Learning to Control Collisions: The Role of Perceptual Attunement...

Learning to Control Collisions: The Role of Perceptual Attunement andAction Boundaries

Brett R. Fajen and Michael C. DevaneyRensselaer Polytechnic Institute

The authors investigated the role of perceptual attunement in an emergency braking task in whichparticipants waited until the last possible moment to slam on the brakes. Effects of the size of theapproached object and initial speed on the initiation of braking were used to identify the optical variableson which participants relied at various stages of practice. In Experiments 1A and 1B, size and speedeffects that were present early in practice diminished but were not eliminated as participants learned toinitiate braking at a rate of optical expansion that varied with optical angle. When size and speed weremanipulated together in Experiment 2, the size effect was quickly eliminated, and participants learned touse a 3rd optical variable (global optic flow rate) to nearly eliminate the speed effect. The authorsconclude that perceptual attunement depends on the range of practice conditions, the availability ofinformation, and the criteria for success.

Keywords: visually guided action, perceptual learning, optic flow, collision avoidance, time-to-contact

What distinguishes experts from novices performing the sameperceptual or perceptual-motor skill? Some researchers believethat the superior performance of experts can be attributed, in part,to the ability to become attuned to more effective optical variableswith practice (E. J. Gibson, 1969; J. J. Gibson, 1966, 1986). Thisform 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 relativeforce exerted by a videotaped or computer-generated figure pullingon a bar. Jacobs et al. used the classic task in which participants areasked to judge the relative mass of two colliding balls. Both studiesshowed that perceptual judgments before practice were based onoptical 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 corre-lated with the relevant property. Perceptual attunement has alsobeen demonstrated using a perceptual-motor task in which observ-ers were instructed to time the release of a pendulum to strike anapproaching ball (Smith, Flach, Dittman, & Stanard, 2001). Duringthe early stages of practice, most participants released the pendu-lum when the rate of optical expansion of the approaching ballreached a critical value, resulting in systematic biases in perfor-mance when ball size and speed were manipulated. After severalsessions of practice, the effects of ball size and speed diminished

as participants learned to rely on a higher order optical variabledefined by a combination of optical angle and expansion rate.

The present study was motivated by considering the role ofperceptual attunement in the context of continuously controlledvisually guided actions, such as braking, steering, and fly ballcatching. Up until this point, the role of perceptual attunement insuch tasks has not been seriously considered because the assump-tion has been that all observers, regardless of level of experience,regulate their actions around the critical value of a single opticalinvariant (see Fajen, 2005b, for a more in-depth discussion).1 Forexample, according to the most widely accepted theory of visuallyguided 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 empir-ical evidence to support the single optical invariant assumption forvisually guided action. Furthermore, this assumption has preventedresearchers from considering the possibility that the poorer per-formance of novices reflects the use of noninvariants and thatimprovement with practice on a visually guided action reflects theability to become attuned to more reliable optical variables.

To understand how attunement might play a role in improvingperformance on a visually guided action such as braking, imaginea driver moving on the highway at a constant speed toward adistant toll booth. When should the driver start braking? Howmuch brake pressure should be applied? The answers depend onseveral factors, such as the distance to the toll booth, the speed ofapproach, the strength of the brake, and the driver’s tolerance forrisk. The driver could initiate braking early and slow down grad-

1 Some readers may question the claim that noninvariants have beenignored in studies of visually guided action. Indeed, it is not uncommon fornoninvariants to be considered in investigations of tasks such as catching,hitting, and avoiding collisions. Our claim regarding the tendency to focusexclusively on optical invariants concerns investigations of continuouslycontrolled visually guided action, such as those mentioned in the text.

Brett R. Fajen and Michael C. Devaney, Department of CognitiveScience, Rensselaer Polytechnic Institute.

This research was supported by Grant BCS 0236734 from the NationalScience Foundation. We thank Andy Peruggi and Parthipan Pathmanapanfor 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, Rens-selaer Polytechnic Institute, 110 8th Street, Troy, NY 12180. E-mail:[email protected]

Journal of Experimental Psychology: Copyright 2006 by the American Psychological AssociationHuman Perception and Performance2006, Vol. 32, No. 2, 300–313

0096-1523/06/$12.00 DOI: 10.1037/0096-1523.32.2.300

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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 orincreases deceleration too gradually, then at some point the decel-eration required to stop will exceed the maximum deceleration ofthe brake and it will no longer be possible to stop within the limitsof the brake.

To control deceleration so that it is always still possible to stop,one must be able to detect information about the decelerationrequired to stop relative to the brake’s maximum possible decel-eration (Fajen, 2005a, 2005c). In terms of spatial variables, theconstant rate of deceleration that would bring the driver to a stopat the toll booth without making any further adjustments is equalto

dideal � v 2/2z, (1)

where v is speed, z is target distance, and v2/2z is the “idealdeceleration” (abbreviated dideal) in the sense that no further ad-justments are necessary as long as current deceleration is equal tov2/2z. Further, v/z is equal to the inverse of the amount of timeremaining until the driver reaches the toll booth assuming constantvelocity (which Lee, 1976, called time-to-contact) and is specifiedby 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 afixed eyeheight, the optical velocity of each point on the groundsurface depends on the point’s azimuth and declination. In addi-tion, the optical velocity of each point is proportional to the ratioof observer speed (v) to eyeheight (e). Thus, v/e is a globalmultiplier that affects the optical motion of all points on the groundsurface in the same way. This ratio (v/e) is referred to as globaloptic flow rate (GOFR; Larish & Flach, 1990; Warren, 1982). Aslong as eyeheight is fixed, which it typically is for the kinds ofactivities that involve visually guided braking (e.g., driving, cy-cling, playing sports), GOFR specifies speed.2

Substituting �̇/� (or 1/�) for v/z and GOFR for v, Equation 1 canbe expressed in terms of optical variables as

dideal � GOFR � �̇/� � GOFR/�. (2)

(Note that the “2” in the denominator of Equation 1 may bedropped in Equation 2 because GOFR � �̇/� is proportional to, notequal to, dideal.) Thus, to avoid a collision, one could adjust brakepressure to keep the perceived ideal deceleration, based onGOFR � �̇/�, below a critical value that is calibrated to maximumdeceleration (see Fajen, 2005c, for more on the role of calibrationin visually guided braking).

GOFR � �̇/� is an example of an optical invariant because ituniquely specifies ideal deceleration across variations in observerspeed and object size. This is illustrated in Figure 1A, which showsthe value of GOFR � �̇/� as a function of time for 25 simulatedapproaches to an object in which speed is constant within eachapproach but varies randomly between 3.6585 and 15.0 m/s be-tween approaches.3 The size (i.e., the radius) of the approachedobject also varies randomly between 0.15 and 0.615 m betweenapproaches. The black dots correspond to the point at which theideal deceleration was equal to 10 m/s2 (the maximum rate ofdeceleration used in the experiments) for each simulated approach.Because GOFR � �̇/� is invariant across changes in speed andsize, its value at this boundary is the same for each trial.

2 Speed is also specified by edge rate (ER), which is defined as thenumber of texture elements that pass by a fixed point of reference in thevisual field per unit of time (Warren, 1982). Unlike GOFR, ER is invariantover changes in eyeheight but not over changes in texture density. Inprinciple, observers could rely on ER rather than, or in addition to, GOFR.However, Dyre (1997) found that perceptual judgments of self-motionwere affected more by GOFR than ER, and Fajen (2005a) found thatGOFR dominated ER in a visually guided braking task. Thus, we mainlyrefer to GOFR in this article but note here that observers could also rely onER.

3 The ranges of initial speeds and object sizes correspond to those usedin the experiments.

Figure 1. Global optic flow rate (GOFR) � �̇/� (A) and �̇ (B) as afunction of time for 25 simulated approaches. Object size (i.e., radius)varied randomly between 0.15 and 0.615 m, and initial speed variedrandomly between 3.6585 and 15.0 m/s. The black dots indicate the pointon each trial at which ideal deceleration was equal to maximumdeceleration.

301LEARNING TO CONTROL COLLISIONS

Although information that specifies ideal deceleration is availablein the optic array, this does not necessarily mean that it is actuallyused. There are also many noninvariants whose value when idealdeceleration is equal to maximum deceleration is affected to at leastsome degree by size and speed. Figure 1B shows the value of onenoninvariant, expansion rate (�̇), as a function of time for the same 25simulated approaches in Figure 1A. Unlike the invariant, the value of�̇ at the moment that the ideal deceleration is equal to the maximumdeceleration (indicated by the black dots in Figure 1B) varies betweenapproaches. Thus, perceiving ideal deceleration on the basis of �̇would result in systematic overestimation or underestimation of idealdeceleration as speed and size vary. However, the reliability of �̇depends on the range of object sizes and initial speeds, and there areother noninvariants that vary less than �̇. So depending on tolerancefor error, performance based on a noninvariant may still be “goodenough.”4

Do observers rely on the invariant or a noninvariant to keepideal deceleration within the limits of the brake? Can improvementin performance be attributed to attunement to more reliable opticalvariables with practice? The research by Michaels and de Vries(1998), Jacobs et al. (2001), and Smith et al. (2001) that wassummarized at the beginning of this article suggests that people dorely on noninvariants at least some of the time, and that theyconverge on more reliable variables with practice under certainconditions. However, the tasks used in those studies were unre-lated to the kinds of visually guided actions that are under contin-uous control, such as braking, steering, and fly ball catching.Demonstrating perceptual attunement in the context of such visu-ally guided actions is a challenge because when actions are con-tinuously regulated, it is usually possible to correct for errors thatarise from systematic overestimations or underestimations result-ing from the use of a noninvariant. Attempting to infer the opticalvariable on which participants relied by looking at the effects ofvarious manipulations (e.g., object size and speed) would not be aseffective for continuously regulated actions as it is for preciselytimed ballistic actions, such as releasing a pendulum to hit anapproaching ball (e.g., Smith et al., 2001).

To investigate the role of perceptual attunement in the context ofbraking, we developed an “emergency braking” task in whichparticipants were instructed to wait until the last possible momentto stop at an object (a stop sign) in the path of motion by initiatingmaximum brake pressure. To perform the task successfully, par-ticipants must “slam on the brakes” at the moment that idealdeceleration is equal to maximum deceleration.5 If participantsrely on the optical invariant (i.e., GOFR � �̇/�) to perceive idealdeceleration, then the ideal deceleration at which braking is initi-ated should be unaffected by the size of the stop sign and the initialapproach speed. On the other hand, if the initiation of braking isaffected by these factors, then participants must be using a non-invariant, and the pattern of errors can be used to make inferencesabout which noninvariant is being used. To compare performanceat different stages of learning, we adopted a design similar to thatused by Smith et al. (2001). The experiments consisted of blocksof trials, and analyses were conducted for each block to determinethe optical variables on which participants relied at each stage ofpractice.

One might wonder whether anything can be learned aboutnormal, regulated braking by studying how people perform anemergency braking task, which is not a visually guided action. If

normal, regulated braking is controlled by keeping the perceivedideal deceleration within the limits of the brake as suggested byFajen (2005a, 2005c), then participants must be able to reliablyperceive ideal deceleration relative to maximum decelerationacross changes in speed and size. Because the emergency brakingtask requires participants to slam on the brakes at the moment thatperceived ideal deceleration equals maximum deceleration, thistask provides a useful way to measure the reliability with whichparticipants perceive ideal deceleration across variations in sizeand speed. Thus, by studying emergency braking, we may be ableto learn something about how normal braking is controlled andwhether improvement with practice is due to perceptualattunement.

Now that we have explained how perceptual attunement mightplay a role in improving performance in a visually guided actionsuch as braking, let us show how data from the emergency brakingtask can be represented in ways that allow us to make simplecomparisons with the predictions of different optical variables.Figure 2 shows ideal deceleration at the onset of braking (based onvonset

2/2zonset) as a function of stop sign radius (Figure 2A) andinitial speed (Figure 2B). If participants rely on the optical invari-ant, then the data should fall along a line with zero slope.6 Ifparticipants initiate deceleration at a fixed rate of optical expan-sion, then the data should fall along a curve that slopes downwardin the sign radius plot and upward in the initial speed plot. That is,braking should be initiated earlier when radius is large and speedis slow. Lastly, if the rate of optical expansion at which braking isinitiated is proportional to optical angle (i.e., if braking is initiatedat a fixed value of �̇ or 1/�), then the data should fall along a flatline in the sign radius plot and an upwardly sloping curve in theinitial speed plot.7

Another useful way to represent the data is to plot expansionrate at onset as a function of optical angle at onset (see Figure 3),which Smith et al. (2001) referred to as optical state space. Oneadvantage of an optical state space representation is that expansionrate and �̇ strategies are easier to visualize. Regardless of whethersign radius (Figure 3A) or initial speed (Figure 3B) is varied, theexpansion rate strategy corresponds to a line in optical state spacewith a zero slope and a positive intercept (dotted line), and the �̇/�strategy corresponds to a line with a positive slope and a zerointercept (dashed line). Visualizing the predictions of the opticalinvariant can be more difficult because optical state space does not

4 For example, �̇/� varies across changes in initial speed but not acrosschanges in object size. If conditions are encountered in which the range ofinitial speeds is narrow, then performance based on �̇/� may be indistin-guishable from performance based on the optical invariant.

5 In practice, observers may initiate emergency braking a split secondbefore ideal deceleration reaches maximum deceleration to compensate forperceptual-motor time delays.

6 The location of the y-intercept relative to the brake’s maximum decel-eration indicates whether there was an overall bias to initiate decelerationtoo early or too late. Thus, if participants are calibrated to the strength ofthe brake and do not exhibit any biases, then the y-intercept shouldcorrespond to the brake’s maximum deceleration.

7 The particular critical value of the corresponding optical variable willaffect the height but not the shape of the curve. The critical values used inFigure 2 would result in an overall bias to stop at or before reaching thestop sign across the range of sign radii and initial speeds.

302 FAJEN AND DEVANEY

include a dimension for GOFR. Rather than adding a third dimen-sion, the predictions for different initial speed conditions (i.e.,different values of GOFR) can be represented as different lines inoptical state space (Figure 3C). If participants rely on the opticalinvariant, then the data for a given initial speed should fall alonga line with a zero intercept and a positive slope inversely propor-tional to GOFR. As initial speed varies, the line’s slope changes,but it always intercepts the y-axis at zero. The solid lines in Figures3A–3B show the predictions of the optical invariant when signradius and initial speed are varied separately. Even though theoptical invariant is composed of three component optical variables,the predictions can be represented by a single line in optical statespace when initial speed is fixed because the value of GOFR isalways the same (Figure 3A). When initial speed varies and signradius is fixed, the predictions can be represented by a curve ratherthan a straight line in optical state space (Figure 3B).

Although these plots are useful for making comparisons be-tween the data and predictions of each model, we did not expectthat the data would necessarily align with the predictions of anyone of these variables. �̇, �̇/�, and GOFR � �̇/� are simply threeout of an infinite number of ways of defining boundaries in opticalstate space. The fact that these three variables can be expressed assimple combinations of component optical variables does notnecessarily mean that actual performance is any more likely tocorrespond to the predictions of one of these models. For example,the data might fall along a line in optical state space that liesbetween the predictions of the �̇ and �̇/� models, or even fall alonga curve. It is just as important to be able to describe and interpretthese possible outcomes.

Smith et al. (2001) recognized this problem and pointed out thatany linear margin (i.e., boundary) in optical state space can beexpressed by the equation �̇ � a� � b, where a is the slope and bis the intercept. This equation provides a convenient way to de-scribe data that do not necessarily conform to the predictions ofany of the idealized models. For example, a line in optical statespace that lies between the predictions of the �̇ and �̇/� modelswould 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 analysesreported below, we fit a line to the data from each block to obtainan estimate of slope and intercept so that actual performance couldbe compared with each of the idealized models.

The other aim of this study was to better understand some of thefactors that influence the optical variables to which one becomesattuned. Previous research has shown that observers who practicethe same task under a different range of conditions can becomeattuned to different optical variables (Jacobs et al., 2001; Smith etal., 2001). Such range effects most likely occur because the reli-ability of any given noninvariant depends on the range of condi-tions encountered by the observer. To illustrate this point in thecontext of the emergency braking task, recall that �̇/� is equivalentto an optical invariant when sign radius varies and initial speed isfixed (see Figure 2A) but not when initial speed varies and signradius is fixed (see Figure 2B). If perceptual attunement dependson the reliability of an optical variable, and reliability is affectedby the range of conditions, then observers who practice underdifferent conditions may learn to rely on different optical variables.This prediction was tested by comparing situations in which signradius varies and initial speed is fixed (Experiment 1A) withsituations in which sign radius is fixed and initial speed varies(Experiment 1B).

Finally, the influence of available information on attunementwas tested by manipulating the presence of the ground plane.When the ground plane was absent, participants could not use anyoptical variable whose components include GOFR, including theoptical invariant (GOFR � �̇/�). The question was whether par-

8 Smith et al. (2001) took this equation a step further and suggested thatperceptual attunement itself was a process in which the parameters a andb were adjusted so as to improve performance. We prefer not to make anycommitments at this point to the mechanisms involved in perceptualattunement, but we use this equation as a convenient way to describe dataand compare it with the predictions of the three idealized models.

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).


ticipants in the ground condition would always use GOFR whenGOFR was available and could be used to improve performance.Recall that �̇/� is effectively an optical invariant in Experiment 1Abecause initial speed is fixed. Thus, optimal performance could beachieved 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 suchinformation can be used to improve performance, then perfor-mance in the ground and air conditions should be similar inExperiment 1A and different in Experiment 1B.

Experiments 1A and 1B

The primary goal of Experiment 1 was to demonstrate thatimprovement in performance on a perceptual-motor task can beattributed (at least, in part) to perceptual attunement. Participantscompleted 10 blocks of 30 trials of the emergency braking task,and analyses were conducted on the data from each block toidentify the optical variable on which observers relied at each stageof practice. Range effects on attunement were also tested bycomparing conditions in which sign radius varied and initial speedwas fixed (Experiment 1A) with conditions in which sign radiuswas fixed and initial speed varied (Experiment 1B). Lastly, theinfluence of available information was tested by manipulating thevisibility of the textured ground plane.

Method

Participants. Twenty students participated in Experiment 1A, and 16different students participated in Experiment 1B. Students were recruitedfrom psychology courses and received extra credit for participating. In bothexperiments, half of the students were randomly assigned to the groundcondition and the other half to the air condition.

Displays and apparatus. Displays were generated using OpenGL run-ning on a Dell Precision 530 Workstation and were rear-projected by aBarco Cine 8 CRT projector onto a large (1.8 m � 1.2 m) screen at a framerate of 60 Hz. The displays, which were similar to those used by Yilmazand Warren (1995), simulated observer movement along a linear pathtoward three red and white octagonal stop signs (see Figure 4, top). The skywas light blue, and a gray cement-textured ground surface 1.1 m below theobserver’s viewpoint was present in the ground condition but not in the aircondition. One stop sign was positioned on the observer’s simulated pathof motion and the other two were positioned on the right and left. Thedistance 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 groundsurface. Floating stop signs were used to provide a stronger test of theeffects 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 wouldhave been constant across changes in size, potentially affecting the sizemanipulation.

In Experiment 1A, initial speed was fixed at 10 m/s, and sign radiusvaried between 0.15, 0.165, 0.195, 0.255, 0.375, and 0.615 m. In Experi-ment 1B, sign radius was fixed at 0.225 m, and initial speed varied between3.6585, 6.0, 8.8235, 11.5385, 13.6364, and 15.0 m/s. The sign radii andinitial speeds were chosen so that the radial travel time (i.e., the time ittakes the observer to travel the distance of one sign radius) were identicalin both experiments (Smith et al., 2001). The advantage of using the sameradial 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 bothexperiments. In other words, the pattern of optic flow that was generated bythe stop sign prior to the onset of braking was identical. However, the

Figure 3. Predictions based on global optic flow rate (GOFR) � �̇/�(solid line), �̇/� (long dashed line), and �̇ (short dashed line) represented inoptical state space (�̇ vs. �). A: Variable sign radius/fixed initial speed. B:Variable initial speed/fixed sign radius. C: Variable sign radius/variableinitial speed. Thin lines in A and B show trajectories through optical statespace for different values of sign radius or initial speed.


consequences of variations in sign radius on final stopping distance aredifferent from the consequences of variations in initial speed. Radial traveltimes 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 bothexperiments so that the center stop sign always occupied the same visualangle (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 ap-peared, and simulated motion toward the stop signs began immediately.Participants were told that the brake was not like a normal brake in thatdeceleration could not be adjusted once braking was initiated. Hence theirtask was to figure out when to start braking so that they would stop asclosely as possible to the stop signs. At the moment that the joystick wasdisplaced from the center neutral position, a fixed deceleration of 10 m/s2

was initiated. Displays ended when participants came to a stop, even if theycollided with the stop sign. The final frame was displayed for 1 s before theintertrial screen appeared.

There were five repetitions per condition in each block, and 10 blocksper session. At the end of each block, a screen summarizing the partici-pant’s performance on each completed block was presented (see Figure 4,bottom). The white vertical line under the stop sign corresponds to the

location of the stop sign. Mean stopping location for each block wasindicated by the short gray line (red in the actual display), and the standarddeviation of stopping distance was indicated by the gray bar (blue in theactual display). Participants were encouraged to monitor their performanceat the end of each block and to keep trying to improve performancethroughout the entire experiment. There were no practice trials prior to thefirst block, and the entire experiment lasted approximately 45 min.

Results and Discussion

Final stopping distance. Mean final stopping distance isplotted as a function of block for Experiments 1A and 1B inFigures 5A and 5B, respectively. A positive final stoppingdistance indicates that the observer stopped before reaching thestop sign. These figures show that there was an overall collisionavoidance bias. That is, despite the instructions to stop asclosely as possible regardless of collision, participants tended toerr on the side of braking too early rather than too late. Asignificant 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 avoidancebias diminished with practice. However, it was present throughall 10 blocks in both conditions of both experiments. Neitherthe main effect of environment nor the Block � Environmentinteraction was significant. Mean standard deviation of finalstopping distance, shown in Figures 5C–5D, also decreased inboth conditions, indicating that participants became more con-sistent with practice, F(9, 162) � 20.04, p � .001, in Experi-ment 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 decel-eration at the onset of braking was calculated using v onset

2 /(2 �zonset), where vonset and zonset are the speed and distance at brakeonset. Figures 6A and 6C show mean ideal deceleration at onsetas a function of sign radius in the ground and air conditions,respectively. Data from Blocks 1 and 10 are shown, along withthe predictions of the �̇, �̇/�, and GOFR � �̇/� models. A 6 (signradius) � 10 (block) � 2 (environment) mixed analysis ofvariance (ANOVA) revealed significant main effects of signradius, F(5, 90) � 88.71, p � .001, and block, F(9, 162) �10.88, p � .001, as well as a significant Sign Radius � Blockinteraction, F(45, 810) � 3.48, p � .001. Neither the maineffect of environment nor any of the interactions involvingenvironment were significant. The main effect of sign radiusindicates 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. Thesignificant Sign Radius � Block interaction indicates that thestrength of the size effect diminished with practice, but thesimple main effect of sign radius in Block 10 was significant inboth the ground, F(5, 45) � 8.56, p � .001, and air, F(5, 45) �9.56, p � .001, conditions, confirming that participants failed tocompletely eliminate the size effect within 10 blocks ofpractice.

Optical state space analysis provides a tool for visualizing suchchanges in performance in terms of optical variables. Data fromeach block were plotted in optical state space, and �̇ was regressedagainst �. Figures 7A, 7C, and 7E show the mean slope, intercept,and r2 values, respectively, of the line in optical state space that

Figure 4. Top: Screen shot of sample trial from the ground condition.Bottom: Screen shot of summary screen shown to participants betweenblocks to indicate mean and standard deviation of final stopping distance.


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, inthe air condition, and intercept, t(9) � 5.05, p � .01, in the groundcondition and t(9) � 4.16, p � .01, in the air condition, weresignificantly (or marginally so) greater than zero, indicating thatperformance fell between the predictions of the �̇ and �̇/� models.Recall that to eliminate the size effect, it was necessary to initiatedeceleration at a higher expansion rate when sign radius was large.In terms of optical variables, the value of �̇ at which decelerationis initiated should increase proportionally with � (i.e., �̇� k�,where k � 0), which is equivalent to initiating deceleration at afixed value of �̇/�. As shown in Figure 7A, the slope of thebest-fitting line in optical state space increased with additionalpractice, indicating that participants learned to initiate decelerationat values of �̇ that increased with �. However, the intercept wasstill 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 notproportional to � at onset.

Although average performance fell between the predictions ofthe �̇ and �̇/� models, one might wonder whether individualparticipants relied on such “in between” variables. In principle, thesame average performance could also occur if some participantsrelied on �̇ while the others relied on �̇/�. Figures 8A–8D show theslope and intercept of the line in optical state space that best fit thedata from Block 10 for each individual participant. Although therewere individual differences, both slope and intercept were consis-tently greater than zero, suggesting that almost all participantswere, in fact, attuned to variables that fell between the predictionsof �̇ 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,

Figure 5. Mean final stopping distance (A and B) and mean standard deviation of final stopping distance (Cand D) as a function of block for the ground and air conditions of Experiments 1A and 1B. Error bars indicate �1 SE.


F(45, 630) � 3.07, p � .001, indicated that the speed effectdiminished with practice, but the simple main effect of initialspeed was still significant on the 10th block, F(5, 70) � 45.27, p �.001. Neither the main effect of environment nor any of theinteractions involving environment were significant. Optical statespace analyses (Figures 7B, 7D, and 7F) indicated that perfor-mance in Block 1 more closely corresponded to the predictions ofthe �̇/� model than the �̇ model; the slope of the best-fitting linewas significantly greater than zero, t(7) � 3.62, p � .01, in theground condition and t(7) � 7.35, p � .05, in the air condition,ruling out the �̇ model. Also, the intercept did not differ signifi-cantly 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 inoptical state space (i.e., slope increased and intercept decreased).Figures 8E–8H indicate that slope was positive and intercept wasnegative for all but a few participants.

In summary, performance improved with practice in both ex-periments: The mean and standard deviation of final stoppingdistance decreased, and the robust size and speed effects that werepresent in Block 1 of both experiments diminished with practice.In terms of optical variables, practice in both experiments resultedin a steeper margin in optical state space, suggesting that partici-pants learned to initiate braking at a rate of expansion that in-creased with optical angle. It is interesting that neither the sizeeffect nor the speed effect was completely eliminated. In Experi-ment 1A, the size effect could have been eliminated by initiatingdeceleration at a value of �̇ that increased proportionally with �(i.e., at a fixed �̇/�). Although performance became more closelyaligned with the predictions of �̇/� model, the size effect persistedthrough the 10th block. Considering the fact that performance inBlocks 6 through 10 was fairly stable (see Figures 7A and 7C), onemight conclude that observers are simply unable to use an opticalvariable that is invariant over changes in size. However, this

Figure 6. Mean ideal deceleration at onset as a function of radius in Experiment 1A (A and C) and as a functionof initial speed in Experiment 1B (B and D). Data from the ground condition are shown in A and B and fromthe air condition in C and D.


explanation can be ruled out by comparing performance in Exper-iment 1A and 1B.

Range effects. Figures 7A–7D show that participants in Ex-periments 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 rateof expansion that increased with �. However, the degree to which�̇ increased with � for both unpracticed and practiced participants

Figure 7. Mean slope (A and B), intercept (C and D), and r2 (E and F) of the best-fitting line in optical statespace as a function of block for the ground (dark lines) and air (gray lines) conditions.


differed between experiments. More important, performance inBlock 1 of Experiment 1B most closely resembled the predictionsof the �̇/� model; the best-fitting line in optical state space had apositive slope and an intercept close to zero. Thus, at a very earlystage of practice, participants in Experiment 1B relied on anoptical variable that is invariant over changes in size—that is, thatwould have resulted in no size effect under the conditions used inExperiment 1A. This confirms that observers are capable of beingattuned to a size-invariant optical variable and rules out the pos-sibility that participants in Experiment 1A failed to rely on �̇/�because they were unable to do so. To confirm that the size effectcan, in fact, be eliminated with practice under the right conditions,sign radius and initial speed were manipulated together in Exper-iment 2. On the basis of the results of Experiment 1B, it wasexpected that participants would quickly become attuned to anoptical variable that is invariant across changes in size.

Effects of available information. The other interesting findingfrom Experiment 1 was the similarity between performance in the

ground and air conditions. The fact that performance in the groundand air conditions was similar in Experiment 1A is not surprisingbecause initial speed was fixed. However, it is at least initiallysurprising that there were no differences in Experiment 1B becauseGOFR could have been used to eliminate the speed effect. Oneplausible explanation is that participants were simply unable to useGOFR together with � and �̇, perhaps because these optical vari-ables originate from different parts of the scene (i.e., the stop signsvs. the ground plane) and are located in different regions of thevisual field. Alternatively, participants in Experiment 1B may havefailed to use GOFR because the range of conditions was so limited.Although initial speed varied in Experiment 1B, it was still pos-sible to perform the task successfully without using GOFR becausesign radius was fixed. As shown in Figure 3B (thick solid curve),perfect performance in Experiment 1B corresponds to a curve inoptical state space that can be closely approximated by a steeplysloped line with a negative intercept. In Experiment 2, in whichboth sign radius and initial speed were varied, performance basedon � and �̇ alone would be considerably worse. This is illustratedin Figure 3C, which shows that perfect performance corresponds toa line in optical state space with a zero intercept and a positiveslope that varies with initial speed. In other words, perfect perfor-mance across changes in both sign radius and initial speed cannotbe approximated by a single line in optical state space. Thus, weexpected that differences between the ground and air conditionswould emerge in Experiment 2.

Experiment 2

Participants in Experiment 1A failed to learn to use �̇/� whendoing so would have eliminated the size effect. Similarly, partic-ipants in Experiment 1B failed to learn to use GOFR when doingso would have eliminated the speed effect. It was suggested thatthese effects persisted not because observers were unable to tune tooptical invariants but because the range of conditions used inExperiments 1A and 1B was so limited. This explanation wastested in Experiment 2 by manipulating sign radius and initialspeed together in the same experiment, rather than in separateexperiments as in Experiment 1. When both sign radius and initialspeed are manipulated, the optical variables that were used inExperiments 1A and 1B would result in poor performance. Hence,it was expected that the size effect would be quickly eliminatedand that differences between the ground and air conditions wouldemerge in Experiment 2. Experiment 2 also included a secondidentical session, which was completed on the day following thefirst session, to determine whether performance continued to im-prove with additional practice.

Method

Participants. Sixteen different undergraduate students, recruited froma psychology course for which they received extra credit, participated inExperiment 2. Half of the participants were randomly assigned to theground condition and the other half to the air condition.

Displays and apparatus. Displays were similar to those used in Ex-periment 1 with a few exceptions. First, the 30 trials in each block werecomposed of six sign radii crossed with five initial speeds. The same signradii and initial speeds used in Experiment 1A and 1B were used inExperiment 2, with the exception that the slowest initial speed was droppedso that the number of trials per block would be the same. As in Experiment

Figure 8. Slope (A, C) and intercept (B, D) of best-fitting line in opticalstate space for Block 10 of Experiment 1A. Each bar represents data from1 participant. (E, G) and (F, H) show the same for Experiment 1B.


1, initial distance was determined by sign radius so that the center stop signalways occupied a visual angle of 0.8° at the beginning of the trial.

Procedure. The procedures and instructions were essentially the sameas those used in Experiment 1. The only difference was the addition of asecond session, which was completed on the day following the firstsession.

Results and Discussion

Size effect. To compare the strength of the size effect acrossblocks in Experiment 2 and with the data from Experiment 1A, wecalculated the mean ideal deceleration at onset as a function of signradius and found the slope of the best-fitting line. When usingslope as a measure of the strength of the size effect, unbiasedperformance is indicated by a zero slope. As shown in Figure 9, thesign radius bias was considerably weaker in Experiment 2 com-pared with Experiment 1A. Whereas the mean slope differedsignificantly ( p � .05) from zero in all 10 blocks of both condi-tions in Experiment 1A, the only block in which the mean slopediffered significantly from zero in Experiment 2 was the very firstblock in the ground condition. Of course, this does not mean thatwe can accept the null hypothesis and conclude on the basis ofthese analyses that there was no size effect beyond Block 1 inExperiment 2. However, the results clearly indicate that the sizeeffect was weaker in Experiment 2 than in Experiment 1A. Inaddition, although slope never differed significantly from zero inthe air condition, it is noteworthy that the mean slope was consis-tently greater than zero on all 10 blocks of the second session.Taken together, the results demonstrate that participants are capa-ble of quickly learning to use optical variables that are invariant (ornearly so) across changes in sign radius by simply practicing underthe right conditions. Thus, it appears that participants in Experi-ment 1A failed to eliminate the size effect, not because they were

unable to use size-invariant optical variables, but because the rangeof conditions used in Experiment 1A was so limited.

Ground condition versus air condition. Unlike Experiment 1,Experiment 2 revealed some striking differences between theground and air conditions. These differences were apparent interms of the optical variables used by both unpracticed participants(i.e., in the early blocks of Session 1) and well-practiced partici-pants (i.e., in Session 2). As with the size effect, the strength of thespeed effect was measured by calculating the ideal deceleration atonset as a function of initial speed and finding the slope of thebest-fitting line (see Figure 10). Whereas the strength of the speedeffect changed very little throughout the experiment in the aircondition, it diminished rapidly in the first few blocks and contin-ued to gradually weaken throughout the rest of the first session inthe ground condition. In Session 1, the main effects of environ-ment, F(1, 14) � 34.29, p � .001, and block F(9, 126) � 2.41, p �.05, were significant. Although the change in slope over blockswas greater in the ground condition, the Environment � Blockinteraction 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 peopleare able to learn to use GOFR together with � and �̇ to improveperformance, and the results provide further support for the hy-pothesis that participants in Experiment 1B failed to use GOFRbecause the range of conditions was so limited. Indeed, whenconditions are encountered that do not permit satisfactory perfor-mance by relying on a single linear margin in optical state space,then participants will quickly learn to use GOFR if it is availableto improve performance.

To better understand how GOFR was used by well-practicedparticipants in the ground condition, the data were collapsed acrossblocks in Session 2 (i.e., after performance stabilized). This al-lowed us to obtain a reliable estimate of the conditions at themoment of braking onset for each combination of sign radius andinitial speed.9 If GOFR is used in a manner suggested by theoptical invariant (GOFR � �̇/�), then braking should be initiated ata value of �̇ that is scaled to GOFR. Figure 11A shows thetime-to-contact (TTC) at brake onset as a function of sign radiusfor each initial speed in the ground condition. In this space, perfectperformance corresponds to a flat line for each initial speed con-dition, whose height increases with initial speed. A 6 (sign ra-dius) � 5 (initial speed) ANOVA revealed significant effects ofboth radius, F(5, 35) � 5.47, p � .05, and initial speed, F(4, 28) �118.91, p � .001. Comparison of the data with the predictionsindicates that braking was initiated too early at all five speeds(especially in the slowest initial speed condition), but the signifi-cant effect of initial speed on TTC at onset clearly indicates thatparticipants were relying on GOFR. Thus, although �̇ at onset wasnot perfectly scaled to either � or GOFR as one would expect ifparticipants were using the optical invariant, it is clear that �̇ wastuned 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. Thepattern of results suggests that braking was initiated at a value of

9 Note that such an analysis cannot be performed for each individualblock because there is only one data point per block for each combinationof sign radius and initial speed.

Figure 9. Mean slope of line that best fits data when ideal deceleration atonset is plotted as a function of sign radius. Mean slope is shown as afunction of block number in ground and air conditions of Experiment 1A(dotted lines) and Experiment 2 (solid lines). Data from both sessions ofExperiment 2 are shown.


�̇ that was roughly proportional to � across changes in sign radius,but that �̇/� at onset did not vary with initial speed as it did in theground condition.

In summary, Experiment 2 revealed interesting differences be-tween the ground and air conditions that were not evident inExperiment 1. Novices quickly learned to use GOFR when it wasavailable, resulting in a weaker speed effect. Although the speedeffect persisted throughout both sessions of the experiment, well-practiced participants did learn to use GOFR to modulate the valueof �̇/� at which braking was initiated. These findings providefurther support for the hypothesis that participants in the groundcondition of Experiment 1B failed to use GOFR because of thelimited range of conditions. Once again, when GOFR was usefulfor improving performance, participants learned to use it.

General Discussion

This study was motivated by consideration of the role of per-ceptual attunement in visually guided action. We used a modifiedbraking task in which participants were instructed to wait until thelast possible moment to slam on the brakes so that they would stopas closely as possible to a stop sign in their path of motion. Signradius and initial speed were manipulated in different experiments(Experiments 1A and 1B, respectively) and together in the sameexperiment (Experiment 2). The optical invariant that yields un-biased performance across changes in both sign radius and initialspeed is GOFR � �̇/�. Other optical variables, such as �̇ and �̇/�,yield predictable biases as sign radius and initial speed vary. Todetermine the optical variables on which participants relied atvarious stages of practice, we analyzed the data from each blockand compared them with the predictions of these three idealizedmodels.

Early in practice, participants exhibited size and speed effectsconsistent with the use of noninvariants. Similar effects have been

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, Atch-ley, & Saidpour, 1999; DeLucia, Bleckley, Meyer, & Bush, 2003),and collision avoidance (DeLucia & Warren, 1994). A primaryfocus of these studies is the optical variable � and its components(� and �̇). One of the novel aspects of the emergency braking taskis that the optical invariant (i.e., GOFR � �̇/�) is a higher ordervariable defined by three components, one of which corresponds toa part of the environment that is separate from the approachedobject (i.e., GOFR is defined by the optical motion of the groundplane, not the approached object). In this sense, the emergencybraking task is a natural extension of the large body of research ontiming tasks to situations in which the optical invariant is definedby a complex combination of multiple components. The results ofExperiment 2 indicate that observers are capable of becomingattuned to such optical variables.

The results also suggest that people can learn to exploit morereliable optical variables with practice. Effects of the size of theapproached object and the initial speed that were present at thebeginning of the experiments diminished with practice. Suchchanges can be easily interpreted in terms of perceptual attune-ment: With practice, participants learned to initiate braking at avalue of �̇ that depended on � and GOFR. In the remainder of thissection, we consider three issues that pertain to the perceptualattunement observed in the present study.

First, the amount of practice is just one of several factors thatinfluences perceptual attunement. Observers in Experiments 1Aand 1B practiced the same task for the same amount of time butbecame attuned to different optical variables. This most likelyreflects the fact that the reliability of any given optical variabledepends on the local constraints of the environment. Similar find-ings have been reported by Jacobs et al. (2001) and Smith et al.

Figure 10. Mean slope of line that best fits data from Experiment 2 whenideal deceleration at onset is plotted as a function of initial speed. Meanslope is shown as a function of block number in the ground and airconditions.

Figure 11. Mean time-to-contact (TTC) at onset as a function of signradius for each condition of initial speed in Experiment 2. Data are from the(A) ground condition and (B) air condition.


(2001) and underscore the significance of the range of practiceconditions on perceptual attunement.

Second, observers in the present study (see also Smith et al.,2001) were often attuned to optical variables that fell between thethree idealized optical models (i.e., �̇, �̇/�, and GOFR � �̇/�). Thisindicates that just because an optical variable can be expressed asa simple combination of component optical variables does notmean that observers are any more likely to use that variable. Themodel proposed by Smith et al. (2001), described in the introduc-tion, provides one possible explanation of attunement to such “inbetween” variables. Other possible mechanisms should be consid-ered in future research.

Third, although participants in our experiments learned to ex-ploit more reliable optical variables with practice, the effects ofsize and speed often persisted even after extensive practice. InExperiment 1A, participants failed to learn to use the opticalinvariant (i.e., �̇) when doing so would have eliminated the sizeeffect. Similarly, participants in Experiment 1B failed to useGOFR when doing so would have eliminated the speed effect. Thepersistence of these effects does not appear to reflect a generalinability to become attuned to the optical invariant. When bothsign radius and initial speed were manipulated together in Exper-iment 2, participants eliminated the size effect within a few blocksof practice and learned to use GOFR when it was available todiminish the speed effect. Although well-practiced participants inExperiment 2 still exhibited a weak speed effect, they clearlylearned to rely on all three component optical variables and usethem in a manner that was qualitatively similar to the opticalinvariant.

If observers are capable of becoming attuned to size-invariantand speed-invariant optical variables, then why didn’t participantsin Experiment 1A completely eliminate the size effect and whydidn’t participants in Experiments 1B and 2 completely eliminatethe speed effect? Although the size and speed effects could only becompletely eliminated by relying on the optical invariant, the taskcould still be performed well on the basis of certain noninvariants,especially across the limited range of conditions used in Experi-ments 1A and 1B. Perceptual attunement may have stabilized onnoninvariants once satisfactory feedback was attained, eventhough small size and speed effects were still present. This doesnot necessarily reflect a lack of motivation on the part of observers.As observers converge on the optical invariant, the informationthat guides perceptual attunement becomes more difficult to detect(Jacobs et al., 2001). Early in practice, errors in performance dueto unreliable noninvariants tend to be large, and hence easy todistinguish from random errors due to perceptual and motor vari-ability. As the observer converges on the optical invariant, errorsdue to perceptual attunement become smaller, and hence moredifficult to distinguish from random errors. The result is thatperceptual attunement will stabilize on optical variables that resultin “good” but not perfect performance across the conditions thatare encountered.

Conclusion

Do the results observed in the emergency braking task used inthe present study have any implications for normal, regulatedbraking? The size and speed effects suggest that ideal decelerationis perceived on the basis of noninvariants, especially by novice

observers. If normal, regulated braking is controlled by keepingthe perceived ideal deceleration within the safe region betweenzero and maximum deceleration as suggested by Fajen (2005a,2005c), then similar effects should emerge in regulated brakingtasks. Furthermore, such effects should diminish with practice asparticipants learn to use more reliable optical variables. We re-cently found that the initiation and the magnitude of individualbrake adjustments in a regulated braking task are influenced bysign radius and initial speed in a manner consistent with the effectsobserved in the present study (Fajen, 2006). That is, braking wasweakly affected or unaffected by sign radius but was initiatedearlier, and brake adjustments were larger when speed was slow.Furthermore, practice on the emergency braking task that results inperceptual attunement transfers to normal, regulated braking. Prac-tice on regulated braking also results in perceptual attunement.Such findings further demonstrate that perceptual attunement playsa significant but often overlooked role in the visual guidance ofaction.

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Received July 11, 2005Revision received September 16, 2005

Accepted September 27, 2005 �


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