Brief Communication 587

Simulated self-motion alters perceived time to collisionR. Gray* and D. Regan†

Many authors have assumed that motor actionsrequired for collision avoidance and for collisionachievement (for example, in driving a car or hitting aball) are guided by monitoring the time to collision(TTC), and that this is done on the basis of moment-to-moment values of the optical variable τ [1–3]. Thisassumption has also motivated the search for singleneurons that fire when τ is a certain value [4–8]. Almostall of the laboratory studies and all the animalexperiments were restricted to the case of stationaryobserver and moving object. On the face of it, thiswould seem reasonable. Even though humans andother animals routinely perform visually guided actionsthat require the TTC of an approaching object to beestimated while the observer is moving, τ provides anaccurate estimate of TTC regardless of whether theapproach is produced by self-motion, object-motion ora combination of both. One might therefore expect thatjudgements of TTC would be independent of self-motion. We report here, however, that simulated self-motion using a peripheral flow field substantiallyaltered estimates of TTC for an approaching object,even though the peripheral flow field did not affect thevalue of τ for the approaching object. This findingpoints to long range interactions between collision-sensitive visual neurons and neural mechanisms forprocessing self-motion.

Addresses: *Nissan Cambridge Basic Research, Four CambridgeCenter, Cambridge, Massachusetts 02142, USA. †Departmentsof Psychology and Biology, York University, Toronto, OntarioM3J 1P3, Canada.

Correspondence: R. GrayE-mail: rgray@cbr.com

Received: 11 February 2000Revised: 23 March 2000Accepted: 23 March 2000

Published: 5 May 2000

Current Biology 2000, 10:587–590

0960-9822/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved.

Results and discussionFigure 1 shows the experimental set-up used. The observersaw a sphere that appeared to be moving towards them.Forward self-motion was simulated by squares movingaway from the centre of the visual display and increasing insize and backward self-motion by squares moving towardsthe centre and contracting. Figure 2a–c shows the meanpercentage error in estimating TTC (that is the percentagedifference between the estimated and calculated TTC) for

three observers. It is clear from Figure 2 that the pattern ofsimulated self-motion had a large effect on estimates ofTTC. Consistent with previous findings with a backgroundof static texture elements, all three observers made small(3–14%) underestimates of TTC in simulated static condi-tions. When forward self-motion was simulated, all threeobservers made larger (by 11%, 13% and 9%) underesti-mates of TTC than in the static condition. Conversely,when backward self-motion was simulated, all threeobservers overestimated TTC. The differences in TTCestimates between backward and static flow were 17%, 23%and 19% for the three observers. Table 1 shows the meanabsolute estimation errors for the three conditions. Arepeated measures analysis of variance (ANOVA) revealed asignificant main effect of flow type (F(2,4) = 149, p < 0.001).

When the size of the moving squares in the flow patternwas held constant, the effect of the flow pattern on TTCestimates was dramatically reduced. Estimation errors forthis condition are shown in Figure 2d–f. In this condition,the forward–static difference was only 3%, 6% and 5% forthe three observers and the backward–static differencewas only 7%, 9% and 2% for observers 1–3, respectively.

In Figure 2a–c, the flow pattern was visible only during apresentation. But TTC judgements were not significantlydifferent when the observer adapted to the flow patternfor 10 minutes prior to beginning the run and the patternremained on throughout the run. For observer 1, % errorsin this condition were –16%, –6% and 12% for the forward,static and backward flow conditions, respectively. Thisfinding suggests that the effect was not chiefly caused byadaptation to the flow pattern.

To examine the lateral spread of the flow effect, we nextvaried the size of the square hole at the focus of the flowpattern (see Figure 1c). We used four hole sizes (9.7°,13.6°, 18.5° and 21.4°). Figure 3 shows TTC estimationerrors for these four hole sizes expressed as the gapbetween the outer edge of the object and the inner edgeof the flow pattern (3.2°, 5.1°, 7.5° and 9°, respectively). Itis clear that the effect of simulated self-motion on per-ceived TTC decreased at an accelerating rate as the sepa-ration between the flow pattern and the simulatedapproaching sphere was increased. A two-factor repeated-measures ANOVA revealed a significant effect of flowcondition (F(1,2) = 452.2, p < 0.01) and a significant inter-action between flow condition and gap size (F(3,6) = 25.2,p < 0.01). At a gap size of 9°, TTC estimates for theforward and backward flow conditions were not signifi-cantly different (observer 1: t(26) = 0.7, p > 0.5; observer 2:t(26) = 0.4, p > 0.5; observer 3: t(26) = 0.6, p > 0.5).

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Psychophysical evidence has been reported for the follow-ing model of visual sensitivity to changing size and TTC[3,9–12]. At the first stage of processing, the oppositeedges of an approaching object’s retinal image stimulate

detectors with small receptive fields that are sensitive tounidirectional motion (for example, elaborated Reichardtdetectors) [13]. At the second stage of processing, theoutputs of pairs of these local-motion detectors are sub-tracted to create a changing-size mechanism that is sensi-tive to expansion along one direction, and has a smallreceptive field (1.5°–2.0°). And at the third stage of pro-cessing, a motion-in-depth signal is generated whose mag-nitude is inversely proportional to TTC, provided that theretinal image expansion is isotropic (that is, withoutchange of shape). The local changing-size detector isexcited when its small receptive field is precisely at thecentre of radially expanding flow pattern, but is notexcited when the centre of the flow pattern is covered byan occluder that creates a 0.5° gap between the outer edgeof its receptive field and the inner edge of the flow pattern[14,15]. Thus, this local changing-size mechanism wouldnot have been directly stimulated when we introduced a5° gap between the outer edge of the simulated approach-ing object and the inner edge of the flow pattern. Yet, asreported above, the effect of the flow pattern on estimatesof TTC were unaffected by the 5° gap. We conclude thatthe effects reported here could not have been caused by adirect effect of the flow pattern upon the local second-stage changing-size mechanism. Rather, we propose thatthe long-range lateral interaction that produced the effectsreported here occurred at a processing stage subsequent tothe changing-size mechanism. In particular, the motion-in-depth signal that supported estimates of TTC was aweighted sum of the motion-in-depth signal generated bystimulating the local changing-size detector and themotion-in-depth signal generated by the flow pattern.

Our finding that the effect of the flow pattern was almostabolished when the size of texture elements was held con-stant brings into question the relevance to everyday life ofthe considerable literature on optic flow in which textureelement size was held constant.

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Figure 2

Mean percentage TTC estimation error for the different flow conditions.Black bars are for forward flow, gray bars are for backward flow andwhite bars are for the static condition. (a–c) Squares grew larger asthey moved radially outwards and vice versa. (d–f) Square size wasconstant. Error bars are standard errors. (a,d) Observer 1;(b,e) observer 2; (c,f) observer 3. Stepwise multiple regressionanalysis revealed that the task-relevant variable, θ/(dθ/dt), accountedfor a high proportion of total variance for all three flow conditions. Forthe three observers, the task-relevant variable accounted for 74–90%of the variance in the forward condition, 81–93% in the staticcondition and 79–86% in the backward condition. Task-irrelevantvariables (θ0, dθ/dt, and ∆θ) accounted for only a small amount ofadditional variance (ranging from 3% to 8%).

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The radially expanding or contracting flow fieldconsisted of a randomly scattered pattern ofsquares whose size and instantaneous speedincreased radially to simulate self-motion.(a) The squares were displayed on a large(80 cm horizontal × 56 cm) electrostaticallydriven display (monitor 1, Hewlett-Packardmodel 1321A) that was viewed through theoptics of an F-18 flight simulator. A large glasssheet (LG) reflected the display onto a large(75 cm horizontal × 90 cm) high-qualityparabolic mirror (PM) so that the displayseemed to be at a great distance, though itsubtended 39° horizontal × 27°. (b) Anapproaching spherical object of luminance16 cd/m2 was simulated on a second monitor(monitor 2, Tektronix model 608 with green

P31 phosphor) that ran at 50 frames/sec. Athin sheet of glass (SG) reflected this seconddisplay into the parabolic mirror so that it alsoseemed to be at a great distance. Note that, forclarity, the glass sheet LG is omitted from (b).

(c) The observer’s view of the approachingobject (gray circle) and flow field (blacksquares). The dashed square (not present inthe actual display) indicates the central area inwhich no flow elements were presented.

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There is a possible ecological role for the interactions wereport here. When a stationary observer attempts to catchan approaching object, there is a clear advantage that aτ-based estimate of TTC should be an underestimation:the unavoidable variability in the estimate will never createthe situation in which there is no time left to acquire thestereo information about TTC that is required to correctlytime the finger flexions that take place during the final tensof milliseconds of a successful catch. It has been shown thatthis stereo information is acquired only when the approach-ing object is within a few metres of the catcher [16]. Whenthe whole body is moving forward (for example, a monkeyswinging from branch to branch) the mass that must becontrolled when using close-range stereo information tomake fine corrective adjustments is very much greater thanwhen remaining stationary. A simple solution would be alateral neural interaction that allows the expanding flowfield produced by self-motion to increase the underestima-tion of TTC based on monocular information only (i.e. τ) tobe even greater than when stationary.

Some neurons in the pigeon’s brain are sensitive to theratio θ/(dθ/dt) (where θ is the angle subtended by theapproaching object and t is time), that is, τ, while others aresensitive to the rate of expansion dθ/dt [4]. By itself, thisfinding leaves the relation between the activities of suchτ-sensitive neurons and the animal’s behaviour a matter ofconjecture. However, if behavioral studies showed that thehuman findings reported here extrapolate to pigeons, astronger link between physiology and behaviour would beestablished if it were found that τ-sensitive neurons wereaffected by flow fields whereas neurons sensitive to rate ofexpansion were not. Electrophysiological studies suggestthat birds have separate mechanisms for processing objectmotion and self-motion (the tectofugal pathway and theaccessory optic system, respectively) [8]. Our findings raisethe possibility that there may be long-range connectionsbetween these ecologically distinct systems.

Materials and methodsBy using the optics of a flight simulator we were able to create a flowpattern that subtended 39° horizontally × 27° while appearing to belocated at a great distance (Figure 1a,b). For forward flow, texture ele-ments flowed radially outward from the focus, simulating forward self-motion; for backward flow, texture elements flowed radially inwardtoward the focus. For the expanding flow pattern, the texture elementsincreased speed and grew larger as they moved radially outwards. Thecontracting (backward) flow pattern was the reverse. Results obtainedwith these two flow patterns were compared with those obtained usinga static condition, in which the squares remained stationary.

We used the optical arrangement shown in Figure 1a,b to simulate asphere moving at a constant speed along a straight line towards apoint between the eyes. A sensation of approaching motion in depthwas created by changing the size of the simulated object appropriately[11]. The simulated approaching sphere was presented at the centre ofthe radial flow pattern. Figure 1c gives a rough impression of what theobserver saw. No texture elements were presented in a central squarearea with a side length of 9°.

ProcedureOur method has been described previously [17]. In brief, each trial con-sisted of one presentation of the simulated approaching sphere with amean duration of 700 msec. The flow pattern was only visible duringthis presentation interval. At the designated time of collision, some timeafter the sphere and flow pattern had been switched off, a brief audi-tory click was generated. The observer’s task was to indicate whetherthe auditory click occurred before or after the simulated approachingsphere would have arrived at their eyes [17]. The initial TTC of the sim-ulated approaching object (θ/(dθ/dt) was varied from trial to trialaccording to a transformed staircase method [18]. The staircase con-verged onto a TTC that gave a 50% probability that the observer wouldjudge that the simulated approaching object would arrive before theauditory click. Nine staircases corresponding to all possible combina-tions of three values of designated TTC (1.8 sec, 2.3 sec and 2.8 sec)and three values of initial angle that the sphere subtends (1.1°, 1.7°

Brief Communication 589

Table 1

Mean absolute errors in TTC estimation.

Observer Flow condition Mean absolute error (msec)

1 Forward –258.8

Static –57.7

Backward 386.0

2 Forward –641.1

Static –337.3

Backward 180.4

3 Forward –321.4

Static –69.2

Backward 316.3

Figure 3

TTC estimation error as a function of the gap between the outer edgeof the object and the inner edge of the flow pattern. Solid, dashed anddotted lines plot TTC estimation errors for observers (obs) 1, 2 and 3,respectively. Circles show TTC estimates for forward flow andtriangles show estimates for backward flow. Small arrows indicate themean estimation error in the static condition for each observer. Errorbars are standard errors.

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and 2.3°) were randomly interleaved. The use of multiple staircases hadthe following two consequences: it was not possible for observers toanticipate trial-to-trial variations in TTC, and after collecting theresponse data we could perform a stepwise regression analysis todetermine which optical variables were used in making estimates ofTTC. This method also has the advantages that it removes any effect ofmotor delay on the TTC estimate as well as any cognitive strategy forcontrolling collisions [19].

AcknowledgementsThe authors wish to thank Laurinda Kwan and Derek Harnanansingh for par-ticipating as observers. This research was supported by Nissan Researchand Development, Inc. and the Natural Science and Engineering ResearchCouncil of Canada (NSERC operating grant to D.R.). Effort sponsored bythe Air Force Office of Scientific Research, Air Force Material Command,USAF, under grant number F40620-97-1-0051. The US Government isauthorized to reproduce and distribute reprints for governmental purposesnotwithstanding any copyright violation thereon. The views and conclusionscontained herein are those of the authors and should not be interpreted asnecessarily representing the official policies or endorsements, eitherexpressed or implied, of the Air Force Office of Scientific Research of theUS Government. D.R. holds the NSERC/CAE Industrial Research Chair inVision and Aviation.

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