In everyday life we often want to predict the moment there is going to be contact between us and some object. These situations include ones in which we
are moving towards some object (e.g., a wall) and those in which an object (e.g., a ball) is approaching us. We might work out the time to contact by dividing our estimate of the object’s distance by our estimate of its speed. However, this would be fairly complex and prone to error because information about speed and distance is not directly available.
Lee (1976, 2009) argued that we do not need to work out the distance or speed of an approaching object to work out the time to contact. Provided we are approaching it (or it is approaching us) at constant velocity, we can make use of tau. Tau is defined as the size of an object’s retinal image divided by its rate of expansion. Tau specifies the time to contact with an approaching object – the faster the rate of expansion, the less time there is to contact.
When driving, the rate of decline of tau over time (tau-dot) indicates whether there is sufficient braking time to stop at the target. More specifically, Lee (1976) argued that drivers brake to hold constant the rate of change of tau. Lee’s tau-dot hypothesis is consistent with Gibson’s approach because it assumes information about time to contact is available from optic flow. In other words, observers can work out time to contact from variables measurable directly by the eye.
Lee’s (1976, 2009) theoretical approach has been highly influential. However, tau has somewhat limited applicability in several ways in the real world (Tresilian, 1999):
• Tau ignores acceleration in object velocity.
• Tau only provides information about the time to contact with the eyes. However, what is important to drivers when braking to avoid an obstacle is the time to contact with their car. If they use tau, they may find the front of their car smashed in!
• Tau is accurate only when applied to spherically symmetrical objects: do not use it when catching a rugby ball!
Findings
Suppose you try to catch an approaching ball. Lee (1976) assumed your judgement of the time to contact would depend crucially on the rate of expansion of the ball’s retinal image. Savelsbergh et al. (1993) tested this hypothesis. They manipulated the rate of expansion by using a deflating ball – its rate of expansion is less than a non-deflating ball. As predicted, the peak grasp closure occurred later to the deflating ball. However, the average difference was only 30 ms, whereas Lee’s hypothesis predicts a difference of 230 ms. Thus, participants used additional sources of information (e.g., depth cues) that minimised the distorting effects of manipulating the rate of expansion.
Hosking and Crassini (2010) showed convincingly that tau is not the only factor determining time-to-contact judgements. Participants judged time to contact for familiar objects (tennis ball and football) presented in their standard size or with their sizes reversed (e.g., tennis ball the size of a football).
Hosking and Crassini also used unfamiliar black spheres.
Hosking and Crassini’s (2010) findings are shown in Figure 4.4. Time-to-contact judgements were influenced by familiar size. This was especially the case when the object was a very small tennis ball, which led participants to overestimate time to contact.
Another factor influencing time-to-contact judgements is binocular disparity. Rushton and Wann (1999) used a virtual reality situation involving catching balls, and manipulated tau and binocular disparity independently. When tau indicated contact with the ball 100 ms before binocular disparity, observers responded 75 ms earlier. When tau indicated contact 100 ms after disparity, the response was delayed by 35 ms. Thus, information about tau is combined with information about binocular disparity, with the source of information specifying the shortest time to contact being given the greatest weight.
Evidence that observers make flexible use of information when predicting time to contact was discussed by DeLucia (2013). She focused on the size-arrival effect: observers mistakenly predict that a large approaching object far away will hit them sooner than a closer small approaching object. This effect occurs because observers attach more importance to relative size than tau. However, when both objects move closer, observers switch to using tau rather than relative size to judge which object will hit them first. Thus, the nature of the information used to judge time to contact changes as objects approach an observer.
Figure 4.4
Errors in time-to-contact judgements for the smaller and the larger object as a function of whether they were presented in their standard size, the reverse size (off-size) or lacking texture (no-texture). Positive values indicate that responses were made too late and negative values that they were made too early.
From Hosking and Crassini (2010). With kind permission from Springer Science + Business Media.
We turn now to research on drivers’ braking decisions. Lee’s (1976) notion that drivers brake to hold constant the rate of change of tau was tested by Yilmaz and Warren (1995). They told participants to stop at a stop sign in a simulated driving task. As predicted, there was generally a linear reduction in tau during braking. However, some participants showed large rather than gradual changes in tau shortly before stopping.
Tijtgat et al. (2008) discovered that stereo vision influences drivers’ braking behaviour to avoid a collision. Drivers with weak stereo vision started breaking earlier than those with normal stereo vision and their peak deceleration also occurred earlier. Those with weak stereo vision found it harder to calculate distances, which caused them to underestimate the time to contact. Thus, deciding when to brake does not depend only on tau.
Evaluation
The notion that tau is used to make time-to-contact judgements is simple and elegant. There is much evidence that such judgements are often strongly influenced by tau. Even when competing factors affect time-to-contact judgements, tau often has the greatest influence on those judgements. Tau is also often used when drivers make decisions about when to brake.
What are the limitations of research in this area? First, judgements of time to contact are typically more influenced by tau or tau-dot with relatively uncluttered visual environments in the laboratory than under more naturalistic conditions (Land, 2009).
Second, tau is not the only factor determining judgement of time to contact. As Land (2009, p. 853) pointed out, “The brain will accept all valid cues in the performance of an action, and weight them according to their current reliability.” As we have seen, these cues can include object familiarity, binocular disparity and relative size. It clearly makes sense to use all the available information in this way.
Third, the tau hypothesis takes no account of the emotional value of the approaching object. However, Brendel et al. (2012) found time-to-contact judgements were shorter for threatening pictures than neutral ones. This makes evolutionary sense – it could be fatal to overestimate how long a very threatening object (e.g., a lion) will take to reach you!
Fourth, the tau and tau-dot hypotheses are too limited in scope. We lack a comprehensive theory indicating how the various factors influencing time-to-contact judgements are combined and integrated.
PLANNING–CONTROL MODEL
How do we use visual information when we want to perform an action with respect to some object (e.g., reaching for a cup of coffee)? This issue was addressed by Glover (2004) in his planning–control model. According to this model, people initially use a planning system followed by a control system, although the two systems often overlap in time. Here are the main features of the two systems:
1 Planning system
• It is used mostly before the initiation of movement.
• It selects an appropriate target (e.g., cup of coffee), decides how it should be grasped and works out the timing of the movement.
• It is influenced by factors such as the individual’s goals, the nature of the target object, the visual context and various cognitive processes.
• It is relatively slow because it makes use of much information and is influenced by conscious processes.
• Planning depends on a visual representation located in the inferior parietal lobule together with motor processes in the frontal lobes and basal ganglia (see Figure 4.5). The inferior parietal lobe is involved in integrating information about object identification and context with motor planning to permit tool and object use.
2 Control system
• It is used during the carrying out of a movement.
• It ensures movements are accurate, making adjustments if necessary based on visual feedback. Efference copy (see Glossary) is used to compared actual with desired movement. Proprioception (sensation relating to the position of one’s body) is also involved.
• It is influenced by the target object’s spatial characteristics (e.g., size, shape, orientation) but not by the surrounding context.
• It is fairly fast because it makes use of little information and is not susceptible to conscious influence.
• Control depends on a visual representation located in the superior parietal lobe combined with motor processes in the cerebellum (see Figure 4.5).
Figure 4.5
Brain areas involved in the planning and control systems within Glover’s theory. IPL = inferior parietal lobe; IT = inferotemporal lobe; M1 = primary motor; PFC = prefrontal cortex; SPL = superior parietal lobe.
From Glover (2004). Copyright © Cambridge University Press. Reproduced with permission.
According to the planning–control model, most errors in human action stem from the planning system. In contrast, the control system typically ensures actions are accurate and achieve their goal. Many visual illusions occur because of the influence of visual context. According to the model, information about visual context is used only by the planning system. Accordingly, responses to visual illusions should typically be inaccurate if they depend on the planning system but accurate if they depend on the control system.
In sum, Glover (2004) argued that independent planning and control systems are involved in producing actions to objects. A crucial assumption is that these two systems are located in different brain regions within the parietal lobe.
There are similarities between the planning–control model and Milner and Goodale’s two-systems model (see Chapter 2). In essence, their vision-for-action system resembles Glover’s control system and their vision-for-perception system overlaps with Glover’s planning system. However, Glover (2004) focused more on the processing changes occurring during the performance of an action. In addition, there are differences between the models in the key
brain areas involved.