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The perception of lead vehicle movement in darkness
Pergamoa Press 1976. Printed inCmt Britain Acrid. Ad. d Pm.,Vol. 8.pp.151-166.
THE PERCEPTION
OF LEAD VEHICLE MOVEMENT IN DARKNESS
WIEL H. JANSSEN, JOHNA.
.MICHoNtand LEWIS0.
HARVEY,
JRS
Institute for Perception TNO, Kampweg 5, Soesterberg, The Netherlands (Received 14 October 1975) Abstract-Three experimental studies are described on the detection of longitudinal lead-vehicle movement in darkness. Experiment I, performed in the laboratory, isolated the relative horizontal angular motion of the lead-vehicle’s taillights as a cue to the detection of relative longitudinal movement. Movement thresholds were determined as a function of initial headway, exposure duration, direction of the movement, and the presence of a background. All these factors except the last had significant effects on the movement threshold. Experiment II, also a laboratory-experiment, isolated changes in apparent size or brightness of the taillights as a cue. Movement thresholds were again found to be a function of the variables investigated in Experiment I. However, thresholds now were much higher than under the isolated angular cue. It was therefore concluded that the relative horizontal angular motion of the lead-vehicle’s taillights is the priminent cue in the detection of relative vehicle motion in depth. Experiment III substantiated this conclusion by confirming the parametric outcomes of Experiment I under realistic night-driving conditions. The practical relevance of the estimates made from the data of two important temporal parameters in car following, viz. time until collision and free time after detection.
INTRODUCTION
Under contract with the Netherlands Institute for Road Safety Research an investigation has been carried out to achieve better understanding of the factors which enter into an automobile driver’s perception of other vehicles moving through his visual field. The problem in general may be analyzed in terms of distal and proximal stimulation. This distinction may be illustrated by considering the night-time driver who is followed a car in front of him. The behavior of the leading car-in absence of other environmental cues such as street lighting-will be inferred primarily from changes in the configuration and location of its taillights. The main distal variables entering into the situation are schematically presented in Fig. 1. The distal stimulus dimensions are presented in physical timespace, and can be specified quite easily, although they can not so easily be manipulated in reality. At the retina, however, the physical stimulus dimensions are entirely different, i.e. the proximal stimuli will be specified in terms of angles, apparent size, and apparent brightness. The characteristic proximal variables, which correspond in a complicated way to the variables in Fig. 1, are depicted in Fig. 2. Usually the proximal stimulus can be simulated in the laboratory. As long as the transformation distal-proximal is complete a subject will not be able to ascertain whether he is looking at a real world or at a laboratory display. Yet in most cases the laboratory situation will quickly betray itself, because of distal variables which are not represented in the simulation. Therefore, laboratory data obtained in a partially simulated reality ultimately will have to be checked against some real-life situation. On the other hand, the laboratory situation gives the investigator the possibility to manipulate the important variables independently. In the present case the potentially most powerful cues to detect relative motion, viz. the angular distance between the lead-vehicle taillights and their apparent size and brightness, have been manipulated independently. On the basis of the results from these experiments a check in the field has subsequently been performed. We will describe three experimental studies on the perception of lead-vehicle movement we have performed and the conclusions that have emerged from them. For the sake of briefness not all procedural details will be discussed; these are contained in the technical reports issued by the Institute for Perception TNO. tNow at the University of Groningen, The Netherlands. SNOWat the University of Colorado, Boulder, Colorado, U.S.A. 151
152
WIEL H. JANSSENef nl. heading
direction t
observer
Fig. I. Distal stimulus situation in car following. The relevant variables are: D-distance; L-lateral distance from the heading direction (median plane); a-the angle between the heading directions of both vehicles; H-the height difference between the plane through vanishing point and the observer’s eye parallel to the horizon, and the taillights of the leading car. medtan plane
!
horizon
Fig. 2. Proximal stimulus situation in car following. Variables are: I-apparent brightness/apparent size; S-angular separation between taillights; y-ditto (vertically); A-angular distance between vanishing point and taillights (horizontally); n-ditto(vertically).
EXPERIMENTAL
STUDIES
Experiment I. The angular cue
The first experiment [Harvey and Michon, 1971, also 19741was designed to measure human sensitivity to the relative horizontal motion of two spots of light. When an observer views, from distance 0, two spots separated by distance d, the visual angle a separating the spots is: a =$rad(n
(1)
If D is changing at a constant rate v the rate of change in a is described by the first derivative of (1) with respect to time: &=- do
D2
Angular speed is accelerating positively when motion is toward the observer (closure) and negatively when it is away from the observer (opening).
The perception of lead vehicle movement in darkness
153
The specific question to be answered experimentally was: “How fast must two spots move relative to each other in order for an observer just to be able to detect the motion?” Performance is then said to be at threshold, Thresholds were determined as a function of: (i) The initial angular separation (Z”, l”, 30’, 15’ or 7*5’,corresponding to D = 40,80,160,320 or 640, respectively, for a (fairly common) intertaillight distance of d = 1.4m). (ii) The exposure duration (t = 0.5,1*0,2~0 or 4-Oset). (iii) The direction of movement (toward or away from the observer). (iv) The presence or absence of a background consisting of vertical lines spaced randomly on a random dot background. The stimulus spots were generated by a mirror system [see Harvey and Michon, 197I, 1974,for details on the apparatus]. On the projection screen the spots had a luminance of 21 cd/m’. They subtended a constant angle of I’, and thus were effectively point sources for an observer sitting at a distance of 25 m. The experiment was done in a dark corridor. For any given experimental condition the distal speed of movement was determined that would allow the subject to detect the movement 75% of the time. A signal detection method was used [Green and Swets, 1%6] which resulted in estimates of the bias-free sensitivity parameter d’ under each of four speeds of movement per experimental condition. Threshold speed t&h was obtained by interpolating at d’ = 1.25 (the bias-free equivalent of the 75% point of classical threshold measurement) on the function relating movement speed to d'. The results were analysed by analysis of variance on the log-transformed values of urh.It was showp, first of all, that the presence of a background made no difference. This is a somewhat unexpected finding given the results of Leibowitz [1955a, b] on the detection of linear movement of single targets, where background did make a difference. Perhaps the presence of a background is simply not effective with two spots moving relative to each other. ~ternativeIy, the 4-see exposure may not have been long enough for background to make an effect. Initial angle, direction of movement and exposure duration all had highly significant effects on t&h. The data, averaged over background conditions, are shown in Figs. 3 and 4. The data show that Z)lhdecreases as exposure increases from 0.5 to 2 set but that further increase to 4 set exposure does not produce much further improvement. A comparison of Figs. 3 and 4 also shows a significant interaction between direction of movement and initial viewing distance. The difference between directions of movement vanishes at the larger viewing distances. Another significant interaction is that between direction of movement and exposure duration, thresholds for closure decreasing faster than thresholds for opening with t increases. init 120
ong 60
5ep
a 30
of0rcJ
hn 15
I
75
1
200"
2L LO
80
160 320 mlt v!ew dist D [ml
610
Fig. 3. Average threshold speed for movement away from the observer as a function of initial angular separation for diierent exposure durations (d = I-40m).
Fig. 4. As Fig. 3, for movement toward the observer.
154
WIEL
i-I.
~NSSEN
et
a!.
One should be careful, however, in drawing conclusions that involve differential effects of direction of movement when the proximal stimulus is really specified in terms of angles. As will be apparent from (1) there exists an Qpriori asymmetry between directions of movement in terms of angular changes accompanying movement in depth. That is, a certain change in angular separation when movement is toward an observer is reached at a lower distal speed than when movement is away from an observer. In fact, when analysis of variance was carried out on the total angular distance traveled at threshold by the spots, the direction of movement became only a marginally significant factor, indicating that the spots had to move a certain angular distance irrespective of direction. Figure 5 shows the data. However, there was a signi~cant interaction indicating that there might be significant differences between directions of movement for longer exposure durations. Weber fractions (threshold angular distance traveled/initial angular separation) increased from 0.042 at 2” to O-060at 7.5’ initial angular separation, with the implication that the center of the fovea is less sensitive than its periphery to movement of the kind studied. Experiment II The size-brightness cue When a flat circular light source moves in depth three stages may be distinguished according to the cue that determines the movement’s detectability. Consider the case where movement is away from an observer. When the light has started its movement its apparent size begins to fafl off with the square of the viewing distance. This does not affect its brightness, however, since the reduction in apparent size runs parallel to the inverse square law governing the magnitude of the light’s illuminance at the observer’s pupil, leaving the amount of light received per unit area at the pupil unaltered. Thus, a change in apparent size is the only cue from which relative movement may be inferred at this stage. This remains true in so far as the light constitutes an area source, i.e. as long as the resoIving power of the eye is indeed sufficient to notice such change. When movement continues, however, a transition zone will be entered at a certain distance wherein the eye changes its mode of operation. When the light has moved out of this zone it is a point source to the eye. Its apparent size is constant now, and since illuminance keeps falling off with the square of the distance a change in brightness is the only cue available for inferring movement in depth. (Sometimes the use of the word “brightness” is restricted to area sources, being employed as an equivalent of the physical concept of luminance. There lies no danger of confusion, however, in speaking of the brightness of both area and point sources when the subjective attribute is meant.) In the experiment [Janssen, 19721 it was tried to determine ark with changes in size or brightness as isolated proximal cues, again as a function of exposure duration (l-0 or 2.0 set), initial viewing distance (40,50,80 or 160m for a light of 15 cm diameter, corresponding to angular sizes of 12+9’,10.2’, 6.4’ and 3.2’, respectively) and direction of movement. A comparison with the results of the first experiment would then yield information on the relative efficiency of the size/brightness cue with respect to the cue of changing angular separation. For technical reasons only movement of a single light could be simulated. The stimulus was formed by an image projected from behind onto a piece of transparent red foil. By having the diaphragm opening made continuously narrower or wider movement in depth could be simulated. The “real” diameter of the moving source was 15 cm, and the luminance of the projected image was about identical to the luminance of the pair of lights used in Experiment I (21 cdfm2). A
Fig. 5. Total angular distance moved at threshold during exposure as a function of angular sepa~tion for movement away from and toward the observer. Curves are the mean across all other experimental conditions.
The perception
of lead vehicle
movement
129 107 ,_,~_6~"~_~_~~_~~~__
in darkneTs
32
]
r
Fig. 6. Threshold
speed for movement in depth of a IS-cm circular source distance for different exposure durations.
:I$ a function
of initial
viewing
procedure similar to that in the preceding experiments resulted in estimates of u,,,. The estimates are shown in Fig. 6. All main effects, but no interactions, were significant. In general, thresholds were much higher than those obtained in the experiment with change in angular separation as a cue, as will appear from a comparison of Fig. 6 with Figs. 3 and 4. It can be shown that the difference is only to a very small extent due to the fact that only one stimulus light was used in the present experiment instead of a pair of lights (whose angular separation would have to be artificially kept constant during movement in order to isolate the size/brightness cue). Application of results on signal detection of the combination of sensory evidence stemming from a number of sources of information [Green and Swets, 1966, p. 2391 shows that threshold velocities on the basis of the size-brightness cue for a pair of lights will only be reduced by an amount that is much smaller than the difference revealed by comparing Fig. 6 with Figs. 3 and 4. We may safely conclude that relative movement will be detected on the basis of a change in angular separation between taillights long before changes in size or brightness can come into play as sources of information. Weber fractions were calculated in order to determine at what angular size a light becomes a point source under the present conditions. It can easily be shown that both the Weber fractions for apparent size and for apparent brightness are equal to
(3) where AD is the distance traveled in depth at threshold. This means that Weber fractions can be calculated without bothering about which cue might be the relevant one in any particular condition. Values of W are displayed in Fig. 7. Analysis of variance showed the direction of movement to be of no significant influence. The remaining main variables still had highly significant effects, and there were no significant interactions. A Newman-Keuls post hoc analysis revealed that the significant effect of the factor “initial angular diameter” was completely due to the effect of the largest diameter, 12.9’. The results of this analysis statistically confirm the presence of a break in W between angular sizes of 10.2’ and 12.9’, thus lending support to an interpretation in terms of two different visual mechanisms. An additional result is that discrimination of apparent size and brightness is enormously more difficult when there is a change of the continuous variety encountered in this experiment than
when change is of the discrete kind most often studied in psychophysics, are seldom higher than 0.20.
where Wcbcr fractions
The purpose of the tield test [Janssen, 19733 was to check the conclusion that ;I change in between a vehicle’s t~lilli~hts, rather- than a change in their apparent size or brightness, must be the dominant cue in the detection of rclativc motion in depth. If this conclusion is valid it should be found that “real-life” thresholds should be equal to those measured in the laboratory with changing angular separation as the single cue (Experiment I). Of course there is a logical difficulty in that changing angular separation must not necessarily have been tile cue if thresholds in the field are indeed found to be equal. However, alternative hypotheses to account for a positive finding certainly would have to bc considerably more complex than the changing angular separation hypothesis. For this reason we decided to prefer the simple hypothesis in case the thresholds would be as predicted. The experimental procedure consisted in having two cars drive at a speed difference found in Experiment I to be at threshold in order to observe whether performance would indeed he at threshold level (defined by d’ = l-25). Ex~~eriment~~l variables included the observati~~n distance D (= 160 and 320 m), the exposure dur~ttion f (= I.0 and 2-O XC), and the direction of relative movement (opening or closure). At the larger observation distance (3X m) only an exposure duration of 2 see was used since the speed difference required for the I-XX condition was too high to be reached within the dimensions of the available track. To control distances between the cars a binocular viewer was mounted in the back of the leading car (Fig. 8). angular separatiotl
The perception of lead vehiclemovement
157
indarkness
It was adapted in such a way that its upper and its lower half-images would exactly coincide at a preset viewing distance chosen by the experimenter. Through the viewer the experimenter watched a construction mounted on the roof of the following car which consisted of a number of bulbs mounted above each other inside a translucent cover of 1 m height. The experimenter, who was seated in the back of the leading car, could switch on the lights of the leading car at the correct viewing distance for a preset exposure duration by means of a push button on the control box. The subjects in the following car had their eyes closed until they were warned by the experimenter, approximately 2 set before stimulus presentation, to open them and watch what happened. Theresults for the four subjects who took part in the experiment are shown in Table 1. There is a clear tendency for the values obtained to be somewhat higher than the predicted value of 1.25. Thus the results seem to contradict the conclusion from the laboratory studies: out of 24 values of d’, 21 are higher than 1.25. We may ask as a start, however, what a difference in d’ of a few tenths of a unit means in terms of the distal speed difference. To answer this question we must know the shape of the function relating d’ to distal speed. Fortunately this function was known from the procedure to estimate the threshold as applied in the laboratory experiments, which in fact consisted in interpolating on this function. The data indicated that the function was very steep, a difference in d’ of a few tenths of a unit corresponding to only a few kilometers per hour on the speed scale. Thus, the departure from the expected values found in the present experiment was probably very minor. Nevertheless it would be valuable if an explanation of even this small departure could be provided. The explanation may lie in a feature of the procedure employed in the experiment. We are referring to the fact that subjects were warned to open their eyes a few seconds before the presentation was given. Thus, the subjects may have had a small advantage from the observation of the leading car’s silhouette before the onset of the actual observation interval. If this interpretation is correct one would expect d’ to be closer to 1.25 with a 2-set than with a I-set exposure interval, at the same viewing distance. This is because if we assume that the subjects started looking at an approximately fixed interval before the onset of the actual exposure interval, they would have little help of auxiliary cues before a 2-set interval. The speed difference just before (and during) this interval was, of course, always smaller than with a I-set interval, since speed differences had been chosen in accordance with the finding from Experiment I that threshold speed decreases with increasing exposure duration. The results presented in Table 1 are in agreement with this interpretation, as will be apparent from the comparison between the 1-set and 2-set data columns for a viewing distance of 160 m. We may conclude that the slight departure of the data from what was expected on the basis of the hypothesis put to test must be due to uncontrolled observations made by the subjects, and that the data essentially tend to support to the hypothesis. Thus, a change in angular separation between taillights indeed appears to be the prominent cue in the detection of vehicle motion in depth. Table LValues of d'inthe fieldexperiment
observation
opening
distance
320 m
160 m exposure interval
closure 160 m
320 m
1 set
2 set
2 set
1 set
2 set
2 set
1
1.84
1.70
0.85
1.57
1.27
1.70
2
1.29
1.35
1.44
1.49
1.36
1.65
subject
m
3
1.56
1.34
1.47
1.47
1.32
1.45
4
1.39
0.74
1.65
1.28
1.34
1.22
average
1.52
1.28
1.35
1.45
1.32
1.50
If8
JANSSENet al.
WIELH. IMPLlCATIONS
FOR THE NIGHT-DRIVING
SITUATION
What are the implications of the empirical results for car-following at night, and how could they give rise to suggestions which may reduce the relatively large risk that accident-liability statistical records show to be associated with night-time driving? This is the question to which we will address ourselves in the remainder of this report [see also Janssen, 19741. Although threshold speeds haye been obtained both for the opening and the closure situation, and although the instability of a traffic system leading to a rear-end collision must be attributed to an interplay of factors from both situations, the discussion will, for reasons of space, be restricted to the closure situation. The relation between threshold speed, initi~ viewing dista~ee (headway) and ex~osafe daratio~
The data from Experiment I looked reasonably linear on log-tog plots (see Fig. 4), and consequently they were fitted by least-squares estimates. The resulting equations were: (t = O-5set)
vrh= 0. 152D”‘6
(4a)
(t = 1-Oset)
vlh= O*079D”‘8
(4b)
(t = 2-Oset)
or,,= O’018D”38
(4c)
(t = 4-Oset)
0th= 0~017D”37
(4d)
(Q, in km/h, D in m). AIthough the exponents in these equations are not identical, they were considered to be sufficientiy close to each other to permit the use of a single exponent under different exposure durations in further computations. The value of the idealized exponent was taken to be 1.25, about the average of the four exponents. We thus take: ii,h= f(t) . g5’4
(5)
as the idealized, smoothed expression to serve as a computational basis; f(t) is constant for a given value of t. After having refitted the original equations to incorporate the idealized exponent the function f(t) can be determined by Ieast-squares. A hyperbolic equation was judged to describe f(t) best:
f(f)= 3672t f- 15.17 Values of f(t) are tabulated below; since f(t) is not dimensionless they are valid if &h is expressed in km/h and D in m. When changing to angular dimensions the time dependent function f(t) can be rewritten into a corresponding function g(t), which again is not dimensionless. Since, according to (2)
d. Vth
a& = -
DZ
Table 2. Values of the coefficient f(f) in eqn (5)
i
t
(set)
i
f(t)
(=I
0.5
0.157
1.0
0.047
2.0
0.034
4.0
0.030
m
0.027
-1
I
we obtain
&$h= g(t) 1r3’* * d = h(t). ff”4. 2”
00
as the idealized equation expressing dlrhtinstead of Q,, as the dependent threshold variable.(The factor h(t) corresponds to g(t) and f(t), but has again different dimensions.) a is the initial viewing angle. An interesting implication of (8) is that the Weber fraction
is not Monsantobut is seen to be finely related to X3”“.Of course this fits the ~nd~~~of ~xp~~rnent I that the Weber fraction increased with decreasing initial angle. The subject to which the above equations obtain is the average one. However, from the raw data tabulated in the appendices to the report by Harvey and Michon [1971]it was apparent that there were large individual differences in the ability to detect motion. Stwas observed from these data that there very commonly was a difference of as much as 100%between the threshold vahres af the most and the least sensitive subjects within an experimental group. We therefore will not only deal with the average subject, but also with the fairly common subject whose thresholds are, let us say, 50% higher. Equation (5) appfies to him with a factor l-5 in front. Time Et&
eo~~~~~ amifmziime
af&
~~e~~ion
From the thresh&! data for efosure, formafized eqn (5)?estimates may be obtaineii of fwo ~m~rtant temporal parameters in ear follo~ng~ viz. time untif collision (T, ) and free time after detention IT,). Time unti1 collision T, is de~n~d as the period of time between the instant the driver has detected that he is closing and the instant that a collision with the leading car will ensue-given that both cars drive on with the same speed. This parameter may be computed from: T _ distance after detection = D c-
%I
l]O, .
Qh
t
.
where o*&follows from (S), Lee 11972)has ~a~~u~at~T, under the assump~o~ of fixed angn~~ ~e~o~~t~ thresholds of S/see and f*lsee, whieh he felt would represent a fair estimate of the range that w&d be encountered in driving in all but dense fog. This is an approximating which is too crude, since angular thresholds are obvious& not fixed but are at least a function of the initial angle at and of t. Thus Lee’s graphs cannot provide very reliable estimates of T,, Figures 9 and 10 do the job somewhat better, since the basic eqn (5)from which they are derived incorporates both a Weber mechanism and a constant related to t. T, is shown both for the average observer (Fig. 9) and for the observer whose thresholds are 50% higher than average (Fig. 10).
WIELH.
zoo
JANSSEN
er al.
LOO
lnlt vww dlst
600 Dim)
Fig. IO. Time until collision after detection of closure (observer whose threshold is 50% higher than the average).
The remarkable feature appearing from these graphs is that T, grows with decreasing viewing distances and drops to rather low values at the larger viewing distances. Thus, owing to the nonlinearity of the relationship between v, and D it appears that following a lead car at a short distance by keeping relative movement at threshold is considerably safer than fo~iowing it so at a long distance. This conclusion stands up even if we recognize that the speed differences required to generate the right-hand parts of the curves in Figs. 10 and 11 are unrealistically high. In particular, of course, the conciusion is seen to bear on observers with low movement sensitivity. Not all of the interval T, can be spent by the driver in merely contemplating about what to do. If the driver is to avoid collision with the lead car there is an ultimate point in time within T, at which maximum braking force must be applied. Free time Tf is defined as the interval from the moment the driver has detected he is closing until the moment he should apply maximum braking force (which at its utmost may be 1.0 g) in order to avoid collision. Although the definition of T, in a strict sense only applies to the case in which none of the vehicles takes any action until the critical moment of full braking it is also interesting to see what becomes of Tf if the lead car changes its movements after the detection of closure has taken place. In particular the case of deceleration would have important consequences to 7” Consider, however, first the case in which both vehicles continue their journey with the speeds they had at the beginning of the observation interval t. In order to avoid collision it is necessary for the following car to (at least) reduce its speed to that of the lead car. Take a (
Fig. I t. Free time after detection of closure (average observer, deceleration -7 m/se?).
The perception of lead vehicle movement in darkness
161
This value must be subtracted from the value of the time until collision T, as given by (9). Moreover a certain interval should be subtracted from T, which it takes the driver of the following car to initiate his braking reaction. A reasonable estimate of this interval is of the order of 0.7 set [Lee, 19721.We find: T, = I; i:-O.7sec
(10)
(a -=z 0, o*)th> 0). Values of Tf computed from (10) are shown in Figs. 1l-14, both for average and underaverage individuals, and for two values of a (-4 and -7mlsec’). As with the graphs for T, the steep rising of the curves with small viewing distances and their gradual drop at the larger distances is clearly apparent. Now consider the case in which the lead vehicle starts decelerating at the very moment the driver of the following car has detected the existence of a speed difference. (There is nothing special about the deceleration supposed to take place at this moment, except that it makes computations slightly simpler.) Denote the magnitude of the lead car’s deceleration by b and suppose that it is maintained for a period t* (we require that t* is much smaller than the time until collision T, in order for the situation to make sense). During the period of deceleration the speed difference between the vehicles will change from aLhto v*=tl,-b.t*
average observer
200
LOO tn,t ww dist
-
(b < 0).
011
Lm/sec”
600
800
0 (ml
Fig. 12.AS Fig. 11,but with a deceleration of -4 m/set*.
Fig. 13. Free time after detection of closure (observer with thresholds 50% higher than average, deceleration -7 m/se?).
LOO bO0 800 #nit vv?wd!st D iml Fig. 14.As Fig. 13,but with a deceleration of - 4 m/se?. 200
J
162
WIEL H. JANSSENet al.
What about the distance D* between the vehicles after the interval t*? Obviously D* equals the distance at the moment of the detection of a speed difference minus the difference between the distances both vehicles have travelled during the deceleration interval. This difference is seen to equal v,,,. t*-;b.
t*=
(12)
so that the distance between the cars after the deceleration interval is
D*=D-vr”*f_v,h.t*+Ib2. t*=. uth
(13)
Time until collision is then seen to be equal to T,
=$+ t*.
(14)
(Observe that t* must be added because the observer in the following car has already survived this deceleration interval.) In order to compute T, we merely have to subtract from T, the time it takes to reduce the speed difference to 0 after the lead car’s deceleration, and also the time it takes to initiate the braking reaction. This yields: T, = T, - ( vrh-,” ’ t *) - 0.7 sec.
(13
From this expression one may get a feeling of how disastrous even a small deceleration of the lead car, applied for only a few seconds, may be on the available free time. Figure 15 shows, as an example, the values of T, resulting from a deceleration of - 2 m/sec2 maintained during 2 set and compares these to the values obtained in the stationary situation without deceleration (Fig. 11). The effect is particularly impressive at the smaller distances, since here the change in relative speed caused by the deceleration is large compared to v,,,. For an observation interval of over O-5set T, is seen to have a maximum at a headway of about 200 m. Size of the natural sampling interval The functions for T, and T, show that the largest increase in these temporal parameters takes
place when exposure duration goes up from 0.5 to 1.0 sec. Relatively little improvement is found if t takes values of over 1.0 sec.
InIt
VIEW
dtst
D lml
Fig. 15. A comparison between free times w’ith and without deceleration of the leading car. Dotted lines: with deceleration of -2 m/se? maintained during 2 sec. The picture represents observers of average sensitivity.
The perception
of lead vehicle movement
163
in darkness
This brings us to the question of what the sampling rate of visual information during driving actually is. Since drivers surely do not continuously pay attention to the road in front of them one would like to have information on how often they do pay attention to environmental features and, still more important for present purposes, what the size of the sampling interval is. The literature, unfortunately, shows a lack on this point. Although a promising approach to visual sampling during driving has been developed by Senders et al. [1%7] it has not yet been used so as to yield results that are appropriate to the present issue. What Senders et al. did was to study sampling rates for given vehicle speeds by periodically raising (at the subject’s desire) and lowering a visor attached to a helmet that subjects wore during driving. They used fixed viewing durations ((of 0.25,0.50 and 1.00 set) and measured the duration of periods of occluded vision. This is a procedure which does not yield an estimate of the natural sampling duration. The reverse procedure, i.e. having a subject drive with unobstructed vision until he indicates that he can do without vision for a while could yield an estimate of sampling durations (although this would be a somewhat artificial thing to do for the subject). For the time being we have only some pilot studies by Senders et al. to rely on. From these studies it appears that a “sampling episode”, consisting of a 0.5set sampling interval every 3 set, can be identified. This means that, of the functions obtained in the present experiments, those generated under the shorter exposure durations should be considered to be the most relevant.
The effect of taillight separation
on speed thresholds
The values of collision and free intervals computed thus far assume that d, the metric distance between taillights, is l-40 m. Since the detectability of relative moment is, however, based on proximal cues we may ask what the effect of variation in d is on the speed thresholds and, consequently, on the temporal parameters of relevance in car-following. What is the effect on &h if we change d into k. d, all other things remaining equal? In order to assess this effect the requirement to be kept in mind is that the movement in depth of the lights (now separated by a distance k . d) must possess a speed which is sufficient to bring angular velocity at the threshold level associated, through the Weber mechanism, with the initial angular separation between the lights. The relationship between angular velocity and initial angular separation we already know from the experiments in which d was, for convenience, chosen to be 1.40m. Hence, we may derive an expression for the size of the ratio of the threshold speeds for any two values of the taillight distance which differ by some factor k. To this purpose compare three situations (see Fig. 16). First, there is the situation with the “old” taillight separation d, observed from a distance D and resulting in a speed threshold L)lh (old). Second, there is the situation with the “new” taillight separation k . d, again observed from a distance D, and resulting in a speed threshold VI,,(new). These are the two situations we wish to compare, i.e. we want to know the ratio u,,,(new)/u,,,(old). To this means we need a third situation
d/20 rod
V
OLD
Fig. 16. Computation
V
STATE
DUMMY
STATE
of the effect on the threshold
NEW
STATE
for closure of a change in taillight
separation
by a factor k.
164
WIEL H. JANSSENet al.
in which the taillight separation is the old d, but in which the initial angle between the taillights is equal to that in the “new” situation. This “dummy” situation we need in order to know the required angular threshold going with a particular initial angle, which we can then translate back to the “new” situation. This means that taillights in this third situation must be at an observation distance D/k; there is a speed threshold uth (dummy). Now we are ready to write expressions for the speed thresholds in each of these three situations by making use of the basic eqn (5) and also of the expression relating &, to distal variables (2). In the “old” situation we have ut,,(old) = f(t) . P
(16)
From the proximal identity of the “new” and the “dummy” states follows the requirement that &h =
d. Vlh(dummy) = k . d. ulh (new) D2 D2 k 0
(17)
Us,,(new) = k . t&h(dummy).
(18)
from which we find that
This says simply that if we double both the distance between lights and the observation distance at the same time, for example, we will need twice the original velocity in depth to maintain the same angular velocity. Since we have ti,,,(dummy) = f(t) . (f)“’
(19)
u,,,(new) = k. f(t).
(20)
and, consequently, (f)5’4
it follows by combining (16) and (20) that
u,,o =
k-l,4
uth(old)
*
(21)
This equation gives the desired ratio of the sizes of the threshold speeds after a certain change in d. We may calculate, for example, that reducing d by 50% increases threshold speed by 19%, or that doubling it decreases threshold speed by 16%. Also observe that the factor 3 by which automobile taillights distances may differ (from appr. 0.75 to 2.25 m) will cause the smaller cars to have a threshold speed for detection of their relative movement in the dark which is +30% higher than that of their big brothers. Obviously this implies a severe reduction in the temporal parameters T, and T,. One might conclude at once that making intertaillight separation as large as possible would be recommended. Conclusions
from the calculation
of temporal parameters
The following may be concluded from the calculations on temporal parameters in car-following which have been presented: (i) Both for individuals of average and underaverage sensitivity to relative motion there are likely to occur situations in night driving in which collision with a lead vehicle is area1 threat. (ii) Factors that in particular will increase the risk of a collision are: (1) decreased braking power of the following car, such as occurs when roads are wet; (2) manoeuvres of the lead car which involve a deceleration, even if it is small and lasts only for a brief period; (3) a small intertaillight separation of the lead car.
The perception of lead vehicle movement in darkness
165
(iii) It is therefore required that measures are taken which have the net effect of improving a driver’s ability to detect a lead car’s relative motion. In other words, we must believe there is a real problem to the driver in the situation, and in order for him to survive it should be solved. A few suggestions to improve the existing situation are listed in the final section of this paper. It is realised that requirements from other problem areas will and must interfere and interact with these suggestions. More comprehensive treatments of the problem of vehicle lighting and signaiing systems are given by Mortimer [1970]. IMPROVING
THE CAPACITY
TO DETECT LEAD CAR MANOEUVRES
Three ways can be distinguished in which the problem of raising detec~biIity capacity could be approached. First, the possibility of training drivers so as to increase their sensitivity could be explored. Second, there is the possibility of developing new systems, demanding major modifications of current vehicle design, which inform surrounding traffic of a vehicle’s ongoing or planned manoeuvres. Third, one might try to modify existing vehicle lighting systems in a relatively minor way so as to be better adapted to the needs of drivers of other vehicles. Between the second and the third alternative there is, of course, only a gradual difference. Improving sensitivity by systematic training is a subject which has not attracted much attention in the literature. This apparently is because the detection of relatively simple stimuli is not considered to be a skill which can be learned and developed. Another reason why the literature is scarce is that researchers working in the field of detection are usually interested only in stable asymptotic performance and have developed a habit of throwing the learning portion of their data away. Blackwell 119531is an exception to the rule. In a large-scale study of visual detection he included an investigation in which he found that subjects displayed training effects in the detection of a spot of light which extended to 6 or 7 sessions of 2 hr each. The final effect was a decrease in threshold luminance of the order of 25-30%. Despite the fact that Blackwell’s experimental set-up differed a great deal from ours there is reason to hope that training might improve driver’s sensitivity to motion, the more so since Blackwell’s subjects did not receive any systematic training but were left at themselves. However, since basic data are still essentially lacking it is difficult to see what form such a training for drivers could possibly take and how it should be inco~orated into driver education as a whole. The second alternative, the development of radical new systems aimed at improving the perceptibility of vehicle manoeuvres, has already been under exploration for several years now. Although it is probably still too early to reach a definitive conclusion the evidence as yet is that this approach has appeared a rather fruitless one in terms of the probability of one of the constructions developed to be ever implemented. Contributing to this impression are the failures to be considered realistic solutions of such reasonable proposals as the application of Doppler radar in order to force the driver into maintaining a fixed headway distance, the application of a signal system which warns for ongoing decelerations and accelerations [Michaels and Solomon, 19621,and the application of signal systems which indicate the severity of braking [e.g. Rutley and Mace, 19701. To the present writers it appears that the direction a solution should take is to improve upon the vehicle-lighting system as it exists today. The following, admittedly rather elementary, suggestions seem worth considering First, taillight separation should be standardized. This is not advice based so much on our own findings as it is on the general consideration that a standard separation would help drivers in judging vehicle manoeuvres. In cars as they are found today distance between taillights may vary by no less than a factor 3 (from 0.75 to 2.25 m). From the point of view of human engineering this is a regrettable state of affairs. Second, taillight separation should be as large as possible. The reason is, as indicated in this paper, that speed thresholds decrease considerably with increasing d. Third, vehicles which presently have only one taillight (motorcycles) should have two, The reason is that the detection of relative speed is easier from angular than from size-brightness cues. Awaiting the implementation of this recommendation one should concentrate on increasing the size of the taillight rather than its brightness. This is because it appeared from the experiment on the efficiency of the size-brightness cue that size discrimination for a moving source is
166
Wax H. JANSSEN er al.
superior to brightness discrimination. This implies that it is valuable to make a tight retain its identity as an area source as long as possible. REFERENCES Blackwell H. R., Psychophysical thresholds: experimental studies of methods of measurement. Bull. Eng. Res. Inst. Michigan
No. 36, 1953.
Green D. M. and Swets J. A., Signal Detection Theory and Psychophysics. New York, Wiley, 1966. Harvey L. 0. Jr. and Michon J. A., Progress Report 1. Effects of viewing distance and angular separation. Institute for Perception TNO. Report Nr. JZF JP7J-C6, 1971. Harvey L. 0. Jr. and Michon J, A., Detectability of relative motion as a function of exposure duration, angular separation, and background. J. Exp. Psycho1 103, 317-325, 1974. Janssen W. H., Progress Report II. Effect of IateraI motion on thresholds for relative sagittal motion. Institute for Perception TNO. Report Nr. IZP J97J-C2t?, 1971. Janssen W. H., Progress Report IV. Perceptib~ty of relative sagittal motion on the basis of changes in apparent size or intensity of taillights. Institute for Perception TNO. Report Nr. JZF J972-C6, 1972. Janssen W. H., Progress Report V. Thresholds for relative vehicle motion in depth: A check in the field. Institute for Perception TNO.~Report fir. IZF 197~CJ2, 1973. Janssen W. H.. Proaress Renort VI (Final reoort). Imnlication of nsvchophvsical threshold measurements for the night-driving situation. Institute for Perception TNO. Report Nr. fZk j974ki2, 1974. Lee D. N., Theory of visual information available for vehicle control. Paper presented at an OECDSymposium,Rome, 1972. Leibowitz H. W., The relation between the rate threshold for the perception of movement and luminance for various durations of exposure. 1. Exp. Psycho/. 49, 209-214, 1955a. Leibowitz H. W., Effect of reference lines on the discrimination of movement. J. Opf. Sot. Am. 4% 829-830.195% Michaels R. M. and Solomon D. M., The effect of speed change information on spacing between vehicles. Public Roads 31, 229-235, 1%2. Mortimer R. G., Automotive rear lightingand signalingresearch. &SRI-report No. Hz&f. University of Michigan, 1970. Rutley K. S. and Mace D. G. W., An evaluation of brakelight display which indicates the severity of braking. Road Research ~aborato~es Report LR .S?, 1969. Senders J. W., K~stofferson A. B., Levison W. H., Dietrich C. W. and Ward J. L., Attentions demand of automob~e driving. Boft, J&ran& and Newman, inc. Report Nr. 1482, 1967.
THE PERCEPTION
OF LEAD VEHICLE MOVEMENT IN DARKNESS
WIEL H. JANSSEN, JOHNA.
.MICHoNtand LEWIS0.
HARVEY,
JRS
Institute for Perception TNO, Kampweg 5, Soesterberg, The Netherlands (Received 14 October 1975) Abstract-Three experimental studies are described on the detection of longitudinal lead-vehicle movement in darkness. Experiment I, performed in the laboratory, isolated the relative horizontal angular motion of the lead-vehicle’s taillights as a cue to the detection of relative longitudinal movement. Movement thresholds were determined as a function of initial headway, exposure duration, direction of the movement, and the presence of a background. All these factors except the last had significant effects on the movement threshold. Experiment II, also a laboratory-experiment, isolated changes in apparent size or brightness of the taillights as a cue. Movement thresholds were again found to be a function of the variables investigated in Experiment I. However, thresholds now were much higher than under the isolated angular cue. It was therefore concluded that the relative horizontal angular motion of the lead-vehicle’s taillights is the priminent cue in the detection of relative vehicle motion in depth. Experiment III substantiated this conclusion by confirming the parametric outcomes of Experiment I under realistic night-driving conditions. The practical relevance of the estimates made from the data of two important temporal parameters in car following, viz. time until collision and free time after detection.
INTRODUCTION
Under contract with the Netherlands Institute for Road Safety Research an investigation has been carried out to achieve better understanding of the factors which enter into an automobile driver’s perception of other vehicles moving through his visual field. The problem in general may be analyzed in terms of distal and proximal stimulation. This distinction may be illustrated by considering the night-time driver who is followed a car in front of him. The behavior of the leading car-in absence of other environmental cues such as street lighting-will be inferred primarily from changes in the configuration and location of its taillights. The main distal variables entering into the situation are schematically presented in Fig. 1. The distal stimulus dimensions are presented in physical timespace, and can be specified quite easily, although they can not so easily be manipulated in reality. At the retina, however, the physical stimulus dimensions are entirely different, i.e. the proximal stimuli will be specified in terms of angles, apparent size, and apparent brightness. The characteristic proximal variables, which correspond in a complicated way to the variables in Fig. 1, are depicted in Fig. 2. Usually the proximal stimulus can be simulated in the laboratory. As long as the transformation distal-proximal is complete a subject will not be able to ascertain whether he is looking at a real world or at a laboratory display. Yet in most cases the laboratory situation will quickly betray itself, because of distal variables which are not represented in the simulation. Therefore, laboratory data obtained in a partially simulated reality ultimately will have to be checked against some real-life situation. On the other hand, the laboratory situation gives the investigator the possibility to manipulate the important variables independently. In the present case the potentially most powerful cues to detect relative motion, viz. the angular distance between the lead-vehicle taillights and their apparent size and brightness, have been manipulated independently. On the basis of the results from these experiments a check in the field has subsequently been performed. We will describe three experimental studies on the perception of lead-vehicle movement we have performed and the conclusions that have emerged from them. For the sake of briefness not all procedural details will be discussed; these are contained in the technical reports issued by the Institute for Perception TNO. tNow at the University of Groningen, The Netherlands. SNOWat the University of Colorado, Boulder, Colorado, U.S.A. 151
152
WIEL H. JANSSENef nl. heading
direction t
observer
Fig. I. Distal stimulus situation in car following. The relevant variables are: D-distance; L-lateral distance from the heading direction (median plane); a-the angle between the heading directions of both vehicles; H-the height difference between the plane through vanishing point and the observer’s eye parallel to the horizon, and the taillights of the leading car. medtan plane
!
horizon
Fig. 2. Proximal stimulus situation in car following. Variables are: I-apparent brightness/apparent size; S-angular separation between taillights; y-ditto (vertically); A-angular distance between vanishing point and taillights (horizontally); n-ditto(vertically).
EXPERIMENTAL
STUDIES
Experiment I. The angular cue
The first experiment [Harvey and Michon, 1971, also 19741was designed to measure human sensitivity to the relative horizontal motion of two spots of light. When an observer views, from distance 0, two spots separated by distance d, the visual angle a separating the spots is: a =$rad(n
(1)
If D is changing at a constant rate v the rate of change in a is described by the first derivative of (1) with respect to time: &=- do
D2
Angular speed is accelerating positively when motion is toward the observer (closure) and negatively when it is away from the observer (opening).
The perception of lead vehicle movement in darkness
153
The specific question to be answered experimentally was: “How fast must two spots move relative to each other in order for an observer just to be able to detect the motion?” Performance is then said to be at threshold, Thresholds were determined as a function of: (i) The initial angular separation (Z”, l”, 30’, 15’ or 7*5’,corresponding to D = 40,80,160,320 or 640, respectively, for a (fairly common) intertaillight distance of d = 1.4m). (ii) The exposure duration (t = 0.5,1*0,2~0 or 4-Oset). (iii) The direction of movement (toward or away from the observer). (iv) The presence or absence of a background consisting of vertical lines spaced randomly on a random dot background. The stimulus spots were generated by a mirror system [see Harvey and Michon, 197I, 1974,for details on the apparatus]. On the projection screen the spots had a luminance of 21 cd/m’. They subtended a constant angle of I’, and thus were effectively point sources for an observer sitting at a distance of 25 m. The experiment was done in a dark corridor. For any given experimental condition the distal speed of movement was determined that would allow the subject to detect the movement 75% of the time. A signal detection method was used [Green and Swets, 1%6] which resulted in estimates of the bias-free sensitivity parameter d’ under each of four speeds of movement per experimental condition. Threshold speed t&h was obtained by interpolating at d’ = 1.25 (the bias-free equivalent of the 75% point of classical threshold measurement) on the function relating movement speed to d'. The results were analysed by analysis of variance on the log-transformed values of urh.It was showp, first of all, that the presence of a background made no difference. This is a somewhat unexpected finding given the results of Leibowitz [1955a, b] on the detection of linear movement of single targets, where background did make a difference. Perhaps the presence of a background is simply not effective with two spots moving relative to each other. ~ternativeIy, the 4-see exposure may not have been long enough for background to make an effect. Initial angle, direction of movement and exposure duration all had highly significant effects on t&h. The data, averaged over background conditions, are shown in Figs. 3 and 4. The data show that Z)lhdecreases as exposure increases from 0.5 to 2 set but that further increase to 4 set exposure does not produce much further improvement. A comparison of Figs. 3 and 4 also shows a significant interaction between direction of movement and initial viewing distance. The difference between directions of movement vanishes at the larger viewing distances. Another significant interaction is that between direction of movement and exposure duration, thresholds for closure decreasing faster than thresholds for opening with t increases. init 120
ong 60
5ep
a 30
of0rcJ
hn 15
I
75
1
200"
2L LO
80
160 320 mlt v!ew dist D [ml
610
Fig. 3. Average threshold speed for movement away from the observer as a function of initial angular separation for diierent exposure durations (d = I-40m).
Fig. 4. As Fig. 3, for movement toward the observer.
154
WIEL
i-I.
~NSSEN
et
a!.
One should be careful, however, in drawing conclusions that involve differential effects of direction of movement when the proximal stimulus is really specified in terms of angles. As will be apparent from (1) there exists an Qpriori asymmetry between directions of movement in terms of angular changes accompanying movement in depth. That is, a certain change in angular separation when movement is toward an observer is reached at a lower distal speed than when movement is away from an observer. In fact, when analysis of variance was carried out on the total angular distance traveled at threshold by the spots, the direction of movement became only a marginally significant factor, indicating that the spots had to move a certain angular distance irrespective of direction. Figure 5 shows the data. However, there was a signi~cant interaction indicating that there might be significant differences between directions of movement for longer exposure durations. Weber fractions (threshold angular distance traveled/initial angular separation) increased from 0.042 at 2” to O-060at 7.5’ initial angular separation, with the implication that the center of the fovea is less sensitive than its periphery to movement of the kind studied. Experiment II The size-brightness cue When a flat circular light source moves in depth three stages may be distinguished according to the cue that determines the movement’s detectability. Consider the case where movement is away from an observer. When the light has started its movement its apparent size begins to fafl off with the square of the viewing distance. This does not affect its brightness, however, since the reduction in apparent size runs parallel to the inverse square law governing the magnitude of the light’s illuminance at the observer’s pupil, leaving the amount of light received per unit area at the pupil unaltered. Thus, a change in apparent size is the only cue from which relative movement may be inferred at this stage. This remains true in so far as the light constitutes an area source, i.e. as long as the resoIving power of the eye is indeed sufficient to notice such change. When movement continues, however, a transition zone will be entered at a certain distance wherein the eye changes its mode of operation. When the light has moved out of this zone it is a point source to the eye. Its apparent size is constant now, and since illuminance keeps falling off with the square of the distance a change in brightness is the only cue available for inferring movement in depth. (Sometimes the use of the word “brightness” is restricted to area sources, being employed as an equivalent of the physical concept of luminance. There lies no danger of confusion, however, in speaking of the brightness of both area and point sources when the subjective attribute is meant.) In the experiment [Janssen, 19721 it was tried to determine ark with changes in size or brightness as isolated proximal cues, again as a function of exposure duration (l-0 or 2.0 set), initial viewing distance (40,50,80 or 160m for a light of 15 cm diameter, corresponding to angular sizes of 12+9’,10.2’, 6.4’ and 3.2’, respectively) and direction of movement. A comparison with the results of the first experiment would then yield information on the relative efficiency of the size/brightness cue with respect to the cue of changing angular separation. For technical reasons only movement of a single light could be simulated. The stimulus was formed by an image projected from behind onto a piece of transparent red foil. By having the diaphragm opening made continuously narrower or wider movement in depth could be simulated. The “real” diameter of the moving source was 15 cm, and the luminance of the projected image was about identical to the luminance of the pair of lights used in Experiment I (21 cdfm2). A
Fig. 5. Total angular distance moved at threshold during exposure as a function of angular sepa~tion for movement away from and toward the observer. Curves are the mean across all other experimental conditions.
The perception
of lead vehicle
movement
129 107 ,_,~_6~"~_~_~~_~~~__
in darkneTs
32
]
r
Fig. 6. Threshold
speed for movement in depth of a IS-cm circular source distance for different exposure durations.
:I$ a function
of initial
viewing
procedure similar to that in the preceding experiments resulted in estimates of u,,,. The estimates are shown in Fig. 6. All main effects, but no interactions, were significant. In general, thresholds were much higher than those obtained in the experiment with change in angular separation as a cue, as will appear from a comparison of Fig. 6 with Figs. 3 and 4. It can be shown that the difference is only to a very small extent due to the fact that only one stimulus light was used in the present experiment instead of a pair of lights (whose angular separation would have to be artificially kept constant during movement in order to isolate the size/brightness cue). Application of results on signal detection of the combination of sensory evidence stemming from a number of sources of information [Green and Swets, 1966, p. 2391 shows that threshold velocities on the basis of the size-brightness cue for a pair of lights will only be reduced by an amount that is much smaller than the difference revealed by comparing Fig. 6 with Figs. 3 and 4. We may safely conclude that relative movement will be detected on the basis of a change in angular separation between taillights long before changes in size or brightness can come into play as sources of information. Weber fractions were calculated in order to determine at what angular size a light becomes a point source under the present conditions. It can easily be shown that both the Weber fractions for apparent size and for apparent brightness are equal to
(3) where AD is the distance traveled in depth at threshold. This means that Weber fractions can be calculated without bothering about which cue might be the relevant one in any particular condition. Values of W are displayed in Fig. 7. Analysis of variance showed the direction of movement to be of no significant influence. The remaining main variables still had highly significant effects, and there were no significant interactions. A Newman-Keuls post hoc analysis revealed that the significant effect of the factor “initial angular diameter” was completely due to the effect of the largest diameter, 12.9’. The results of this analysis statistically confirm the presence of a break in W between angular sizes of 10.2’ and 12.9’, thus lending support to an interpretation in terms of two different visual mechanisms. An additional result is that discrimination of apparent size and brightness is enormously more difficult when there is a change of the continuous variety encountered in this experiment than
when change is of the discrete kind most often studied in psychophysics, are seldom higher than 0.20.
where Wcbcr fractions
The purpose of the tield test [Janssen, 19733 was to check the conclusion that ;I change in between a vehicle’s t~lilli~hts, rather- than a change in their apparent size or brightness, must be the dominant cue in the detection of rclativc motion in depth. If this conclusion is valid it should be found that “real-life” thresholds should be equal to those measured in the laboratory with changing angular separation as the single cue (Experiment I). Of course there is a logical difficulty in that changing angular separation must not necessarily have been tile cue if thresholds in the field are indeed found to be equal. However, alternative hypotheses to account for a positive finding certainly would have to bc considerably more complex than the changing angular separation hypothesis. For this reason we decided to prefer the simple hypothesis in case the thresholds would be as predicted. The experimental procedure consisted in having two cars drive at a speed difference found in Experiment I to be at threshold in order to observe whether performance would indeed he at threshold level (defined by d’ = l-25). Ex~~eriment~~l variables included the observati~~n distance D (= 160 and 320 m), the exposure dur~ttion f (= I.0 and 2-O XC), and the direction of relative movement (opening or closure). At the larger observation distance (3X m) only an exposure duration of 2 see was used since the speed difference required for the I-XX condition was too high to be reached within the dimensions of the available track. To control distances between the cars a binocular viewer was mounted in the back of the leading car (Fig. 8). angular separatiotl
The perception of lead vehiclemovement
157
indarkness
It was adapted in such a way that its upper and its lower half-images would exactly coincide at a preset viewing distance chosen by the experimenter. Through the viewer the experimenter watched a construction mounted on the roof of the following car which consisted of a number of bulbs mounted above each other inside a translucent cover of 1 m height. The experimenter, who was seated in the back of the leading car, could switch on the lights of the leading car at the correct viewing distance for a preset exposure duration by means of a push button on the control box. The subjects in the following car had their eyes closed until they were warned by the experimenter, approximately 2 set before stimulus presentation, to open them and watch what happened. Theresults for the four subjects who took part in the experiment are shown in Table 1. There is a clear tendency for the values obtained to be somewhat higher than the predicted value of 1.25. Thus the results seem to contradict the conclusion from the laboratory studies: out of 24 values of d’, 21 are higher than 1.25. We may ask as a start, however, what a difference in d’ of a few tenths of a unit means in terms of the distal speed difference. To answer this question we must know the shape of the function relating d’ to distal speed. Fortunately this function was known from the procedure to estimate the threshold as applied in the laboratory experiments, which in fact consisted in interpolating on this function. The data indicated that the function was very steep, a difference in d’ of a few tenths of a unit corresponding to only a few kilometers per hour on the speed scale. Thus, the departure from the expected values found in the present experiment was probably very minor. Nevertheless it would be valuable if an explanation of even this small departure could be provided. The explanation may lie in a feature of the procedure employed in the experiment. We are referring to the fact that subjects were warned to open their eyes a few seconds before the presentation was given. Thus, the subjects may have had a small advantage from the observation of the leading car’s silhouette before the onset of the actual observation interval. If this interpretation is correct one would expect d’ to be closer to 1.25 with a 2-set than with a I-set exposure interval, at the same viewing distance. This is because if we assume that the subjects started looking at an approximately fixed interval before the onset of the actual exposure interval, they would have little help of auxiliary cues before a 2-set interval. The speed difference just before (and during) this interval was, of course, always smaller than with a I-set interval, since speed differences had been chosen in accordance with the finding from Experiment I that threshold speed decreases with increasing exposure duration. The results presented in Table 1 are in agreement with this interpretation, as will be apparent from the comparison between the 1-set and 2-set data columns for a viewing distance of 160 m. We may conclude that the slight departure of the data from what was expected on the basis of the hypothesis put to test must be due to uncontrolled observations made by the subjects, and that the data essentially tend to support to the hypothesis. Thus, a change in angular separation between taillights indeed appears to be the prominent cue in the detection of vehicle motion in depth. Table LValues of d'inthe fieldexperiment
observation
opening
distance
320 m
160 m exposure interval
closure 160 m
320 m
1 set
2 set
2 set
1 set
2 set
2 set
1
1.84
1.70
0.85
1.57
1.27
1.70
2
1.29
1.35
1.44
1.49
1.36
1.65
subject
m
3
1.56
1.34
1.47
1.47
1.32
1.45
4
1.39
0.74
1.65
1.28
1.34
1.22
average
1.52
1.28
1.35
1.45
1.32
1.50
If8
JANSSENet al.
WIELH. IMPLlCATIONS
FOR THE NIGHT-DRIVING
SITUATION
What are the implications of the empirical results for car-following at night, and how could they give rise to suggestions which may reduce the relatively large risk that accident-liability statistical records show to be associated with night-time driving? This is the question to which we will address ourselves in the remainder of this report [see also Janssen, 19741. Although threshold speeds haye been obtained both for the opening and the closure situation, and although the instability of a traffic system leading to a rear-end collision must be attributed to an interplay of factors from both situations, the discussion will, for reasons of space, be restricted to the closure situation. The relation between threshold speed, initi~ viewing dista~ee (headway) and ex~osafe daratio~
The data from Experiment I looked reasonably linear on log-tog plots (see Fig. 4), and consequently they were fitted by least-squares estimates. The resulting equations were: (t = O-5set)
vrh= 0. 152D”‘6
(4a)
(t = 1-Oset)
vlh= O*079D”‘8
(4b)
(t = 2-Oset)
or,,= O’018D”38
(4c)
(t = 4-Oset)
0th= 0~017D”37
(4d)
(Q, in km/h, D in m). AIthough the exponents in these equations are not identical, they were considered to be sufficientiy close to each other to permit the use of a single exponent under different exposure durations in further computations. The value of the idealized exponent was taken to be 1.25, about the average of the four exponents. We thus take: ii,h= f(t) . g5’4
(5)
as the idealized, smoothed expression to serve as a computational basis; f(t) is constant for a given value of t. After having refitted the original equations to incorporate the idealized exponent the function f(t) can be determined by Ieast-squares. A hyperbolic equation was judged to describe f(t) best:
f(f)= 3672t f- 15.17 Values of f(t) are tabulated below; since f(t) is not dimensionless they are valid if &h is expressed in km/h and D in m. When changing to angular dimensions the time dependent function f(t) can be rewritten into a corresponding function g(t), which again is not dimensionless. Since, according to (2)
d. Vth
a& = -
DZ
Table 2. Values of the coefficient f(f) in eqn (5)
i
t
(set)
i
f(t)
(=I
0.5
0.157
1.0
0.047
2.0
0.034
4.0
0.030
m
0.027
-1
I
we obtain
&$h= g(t) 1r3’* * d = h(t). ff”4. 2”
00
as the idealized equation expressing dlrhtinstead of Q,, as the dependent threshold variable.(The factor h(t) corresponds to g(t) and f(t), but has again different dimensions.) a is the initial viewing angle. An interesting implication of (8) is that the Weber fraction
is not Monsantobut is seen to be finely related to X3”“.Of course this fits the ~nd~~~of ~xp~~rnent I that the Weber fraction increased with decreasing initial angle. The subject to which the above equations obtain is the average one. However, from the raw data tabulated in the appendices to the report by Harvey and Michon [1971]it was apparent that there were large individual differences in the ability to detect motion. Stwas observed from these data that there very commonly was a difference of as much as 100%between the threshold vahres af the most and the least sensitive subjects within an experimental group. We therefore will not only deal with the average subject, but also with the fairly common subject whose thresholds are, let us say, 50% higher. Equation (5) appfies to him with a factor l-5 in front. Time Et&
eo~~~~~ amifmziime
af&
~~e~~ion
From the thresh&! data for efosure, formafized eqn (5)?estimates may be obtaineii of fwo ~m~rtant temporal parameters in ear follo~ng~ viz. time untif collision (T, ) and free time after detention IT,). Time unti1 collision T, is de~n~d as the period of time between the instant the driver has detected that he is closing and the instant that a collision with the leading car will ensue-given that both cars drive on with the same speed. This parameter may be computed from: T _ distance after detection = D c-
%I
l]O, .
Qh
t
.
where o*&follows from (S), Lee 11972)has ~a~~u~at~T, under the assump~o~ of fixed angn~~ ~e~o~~t~ thresholds of S/see and f*lsee, whieh he felt would represent a fair estimate of the range that w&d be encountered in driving in all but dense fog. This is an approximating which is too crude, since angular thresholds are obvious& not fixed but are at least a function of the initial angle at and of t. Thus Lee’s graphs cannot provide very reliable estimates of T,, Figures 9 and 10 do the job somewhat better, since the basic eqn (5)from which they are derived incorporates both a Weber mechanism and a constant related to t. T, is shown both for the average observer (Fig. 9) and for the observer whose thresholds are 50% higher than average (Fig. 10).
WIELH.
zoo
JANSSEN
er al.
LOO
lnlt vww dlst
600 Dim)
Fig. IO. Time until collision after detection of closure (observer whose threshold is 50% higher than the average).
The remarkable feature appearing from these graphs is that T, grows with decreasing viewing distances and drops to rather low values at the larger viewing distances. Thus, owing to the nonlinearity of the relationship between v, and D it appears that following a lead car at a short distance by keeping relative movement at threshold is considerably safer than fo~iowing it so at a long distance. This conclusion stands up even if we recognize that the speed differences required to generate the right-hand parts of the curves in Figs. 10 and 11 are unrealistically high. In particular, of course, the conciusion is seen to bear on observers with low movement sensitivity. Not all of the interval T, can be spent by the driver in merely contemplating about what to do. If the driver is to avoid collision with the lead car there is an ultimate point in time within T, at which maximum braking force must be applied. Free time Tf is defined as the interval from the moment the driver has detected he is closing until the moment he should apply maximum braking force (which at its utmost may be 1.0 g) in order to avoid collision. Although the definition of T, in a strict sense only applies to the case in which none of the vehicles takes any action until the critical moment of full braking it is also interesting to see what becomes of Tf if the lead car changes its movements after the detection of closure has taken place. In particular the case of deceleration would have important consequences to 7” Consider, however, first the case in which both vehicles continue their journey with the speeds they had at the beginning of the observation interval t. In order to avoid collision it is necessary for the following car to (at least) reduce its speed to that of the lead car. Take a (
Fig. I t. Free time after detection of closure (average observer, deceleration -7 m/se?).
The perception of lead vehicle movement in darkness
161
This value must be subtracted from the value of the time until collision T, as given by (9). Moreover a certain interval should be subtracted from T, which it takes the driver of the following car to initiate his braking reaction. A reasonable estimate of this interval is of the order of 0.7 set [Lee, 19721.We find: T, = I; i:-O.7sec
(10)
(a -=z 0, o*)th> 0). Values of Tf computed from (10) are shown in Figs. 1l-14, both for average and underaverage individuals, and for two values of a (-4 and -7mlsec’). As with the graphs for T, the steep rising of the curves with small viewing distances and their gradual drop at the larger distances is clearly apparent. Now consider the case in which the lead vehicle starts decelerating at the very moment the driver of the following car has detected the existence of a speed difference. (There is nothing special about the deceleration supposed to take place at this moment, except that it makes computations slightly simpler.) Denote the magnitude of the lead car’s deceleration by b and suppose that it is maintained for a period t* (we require that t* is much smaller than the time until collision T, in order for the situation to make sense). During the period of deceleration the speed difference between the vehicles will change from aLhto v*=tl,-b.t*
average observer
200
LOO tn,t ww dist
-
(b < 0).
011
Lm/sec”
600
800
0 (ml
Fig. 12.AS Fig. 11,but with a deceleration of -4 m/set*.
Fig. 13. Free time after detection of closure (observer with thresholds 50% higher than average, deceleration -7 m/se?).
LOO bO0 800 #nit vv?wd!st D iml Fig. 14.As Fig. 13,but with a deceleration of - 4 m/se?. 200
J
162
WIEL H. JANSSENet al.
What about the distance D* between the vehicles after the interval t*? Obviously D* equals the distance at the moment of the detection of a speed difference minus the difference between the distances both vehicles have travelled during the deceleration interval. This difference is seen to equal v,,,. t*-;b.
t*=
(12)
so that the distance between the cars after the deceleration interval is
D*=D-vr”*f_v,h.t*+Ib2. t*=. uth
(13)
Time until collision is then seen to be equal to T,
=$+ t*.
(14)
(Observe that t* must be added because the observer in the following car has already survived this deceleration interval.) In order to compute T, we merely have to subtract from T, the time it takes to reduce the speed difference to 0 after the lead car’s deceleration, and also the time it takes to initiate the braking reaction. This yields: T, = T, - ( vrh-,” ’ t *) - 0.7 sec.
(13
From this expression one may get a feeling of how disastrous even a small deceleration of the lead car, applied for only a few seconds, may be on the available free time. Figure 15 shows, as an example, the values of T, resulting from a deceleration of - 2 m/sec2 maintained during 2 set and compares these to the values obtained in the stationary situation without deceleration (Fig. 11). The effect is particularly impressive at the smaller distances, since here the change in relative speed caused by the deceleration is large compared to v,,,. For an observation interval of over O-5set T, is seen to have a maximum at a headway of about 200 m. Size of the natural sampling interval The functions for T, and T, show that the largest increase in these temporal parameters takes
place when exposure duration goes up from 0.5 to 1.0 sec. Relatively little improvement is found if t takes values of over 1.0 sec.
InIt
VIEW
dtst
D lml
Fig. 15. A comparison between free times w’ith and without deceleration of the leading car. Dotted lines: with deceleration of -2 m/se? maintained during 2 sec. The picture represents observers of average sensitivity.
The perception
of lead vehicle movement
163
in darkness
This brings us to the question of what the sampling rate of visual information during driving actually is. Since drivers surely do not continuously pay attention to the road in front of them one would like to have information on how often they do pay attention to environmental features and, still more important for present purposes, what the size of the sampling interval is. The literature, unfortunately, shows a lack on this point. Although a promising approach to visual sampling during driving has been developed by Senders et al. [1%7] it has not yet been used so as to yield results that are appropriate to the present issue. What Senders et al. did was to study sampling rates for given vehicle speeds by periodically raising (at the subject’s desire) and lowering a visor attached to a helmet that subjects wore during driving. They used fixed viewing durations ((of 0.25,0.50 and 1.00 set) and measured the duration of periods of occluded vision. This is a procedure which does not yield an estimate of the natural sampling duration. The reverse procedure, i.e. having a subject drive with unobstructed vision until he indicates that he can do without vision for a while could yield an estimate of sampling durations (although this would be a somewhat artificial thing to do for the subject). For the time being we have only some pilot studies by Senders et al. to rely on. From these studies it appears that a “sampling episode”, consisting of a 0.5set sampling interval every 3 set, can be identified. This means that, of the functions obtained in the present experiments, those generated under the shorter exposure durations should be considered to be the most relevant.
The effect of taillight separation
on speed thresholds
The values of collision and free intervals computed thus far assume that d, the metric distance between taillights, is l-40 m. Since the detectability of relative moment is, however, based on proximal cues we may ask what the effect of variation in d is on the speed thresholds and, consequently, on the temporal parameters of relevance in car-following. What is the effect on &h if we change d into k. d, all other things remaining equal? In order to assess this effect the requirement to be kept in mind is that the movement in depth of the lights (now separated by a distance k . d) must possess a speed which is sufficient to bring angular velocity at the threshold level associated, through the Weber mechanism, with the initial angular separation between the lights. The relationship between angular velocity and initial angular separation we already know from the experiments in which d was, for convenience, chosen to be 1.40m. Hence, we may derive an expression for the size of the ratio of the threshold speeds for any two values of the taillight distance which differ by some factor k. To this purpose compare three situations (see Fig. 16). First, there is the situation with the “old” taillight separation d, observed from a distance D and resulting in a speed threshold L)lh (old). Second, there is the situation with the “new” taillight separation k . d, again observed from a distance D, and resulting in a speed threshold VI,,(new). These are the two situations we wish to compare, i.e. we want to know the ratio u,,,(new)/u,,,(old). To this means we need a third situation
d/20 rod
V
OLD
Fig. 16. Computation
V
STATE
DUMMY
STATE
of the effect on the threshold
NEW
STATE
for closure of a change in taillight
separation
by a factor k.
164
WIEL H. JANSSENet al.
in which the taillight separation is the old d, but in which the initial angle between the taillights is equal to that in the “new” situation. This “dummy” situation we need in order to know the required angular threshold going with a particular initial angle, which we can then translate back to the “new” situation. This means that taillights in this third situation must be at an observation distance D/k; there is a speed threshold uth (dummy). Now we are ready to write expressions for the speed thresholds in each of these three situations by making use of the basic eqn (5) and also of the expression relating &, to distal variables (2). In the “old” situation we have ut,,(old) = f(t) . P
(16)
From the proximal identity of the “new” and the “dummy” states follows the requirement that &h =
d. Vlh(dummy) = k . d. ulh (new) D2 D2 k 0
(17)
Us,,(new) = k . t&h(dummy).
(18)
from which we find that
This says simply that if we double both the distance between lights and the observation distance at the same time, for example, we will need twice the original velocity in depth to maintain the same angular velocity. Since we have ti,,,(dummy) = f(t) . (f)“’
(19)
u,,,(new) = k. f(t).
(20)
and, consequently, (f)5’4
it follows by combining (16) and (20) that
u,,o =
k-l,4
uth(old)
*
(21)
This equation gives the desired ratio of the sizes of the threshold speeds after a certain change in d. We may calculate, for example, that reducing d by 50% increases threshold speed by 19%, or that doubling it decreases threshold speed by 16%. Also observe that the factor 3 by which automobile taillights distances may differ (from appr. 0.75 to 2.25 m) will cause the smaller cars to have a threshold speed for detection of their relative movement in the dark which is +30% higher than that of their big brothers. Obviously this implies a severe reduction in the temporal parameters T, and T,. One might conclude at once that making intertaillight separation as large as possible would be recommended. Conclusions
from the calculation
of temporal parameters
The following may be concluded from the calculations on temporal parameters in car-following which have been presented: (i) Both for individuals of average and underaverage sensitivity to relative motion there are likely to occur situations in night driving in which collision with a lead vehicle is area1 threat. (ii) Factors that in particular will increase the risk of a collision are: (1) decreased braking power of the following car, such as occurs when roads are wet; (2) manoeuvres of the lead car which involve a deceleration, even if it is small and lasts only for a brief period; (3) a small intertaillight separation of the lead car.
The perception of lead vehicle movement in darkness
165
(iii) It is therefore required that measures are taken which have the net effect of improving a driver’s ability to detect a lead car’s relative motion. In other words, we must believe there is a real problem to the driver in the situation, and in order for him to survive it should be solved. A few suggestions to improve the existing situation are listed in the final section of this paper. It is realised that requirements from other problem areas will and must interfere and interact with these suggestions. More comprehensive treatments of the problem of vehicle lighting and signaiing systems are given by Mortimer [1970]. IMPROVING
THE CAPACITY
TO DETECT LEAD CAR MANOEUVRES
Three ways can be distinguished in which the problem of raising detec~biIity capacity could be approached. First, the possibility of training drivers so as to increase their sensitivity could be explored. Second, there is the possibility of developing new systems, demanding major modifications of current vehicle design, which inform surrounding traffic of a vehicle’s ongoing or planned manoeuvres. Third, one might try to modify existing vehicle lighting systems in a relatively minor way so as to be better adapted to the needs of drivers of other vehicles. Between the second and the third alternative there is, of course, only a gradual difference. Improving sensitivity by systematic training is a subject which has not attracted much attention in the literature. This apparently is because the detection of relatively simple stimuli is not considered to be a skill which can be learned and developed. Another reason why the literature is scarce is that researchers working in the field of detection are usually interested only in stable asymptotic performance and have developed a habit of throwing the learning portion of their data away. Blackwell 119531is an exception to the rule. In a large-scale study of visual detection he included an investigation in which he found that subjects displayed training effects in the detection of a spot of light which extended to 6 or 7 sessions of 2 hr each. The final effect was a decrease in threshold luminance of the order of 25-30%. Despite the fact that Blackwell’s experimental set-up differed a great deal from ours there is reason to hope that training might improve driver’s sensitivity to motion, the more so since Blackwell’s subjects did not receive any systematic training but were left at themselves. However, since basic data are still essentially lacking it is difficult to see what form such a training for drivers could possibly take and how it should be inco~orated into driver education as a whole. The second alternative, the development of radical new systems aimed at improving the perceptibility of vehicle manoeuvres, has already been under exploration for several years now. Although it is probably still too early to reach a definitive conclusion the evidence as yet is that this approach has appeared a rather fruitless one in terms of the probability of one of the constructions developed to be ever implemented. Contributing to this impression are the failures to be considered realistic solutions of such reasonable proposals as the application of Doppler radar in order to force the driver into maintaining a fixed headway distance, the application of a signal system which warns for ongoing decelerations and accelerations [Michaels and Solomon, 19621,and the application of signal systems which indicate the severity of braking [e.g. Rutley and Mace, 19701. To the present writers it appears that the direction a solution should take is to improve upon the vehicle-lighting system as it exists today. The following, admittedly rather elementary, suggestions seem worth considering First, taillight separation should be standardized. This is not advice based so much on our own findings as it is on the general consideration that a standard separation would help drivers in judging vehicle manoeuvres. In cars as they are found today distance between taillights may vary by no less than a factor 3 (from 0.75 to 2.25 m). From the point of view of human engineering this is a regrettable state of affairs. Second, taillight separation should be as large as possible. The reason is, as indicated in this paper, that speed thresholds decrease considerably with increasing d. Third, vehicles which presently have only one taillight (motorcycles) should have two, The reason is that the detection of relative speed is easier from angular than from size-brightness cues. Awaiting the implementation of this recommendation one should concentrate on increasing the size of the taillight rather than its brightness. This is because it appeared from the experiment on the efficiency of the size-brightness cue that size discrimination for a moving source is
166
Wax H. JANSSEN er al.
superior to brightness discrimination. This implies that it is valuable to make a tight retain its identity as an area source as long as possible. REFERENCES Blackwell H. R., Psychophysical thresholds: experimental studies of methods of measurement. Bull. Eng. Res. Inst. Michigan
No. 36, 1953.
Green D. M. and Swets J. A., Signal Detection Theory and Psychophysics. New York, Wiley, 1966. Harvey L. 0. Jr. and Michon J. A., Progress Report 1. Effects of viewing distance and angular separation. Institute for Perception TNO. Report Nr. JZF JP7J-C6, 1971. Harvey L. 0. Jr. and Michon J, A., Detectability of relative motion as a function of exposure duration, angular separation, and background. J. Exp. Psycho1 103, 317-325, 1974. Janssen W. H., Progress Report II. Effect of IateraI motion on thresholds for relative sagittal motion. Institute for Perception TNO. Report Nr. IZP J97J-C2t?, 1971. Janssen W. H., Progress Report IV. Perceptib~ty of relative sagittal motion on the basis of changes in apparent size or intensity of taillights. Institute for Perception TNO. Report Nr. JZF J972-C6, 1972. Janssen W. H., Progress Report V. Thresholds for relative vehicle motion in depth: A check in the field. Institute for Perception TNO.~Report fir. IZF 197~CJ2, 1973. Janssen W. H.. Proaress Renort VI (Final reoort). Imnlication of nsvchophvsical threshold measurements for the night-driving situation. Institute for Perception TNO. Report Nr. fZk j974ki2, 1974. Lee D. N., Theory of visual information available for vehicle control. Paper presented at an OECDSymposium,Rome, 1972. Leibowitz H. W., The relation between the rate threshold for the perception of movement and luminance for various durations of exposure. 1. Exp. Psycho/. 49, 209-214, 1955a. Leibowitz H. W., Effect of reference lines on the discrimination of movement. J. Opf. Sot. Am. 4% 829-830.195% Michaels R. M. and Solomon D. M., The effect of speed change information on spacing between vehicles. Public Roads 31, 229-235, 1%2. Mortimer R. G., Automotive rear lightingand signalingresearch. &SRI-report No. Hz&f. University of Michigan, 1970. Rutley K. S. and Mace D. G. W., An evaluation of brakelight display which indicates the severity of braking. Road Research ~aborato~es Report LR .S?, 1969. Senders J. W., K~stofferson A. B., Levison W. H., Dietrich C. W. and Ward J. L., Attentions demand of automob~e driving. Boft, J&ran& and Newman, inc. Report Nr. 1482, 1967.