Tables and Graphs
Humans to Optically Track
and Catch Moving Objects
by: Matt Hodgens
When a ball is hit at a baseball outfielder, it appears as if they already know where to run in order to catch the ball. Part of this is inevitably connected with how experienced the outfielder is and the amount of training that the outfielder has had. Initially, the ball is distant enough so that major depth cues such as stereo, accommodation and size change are all inoperable. The further away an object is from you, the more difficult it is for your eyes to perceive what the object is doing in terms of motion. At a distance of more than 30 meters, visual cues such as motion and disparity not useful (Goldstein,B.E.,1999). These cues are only useful towards the end of the trajectory when the outfielder is making final adjustments. Thus, the only valid cues, which the outfielder uses to track the flight of the ball, are temporal and spatial changes in the optical trajectory of the ball (Shaffer, McBeath, 2002).
The First concrete theory as to how baseball outfielders catch fly balls involves temporal and spatial changes in the trajectory of the ball, and it is called the Optical Acceleration Cancellation (OAC) model (Chapman, 1968). The OAC model states that the outfielder will be able to track and catch the ball using an unconscious two-step approach. First, the outfielder must align him/herself horizontally with the ballís path of flight. The second step is for the fielder to run towards the ball at a speed, which makes the ball appear as if it is rising vertically at a constant rate. In order for this to work, the fielder must find the correct speed at which to run, so that they cancel out the balls acceleration. If the fielder runs too slowly, then the ball will appear to slow down and will land in front of them. By slow down, it is meant that the ball that the optical ball speed has changed because the outfielder has selected the incorrect running path. Conversely, if the fielder runs to fast and overruns the ball, then the ball will appear to speed up and will land behind them. For this theory to work, it is necessary that the outfielder choose a running path that keeps the optical ball speed constant, thus achieving Optical Acceleration Cancellation. Although the OAC model does have some valid points, it is also flawed. Prior research suggests that on average, outfielders are not very proficient when it comes to accelerational discrimination as it matters in accurately catching fly balls (McBeath, Shaffer, Kaiser, 1995). In addition, the OAC model suggests that the simplest ball to catch would be a ball hit directly at the outfielder, when it is actually the most difficult ball to catch. Anyone who has played baseball or who has caught a ball that is coming directly at them, knows that it is difficult to determine the speed of the ball and the pace at which it is coming. It is much easier to take a step to one side or another and then judge the speed of the ball. This is commonly seen in baseball, as you will see outfielders take a step to one side or another when catching a ball hit directly at them. The OAC model does not take into account that humans are not very good at detecting changes in acceleration. The reason that you will see outfielders taking a step to the side is so that they can gain a lateral visual angle on the ball, which will tell them if the ball is actually speeding up or slowing down. Thus, the OAC model does not match up with the strategies used by baseball outfielders.
There are many problems that can be clearly seen when looking at the OAC model. It is dependent upon the fielderís ability to discriminate between optical acceleration, a task in which humans do not appear to excel at (McBeath, Shaffer, Kaiser, 1995). A second theory that does not depend on the fielderís ability to precisely detect accelerational changes is the Linear Optical Trajectory (LOT) model (McBeath, Shaffer, Kaiser, 1995). The LOT assesses the weaknesses of the OAC, as the OAC model breaks the optical information available to the outfielder into two separate components of vertical and horizontal. The LOT theory simplified this process and made it into a unified two-dimensional image. Because people are not very good at detecting changes in acceleration, which is a temporal task, the LOT theory changes the problem into a spatial task which involves detecting optical curvature, which is something that people are very good at. The LOT model states that the outfielder selects a running path that maintains a Linear Optical Trajectory (LOT) for the ball, which is relative to the home plate and background scenery (McBeath, Shaffer, Kaiser, 1995).
The OAC model concentrates on the path that the fielder chooses to run. The LOT model is more concentrated on the fielderís ability to keep the ball on the same part of his/her retina and in making appropriate adjustments in speed and in running path in coordination with the ballís flight path. By keeping the ball on the same part of the retina, the fielder is attempting to maintain a consistency between the rate of change in the vertical visual angle and the horizontal visual angle. If the rate of change between the two visual angles is kept constant, then the optical trajection of the ball will appear to continually ascend on the retina of the fielder throughout the entire flight of the ball. Unlike the OAC model, which says that the fielder will choose to run in a straight path to catch the ball, the LOT theory says that the fielder will run in a curved path to cancel out the curvature of the ballís trajectory. This makes the ball appear as if itís moving in a straight line against the visual background. Essentially, while tracking a ball, the fielderís eyes are taking split-second snapshots of the ball against the visual background. As the fielder runs at a curved angle in order to cancel out the curvature of the ballís trajectory, these snapshots that his eyes are taking, add up to form a straight line that continually rises for the entire flight of the ball. If the fielder makes the proper adjustments in their running path and speed, they should be able to get to the proper position in order to catch the ball. You will often see a baseball outfielder start off by running fast and then slow down and then speed up and so on and so forth as the ball approaches them. Once again, if the ball appears to rise in their visual field, then it is going over their head and the fielder must move back until they can get the ball back onto the same part of the retina. Likewise, if the ball begins to fall in their visual field, then the fielder must move forward in order to catch it.
The OAC model is mathematically sound and has some empirical support in cases of balls headed straight towards the outfielder (Babler, Dannemiller, 1993). The main problem with the OAC model is that it says that the ball hit straight at the outfielder should be the most simple to catch, when it is actually the most difficult (Shaffer, Kaiser, 1997). As stated earlier, when a ball is hit directly to an outfielder, he/she will usually take a step or two to one side of the ball in order to gain a new visual angle on the ball. The OAC model has some weaknesses when it comes to balls that are hit to the side of an outfielder. As mentioned before, the OAC alignment strategy assumes that people are good at discriminating rates of acceleration, but this is not consistent with laboratory evidence (Calderone, Kaiser, 1989). The OAC strategy does not include a method for navigating laterally. In cases where a fielder would have to move laterally, the OAC model would presumably say that catching a fly ball hit off the side is more difficult. Only this is not true, because baseball outfielders commonly report that a ball hit to the side of them is easier to catch (Shaffer, McBeath,1997).
The LOT model on the other hand, says that the primary task of the fielder is to discriminate a straight trajectory from a curved trajectory, as opposed to discriminating between accelerational changes. Empirical evidence suggests that people are very good at discriminating small changes in optical curvature (Riggs, 1973). The LOT model does not address the need of the fielder to maintain lateral location of the ball, only that they calibrate lateral against vertical movement as a simplifying constraint. Use of a LOT doesnít negate OAC, it merely gives the fielder an additional cue for balls hit to the side of them. Previous findings show that when directly measuring the relationship between playerís movements on the field and the optical trajectory of caught balls, fielders maintain both a LOT and OAC (McBeath, Shaffer, Kaiser, 1995).
Both The OAC and LOT models help to explain how baseball outfielders visually track and catch fly balls that are hit at them. This concept of viewer-based tracking strategies can be applied to many other areas outside of baseball. Airplane pilots have been found to be extremely precise in spatial error-nulling tasks, and in pursuit tracking tasks that require them to hold a constant angle position that is consistent with their target (Krauchunas, Shaffer, Eddy, McBeath, 2002). Other example of viewer-based tracking strategies which focus on constancy of angles can be witnessed in nature all of the time. ďPredators that are tracking their prey have also exhibited behaviors in which they adjust their position to maintain consistency of the angle of motion between them and their prey. Research involving the tracking of houseflies (Fannia canicularis) and teleost fish (Acanthaluteres spilomelanurus) have shown these organisms lock on to the motion of their target in such a way that maintains optical angle constancy (Collett & Land, 1975; Lanchester & Mark, 1975; Land & Collett, 1974). When a predator is tracking down itís prey, it does not know exactly where itís prey is going to run, and is forced to make predictions and constantly change its speed and running path in order to maintain its pursuit. How successful the animal is in catching its food depends on a number of factors. For one, it must have a good tracking strategy that allows it to keep its prey in its field of vision. Other factors include how experienced the predator is and how skillful they are.
The current experiment was designed to determine how people navigate to track and catch unpredictable target trajectories, in particular, that of a Frisbee®. It is also questioning whether humans will use LOT predictions as seen by baseball outfielders, while catching Frisbees®. My experiment is an extension of an experiment conducted by Krauchunas, Eddy, and Shaffer (2000). In the previous study, Krauchunas and Eddy used a special video camera to record the visual field of a dog as it tracked down and caught Frisbees® which were thrown trough the air. The Lot with OAC is a strategy that can be used by a predator who is tracking its prey. When the trajectory of the Frisbee® changed suddenly and dramatically, the dog simply chose a new LOT and continued to track the Frisbee® (Krauchunas, Shaffer, Eddy, McBeath, 2000). It is hypothesized in this study that people will employ a visual tracking strategy similar to that of the dog, when catching Frisbees® thrown at them. How accurately they are able to track and catch the Frisbee® will depend on a number of factors, but most importantly it will depend of the subjects ability to keep the Frisbee® of the same part of their retina as it travels through the air.
Both the non-expert and the expert subjects were tested individually, one after the other. The Frisbees® were thrown one at a time and the subjects ran in all various directions to track and catch them. The first subject to catch was the non-expert. He was asked to go first so that he would not use the expertís trials as a sort of self-instruction. The subject was given fifteen throws, which all varied in nature. The subject then tried his best to run after and catch each of the Frisbees® to the best of his ability. Throws went out to both sides of the subject; some of them were thrown short and some them were thrown long. In addition, some throws would go high up in the air and off to the side, so that they would return at various angles. The purpose of varying all of the throws was that the trajectory of a Frisbee® can often be quite unpredictable, especially if one has never caught Frisbees® before. Each throw was recorded on the video recorder through the camera mounted on the subject's head.
After this initial aspect of the experiment was completed, the trials were then viewed on a Super VHS ET Professional Series VHS VCR and television screen. A transparency was placed on the screen and the position of the Frisbee® on the screen was plotted using a marker. The VCR worked at a pace of thirty frames per second. Each trial was viewed one frame at a time and the Frisbee®, as the subject was tracking it, was plotted on the transparency for each frame. The point of the transparency represented the subjectsí visual pursuit of the Frisbee® and determined what and where they were looking at while tracking the Frisbee®. After each trial was coded, the transparencies were transferred to graph paper. Then each point of every trial was assigned a coordinate for a vertical visual angle and a horizontal visual angle. This information was then entered into the computer on a Microsoft Excel spreadsheet, and then put onto a program called Sigma plot. At this point, linear regressions were applied and Rsqr values were assigned to each trial, which helped determine how much each trial varied from a straight line that was placed to it. Graphs were then made. It was also noted whether or not the subject caught the Frisbee® for each trial.
It was decided that the trial would be considered significant if the Rsqr value was above 75%, which matched the criterion of the dog study. The non-expert was above the Rsqr value of 75% for eight of his fifteen trials. The expert was above the Rsqr 75% for ten of his fifteen trials. The non-expert had a Median Rsqr value of 81.5900%. The expert had a Median Rsqr vale of 78.3500%. Z scores were then calculated to determine if the number of trials that fit the 75% prediction related to the total number of trials. For example, the non-expert had eight trials that fit the 75% criterion, while the expert had ten trials that fit the 75% criterion. For the non-expert, it was Z=2.5179. With a .05 criterion, this makes the non-expertís significance=0.001. For the expert, Z=3.6083. With the same .05 criterion, this made the expertís significance=0.001.
In my research I found that for many of the trials, the optical trajectories of the subject would begin in a straight line that went up, only towards the end of the trial it would fall drastically and come back down as seen in Figure 3. This was not what I had expected to happen, as in theory, the visual track of the Frisbee® should have stayed in a straight line that went up and did not come back down for the duration of the Frisbees® flight. In the dog study, the dog would typically choose a running path and visual tracking style that would match the change in both the lateral visual angle and the vertical visual angle. This strategy that the dog employed, produced a straight line for most of its trials that supported the Linear Optical Trajectory (LOT) theory. This was much like the linear optical trajectories that is used by baseball outfielders who are running to catch fly balls. When we saw that the optical trajectories of my subjects were falling off in the manner that they were, we were concerned as to why this was happening.
The observation that this was happening on both the expert and the non-expert trials meant that it was not necessarily a matter of one subject doing something wrong, as they were both processing similar things. What we found was that the last points in each of the trials were spaced out much further than the rest of the points in the trial. As you can see in Figure 1, the points at the start of the trial are much closer together and bunched up than the points towards the end of the trial, where they are much more spread out and further apart. The reason for this, is that the further away the object is that you are looking at, the smaller it is our your retina and as a result it will not jump that much from one point to the next. Conversely, the closer the object is to you, the larger it will be on your retina and as a result it will move much more quickly through space from one point to the next.
However, this still did not explain why the lines of the trials were dropping off so drastically. One big difference between dogs and humans is that dogs catch with their mouths and humans catch with their hands. This gives humans a large advantage over dogs, as their ability to extend their arms and make last second lunges or bursts in order to catch the Frisbee® is something that a dog will not be able to do. This characteristic of humans was something that we considered carefully. We then thought that the reason for all of drop off that we were seeing was a result of the subjects making last second adjustments and lunging at the Frisbee® with a quick burst of speed. Since the points towards the end of the trial were so spread out, it took only a few points to make for these large drop-offs in trajectory that were occurring. Because this was happening, we decided that the last few points in each trial were not representative of what was actually happening over the subjects entire tracking of the Frisbee®. As a result, we decided to drop the last five points of each trial in order to maintain some consistency for what the subjects were truly experiencing while they tracked the Frisbee®, and not what their last second lunge or burst of speed was. In almost every trial this made a significant difference in what the eventual Rsqr value was.
The differences in tracking styles between the expert and non-expert were not very large. However, the expert did catch fourteen out of his fifteen trials, while the non-expert caught only eight of his fifteen trials. As seen in Table 1, the expert averaged a mean Rsqr value of 75.5767%, as the non-expert had a mean Rsqr value of 57.1253%. The non-expertís Rsqr values had a range of 95.63, as he had a minimum Rsqr score of 3.63%, and a maximum Rsqr value of 99.26%. This gave the non-expert a Sd=41.6841. The expertís Rsqr values had a range of 56.85%, as he had a minimum Rsqr score of 42.78% and a maximum Rsqr score of 99.63%. This gave the expert a Sd=18.3083. This is considerably smaller than the non-experts Sd and that is most likely due to the expertís advantage of experience over the non-expert.
The non-expert was important in this experiment because he represented a neutral person who had almost no prior experience in catching Frisbees®. As the expert subject had much experience in the various trajectories that Frisbees® can take when thrown at various angles, the non-expert had very little knowledge of such trajectories. This was apparent from the beginning of the non-expertís trials, as he dropped four of his first five attempts. Figure 4 is a good example of the non-experts lack of experience in catching Frisbees®. This throw did not have much horizontal movement, as it went up fairly high down the middle, and then dropped back down faster than he expected it to. The reason for all of the seemingly erratic movement is because the trajectory is condensed into a very small horizontal field. However, he did catch his fifth trial, as seen in Figure 5, and he did so extremely well. This clearly supports the Linear Optical Trajectory theory, as the non-expert had no experience with catching Frisbees®, but he still kept the Frisbee® in a straight line that continued to rise throughout the entire trajectory. It also supports the Optical Acceleration Cancellations strategy, as he appeared to run along a path that kept the optical speed of the ball consistent with its vertical movement.
The expertís trials were much more consistent than the non-expertís
trials, and for good reason. The expert was very confident in his
ability to catch the Frisbee® and also in his decision-making.
One thing that we noticed about the expert was that on a few of his trials
he would catch the Frisbee® with apparent ease, only the Rsqr value
would be uncharacteristically low. For example, on his fifth trial,
the throw went up high to the right, and as he tracked the Frisbees®
trajectory, he came to a point where he decided the Frisbee® was going
to land and he stayed there until it came down to him. As seen in
Table 1, His Rsqr value for trial 10 was 45.06%, which is unusually low
for a catch. This may have been due to the fact that he was idle
for a certain amount of time during the flight of the Frisbee®.
Thus, his eye movement may have changed momentarily or he may have simply
stopped tracking the Frisbee® as carefully because he was confident
in his ability to catch it regardless. However, the expert displayed
tracking strategies for most of his trials that were consistent with both
the LOT and OAC strategies. As seen in Figure 1, he kept the trajectory
of the Frisbee® on a straight line that continued to rise and he ran
along a path that maintained the Frisbees® vertical movement.
In conclusion, my original hypothesis that people would employ similar
visual tracking strategies to that of dogs when catching Frisbees®
was found to be significant. Both the LOT and OAC strategies were
found to be jointly and successfully used during the subjectís visual tracking
of the Frisbee®. It should be noted that the LOT with OAC is
a strategy that can be used by a pursuer to optically navigate towards
a target that is in its sight. Not only is this strategy useful for
predictable targets, such as a baseball, but it is also useful for unpredictable
targets, such as the Frisbee® and for other targets that occur in the
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Rsqr values for subjects trials and related statistical scores.