and mean standard deviation of final stopping distance (C
and D) as a function of block for the ground and air conditions of Experiments 1A and 1B. Error bars indicate ⫾
1 SE.
best fit the data from each block. In Block 1, both slope, t(9) ⫽
2.16, p ⫽ .06, in the ground condition and t(9) ⫽ 2.59, p ⬍ .05, in
the air condition, and intercept, t(9) ⫽ 5.05, p ⬍ .01, in the ground
condition and t(9) ⫽ 4.16, p ⬍ .01, in the air condition, were
significantly (or marginally so) greater than zero, indicating that
performance fell between the predictions of the ␪˙ and ␪˙ /␪ models.
Recall that to eliminate the size effect, it was necessary to initiate
deceleration at a higher expansion rate when sign radius was large.
In terms of optical variables, the value of ␪˙ at which deceleration
is initiated should increase proportionally with ␪ (i.e., ␪˙ ⫽ k␪,
where k ⬎ 0), which is equivalent to initiating deceleration at a
fixed value of ␪˙ /␪. As shown in Figure 7A, the slope of the
best-fitting line in optical state space increased with additional
practice, indicating that participants learned to initiate deceleration
at values of ␪˙ that increased with ␪. However, the intercept was
still significantly greater than zero on the 10th block, t(9) ⫽ 4.40,
p ⬍ .01, in the ground condition, and t(9) ⫽ 5.00, p ⬍ .01, in the
air condition (see Figure 7C), indicating that ␪˙ at onset was not
proportional to ␪ at onset.
Although average performance fell between the predictions of
the ␪˙ and ␪˙ /␪ models, one might wonder whether individual
participants relied on such “in between” variables. In principle, the
same average performance could also occur if some participants
relied on ␪˙ while the others relied on ␪˙ /␪. Figures 8A– 8D show the
slope and intercept of the line in optical state space that best fit the
data from Block 10 for each individual participant. Although there
were individual differences, both slope and intercept were consistently greater than zero, suggesting that almost all participants
were, in fact, attuned to variables that fell between the predictions
of ␪˙ and ␪˙ /␪.
Effects of initial speed in Experiment 1B. In Experiment 1B,
deceleration was initiated earlier when initial speed was slow,
resulting in a significant speed effect (see Figures 6B and 6D), F(5,
70) ⫽ 152.79, p ⬍ .001. An Initial Speed ⫻ Block interaction,
LEARNING TO CONTROL COLLISIONS
307
Figure 6. Mean ideal deceleration at onset as a function of radius in Experiment 1A (A and C) and as a function
of initial speed in Experiment 1B (B and D). Data from the ground condition are shown in A and B and from
the air condition in C and D.
F(45, 630) ⫽ 3.07, p ⬍ .001, indicated that the speed effect
diminished with practice, but the simple main effect of initial
speed was still significant on the 10th block, F(5, 70) ⫽ 45.27, p ⬍
.001. Neither the main effect of environment nor any of the
interactions involving environment were significant. Optical state
space analyses (Figures 7B, 7D, and 7F) indicated that performance in Block 1 more closely corresponded to the predictions of
the ␪˙ /␪ model than the ␪˙ model; the slope of the best-fitting line
was significantly greater than zero, t(7) ⫽ 3.62, p ⬍ .01, in the
ground condition and t(7) ⫽ 7.35, p ⬍ .05, in the air condition,
ruling out the ␪˙ model. Also, the intercept did not differ significantly from zero in the ground condition, t(7) ⫽ –1.13, p ⫽ .294,
and was significantly less than zero in the air condition, t(7) ⫽
⫺2.71, p ⬍ .05. Additional practice resulted in a steeper margin in
optical state space (i.e., slope increased and intercept decreased).
Figures 8E– 8H indicate that slope was positive and intercept was
negative for all but a few participants.
In summary, performance improved with practice in both experiments: The mean and standard deviation of final stopping
distance decreased, and the robust size and speed effects that were
present in Block 1 of both experiments diminished with practice.
In terms of optical variables, practice in both experiments resulted
in a steeper margin in optical state space, suggesting that participants learned to initiate braking at a rate of expansion that increased with optical angle. It is interesting that neither the size
effect nor the speed effect was completely eliminated. In Experiment 1A, the size effect could have been eliminated by initiating
deceleration at a value of ␪˙ that increased proportionally with ␪
(i.e., at a fixed ␪˙ /␪). Although performance became more closely
aligned with the predictions of ␪˙ /␪ model, the size effect persisted
through the 10th block. Considering the fact that performance in
Blocks 6 through 10 was fairly stable (see Figures 7A and 7C), one
might conclude that observers are simply unable to use an optical
variable that is invariant over changes in size. However, this
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FAJEN AND DEVANEY
Figure 7. Mean slope (A and B), intercept (C and D), and r2 (E and F) of the best-fitting line in optical state
space as a function of block for the ground (dark lines) and air (gray lines) conditions.
explanation can be ruled out by comparing performance in Experiment 1A and 1B.
Range effects. Figures 7A–7D show that participants in Experiments 1A and 1B, who were given identical amounts of prac-
tice on the same task, learned to rely on different optical variables.
Participants in both experiments learned to initiate braking at a rate
of expansion that increased with ␪. However, the degree to which
␪˙ increased with ␪ for both unpracticed and practiced participants
LEARNING TO CONTROL COLLISIONS
309
ground and air conditions. The fact that performance in the ground
and air conditions was similar in Experiment 1A is not surprising
because initial speed was fixed. However, it is at least initially
surprising that there were no differences in Experiment 1B because
GOFR could have been used to eliminate the speed effect. One
plausible explanation is that participants were simply unable to use
GOFR together with ␪ and ␪˙ , perhaps because these optical variables originate from different parts of the scene (i.e., the stop signs
vs. the ground plane) and are located in different regions of the
visual field. Alternatively, participants in Experiment 1B may have
failed to use GOFR because the range of conditions was so limited.
Although initial speed varied in Experiment 1B, it was still possible to perform the task successfully without using GOFR because
sign radius was fixed. As shown in Figure 3B (thick solid curve),
perfect performance in Experiment 1B corresponds to a curve in
optical state space that can be closely approximated by a steeply
sloped line with a negative intercept. In Experiment 2, in which
both sign radius and initial speed were varied, performance based
on ␪ and ␪˙ alone would be considerably worse. This is illustrated
in Figure 3C, which shows that perfect performance corresponds to
a line in optical state space with a zero intercept and a positive
slope that varies with initial speed. In other words, perfect performance across changes in both sign radius and initial speed cannot
be approximated by a single line in optical state space. Thus, we
expected that differences between the ground and air conditions
would emerge in Experiment 2.
Experiment 2
Figure 8. Slope (A, C) and intercept (B, D) of best-fitting line in optical
state space for Block 10 of Experiment 1A. Each bar represents data from
1 participant. (E, G) and (F, H) show the same for Experiment 1B.
differed between experiments. More important, performance in
Block 1 of Experiment 1B most closely resembled the predictions
of the ␪˙ /␪ model; the best-fitting line in optical state space had a
positive slope and an intercept close to zero. Thus, at a very early
stage of practice, participants in Experiment 1B relied on an
optical variable that is invariant over changes in size—that is, that
would have resulted in no size effect under the conditions used in
Experiment 1A. This confirms that observers are capable of being
attuned to a size-invariant optical variable and rules out the possibility that participants in Experiment 1A failed to rely on ␪˙ /␪
because they were unable to do so. To confirm that the size effect
can, in fact, be eliminated with practice under the right conditions,
sign radius and initial speed were manipulated together in Experiment 2. On the basis of the results of Experiment 1B, it was
expected that participants would quickly become attuned to an
optical variable that is invariant across changes in size.
Effects of available information. The other interesting finding
from Experiment 1 was the similarity between performance in the
Participants in Experiment 1A failed to learn to use ␪˙ /␪ when
doing so would have eliminated the size effect. Similarly, participants in Experiment 1B failed to learn to use GOFR when doing
so would have eliminated the speed effect. It was suggested that
these effects persisted not because observers were unable to tune to
optical invariants but because the range of conditions used in
Experiments 1A and 1B was so limited. This explanation was
tested in Experiment 2 by manipulating sign radius and initial
speed together in the same experiment, rather than in separate
experiments as in Experiment 1. When both sign radius and initial
speed are manipulated, the optical variables that were used in
Experiments 1A and 1B would result in poor performance. Hence,
it was expected that the size effect would be quickly eliminated
and that differences between the ground and air conditions would
emerge in Experiment 2. Experiment 2 also included a second
identical session, which was completed on the day following the
first session, to determine whether performance continued to improve with additional practice.
Method
Participants. Sixteen different undergraduate students, recruited from
a psychology course for which they received extra credit, participated in
Experiment 2. Half of the participants were randomly assigned to the
ground condition and the other half to the air condition.
Displays and apparatus. Displays were similar to those used in Experiment 1 with a few exceptions. First, the 30 trials in each block were
composed of six sign radii crossed with five initial speeds. The same sign
radii and initial speeds used in Experiment 1A and 1B were used in
Experiment 2, with the exception that the slowest initial speed was dropped
so that the number of trials per block would be the same. As in Experiment
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FAJEN AND DEVANEY
1, initial distance was determined by sign radius so that the center stop sign
always occupied a visual angle of 0.8° at the beginning of the trial.
Procedure. The procedures and instructions were essentially the same
as those used in Experiment 1. The only difference was the addition of a
second session, which was completed on the day following the first
session.
Results and Discussion
Size effect. To compare the strength of the size effect across
blocks in Experiment 2 and with the data from Experiment 1A, we
calculated the mean ideal deceleration at onset as a function of sign
radius and found the slope of the best-fitting line. When using
slope as a measure of the strength of the size effect, unbiased
performance is indicated by a zero slope. As shown in Figure 9, the
sign radius bias was considerably weaker in Experiment 2 compared with Experiment 1A. Whereas the mean slope differed
significantly ( p ⬍ .05) from zero in all 10 blocks of both conditions in Experiment 1A, the only block in which the mean slope
differed significantly from zero in Experiment 2 was the very first
block in the ground condition. Of course, this does not mean that
we can accept the null hypothesis and conclude on the basis of
these analyses that there was no size effect beyond Block 1 in
Experiment 2. However, the results clearly indicate that the size
effect was weaker in Experiment 2 than in Experiment 1A. In
addition, although slope never differed significantly from zero in
the air condition, it is noteworthy that the mean slope was consistently greater than zero on all 10 blocks of the second session.
Taken together, the results demonstrate that participants are capable of quickly learning to use optical variables that are invariant (or
nearly so) across changes in sign radius by simply practicing under
the right conditions. Thus, it appears that participants in Experiment 1A failed to eliminate the size effect, not because they were
Figure 9. Mean slope of line that best fits data when ideal deceleration at
onset is plotted as a function of sign radius. Mean slope is shown as a
function of block number in ground and air conditions of Experiment 1A
(dotted lines) and Experiment 2 (solid lines). Data from both sessions of
Experiment 2 are shown.
unable to use size-invariant optical variables, but because the range
of conditions used in Experiment 1A was so limited.
Ground condition versus air condition. Unlike Experiment 1,
Experiment 2 revealed some striking differences between the
ground and air conditions. These differences were apparent in
terms of the optical variables used by both unpracticed participants
(i.e., in the early blocks of Session 1) and well-practiced participants (i.e., in Session 2). As with the size effect, the strength of the
speed effect was measured by calculating the ideal deceleration at
onset as a function of initial speed and finding the slope of the
best-fitting line (see Figure 10). Whereas the strength of the speed
effect changed very little throughout the experiment in the air
condition, it diminished rapidly in the first few blocks and continued to gradually weaken throughout the rest of the first session in
the ground condition. In Session 1, the main effects of environment, F(1, 14) ⫽ 34.29, p ⬍ .001, and block F(9, 126) ⫽ 2.41, p ⬍
.05, were significant. Although the change in slope over blocks
was greater in the ground condition, the Environment ⫻ Block
interaction did not reach significance, F(9, 126) ⫽ 1.32, p ⫽ .23.
In Session 2, only the main effect of environment was significant,
F(1, 14) ⫽ 61.81, p ⬍ .001. These results demonstrate that people
are able to learn to use GOFR together with ␪ and ␪˙ to improve
performance, and the results provide further support for the hypothesis that participants in Experiment 1B failed to use GOFR
because the range of conditions was so limited. Indeed, when
conditions are encountered that do not permit satisfactory performance by relying on a single linear margin in optical state space,
then participants will quickly learn to use GOFR if it is available
to improve performance.
To better understand how GOFR was used by well-practiced
participants in the ground condition, the data were collapsed across
blocks in Session 2 (i.e., after performance stabilized). This allowed us to obtain a reliable estimate of the conditions at the
moment of braking onset for each combination of sign radius and
initial speed.9 If GOFR is used in a manner suggested by the
optical invariant (GOFR ⫻ ␪˙ /␪), then braking should be initiated at
a value of ␪˙ that is scaled to GOFR. Figure 11A shows the
time-to-contact (TTC) at brake onset as a function of sign radius
for each initial speed in the ground condition. In this space, perfect
performance corresponds to a flat line for each initial speed condition, whose height increases with initial speed. A 6 (sign radius) ⫻ 5 (initial speed) ANOVA revealed significant effects of
both radius, F(5, 35) ⫽ 5.47, p ⬍ .05, and initial speed, F(4, 28) ⫽
118.91, p ⬍ .001. Comparison of the data with the predictions
indicates that braking was initiated too early at all five speeds
(especially in the slowest initial speed condition), but the significant effect of initial speed on TTC at onset clearly indicates that
participants were relying on GOFR. Thus, although ␪˙ at onset was
not perfectly scaled to either ␪ or GOFR as one would expect if
participants were using the optical invariant, it is clear that ␪˙ was
tuned to both ␪ and GOFR in the ground condition.
In the air condition (Figure 11B), neither the sign radius effect
(F ⬍ 1) nor the initial speed effect (F ⬍ 1) was significant. The
pattern of results suggests that braking was initiated at a value of
9
Note that such an analysis cannot be performed for each individual
block because there is only one data point per block for each combination
of sign radius and initial speed.
LEARNING TO CONTROL COLLISIONS
Figure 10. Mean slope of line that best fits data from Experiment 2 when
ideal deceleration at onset is plotted as a function of initial speed. Mean
slope is shown as a function of block number in the ground and air
conditions.
␪˙ that was roughly proportional to ␪ across changes in sign radius,
but that ␪˙ /␪ at onset did not vary with initial speed as it did in the
ground condition.
In summary, Experiment 2 revealed interesting differences between the ground and air conditions that were not evident in
Experiment 1. Novices quickly learned to use GOFR when it was
available, resulting in a weaker speed effect. Although the speed
effect persisted throughout both sessions of the experiment, wellpracticed participants did learn to use GOFR to modulate the value
of ␪˙ /␪ at which braking was initiated. These findings provide
further support for the hypothesis that participants in the ground
condition of Experiment 1B failed to use GOFR because of the
limited range of conditions. Once again, when GOFR was useful
for improving performance, participants learned to use it.
311
reported elsewhere in studies of TTC judgment (Caird & Hancock,
1994; DeLucia, 1991), catching (van der Kamp, Savelsbergh, &
Smeets, 1997), hitting (Michaels, Zeinstra, & Oudejans, 2001;
Smith et al., 2001), collision detection (Andersen, Cisneros, Atchley, & Saidpour, 1999; DeLucia, Bleckley, Meyer, & Bush, 2003),
and collision avoidance (DeLucia & Warren, 1994). A primary
focus of these studies is the optical variable ␶ and its components
(␪ and ␪˙ ). One of the novel aspects of the emergency braking task
is that the optical invariant (i.e., GOFR ⫻ ␪˙ /␪) is a higher order
variable defined by three components, one of which corresponds to
a part of the environment that is separate from the approached
object (i.e., GOFR is defined by the optical motion of the ground
plane, not the approached object). In this sense, the emergency
braking task is a natural extension of the large body of research on
timing tasks to situations in which the optical invariant is defined
by a complex combination of multiple components. The results of
Experiment 2 indicate that observers are capable of becoming
attuned to such optical variables.
The results also suggest that people can learn to exploit more
reliable optical variables with practice. Effects of the size of the
approached object and the initial speed that were present at the
beginning of the experiments diminished with practice. Such
changes can be easily interpreted in terms of perceptual attunement: With practice, participants learned to initiate braking at a
value of ␪˙ that depended on ␪ and GOFR. In the remainder of this
section, we consider three issues that pertain to the perceptual
attunement observed in the present study.
First, the amount of practice is just one of several factors that
influences perceptual attunement. Observers in Experiments 1A
and 1B practiced the same task for the same amount of time but
became attuned to different optical variables. This most likely
reflects the fact that the reliability of any given optical variable
depends on the local constraints of the environment. Similar findings have been reported by Jacobs et al. (2001) and Smith et al.
General Discussion
This study was motivated by consideration of the role of perceptual attunement in visually guided action. We used a modified
braking task in which participants were instructed to wait until the
last possible moment to slam on the brakes so that they would stop
as closely as possible to a stop sign in their path of motion. Sign
radius and initial speed were manipulated in different experiments
(Experiments 1A and 1B, respectively) and together in the same
experiment (Experiment 2). The optical invariant that yields unbiased performance across changes in both sign radius and initial
speed is GOFR ⫻ ␪˙ /␪. Other optical variables, such as ␪˙ and ␪˙ /␪,
yield predictable biases as sign radius and initial speed vary. To
determine the optical variables on which participants relied at
various stages of practice, we analyzed the data from each block
and compared them with the predictions of these three idealized
models.
Early in practice, participants exhibited size and speed effects
consistent with the use of noninvariants. Similar effects have been
Figure 11. Mean time-to-contact (TTC) at onset as a function of sign
radius for each condition of initial speed in Experiment 2. Data are from the
(A) ground condition and (B) air condition.
FAJEN AND DEVANEY
312
(2001) and underscore the significance of the range of practice
conditions on perceptual attunement.
Second, observers in the present study (see also Smith et al.,
2001) were often attuned to optical variables that fell between the
three idealized optical models (i.e., ␪˙ , ␪˙ /␪, and GOFR ⫻ ␪˙ /␪). This
indicates that just because an optical variable can be expressed as
a simple combination of component optical variables does not
mean that observers are any more likely to use that variable. The
model proposed by Smith et al. (2001), described in the introduction, provides one possible explanation of attunement to such “in
between” variables. Other possible mechanisms should be considered in future research.
Third, although participants in our experiments learned to exploit more reliable optical variables with practice, the effects of
size and speed often persisted even after extensive practice. In
Experiment 1A, participants failed to learn to use the optical
invariant (i.e., ␪˙ ) when doing so would have eliminated the size
effect. Similarly, participants in Experiment 1B failed to use
GOFR when doing so would have eliminated the speed effect. The
persistence of these effects does not appear to reflect a general
inability to become attuned to the optical invariant. When both
sign radius and initial speed were manipulated together in Experiment 2, participants eliminated the size effect within a few blocks
of practice and learned to use GOFR when it was available to
diminish the speed effect. Although well-practiced participants in
Experiment 2 still exhibited a weak speed effect, they clearly
learned to rely on all three component optical variables and use
them in a manner that was qualitatively similar to the optical
invariant.
If observers are capable of becoming attuned to size-invariant
and speed-invariant optical variables, then why didn’t participants
in Experiment 1A completely eliminate the size effect and why
didn’t participants in Experiments 1B and 2 completely eliminate
the speed effect? Although the size and speed effects could only be
completely eliminated by relying on the optical invariant, the task
could still be performed well on the basis of certain noninvariants,
especially across the limited range of conditions used in Experiments 1A and 1B. Perceptual attunement may have stabilized on
noninvariants once satisfactory feedback was attained, even
though small size and speed effects were still present. This does
not necessarily reflect a lack of motivation on the part of observers.
As observers converge on the optical invariant, the information
that guides perceptual attunement becomes more difficult to detect
(Jacobs et al., 2001). Early in practice, errors in performance due
to unreliable noninvariants tend to be large, and hence easy to
distinguish from random errors due to perceptual and motor variability. As the observer converges on the optical invariant, errors
due to perceptual attunement become smaller, and hence more
difficult to distinguish from random errors. The result is that
perceptual attunement will stabilize on optical variables that result
in “good” but not perfect performance across the conditions that
are encountered.
Conclusion
Do the results observed in the emergency braking task used in
the present study have any implications for normal, regulated
braking? The size and speed effects suggest that ideal deceleration
is perceived on the basis of noninvariants, especially by novice
observers. If normal, regulated braking is controlled by keeping
the perceived ideal deceleration within the safe region between
zero and maximum deceleration as suggested by Fajen (2005a,
2005c), then similar effects should emerge in regulated braking
tasks. Furthermore, such effects should diminish with practice as
participants learn to use more reliable optical variables. We recently found that the initiation and the magnitude of individual
brake adjustments in a regulated braking task are influenced by
sign radius and initial speed in a manner consistent with the effects
observed in the present study (Fajen, 2006). That is, braking was
weakly affected or unaffected by sign radius but was initiated
earlier, and brake adjustments were larger when speed was slow.
Furthermore, practice on the emergency braking task that results in
perceptual attunement transfers to normal, regulated braking. Practice on regulated braking also results in perceptual attunement.
Such findings further demonstrate that perceptual attunement plays
a significant but often overlooked role in the visual guidance of
action.
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Received July 11, 2005
Revision received September 16, 2005
Accepted September 27, 2005 䡲