Learning to Control Collisions: The Role of Perceptual Attunement and Action Boundaries

Transcription

1 Journal of Experimental Psychology: Human Perception and Performance 2006, Vol. 32, No. 2, Copyright 2006 by the American Psychological Association /06/$12.00 DOI: / 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 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 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 fajenb@rpi.edu 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- 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

2 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 d ideal v 2 /2z, (1) where v is speed, z is target distance, and v 2 /2z is the ideal deceleration (abbreviated d ideal ) 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 d ideal 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, d ideal.) 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 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 m between approaches. The black dots correspond to the point at which the ideal deceleration was equal to 10 m/s 2 (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 m, and initial speed varied randomly between 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.

3 302 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 v onset 2 /2z onset ) 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.

4 LEARNING TO CONTROL COLLISIONS 303 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). 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 par- 8 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.

5 304 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 m. In Experiment 1B, sign radius was fixed at m, and initial speed varied between , 6.0, , , , 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

6 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, , , , , and 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/s 2 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 deceleration at the onset of braking was calculated using v onset /(2 2 z onset ), where v onset and z onset 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 d ideal ) 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 r 2 values, respectively, of the line in optical state space that

7 306 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) , p.001. An Initial Speed Block interaction,

8 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

9 308 FAJEN AND DEVANEY Figure 7. Mean slope (A and B), intercept (C and D), and r 2 (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 practice 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

10 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

11 310 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) , 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.

12 LEARNING TO CONTROL COLLISIONS 311 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. 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.