碰撞时间估计任务中不同线索的作用比较
摘要
上个世纪70年代,针对动物如何估计运动时间并利用其来控制自己的运动以及躲避其他物体运动的行为,研究者提出了一种新的理论来进行解释。这种理论认为,动物和人类不需要对物体与自身的动态距离和速度进行估计,从而计算剩余的时间。相反,他们可以使用物体在视网膜上的映像的相对扩张率τ来直接完成这种估计。为了将这种新的理论与以往的通过距离和速度对时间进行间接估计的方式进行区分,研究者将这种方式称为τ理论(Lee,1976)。T理论的支持者认为,观察者只需要使用τ变量即可完成所有情况下的时间估计任务,而且这个过程是无需耗费知觉时间的,因而这种方式要比通过距离和速度来间接进行计算的方式更具有优势,也更能够解释在紧急情况下动物所做出的与运动时间有着密切关系的各种行为。由于τ理论所具备的直接、准确等特点,研究者认为其证实了直接知觉理论能够引导动物和人类的运动(Gibson,1965)。
τ理论的提出吸引了很多研究者的兴趣,也成为了深度运动领域的一个重要的研究课题。然而不同的研究发现,并不是所有的研究结果都支持τ理论,不同的研究者甚至得到了两种完全不同的结论。此外,T理论自身要受到很多前提条件的限制并且并不是在任何情况下都成立,因而这样的一种理论并不能够被看作一种完全正确的理论。而另一方面,这样的一种不准确的理论又经常被用作一种典型的证据来证明直接知觉理论的正确性。因此,从直接知觉理论的角度上来看,这样的一种有缺陷的证据是无法成为其自身的基础的。
因此,鉴于以上对于τ理论的普遍认识,人们开始重新审视各种支持τ理论的实验证据,并试图从多个角度对运动时间估计的规律进行重新的解释。尽管已有研究的结论已经普遍认为τ变量自身并不能够完全解释人类的时间估计行为,在这个过程中可能存在着多个变量对动物的时间估计产生影响。然而,由于各种变量之间存在着的各种错综复杂的关系,因而在对不同的研究进行重新的检验时,研究者需要小心地对这些支持或者反对T理论的研究结论进行解释。
通过对以往研究进行分析发现,对研究中存在着的不同混淆变量进行有效的区分的一类实验来自于“正交分离范式”。在这一范式中,将互相关联的2个或者多个变量中的每一个均沿着相互垂直的一个维度进行变化。在结果中,根据被试对不同变量变化的判断成绩,可以得到其对某一特定变量的心理物理函数,并进一步地根据这些变量的函数曲线的倾斜度来推断被试对该变量的敏感性。在以往的研究中,研究者使用这样的一种方法对一些视觉变量进行了详细地分离。这些视觉变量包括,视角大小,视角变化率以及二者的比值τ等。然而,在一个典型的环境中,当观察者观察物体运动时,他们不仅直接利用视觉变量来得到运动时间,还有可能使用其他的一些与环境有关的中间变量来估计,例如,深度距离,速度等。尽管这些研究中对视觉变量进行了正交分离以验证各种变量的作用,然而对于深度距离等环境变量的作用,目前尚无研究对其进行比较和分析。
鉴于上述深度距离等变量有可能也会对时间估计任务产生影响,本研究中对这些与环境有关的变量的潜在作用进行了分析。研究中对“正交分离范式”进行了进一步的改进,从而将时间变量与深度距离、速度以及物体的物理大小等几种变量沿着不同的正交维度进行分离,从而得以验证各种变量的准确作用。
实验一中,我们主要探讨了被试对不同的变量的敏感性,如果被试确实受到某一变量的影响,那么在实验过程中,被试的成绩会随着该变量的变化而发生相应的变化,同时,我们还从另外的一个角度来验证实验中的不同变量的作用。由于物体的实际大小会发生变化,而同时其在地面上投射的阴影的位置则并没有随着物体的大小而变化。因此,地面提供的阴影信息是一种更加有效的深度距离信息。如果被试确实需要使用这种深度信息,那么当地面信息被人为去除时,被试的反应成绩则会由于无法使用这些深度距离信息而显著地变差。
实验一的结果说明,被试在判断碰撞时间过程中主要使用时间线索,其对时间线索的敏感性最高。同时他们很少甚至并没有使用非时间线索,表现为他们对非时间线索的变化基本上不敏感。实验一的不同线索的正交分离和有无地面线索的比较两种方式都显示了同样的结论。
实验二在实验一的基础上,探讨了时间线索的来源。在实验一中,已经看到,被试主要使用时间线索而完全或者部分忽略非时间线索。而进一步的研究问题则是,时间变量线索存在着至少两种来源：T变量或者距离与速度比值。仅凭实验一的结果无法推断被试是否只是依赖于其中的一种来源还是需要综合二者以得到共同的行为反应。由于通常情况下它们提供的是始终一致且正确的时间变量,因而正常情况下无法区分哪一种才是真正的来源。
结果显示,被试在实验二中确实是主要使用了被操纵的τ变量,而不是实验过程中无变化的非τ变量。将实验结果进行的数量化分析表明,尽管T变量的变化能够影响被试的反应结果的很大一部分,距离和速度比值的时间信息仍然能够决定少部分的实验结果。
实验三检验了实验中提供的其他各种实验刺激等的有效性。结果显示,被试可以很准确地估计出物体的运动速度的相对快慢,并且此过程中不受到其他非速度线索的影响。其对非速度变量的差别阈限是其对速度变量的多倍甚至几十倍。与此同时,我们也检验了实验二中的“线索操纵范式”对时间变量来源的操纵是否也影响到被试对距离和时间信息的知觉。结果发现,同样的“线索操纵范式”下的被试反应结果并没有太大的差异,因而我们推论该过程中的非时间变量并没有受到“线索操纵范式”的影响。
由此,我们得出结论,被试确实是主动的忽视距离和速度信息,而不是由于实验模拟的有效程度原因。即实验操纵的方式是有效的,被试对实验一和二中的任务相关变量敏感,而且对其它变量不敏感。
实验四主要针对实验结论的适用范围问题进行了探讨。选用新被试对同样的结果进行了研究,并尽可能地缩短被试对实验刺激的接触时间,以减少练习效应的影响。通过这些新的方式验证实验一和二中的结果的稳定性。结果显示,新被试的平均反应成绩与已有的实验结果非常接近,被试对时间变量的心理物理曲线同样是最陡的一条曲线,被试对其他的非时间变量的心理物理曲线则要明显的平坦。进一步地,被试的心理物理曲线朝向τ变量变化导致的理论值偏移程度80%左右。因此这个结果与之前的结论类似,即被试主要使用T变量作为自己的时间估计的基础,但是在此过程中,很有可能还会使用其他的线索以获得整合的时间变量。
最后,本研究还对判断过程中存在的有可能影响实验结果的其他变量的作用进行了分析。首先,实验过程中被试可以获得多种单眼视觉线索,包括视角大小,视角变化率以及T等。此外,尽管本研究预期被试仅使用阴影所提供的距离信息来完成相对应的深度信息估计。然而,由于实验中需要模拟一种自然的场景,物体与阴影的大小同样在行进的过程中逐渐变大。因而阴影不可避免地也提供了与物体同样的T信息,从而无法排除被试使用来自阴影的τ而不是来自于物体自身的视觉信息的τ变量的可能性。
实验结果显示,大部分的被试在τ变量变化时差别阂限最小。而当τ变量的值被保持恒定(即该变量的作用被排除)时,这些被试的差别阈限也变得非常大,形成与τ变量作用未排除时的差别阈限的一种显著的对比。同样,对于视角大小、视角变化率与τ变量的变化结果显示,被试的成绩受到τ变量是否恒定的影响。因此,根据这种结果,我们推论,被试在实验过程中主要使用τ变量来作为自己反应的基础,当T变量的作用被排除时,被试的敏感性显著地下降,导致其反应成绩很差。
另一方面,对于不同的阴影τ线索,结果发现,当被用于绝对判断时,不同的阴影τ变量的误差相差比较大,有的非常准确,而有的则完全无法满足被试日常行为中的需求。然而所有的阴影τ变量的绝对误差均要比物体自身的τ变量大。据此推论,被试可能不会使用一种比物体自身τ的误差更大的视觉变量作为自己的行为反应基础。同时,相对误差的结果也说明,不同的阴影τ变量的相对误差与物体自身的τ变量相比,准确性仍然比较差,即阴影τ并不比物体自身τ具有优势。进一步地,使用“线索分离范式”造成的物体τ与阴影的τ不同的实验结果也同样表明了被试可能主要利用物体自身的τ变量,而不是各种阴影τ线索。
以往的碰撞时间研究中大部分仅仅使用定性研究,并没有使用量化研究。即研究者仅仅确定某一种或者几种变量是否会影响被试的行为输出,但是并没有在数量上进行量化分析。本研究不仅从性质上研究了不同的变量对运动时间知觉的影响作用,更进一步地,还分析了这些不同种类的线索对被试的时间判断输出的相对贡献值大小。由于定性研究仅仅能够确定一种或者多种线索是否对被试的判断产生影响,量化研究则为比较不同线索的相对作用大小提供了更准确地依据。结果说明,被试能够根据任务的属性来综合调整不同变量的相对权重,从而形成以一种最有效的知觉输出。
研究结论：整个时间判断的过程是一个信息整合的过程,尽管我们无法推断出决定信息整合的确切规律,然而对不同的线索的相对作用的比较发现。τ线索是相对比较任务中的一种最为有效的时间估计线索。观察者在进行运动时间观察时,不仅依靠τ线索,并且还要在一定程度上依靠其他的各种变量来完成时间估计任务。
Humans and animals constantly interact with a dynamic environment. These interactions can include an observer moving towards a stationary object, an object moving towards a stationary observer or a combination of both thereof. Over the past few decades, numerous studies have tried to elucidate which sources of information are used to mediate these types of interactions. Given that the time required for performing an action is biologically constrained and often fixed (i.e. resulting from a sequence of muscle movements), it is possible that humans and animals use predictive timing information specified by visual information to guide their actions. One potential source of information often focused on in the literature is time-to-collision (alternatively time-to-contact; TTC). TTC is defined as the time remaining before contact between the observer and object, and can be derived in several ways.
Among the different ways of perceiving TTC, an optic variable "tau" (Lee,1976) was particularly focused on in the literature. Tau is often regarded as an invariant; and as such, it is veridical and independent of other variables, such as the distance and velocity of the incoming object. Tau theory has argued that a tau strategy is necessary and sufficient to perceive TTC. Compared to the time-consuming and less accurate computation of distance to collision (DTC) and speed, tau provides a more direct and accurate estimate of TTC. The capability to perceive tau, as such, would be especially useful in situations which require immediate and accurate responses.
Some laboratory studies have suggested that tau is used to perform a variety of TTC estimation tasks. Others, however, have argued that other variables can also impact these estimations.
To evaluate the contribution of individual sources to TTC perception, it is necessary to first dissociate different co-varying variables that may have influenced TTC judgments. Among the studies that investigated the use of tau, two groups of studies deserve special considerations for their methods used in controlling visual information. The first group of studies devised a novel and systematic approach to isolate tau from other related optical variables. For instance, in an attempt to dissociate tau and rate of expansion at the moment of object presentation (see Equation 2), A two-dimensional matrix was created in which the two variables were systematically varied, one along each dimension, at the start of object trajectory. Cells of the matrix then formed trials using the values of these two variables as parameters. By examining responses to relative judgments of TTC, results showed that the observer was consistent with the use of a tau strategy, and that his judgment was independent of rate of expansion. Additionally, it was also found that the observer was able to specifically judge rate of expansion, which was done independently of tau. Thus, a conclusion was reached that separate and independent systems exist for estimating TTC and rate of expansion.
Using systematic variations and well-controlled dissociation of movement parameters, along with the incorporation of cue conflict between the two sources of information that specify TTC; the current study aimed to quantify the relative contributions of tau and other variables such as DTC, speed and physical size of the incoming object during a TTC judgment task. In Experiment 1, the availability of distance information through the presence of ground was manipulated in order to better investigate the effects of DTC and speed. When distance information was presented, the target approached in a direction parallel to the ground surface, and projected a shadow directly underneath. In this situation, both target and its shadow provided potential depth information. However, as we varied target size between trials, DTC and speed information were most saliently provided by the contrast of the moving object and shadow along the ground, which could then be used to estimate TTCd. Responses in these conditions were then compared to when ground and shadow information were unavailable. In Experiments 2 and 3, we continued to provide ground depth information, but further manipulated the physical size of the object during some of the approaches. This TTCt manipulation led to inconsistencies between TTC specified by tau and TTC specified by the distance/speed ratio. Changes in responses due to these manipulations then allowed us to quantify the extent observers used tau.
In Experiment 1. we investigated the contribution of four variables-TTC, DTC, target speed and physical size-during a relative TTC judgment task. Our results showed that participants could accurately discriminate trial-to-trial TTC differences based on TTC information. Discrimination thresholds revealed that TTC information was the most effective information for making TTC judgments compared to the other three variables, and that these results were consistent among all observers.
Moreover, there was no noticeable difference between responses in with-ground and without-ground conditions. Altogether, our results suggested that depth information provided by the ground surface and target shadow, for the most part, did not influence TTC estimations. Thus, we concluded that DTC and speed information derived from ground presence affects little, if at all, the perception of TTC.
Similar to Experiment 1, Experiment 2a showed that participants were most sensitive to trial-to-trial differences in TTC during a TTC estimation task, and not sensitive to variations of DTC, speed and target size. Weber fractions of curves based on TTC information were less than those produced by other variables. Additionally, we dissociated the effects of TTC by tau (TTCt) from TTC by DTC-speed (TTCd). If observers relied on tau (TTCt) to guide their judgments, responses would have differed between the three TTCt manipulation conditions. Responses, on the other hand, would have remained unchanged if observers relied instead on TTC specified by distance (TTCd) or other non-tau sources. Our results showed that responses were mostly affected by tau, and that manipulating TTCt reliably influenced TTC judgments. Specifically, enlarging the physical size of the target during approach caused observers to perceive a sooner arriving object. In contrast, decreasing the physical size of the target during approach caused participants to view the object as arriving later. The extent that individuals utilized tau, however, remained uncertain. While the present experiment only examined four observers, it was demonstrated that at least in the TTC-speed-size array, participants did not fully shift their responses to the extent we would expect had observers only used tau.
Results in Experiment 3 indicated that participants could in fact discriminate trial-to-trial differences in DTC and speed. Therefore, the lack of sensitivity to DTC and speed observed in Experiment 2 was not due to inability to perceive the two variables. We also demonstrated that TTCt manipulations did not noticeably influence DTC and speed perception in the present study, thus confirming the validity of our manipulations.
Experiment 4 demonstrated that even for a larger sample of naive participants, reducing the number of manipulations did not greatly change the pattern of results. Results consistently revealed that tau was the most effective and utilized source of information for judging TTC. When tau conflicted with ground-based depth information, these new participants continued to base their judgment to a large extent on tau. Tau by itself could not account for the total difference in response following manipulation (approximately 80%). Statistical analyses showed that this observed shift was different, although only marginally, to the expected 100% shift we would expect if observers had based their judgments entirely on tau. This suggested that observers relied on tau primarily for TTC estimations, but also used other variables, albeit to a smaller extent.
In summary, the present study used an orthogonal design and cue-conflict paradigm to investigate how participants made relative TTC judgments when non-time variables and different sources of TTC were available. Results from Experiment 1 showed that when judging TTC of an approaching target, participants were most sensitive to TTC and much less sensitive to variations of other non-time variables such as the approaching target's DTC, speed and physical size. Similar performances in with-ground and without-ground conditions further confirmed that participants relied mostly on TTC information during these estimations. Given that TTC information is used, we were also interested in what source of time information drove this sensitivity. Our results in Experiments 2 and 4 demonstrated that when different sources provided conflicting TTC information, observers were largely influenced by tau, and biased their judgments more towards the extent tau was manipulated. Altogether, we conclude that tau variable was the most useful cue when making relative TTC judgments, and others were less effective.
τ理论的提出吸引了很多研究者的兴趣,也成为了深度运动领域的一个重要的研究课题。然而不同的研究发现,并不是所有的研究结果都支持τ理论,不同的研究者甚至得到了两种完全不同的结论。此外,T理论自身要受到很多前提条件的限制并且并不是在任何情况下都成立,因而这样的一种理论并不能够被看作一种完全正确的理论。而另一方面,这样的一种不准确的理论又经常被用作一种典型的证据来证明直接知觉理论的正确性。因此,从直接知觉理论的角度上来看,这样的一种有缺陷的证据是无法成为其自身的基础的。
因此,鉴于以上对于τ理论的普遍认识,人们开始重新审视各种支持τ理论的实验证据,并试图从多个角度对运动时间估计的规律进行重新的解释。尽管已有研究的结论已经普遍认为τ变量自身并不能够完全解释人类的时间估计行为,在这个过程中可能存在着多个变量对动物的时间估计产生影响。然而,由于各种变量之间存在着的各种错综复杂的关系,因而在对不同的研究进行重新的检验时,研究者需要小心地对这些支持或者反对T理论的研究结论进行解释。
通过对以往研究进行分析发现,对研究中存在着的不同混淆变量进行有效的区分的一类实验来自于“正交分离范式”。在这一范式中,将互相关联的2个或者多个变量中的每一个均沿着相互垂直的一个维度进行变化。在结果中,根据被试对不同变量变化的判断成绩,可以得到其对某一特定变量的心理物理函数,并进一步地根据这些变量的函数曲线的倾斜度来推断被试对该变量的敏感性。在以往的研究中,研究者使用这样的一种方法对一些视觉变量进行了详细地分离。这些视觉变量包括,视角大小,视角变化率以及二者的比值τ等。然而,在一个典型的环境中,当观察者观察物体运动时,他们不仅直接利用视觉变量来得到运动时间,还有可能使用其他的一些与环境有关的中间变量来估计,例如,深度距离,速度等。尽管这些研究中对视觉变量进行了正交分离以验证各种变量的作用,然而对于深度距离等环境变量的作用,目前尚无研究对其进行比较和分析。
鉴于上述深度距离等变量有可能也会对时间估计任务产生影响,本研究中对这些与环境有关的变量的潜在作用进行了分析。研究中对“正交分离范式”进行了进一步的改进,从而将时间变量与深度距离、速度以及物体的物理大小等几种变量沿着不同的正交维度进行分离,从而得以验证各种变量的准确作用。
实验一中,我们主要探讨了被试对不同的变量的敏感性,如果被试确实受到某一变量的影响,那么在实验过程中,被试的成绩会随着该变量的变化而发生相应的变化,同时,我们还从另外的一个角度来验证实验中的不同变量的作用。由于物体的实际大小会发生变化,而同时其在地面上投射的阴影的位置则并没有随着物体的大小而变化。因此,地面提供的阴影信息是一种更加有效的深度距离信息。如果被试确实需要使用这种深度信息,那么当地面信息被人为去除时,被试的反应成绩则会由于无法使用这些深度距离信息而显著地变差。
实验一的结果说明,被试在判断碰撞时间过程中主要使用时间线索,其对时间线索的敏感性最高。同时他们很少甚至并没有使用非时间线索,表现为他们对非时间线索的变化基本上不敏感。实验一的不同线索的正交分离和有无地面线索的比较两种方式都显示了同样的结论。
实验二在实验一的基础上,探讨了时间线索的来源。在实验一中,已经看到,被试主要使用时间线索而完全或者部分忽略非时间线索。而进一步的研究问题则是,时间变量线索存在着至少两种来源：T变量或者距离与速度比值。仅凭实验一的结果无法推断被试是否只是依赖于其中的一种来源还是需要综合二者以得到共同的行为反应。由于通常情况下它们提供的是始终一致且正确的时间变量,因而正常情况下无法区分哪一种才是真正的来源。
结果显示,被试在实验二中确实是主要使用了被操纵的τ变量,而不是实验过程中无变化的非τ变量。将实验结果进行的数量化分析表明,尽管T变量的变化能够影响被试的反应结果的很大一部分,距离和速度比值的时间信息仍然能够决定少部分的实验结果。
实验三检验了实验中提供的其他各种实验刺激等的有效性。结果显示,被试可以很准确地估计出物体的运动速度的相对快慢,并且此过程中不受到其他非速度线索的影响。其对非速度变量的差别阈限是其对速度变量的多倍甚至几十倍。与此同时,我们也检验了实验二中的“线索操纵范式”对时间变量来源的操纵是否也影响到被试对距离和时间信息的知觉。结果发现,同样的“线索操纵范式”下的被试反应结果并没有太大的差异,因而我们推论该过程中的非时间变量并没有受到“线索操纵范式”的影响。
由此,我们得出结论,被试确实是主动的忽视距离和速度信息,而不是由于实验模拟的有效程度原因。即实验操纵的方式是有效的,被试对实验一和二中的任务相关变量敏感,而且对其它变量不敏感。
实验四主要针对实验结论的适用范围问题进行了探讨。选用新被试对同样的结果进行了研究,并尽可能地缩短被试对实验刺激的接触时间,以减少练习效应的影响。通过这些新的方式验证实验一和二中的结果的稳定性。结果显示,新被试的平均反应成绩与已有的实验结果非常接近,被试对时间变量的心理物理曲线同样是最陡的一条曲线,被试对其他的非时间变量的心理物理曲线则要明显的平坦。进一步地,被试的心理物理曲线朝向τ变量变化导致的理论值偏移程度80%左右。因此这个结果与之前的结论类似,即被试主要使用T变量作为自己的时间估计的基础,但是在此过程中,很有可能还会使用其他的线索以获得整合的时间变量。
最后,本研究还对判断过程中存在的有可能影响实验结果的其他变量的作用进行了分析。首先,实验过程中被试可以获得多种单眼视觉线索,包括视角大小,视角变化率以及T等。此外,尽管本研究预期被试仅使用阴影所提供的距离信息来完成相对应的深度信息估计。然而,由于实验中需要模拟一种自然的场景,物体与阴影的大小同样在行进的过程中逐渐变大。因而阴影不可避免地也提供了与物体同样的T信息,从而无法排除被试使用来自阴影的τ而不是来自于物体自身的视觉信息的τ变量的可能性。
实验结果显示,大部分的被试在τ变量变化时差别阂限最小。而当τ变量的值被保持恒定(即该变量的作用被排除)时,这些被试的差别阈限也变得非常大,形成与τ变量作用未排除时的差别阈限的一种显著的对比。同样,对于视角大小、视角变化率与τ变量的变化结果显示,被试的成绩受到τ变量是否恒定的影响。因此,根据这种结果,我们推论,被试在实验过程中主要使用τ变量来作为自己反应的基础,当T变量的作用被排除时,被试的敏感性显著地下降,导致其反应成绩很差。
另一方面,对于不同的阴影τ线索,结果发现,当被用于绝对判断时,不同的阴影τ变量的误差相差比较大,有的非常准确,而有的则完全无法满足被试日常行为中的需求。然而所有的阴影τ变量的绝对误差均要比物体自身的τ变量大。据此推论,被试可能不会使用一种比物体自身τ的误差更大的视觉变量作为自己的行为反应基础。同时,相对误差的结果也说明,不同的阴影τ变量的相对误差与物体自身的τ变量相比,准确性仍然比较差,即阴影τ并不比物体自身τ具有优势。进一步地,使用“线索分离范式”造成的物体τ与阴影的τ不同的实验结果也同样表明了被试可能主要利用物体自身的τ变量,而不是各种阴影τ线索。
以往的碰撞时间研究中大部分仅仅使用定性研究,并没有使用量化研究。即研究者仅仅确定某一种或者几种变量是否会影响被试的行为输出,但是并没有在数量上进行量化分析。本研究不仅从性质上研究了不同的变量对运动时间知觉的影响作用,更进一步地,还分析了这些不同种类的线索对被试的时间判断输出的相对贡献值大小。由于定性研究仅仅能够确定一种或者多种线索是否对被试的判断产生影响,量化研究则为比较不同线索的相对作用大小提供了更准确地依据。结果说明,被试能够根据任务的属性来综合调整不同变量的相对权重,从而形成以一种最有效的知觉输出。
研究结论：整个时间判断的过程是一个信息整合的过程,尽管我们无法推断出决定信息整合的确切规律,然而对不同的线索的相对作用的比较发现。τ线索是相对比较任务中的一种最为有效的时间估计线索。观察者在进行运动时间观察时,不仅依靠τ线索,并且还要在一定程度上依靠其他的各种变量来完成时间估计任务。
Humans and animals constantly interact with a dynamic environment. These interactions can include an observer moving towards a stationary object, an object moving towards a stationary observer or a combination of both thereof. Over the past few decades, numerous studies have tried to elucidate which sources of information are used to mediate these types of interactions. Given that the time required for performing an action is biologically constrained and often fixed (i.e. resulting from a sequence of muscle movements), it is possible that humans and animals use predictive timing information specified by visual information to guide their actions. One potential source of information often focused on in the literature is time-to-collision (alternatively time-to-contact; TTC). TTC is defined as the time remaining before contact between the observer and object, and can be derived in several ways.
Among the different ways of perceiving TTC, an optic variable "tau" (Lee,1976) was particularly focused on in the literature. Tau is often regarded as an invariant; and as such, it is veridical and independent of other variables, such as the distance and velocity of the incoming object. Tau theory has argued that a tau strategy is necessary and sufficient to perceive TTC. Compared to the time-consuming and less accurate computation of distance to collision (DTC) and speed, tau provides a more direct and accurate estimate of TTC. The capability to perceive tau, as such, would be especially useful in situations which require immediate and accurate responses.
Some laboratory studies have suggested that tau is used to perform a variety of TTC estimation tasks. Others, however, have argued that other variables can also impact these estimations.
To evaluate the contribution of individual sources to TTC perception, it is necessary to first dissociate different co-varying variables that may have influenced TTC judgments. Among the studies that investigated the use of tau, two groups of studies deserve special considerations for their methods used in controlling visual information. The first group of studies devised a novel and systematic approach to isolate tau from other related optical variables. For instance, in an attempt to dissociate tau and rate of expansion at the moment of object presentation (see Equation 2), A two-dimensional matrix was created in which the two variables were systematically varied, one along each dimension, at the start of object trajectory. Cells of the matrix then formed trials using the values of these two variables as parameters. By examining responses to relative judgments of TTC, results showed that the observer was consistent with the use of a tau strategy, and that his judgment was independent of rate of expansion. Additionally, it was also found that the observer was able to specifically judge rate of expansion, which was done independently of tau. Thus, a conclusion was reached that separate and independent systems exist for estimating TTC and rate of expansion.
Using systematic variations and well-controlled dissociation of movement parameters, along with the incorporation of cue conflict between the two sources of information that specify TTC; the current study aimed to quantify the relative contributions of tau and other variables such as DTC, speed and physical size of the incoming object during a TTC judgment task. In Experiment 1, the availability of distance information through the presence of ground was manipulated in order to better investigate the effects of DTC and speed. When distance information was presented, the target approached in a direction parallel to the ground surface, and projected a shadow directly underneath. In this situation, both target and its shadow provided potential depth information. However, as we varied target size between trials, DTC and speed information were most saliently provided by the contrast of the moving object and shadow along the ground, which could then be used to estimate TTCd. Responses in these conditions were then compared to when ground and shadow information were unavailable. In Experiments 2 and 3, we continued to provide ground depth information, but further manipulated the physical size of the object during some of the approaches. This TTCt manipulation led to inconsistencies between TTC specified by tau and TTC specified by the distance/speed ratio. Changes in responses due to these manipulations then allowed us to quantify the extent observers used tau.
In Experiment 1. we investigated the contribution of four variables-TTC, DTC, target speed and physical size-during a relative TTC judgment task. Our results showed that participants could accurately discriminate trial-to-trial TTC differences based on TTC information. Discrimination thresholds revealed that TTC information was the most effective information for making TTC judgments compared to the other three variables, and that these results were consistent among all observers.
Moreover, there was no noticeable difference between responses in with-ground and without-ground conditions. Altogether, our results suggested that depth information provided by the ground surface and target shadow, for the most part, did not influence TTC estimations. Thus, we concluded that DTC and speed information derived from ground presence affects little, if at all, the perception of TTC.
Similar to Experiment 1, Experiment 2a showed that participants were most sensitive to trial-to-trial differences in TTC during a TTC estimation task, and not sensitive to variations of DTC, speed and target size. Weber fractions of curves based on TTC information were less than those produced by other variables. Additionally, we dissociated the effects of TTC by tau (TTCt) from TTC by DTC-speed (TTCd). If observers relied on tau (TTCt) to guide their judgments, responses would have differed between the three TTCt manipulation conditions. Responses, on the other hand, would have remained unchanged if observers relied instead on TTC specified by distance (TTCd) or other non-tau sources. Our results showed that responses were mostly affected by tau, and that manipulating TTCt reliably influenced TTC judgments. Specifically, enlarging the physical size of the target during approach caused observers to perceive a sooner arriving object. In contrast, decreasing the physical size of the target during approach caused participants to view the object as arriving later. The extent that individuals utilized tau, however, remained uncertain. While the present experiment only examined four observers, it was demonstrated that at least in the TTC-speed-size array, participants did not fully shift their responses to the extent we would expect had observers only used tau.
Results in Experiment 3 indicated that participants could in fact discriminate trial-to-trial differences in DTC and speed. Therefore, the lack of sensitivity to DTC and speed observed in Experiment 2 was not due to inability to perceive the two variables. We also demonstrated that TTCt manipulations did not noticeably influence DTC and speed perception in the present study, thus confirming the validity of our manipulations.
Experiment 4 demonstrated that even for a larger sample of naive participants, reducing the number of manipulations did not greatly change the pattern of results. Results consistently revealed that tau was the most effective and utilized source of information for judging TTC. When tau conflicted with ground-based depth information, these new participants continued to base their judgment to a large extent on tau. Tau by itself could not account for the total difference in response following manipulation (approximately 80%). Statistical analyses showed that this observed shift was different, although only marginally, to the expected 100% shift we would expect if observers had based their judgments entirely on tau. This suggested that observers relied on tau primarily for TTC estimations, but also used other variables, albeit to a smaller extent.
In summary, the present study used an orthogonal design and cue-conflict paradigm to investigate how participants made relative TTC judgments when non-time variables and different sources of TTC were available. Results from Experiment 1 showed that when judging TTC of an approaching target, participants were most sensitive to TTC and much less sensitive to variations of other non-time variables such as the approaching target's DTC, speed and physical size. Similar performances in with-ground and without-ground conditions further confirmed that participants relied mostly on TTC information during these estimations. Given that TTC information is used, we were also interested in what source of time information drove this sensitivity. Our results in Experiments 2 and 4 demonstrated that when different sources provided conflicting TTC information, observers were largely influenced by tau, and biased their judgments more towards the extent tau was manipulated. Altogether, we conclude that tau variable was the most useful cue when making relative TTC judgments, and others were less effective.
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