There are numerous situations in which we want to know when we are going to reach some object (e.g., the car immediately in front of us). We could make these calculations by estimating the initial distance away of the object (e.g., car; ball), estimating our speed, and then combining these two estimates into an overall estimate of the time to contact by dividing distance by speed. However, there are two possible sources of error in such calculations, and it is fairly complex to combine the two kinds of information.
Lee (1980) argued that it is not necessary to perceive either the distance or speed of an object we are approaching to work out the time to contact, provided we are approaching it with constant velocity. Time to contact can be calculated using only a single variable, namely the rate of expansion of the object's retinal image: the faster the image is expanding, the less time there is to contact. Lee used this notion to propose a measure of time to contact called T or tau, and which is defined as the inverse of the rate of expansion of the retinal image of the object: T=1/(rate of expansion of object's retinal image). This theory is in general agreement with Gibson's approach, because it is assumed that information about time to contact is directly available.
According to Lee, information about tau is used when an object is approaching us as well as when we are approaching an object. It is also used in various sports when we need to be prepared to catch or hit an approaching ball, when long-jumpers approach the take-off board, and so on. For the present, we are concerned with time to contact when a person is moving towards an object. Later in the chapter, we will turn to the issue of time to contact when it is the object that is in movement.
Cavallo and Laurent (1988) tested Lee's (1976) theory in a study in which experienced drivers and beginners indicated when they expected a collision with a stationary obstacle to occur. Cavallo and Laurent manipulated how easy it was to assess speed by comparing normal and restricted visual fields, and they manipulated ease of distance assessment by comparing binocular and monocular vision. Their findings did not indicate that the rate of expansion of the obstacle's retinal image was the major determinant of time-to-contact judgements. Accuracy of time-to-contact estimation was greater when speed and distance were relatively easy to assess. The beginners made use of both speed and distance information in their estimates, whereas experienced drivers made more use of distance than of speed information.
Research on US Air Force pilots by Kruk and Regan (1983) may be relevant to Lee's (1976) theory. They assessed the pilots' sensitivity to change in the size of a square which changed size in an unpredictable way. As calculation of tau involves making use of information about size expansion, sensitivity to size changes is an indirect measure of sensitivity to tau. Kruk and Regan also assessed the pilots' ability to land a plane smoothly using a cockpit simulator. The pilots who produced the smoothest landings had the greatest sensitivity to size changes. It is thus possible that individual differences in pilots' landing abilities reflect their sensitivity to tau.
Walking and running seem like very simple and automatic activities requiring only limited visual information. In fact, a considerable amount of visual monitoring of the environment is often needed. Anyone who has walked over rough ground at night under poor lighting conditions will probably remember that it can be a hard and uncomfortable experience.
Hollands et al. (1995) studied the eye movements of walkers walking on irregularly positioned stepping stones. The typical pattern was that there was an eye movement towards the next landing place of each leg before it was lifted into the air. Thus, the participants seemed to plan the complete movement of each leg before starting to move it.
Some of the processes involved in running were studied by Lee, Lishman, and Thomson (1982). They took films of female long-jumpers during their run-up. Jumps are disqualified if the long-jumper oversteps the take-off board, so precise positioning of the feet is important. Most coaches and athletes used to assume that expert long-jumpers develop a stereotyped stride pattern that is repeated on each run-up, and which relies very little on visual information. In contrast, Lee et al. (1982, p. 456) argued there are two major processes involved: (1) control consists "in regulating just one kinetic [relating to motion] parameter, the vertical impulse of the step—keeping it constant during the approach phase and then adjusting it to regulate flight time in order to strike the board"; and (2) tau is used late in the run-up, because time-to-arrival at the board "is specified directly by a single optical parameter, the inverse of the rate of dilation of the image of the board."
Lee et al. (1982) obtained evidence in favour of their theoretical position. The athletes showed reasonable consistency in their stride patterns during most of the run-up, but there was a marked increase in the variability of stride lengths over the last three strides. This seemed to be due to alterations in the leap or vertical thrust of the take-off, which affected the flight length for each leg. This allowed the athletes' last stride to land appropriately with respect to the take-off board. According to Lee et al., these adjustments are visually guided by tau and they concluded that most of a long-jumper's run-up is determined by internal processes, with visual processes assuming great importance only in the last few strides.
In subsequent research, Warren, Young, and Lee (1986) trained athletes to place their feet on irregularly spaced targets while running on a treadmill. They confirmed the importance of varying flight length as a strategy for placing the feet in the desired place.
Berg, Wade, and Greer (1994) pointed out that Lee et al. (1982) had used only three jumpers, and had tested them under non-competitive conditions. However, Berg et al.'s findings with expert long-jumpers under competitive conditions were comparable to those of Lee et al. (1982). They also found that novice long-jumpers had similar run-up patterns, suggesting that using tau to regulate stride pattern occurs naturally.
Car driving is a skill that is not normally acquired until at least the late teens. In addition, it involves making decisions about steering, braking, and so on while the driver is moving at speed. These considerations suggest that drivers need to develop special strategies for using visual information. In the specific case of braking, it might be imagined that drivers would be influenced by the speed of their car, the speed of the car in front, and the distance between the two cars. However, Lee (1976) argued that decisions about decelerating or braking are based on the rate of angular expansion of either the car in front or its rear lights. He reported evidence consistent with this hypothesis, but did not show that other factors are not involved. Stewart, Cudworth, and Lishman (1993) argued that the driver's speed and the apparent distance of an obstacle also influenced braking behaviour.
Land and Lee (1994) recorded information about drivers' direction of gaze and the angle of the steering wheel as they approached and drove through bends. Immediately before they turned the steering wheel, drivers fixated on the inside edge (tangent point) of the approaching bend even though they were unaware of doing so. Why do they do this? According to Land and Lee, drivers may use the visual angle between the tangent point and the direction of heading to decide how much to turn the steering wheel.
The notion that we can estimate time to contact accurately on the basis of fairly simple information related to the rate of expansion of the retinal image is appealing. It is of theoretical interest because tau appears to be a good example of the kind of high-level invariant emphasised by Gibson. At the empirical level, research carried out in several situations has provided support for Lee's (1976) theoretical position.
However, there are various problems with the tau-based approach. First, as Cumming (1994, p. 355) pointed out, "It is very difficult to determine experimentally whether human subjects use tau to estimate time-to-contact directly. Furthermore, none of the experiments.excludes the possibility that other strategies are used for timing the actions studied."
Second, there has been a failure to consider alternative factors that might influence time-to-contact judgements. As Wann (1996, p. 1040) pointed out, "Recent trends in perceptual research have tended to ignore depth cues as reliable information for the control of action." In the specific case of car drivers, they may use information about their own speed and about the distance between them and the car in front to work out time to contact.
Third, tau provides information about the time to contact or reach the eyes of the observer. In many situations (e.g., driving a car), this information is insufficient. For example, a driver who used tau to brake in order to avoid an obstacle might find that the front of his or her car has been smashed in (Cumming, 1994)!
Fourth, it is only a starting point to argue that tau is calculated in order to establish time to contact. What remains to be discovered are the precise processes involved in its calculation.
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