Pictorial and Motion-based Depth Information During Active Control of Self-motion- Size-Arrival...

8/19/2019 Pictorial and Motion-based Depth Information During Active Control of Self-motion- Size-Arrival Effects on Collision …

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Journal of Experimental Psychology:Hu man Perception and Performance1994, Vol. 20, No. 4, 783-798

Copyright 1994 by the American Psychological Association, Inc.F 0096-1523/94/$3.00

Pictorial and Motion-Based Depth Information During Active Control ofSelf-Motion: Size-Arrival Effects on Collision Avoidance

Patricia R. DeLucia and Rik Warren

With computer simulations of self-motion , Ss controlled their altitude as they approached a floatingobject and, after getting as close as possible to the object, tried to jump over it without collision.Ss jumped significantly later for small objects, compared with larger objects that were approachedfrom equal distances a t equal speeds and were positioned at equal clearance heights. This occurredeven when accretion-deletion information w as present an d when object width a nd length werevaried independently. Results were consistent with studies in which Ss judged a large farapproaching object to hit the viewpoint before a small near object that would have arrived sooner(P. R. DeLucia, 199la, 1991b). Results suggest that pictorial information such as relative sizecontributes to active collision-avoidance tasks an d must be considered in models of perceiveddistance and time-to-arrival.

DeLucia (1989, 199la, 1991b) reported that when com-puter-generated floating objects approached a viewpoint, alarge far object appeared to be closer than a small nearobject an d appeared to hit the viewpoint before th e smallobject, which was specified to arrive sooner by time-to-contact information (tau; e.g., Lee, 1980a; see also Tresil-ian, 1991). Judgments were consistent with pictorial depthinformation of relative size, rather than with time-to-contactinformation, an d occurred even when motion-based infor-mation was potentially above threshold. These findingswere referred to as the effects of relative size on judgmentsof relative depth (ERS depth ) and arrival time (ERS.,̂ .,,),respectively (DeLucia, 199la). Such effects were replicatedwith textured objects, relatively long display durations, an dhigh-resolution photographic animations of approaching ob -jects (DeLucia, 1991a, 1991b), suggesting that the effectsare not merely a result of using impoverished displays.Furthermore, ERS depth and ERŜ^ occurred but werereduced with simulations of self-motion as well as objectmotion during self-motion (DeLucia, 199 Ib). Finally,

^ occurred when observers made judgments about

Patricia R. DeLucia, Armstrong Laboratory, Wright-PattersonAir Force Base, Dayton, Ohio, and Department of Psychology,Texas Tech University; Rik Warren, Armstrong Laboratory,Wright-Patterson Air Force Base, Dayton, Ohio.

Portions of this research were completed while Patricia R.DeLucia held a National Research Council-U.S. Air Force Arm-strong Laboratory Research Associateship and were presented byhe r at the 1992 Annual Meeting of the Association for Research inVision and Ophthalmology in Sarasota, Florida. We are grateful toDavid N. Lee for generous discussions of his theory. We alsothank Jeff Maresh and Robert Todd of Engineering Solutions, Inc.,for technical assistance and James R. Tresilian and three anony-mous reviewers for comments on an earlier version of this article.

Correspondence concerning this article should be addressed toPatricia R. DeLucia, Department of Psychology, Texas Tech Uni-versity, Lubbock, Texas 79409-2051. Electronic mail may be sentto [email protected].

whether two computer-generated cubes would collide witheach other: Compared to two same-sized cubes, different-sized cubes were predicted more often not to collide, evenwhen collision was imminent (DeLucia, 1991b).

Thus, ERS depth and ERS arrjva , can occur under a variety ofdisplay an d judgment conditions. These effects, particularlyERS depth , can be considered related to size-distance rela-tionships reported earlier (e.g., Epstein, Park, & Casey,1961; Ittelson, 1951a, 1951b; Kilpatrick & Ittelson, 1951).For ease of discourse we refer to ERŜ^ as the size-arrival effect.

The size-arrival effect seems contrary to predictions thatare based on the general assertion that, in ordinary veridicalperception, motion-based depth information supersedes thetraditional static pictorial depth cues (e.g., Gibson, 1979).That pictorial information may not always be superseded bymotion-based information has previously been demon-strated in the area of form perception (Dosher, Sperling, &Wurst, 1986).

In the above studies, however, observers did not controlany aspects of the displays; in other words, the observerswere passive rather than active (Flach, 1990; Gibson, 1979;Warren, 1990; Warren & McMillan, 1984; see also com-ments by Hochberg, 1982, p. 203). Some studies suggestthat active perceptual judgments are better than their anal-ogous passive judgments (e.g., Gibson, 1962), but equivocalevidence has been reported (Flach, Allen, Brickman, &

Hutton, 1992). In this article we demonstrate that the size-arrival effect that w as reported with passive judgments(DeLucia, 199la, 1991b) can occur when observers tryactively to avoid collisions with objects during simulationsof self-motion.

Experiment 1The purpose of Experiment 1 was to determine whether

an observer moving at a constant speed toward an objectwould jump sooner to avoid collision with a large sta-tionary object, compared with smaller objects at the same

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784 PATRICIA R. DELU CIA AND RIK WARREN

distance and clearance height. An analysis of visual infor-mation that is available to guide the act of jumping wasprovided by Lee (1974, 1980b; see also Laurent, Dinh-Phung, & Ripoll, 1989; Lee, Lishman, & Thom son, 1982;Warren, Young, & Lee, 1986).

For example, Lee (1974, 1980b) defined a maximallyefficient jump as one in which the zenith of the jump isdirectly above the top of the obstacle. Such a jum p requiresthat a minimum energy, E min , be expended at takeoff toraise the center of gravity a height h) just enough to clearthe wall. E m in is essentially proportional to h. The positioncoordinates of any visible texture element are specified inunits of the observer's height above the ground; thus , body-scaled spatial information about the size of the obstacle isavailable in the optic flow field. It is assumed that suchbody-scaled information could be used to judge E m in (1974,p. 263).

The jump also must be initiated at the right time so thatthe observer reaches the obstacle as the peak of the jump is

reached. In other words, the time to reach the obstacle(measured from takeoff) must equal the time to reach thezenith (D. N. Lee, personal com mu nication, October 14,1993). The time between takeoff and zenith is essentiallyproportional to the square root of h and could be judgedusing body-scaled information (Lee, 1974, p. 263). For anygiven takeoff point, the time it would take to reach theobstacle is the current time-to-contact with the obstacle,which is specified optically by tau. To initiate the jump atthe right time, therefore, the jump er m ust mon itor the time-to-contact with the obstacle (possibly via tau) and initiatethe jump just as the time-to-contact reaches the time fromtakeoff to zenith (D. N. Lee, personal communication, Oc-

tober 14, 1993). Thus, Lee's analysis indicates that tauprovides potentially useful information to guide the timingof a jump.

Lee's (1974) model does not predict that a jum p wou ld beaffected by the width (i.e., horizontal extent) or length (i.e.,vertical extent) of the obstacle if the altitude of the top o f theobstacle is constant; perceived time-to-contact with the ob-stacle should be the same regardless of length, assumingthat the observer m oves forward on a level path at a con stanthorizontal velocity (D. N. L ee, personal com mun ication,October 14, 1993). In the displays used in our s tudy, objectsof different sizes had the same time-to-contact and height.One could argue that, if our observers timed their jum ps onthe basis of optical information about time-to-contact asdescribed in Lee's analysis of jumping, they should starttheir jum p at the same time for objects of different sizes.Our observers were not instructed explicitly to complete themaximally efficient ju m p defined by Lee; rather, they wereinstructed to get as close as possible to the object beforejumping in order to avoid collision (see Procedure anddesign in the Method section). Nevertheless, such a jum pmust be initiated at the right time to avoid collision, and thistime should not vary with object size when clearance heightand time-to-contact remain constant; optical time-to-contactinformation (possibly tau) is a viable source of informationfor such a task.

We gave observers practice with jumpin g in an attempt toprovide body-scaled information about height, that is, in-formation about the relationship between co ntrol-stick inputand displayed output. We acknowledge that the observer's jump was merely a simulation. Thus, we can only assumethat adequate body-scaled information about height wasavailable. Moreover, we assessed the effect of obstacle sizeon jumping only when the altitude of the tops of the differ-ent-sized objects was the same.

Even though Lee's (1974) model does not predict aneffect of object size on jumping, it is possible that the sizeof the object will influence perceived distance through thesame mechanism that operates in pictorial size-distancerelationships (e.g., Epstein et al., 1961; Ittelson, 195la,1951b; Kilpatrick & Ittelson, 1951) and thus affect thetiming of the jump; that is, a size-arrival effect may occur.If so , results would be consistent with the previously de-scribed passive studies and may indicate that pictorial sizeca n affect perception-action even when veridical time-to-

contact information (tau) is available.

Method

Participants. Ten paid observers had normal or corrected vi-sual acuity and were naive as to the experimental hypotheses.

Apparatus and displays. Com puter sim ulations were createdwith an MS-DOS 386/33MHz computer equipped with an XTARFalcon-4000 array processor and an XTAR PG-2000 displayboard. Displays had 1024 X 768 pixel resolution and were shownat a presentation speed of 30 frames/s on a 60 Hz, 48.26 cm(19-in.) monitor. Scenes were based on the slow-expansion scenedescribed by DeLucia (199la) and are represented in Figure 1.Simulations represented self-motion toward a black square thatwas suspended above an islandlike ground plane. For ease ofdescription, we give most lengths in feet (meters), but rescaling toother units is geometrically possible. T he virtual ground plane was10,000 ft wide X 20,000 ft long (i.e., about 3,030 m wide X 6,060m long); was covered w ith random ly patterned, solid-coloredsquares; and was located against a green background or sea.Above the sea was a blue sky; an explicit horizon line was present.The virtual square was either 16 ft, 72 ft, or 128 ft (4.85 m, 21.82m, or 38.78 m) in size, and was centered h orizontally and verticallyalong the principal line o f sight (the forward o r z axis). Th e virtualeye (self) always began 128 ft (38.78 m) above the ground plane

Figure I. Ex periment 1: Schematic representation of a self-motion scene. (The actual scenes were in color.)


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SIZE-ARRIVAL EFFECTS ON COLLISION AVOIDANCE 785

(one eyeheight). At the beginning of each trial a single square waslocated 1,280 ft (387.84 m ) from the viewpoint along the forwardor z axis, and self-motion was forward at a constant speed of 150ft/s (45.45 m/s). All squares were initially at the same distance, andself-motion was always at the same speed toward all squares.

Procedure and design. Using a chin rest, participants viewed

the displays binocularly from the projectively correct viewingposition (36-cm distance). If participants did nothing, they would fly straight and level and collide with a stationary square (exceptwhen the top of the smallest square was aligned with the tops ofthe medium-sized or largest square; see below). However, partic-ipants were instructed to fly over the square, first getting as closeas possible to the square before launching themselves to avoidcollision. Once past the square they were to lower their altitude. Ineffect, they were to follow the side profile of the square. Theseinstructions were used to discourage observers from initially flyinghigh enough to clear the square and then remaining at that altitudeto avoid collision.

Participants controlled their simulated altitude but not their pitchor forward speed: They pushed a control stick back in order toascend and forward in order to descend, as in an airplane, exceptthat the horizon always remained vertically centered on the screen;the maximum vertical velocity was 100 ft/s (30.3 m/s). Altitudecontrol was possible at the start of the trial and lasted for 9.87 s,during which altitude was sampled at 10 Hz. The time between thebeginning of the trial and potential contact with the square was8.53 s.

It w as expected that the height of the square would affect theparticipant's initiation of the jump. Therefore, it was important tocompare jumps for different-sized squares only when the tops ofthe squares were aligned (i.e., had the same height). Thus, addi-tional scenes were created: For each scene in which a square wascentered on the principal line o f sight, th e other squares' heightswere adjusted, in separate scenes, so that all tops were aligned.This is referred to as the square-top factor, which had three levels,one for each square size. There were nine unique scenes, and eachscene was replicated 10 times in a random order for a total of 90trials. Intertrial duration was self-paced, and feedback was notprovided. To familiarize the participants with the task and thedynamics of the control stick, we provided 6 practice trials (moreon request); these were no t included in the analyses.

The main objective of this study was to determine whetherparticipants would jump sooner to avoid collision with largersquares than they would with smaller squares, presumably becausethe larger squares appeared closer (DeLucia, 1989, 1991a, 1991b);this w as evaluated primarily with measures o f launch time, definedbelow. Other dependent variables were also obtained from thesampled altitude time history:

1. Peak altitude is the maximum altitude that occurred after 6 sfrom the start of the trial. This w as done to exclude early falsejumps.

2. Time at peak altitude is the time at which peak altitudeoccurred.

3. Launch time is the amount of time that elapsed after the startof th e trial when the jump w as initiated. Launch time also reflectsthe distance between the self and the square at the time of thejump. That is, greater or later launch times indicate smaller dis-tances between the self and square. To compute launch time, analgorithm looked backward in time from the occurrence of peakaltitude and computed the percentage change in altitude at eachsampled point in time (i.e., the slope of the altitude). Launch timewas defined as the time at which the slope exceeded 1%. Thismeasure corresponded to estimates of launch time on the basis ofvisual inspection of the mean time histories (e.g., Figure 2).

4. Altitude at launch is altitude at the time of launch.5. Clearance is the difference in altitude between the top of the

square and the self, when the self was directly over the square.Clearance indicates how far above the square the jump occurred.

6. Frequency of crashes is the number of trials in which the selfand square were ever at the same place at the same time; it was

measured as a percentage of the trials. This measure was notaffected significantly by any of the variables in Experiments 1-5.

Results

Figure 2 shows the mean time histories (the altitude as afunction of time) for each condition averaged across repli-cations and participants. Figure 3 show s the m eans of eachdependent measure for each square size and top condition,averaged across Experiments 1, 2, and 4; these experimentsshared the same pattern of results, as indicated by the resultsof an analysis of variance (ANOVA). Each dependent vari-able in Experiment 1 was analyzed with a 3 X 3 (Square

Size X Altitude of Square Top) completely repeated mea-sures ANOVA.1

Launch time. Only square size affected launch time,F(2, 18) = 62.14, p < .0001, w2 = 40.16%, which in-creased as size decreased. In other words, people ap-proached the smaller squares more closely before launch-ing themselves to avoid collision. Conversely, peoplelaunched themselves sooner when approaching largersquares. Means were 7.80 s, 7.39 s, and 6.89 s for 16-, 72-,and 128-ft (4.85-m, 21.82-m, and 38.78-m, respectively)squares, respectively, with all comparisons significant, p <.05. (Recall that collision with the square would occur 8.53s after the beginning of the trial.)

Altitude at launch. Analyses indicated a main effect ofsquare top, F(2, 18) = 16.67, p < .002, to

2 = 18.42%, and

square size, F(2, 18) = 13.32, p < .004, o >

= 23.68%.There was also a significant Square Top X Square Sizeinteraction, F(4,36) = 8.44, p < .001, « 2 = 1.94%. Launchaltitude increased as size decreased and as the altitude ofsquare top increased.

Time at peak altitude. There was an effect only ofsquare size, F(2, 18) = 20.10, p < .0001, o > = 21.36%.Time increased as square size decreased, with all pairwisecomparisons significant p < .05), except between 16-ft(4.85-m) and 72-ft (21.82-m) squares. Thus, participantsreached their peak altitude later for the smaller squares thanthey did for the larger squares, which is not surprisingbecause launch time was also later for smaller squares.

Peak altitude. Analyses indicated a main effect ofsquare top, F(2, 18) = 290.51, p < .0001, to2 = 52.62%,and square size, F(2, 18 ) = 16.36, p < .0002, < a = 4.40%,but no interaction. As would be expected, peak altitudeincreased as the altitude of square tops increased; Tukey'shonestly significant difference (HSD) tests indicated that allpairwise comparisons were significant p < .05). Peakaltitude increased as square size increased, with significant

1 Al l probability values from the results of the ANOVAs reflectGreenhouse-Geiser corrections.


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SIZE-ARRIVAL EFFECTS ON COLLISION AVOIDANCE 78 7

differences among all sizes, p < .05, except between 16-ft(4.85-m) and 72-ft (21.82-m) squares.

Clearance. Results indicated only a Square Top^ XSquare Size interaction,1.46%.

F(4, 36) = 3.32, p < .04, w2 =

Discussion

As shown by the means for launch time in the top leftpanel of Figure 3, participants jumped sooner for largersquares compared with smaller squares approached fromequal distances at equal speeds. Accordingly, the smallerthe square, the closer the approach before the launch w asinitiated. This could have occurred because the smallsquares appeared relatively farther away, as would be con-sistent with the previously described passive judgments(DeLucia, 1989, 1991a, 1991b).

In addition, participants began their jumps at lower alti-tudes for larger squares than they did for smaller squares(see the top middle panel of Figure 3 ), which could have ledto relatively earlier launch times and peak altitudes forlarger squares (but see Experiment 5). Lower launch alti-tudes for larger squares occurred even when altitudes of allsquare tops were aligned and thus m ay indicate a misper-ception of height due to square size; this is consistent withinformal observations made during the development of thedisplays that smaller squares appeared higher. Once partic-ipants began their ascent and attained more optical infor-mation, however, they may have realized that they hadoverestimated the small square's height and made an ad-justment; this would account for the lower peak altitudes for

smaller squares than for larger squares (see the bottom leftpanel of Figure 3).

Experiment 2

The earlier launch times for the large squares m ay haveoccurred because the larger squares occluded the groundplane at lower positions compared to the smaller squares,thus providing information that the large squares werenearer. In Experiment 2, the ground plane w as eliminated.

Method

Ten new participants having the same characteristics as theparticipants in Experiment 1 completed Experiments 2 and 3. Halfof the participants completed Experiment 2 first. Computer simu-lations were the same as in Experiment 1 except that the squareswere located against a solid blue background; neither a groundplane nor a horizon line was present. The participant's task wasidentical to that in Experiment 1.

Results and Discussion

The F, p, and o > values from the ANOVA are shown inTable 1. The pattern of results was the same as in Experi-ment 1, except for clearance: Only square size affectedclearance, which increased as size increased; the differencebetween 72-ft (21.82-m) and 128-ft (38.78-m) squares wasno t significant. Mean launch times were 7.94 s, 7.49 s, and7.15 s for the 16-ft (4.85-m), 72-ft (21.82-m), and 128-ft(38.78-m) squares, respectively, with all pairwise compari-sons significant p < .05). These results suggest that thedifferences among the positions of the squares' occlusionsof the ground texture do not account for the data fromExperiment 1. Th e effect of size on clearance in Experiment2 may indicate that the potential misperception of squareheight, discussed in Experiment 1, is exacerbated whenbackground texture is not present.

Experiment 3

In Experiments 1 and 2, the height of the bottoms of thesquares varied when square size and the altitude of squaretop varied. In Experiment 3 we determined whether effectsof size on collision avoidance would occur when the altitudeof either square top or square bottom remained constant.

Method

The 10 participants from Experiment 2 performed the same taskas in Experiment 1. The scenes were similar to Experiment 1 inthat a textured ground plane and horizon line were present. How-ever, the altitude or height of the top of the square, or of the bottomof the square, was systematically kept constant while the size ofthe square varied. In three separate scenes, the top of the squarewas always 148 ft (44.84 m) above the ground and the size of thesquare was either 36 ft (10.91 m), 90 ft (27.27 m), or 144 ft (43.63m); on such trials the altitude of the square's bottom also varied.In three additional scenes the bottom of the square was heldconstant at 100 ft (30.3 m) above the ground, and the size of thesquare was either 36 ft (10.91 m), 90 ft (27.27 m), or 144 ft (43.63m ); on such trials, the altitude of the square's top varied. Partici-pants completed a total of 6 unique scenes and 60 trials in arandom order.

Results

Mean time histories are shown in Figure 4. Data were

analyzed with a 2 X 3 completely repeated measuresANOVA. In this design there were three square sizes andtw o levels of a factor referred to as fixed. The two levelsof the fixed factor were altitudes of square top and squarebottom.

Launch time Only square size affected launch time,F(2, 18) = 56.34, p < .0001, < o

= 51.03%. As in Exper-

iments 1 and 2, launch time increased or occurred later as

Figure 2 opposite). Experiment 1: Altitude as a function of time, averaged over replications and participants, for each square size andsquare top condition. (Vertical lines represent a side view of the squares.)


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Table 1Results of Experiments 2 and 4

Independentvariables

Square sizeF(2, 18)

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F 2, 18)P<OT (%)

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Method

Ten new participants had the same characteristics and viewedthe same computer simulations as in Experiment 1. Participantscompleted the task described in Experiment 1, but they wereinstructed first to perform three additional maneuvers as rapidly as

possible: (a) bring the top of the square below the horizon, (b)bring the bottom of the square above the horizon, and (c) cen ter thesquare on the horizon. Participants were told that by completingthese m aneuvers, the square would cover and uncover the textureon the ground plane, which would provide information about thedistance of the square that could be used to complete the jump.After completing the three maneuvers, participants completed thecollision-avoidance task described in Experiment 1.


Mean time histories are shown in Figure 5, and results ofthe ANOVA are shown in Table 1. The same pattern of

results occurred as in Experiment 1, except that the SquareSize X Square Top interaction (on launch altitude) was notsignificant. Also, clearance measures indicated the samepatterns as in Experiment 2. Mean launch times were 8.22 s,7.71 s, and 7.27 s for 16-ft (4.85-m), 72-ft (21.82-m), and128-ft (38.78-m) squares, respectively, with all comparisonssignificant p < .05). Even when participants were informedthat, by varying their altitude, accretion-deletion informa-tion would become available and provide information aboutthe distance of the square, they still jumped later for thesmaller squares than they did for the larger squares. Suchresults suggest that accretion-deletion information was notas effective as pictorial size in this task.

Optical Analyses: Experiments 1-3

Even though tau and its first derivative were the same fordifferent-sized squares, participants jumped significantlysooner for large squares than for smaller squares, suggestingthat such optical information was not the dominant opticalbasis for the timing of the jump. Additional optical variablesof magnitude of visual angle, absolute change in visualangle, rate of change in visual angle (i.e., rate of expansion),and elevation angle were estimated from mean launch timesand launch altitudes for the smallest and largest squares ineach square top condition of Experiments 1-3. 2 Elevationangle refers to the angle between the horizon line and top ofthe square, and it seemed to be a viable source of informa-tion about square height. For each of these variables wecomputed the ratio of large-to-small squares at the begin-ning of the trial and again at launch time. 3

If participants waited for a particular optical variable toreach the same value for the small and large squares beforejumping, then the ratio of the value for small to largesquares would approach 1 at launch time. As represented inFigure 6 (left panel), the ratios for visual angle, change inangle, and rate of expansion were relatively closer to unityat launch time compared to the start of the trial, whereas

the ratio for time-to-contact information began at, andthen diverged from, unity. This m ay suggest that visualangle of the square, change in visual angle, and/or rate ofexpansion affected the timing of the jump more than didtime-to-contact information (but see the General Discus-sion section).

Furthermore, the mean ratio for elevation angle remainedmos t stable across time, possibly because the squares' topsbegan at the same altitudes. We note that launch altitudeswere higher and launch times were later for the smallersquares than for the larger squares, possibly indicating amisperception of height and distance, respectively. Moreimportant, higher launch altitudes coupled with later launchtimes would correspond to a decrease and an increase,respectively, in elevation angle, thereby potentially account-ing for a stable elevation angle. Thus, participants may haveadjusted their altitude to a perceived optimal value prior tothe jump, possibly based on elevation angle and the square'sapparent height. We hypothesize further that once partici-

pants began their jump, they realized that the small objectw as lower than they initially perceived and then compen-sated, thereby accounting for the lower peak altitudes ob-tained with smaller objects.

The same pattern of results occurred for all experimentsexcept in Experiment 3, when square bottoms began at thesame altitude (refer to Figure 6, right panel): the ratio forelevation angle showed a decrease at launch time. In otherwords, participants increased their altitude more beforejumping over the larger squares, which is not surprisingbecause the tops of the larger squares started higher thanthose for the smaller squares.

Experiment 5

In Experiments 1-4, square size was varied by increasingthe width and length of the square by the same magnitude.In Experiment 5 we tested whether size-arrival effectswould occur when either object width or object length alonewas varied. The results of the experiment demonstrated thatsuch parameters do not both have to change for size-arrivaleffects to occur.

Method

Ten new participants viewed the same displays as in Experiment1, except that the object's width and length were varied indepen-

dently while the altitude of the object's top remained fixed at 164ft (49.69 m). The virtual object was either 16 ft (4.85 m), 72 ft(21.82 m), or 128 ft (38.78 m) w ide and fixed in length, or was 16ft (4.85 m), 72 ft (21.82 m), or 128 ft (38.78 m) long and fixed inwidth; width and length factors were completely crossed. Details

2 Visual angles were estimated from the full size of the virtualobject even though, at launch time, the bottom of the medium-sized and largest squares were typically beyond the bottom of thecomputer screen.

3 The start of the trial is defined here as 1 s after the trial beganhad there been no change in altitude; time-history plots indicatedminimal change.


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Figure 6. Magnitude of several optical variables at 1 s after the beginning of the trial and at meanlaunch time, expressed as the ratio of the largest and smallest squares. Left: Representative examplefor Experiment 1 (square top = 164); right: Experiment 3 (fixed square bottoms).

of the displays, procedure, and data analyses were the same asthose described in Experiment 1.


Figure 7 shows the means of launch time, time at peakaltitude, and peak altitude for each width and length condi-tion. Dependent measures were analyzed with a 3 X 3(Object Width X Object Length) completely repeated mea-

sures ANOVA.Launch time. Analyses indicated effects of object width,

F 2, 18) = 27.55, p < .0001, w2 = 3.4%, and object length,F(2, 18) = 9.9l,p < .0049, w 2 = 7.80%, but no interaction.Launch time increased as object width decreased, with allpairwise comparisons significant p < .05). Launch timeincreased as object length decreased from 128 ft (38.78 m)to either 16 ft (4.85 m) or 72 ft (21.82 m; p < .05); othercomparisons were not significant. Mean launch times were7.14 s, 7.01 s, and 6.87 s for the 16-ft (4.85-m), 72-ft(21.82-m), and 128-ft (38.78-m) widths, respectively.Means were 7.06 s, 7.19 s, and 6.77 s for correspondingobject lengths.

Altitude at launch. No significant effects occurred.Time at peak altitude. There were significant effects of

object width, F 2, 18) = 10.84, p < .0029, w2 = 4.20%, andobject length, F(2, 18) = 7.25, p < .0082, co2 = 11.29%.Time at peak altitude increased as object width decreasedfrom 128 ft (38.78 m) to 16 ft (4.85 m), p < .05, and asobject length decreased from 128 ft (38.78 m) to 72 ft(21.82 m; /7 < .05); other comparisons were not significant.

Peak altitude. Results indicated effects of object width,F(2, 18) = 16.70, p < .0002, w 2 = 1.24%, and objectlength, F 2, 18) = 11.51, p < .0045, w2 = 3.25%. Peakaltitude increased as object width increased from 16 ft (4.85m) to 72 ft (21.82 m) or 128 ft (38.78 m; p < .05). Peak

altitude increased as object length increased from 16 ft (4.85m) or 72 ft (21.82 m) to 128 ft (38.78 m) p < .05); othercomparisons were not significant.

Clearance. Results indicated a significant effect of ob-ject width only, F(2, 18) = 5.44, p < .0246, w2 = .57%;clearance increased as object width increased, with signifi-cant differences between 16-ft (4.85-m) and 128-ft(38.78-m) widths only.

The results of Experiment 5 are consistent with those ofExperiments 1-4; size-arrival effects can occur when eitheran object's width or length varies. Furthermore, the lack ofinteractive effects of width and length on performance sug-gests that such effects combine additively in our collision-avoidance task. Indeed, the amount of variance in meanlaunch time attributed to object size in Experiments 1-4was much greater than that attributed to either length orwidth in Experiment 5. The relatively smaller effects inExperiment 5 can be observed by comparing the top leftpanels of Figures 7 and 3. These results may reflect an effectof the object's area on launch time, but further study isneeded before such a conclusion can be drawn. Finally,object width or length did not affect launch altitude, as didsquare size in Experiments 1-4. Such results suggest thatthe lower launch altitudes for larger squares that occurred inthe previous experiments do not account for the correspond-ing earlier launch times and peak altitudes, which alsooccurred in Experiment 5.

General Discussion

The present results demonstrate robust size-arrival effectson active collision-avoidance tasks. Participants jumpedearlier and higher to avoid collision with large objects,compared with smaller objects. Such results occurred when


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794 PATRICIA R. DfiLUCIA AND RIK WARREN

10Object Width

—D— Sma—A— fcbcim—•— Lage Time of Contact

0S3

1S3

2S3

16 72 128

CbpctLengfri®

260

160

Object Width

— O— Srel— Aim—•- Lap

16 72 138

Object Length (ft)

Figure 7. Experiment 5: Results for each object length and object width condition. Error barsindicate ± 1 standard error of the mean. Top, left: Launch time; top, right: Time at peak altitude;bottom: Peak altitude.

time-to-contact and the clearance heights of the objectsremained constant as object size varied. Th e same resultswere obtained when objects varied in length or width, orboth, and occurred even when accretion-deletion informa-tion was available and noted to participants. The presentfindings are consistent with previous studies in which ob-servers made passive judgments about the relative arrivaltime of two computer-generated approaching objects (De-Lucia, 1991a, 1991b, 1992). We consider several potentialexplanations of such effects.

Motion-Based Information Is Below Threshold

It could be argued that motion-based information such asoptical expansion or tau was below threshold for smallerobjects compared with larger objects, perhaps due to com-puter aliasing or because of smaller optical sizes. 4 Such anexplanation does no t seem tenable for several reasons. First,

as early as 1 s after a trial began, the change in the visualangle that the objects projected to the eye was above tradi-tional thresholds for displacement of a target (20 s arc;Easier, 1906; cf. Graham, 1965) and for detection of sizechange of a simulated object moving in depth (1 min arc;Hills, 1975). DeLucia (1991a) also reported that size-arrival

effects occurred w hen such thresholds were exceeded. Sec-ond, in Experiments 1-4 mean launch times increased asobject size decreased, and all pairwise comparisons of sizewere s ignificant. Thus, a threshold-based explanation w ouldimply that time-to-contact information for the medium-sized object was above threshold when it resulted in a lower

4 DeLucia (199la) concluded from empirical data that potentialeffects of computer aliasing on tau and motion thresholds do notaccount for size-arrival effects in passive tasks. (Here, aliasingrefers to effects of the computer's digitization process rather thanto technical meanings assigned by signal-analysis theory.)


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mean launch time than the smallest object, but that the sametime-to-contact information was below threshold when themedium-size object resulted in a greater mean launch timethan the largest object. Such an argument is not internallyconsistent. Finally, results of previous studies suggest theimportance of critical perceptual-motor adjustments in thelast 4 s prior to contact, and die nonuse of tau when the latteris beyond 10 s (Schiff & Detwiler, 1979). In Experiments1-4, mean launch times occurred when time-to-contact wasbetween .32 s and .85 s for the smallest object and between1.21 s and 1.82 s for the largest object, when tau was wellwithin its usable range. It would seem, therefore, thatsize-arrival effects occurred when motion-based informa-tion was above threshold.

Tau Is Less Detectable for Smaller Objects

The following explanation of size-arrival effects was

suggested by an anonymous reviewer5

: Time-to-contact isgiven optically as the ratio of image size to the temporalderivative of image size. For two different-sized objectswith the same time-to-contact, the image size and temporalderivative of image size is smaller and therefore necessarilyless detectable for a smaller object. Therefore, tau is rela-tively less detectable for a small object that has the sameobjective time-to-contact as a larger object. According tothis argument, detectability is considered a continuous func-tion, that is, optical size and rate of expansion are abovethreshold but are relatively less detectable for smallerobjects.

This explanation m ust be worked ou t further before it canbe evaluated completely; Lee's (1980a) model of time-to-contact does not address how time-to-contact informationmay be extracted or detected from the optic array (for arecent discussion of this issue, see Tresilian, 1993). Rather,the model shows that information about time-to-contact isavailable directly in the optic array and need not be com-puted from distance and velocity. As such, parsimony is aprimary strength of Lee's model. In contrast, a detectabilitymodel, as we understand it, suggests that apparent time-to-contact is based on two separate functions: detectability ofan object's optical size and detectability of an object's rateof optical expansion, both of which determine the detect-ability of tau. It is difficult to see how parsimony can bemaintained with such a hypothesis. Moreover, previousstudies suggest that observers are sensitive to tau indepen-dently of optical size or rate of expansion (e.g., Regan &Hamstra, 1991; Todd, 1981; see also Wang & Frost, 1992).Finally, we note that small fast-moving objects may haverelatively less detectable optical sizes but more detectablerates of expansion compared with large slow-moving ob-jects that have more detectable optical sizes but less detect-able rates of expansion, and w hich have the same time-to-contact. It is not clear what a detectability model wouldpredict in such cases. In conclusion, although we cannotrule out a detectability interpretation of our results, furtherspecification of such a model is needed before it can beevaluated completely.

Floating Objects Present MisleadingOptical Information

It has been argued that under ordinary circumstances,optical contact of an object with the ground specifies theobject's physical contact with the ground unless there isinformation to indicate otherwise (Gibson, 1950; Sedgwick,1983). Furthermore, the relative distance of any two loca-tions along the ground (e.g., the bottom of two objects) isspecified optically by the ratio of the respective anglesbetween the horizon line and the line o f regard to a locationon the ground (for small angles; see Sedgwick, 1983, p. 452,Figure 22). It could be argued, therefore, that because theobjects in the present study were floating, such opticalinformation about the relative depth of the different-sizedobjects was deceptive in specifying that the larger objectswere nearer (see Sedgwick, 1983, Figure 6). When thebottoms of the objects were at a fixed altitude as size variedin Experiment 3, however, such angles specified that all

three distances were the same; nevertheless, size-arrivaleffects occurred. Moreover, size-arrival effects occurred inExperiment 5 when the altitude of the objects's top andbottom were fixed as width varied. This argument, there-fore, does not seem to explain our data.

Larger Objects Appear to Require Higher Jumps

J. R. Tresilian (personal c omm unication, November 2,1992) offered the following explanation of our results: Atthe same time-to-contact, larger objects appear to requirehigher jumps than smaller objects; thus, the latter result inlater jum ps. T his is consistent with our finding that partic-ipants jumped higher for larger objects (see results regard-ing peak altitude). However, it is unclear w hy larger objectswould appear to require higher jumps than do smaller ob-jects; the tops of the objects were at the same altitude whenthe object's width and/or length varied.

Nevertheless, w e m easured judgmen ts of time-to-contactas a function of object size in a control experiment in whichthe jum ping task was eliminated; such judgme nts could notbe based on the perception that larger objects require higherjumps per se. Specifically, 10 students from Texas TechUniversity viewed computer simulations of self-motion to-ward a square object. They were instructed to press a keywhen they thought they would collide with the object(Schiff & Detwiler, 1979; see also DeLucia, 1991a, Exper-

iment 2). Displays were created with an MS-DOS 486750MHz computer and were presented in 640 X 350 pixelresolution at a speed of 35 frames/s on a 35.56 cm (14-in.)monitor. The parameters of the scenes were as described in

5 The same reviewer suggested that size-arrival effects m ayoccur because people are just m ore nonchalant about running intosomething small (i.e., less worried about it and therefore lesscareful). This would imply that ou r participants made inferencesabout the objects' virtual sizes a nd did not use the same criteria infollowing the instructions for the three objects. Although ou rresults do not provide evidence for such hypotheses, our experi-ments were no t aimed to address these issues.


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796 PATRICIA R. DELUCIA AN D RIK WARREN

Experiments 1-2 (e.g., the same three levels of square sizeand altitude of square top), except that the objects consistedof white square outlines inscribed with a cross and wereshown against a black background. The scene was termi-nated after 7 s so that observers did not see wh en the objectmoved com pletely beyond the edges of the computer screen.The time between the beginning of the trial and keypresswas recorded.

A 3 X 3 repeated measures ANOVA indicated an effectof square size only, F(2, 18) = 6.17, p < .03. Estimates oftime-to-contact increased as square size decreased; meanswere 8.77 s, 8.47 s, and 8.29 s, respectively. Tukey's HSDtests indicated a significant difference between only thesmallest and largest squares, p < .05. Thus, consistent withthe results of Experiments 1-5, observers reported relativelyearlier collision times for larger objects— even when thejumping task was eliminated. Such results make it difficultto apply the argu ment that earlier launch times occurred forlarger objects in Experiments 1-5 because they appeared to

require higher jum ps. The results of the control experimentindicate that larger squares were perceived as closer in timethan smaller squares, which may account for the earlierlaunch times in Experimen ts 1-5.

Apparent Size-Distance Couplings

It could be argued that participants jumped earlier forlarge objects because they projected a relatively larger im-age, and because observers assumed the objects were thesame virtual size; thus, larger objects appeared closer thandid the smaller objects. Such an explanation is consistentwith our observations of the displays and with traditionalstudies of apparent size-distance relationships (e.g., Epsteinet al., 1961; Hastorf, 1950; Ittelson, 1951a, 1951b; Kil-patrick & Ittelson, 1951). In addition, DeLucia (1991a,1991b) reported that when computer-generated floating ob-jects approached a viewpoint, observers judged a large farobject as closer than a small near object that would havearrived sooner.

In the present study, familiar size information about theobjects w as not available. Pictorial relative size informationwas present: At any given value of time-to-contact in thedifferent scenes, the smaller object projected a smaller im -age than the larger object.6 Accordingly, if both objectswere assumed to be equal in virtual size, the object that

projected the smaller visual angle would have appearedfarther, thereby potentially accounting for later jumps. Fur-ther analyses suggest, however, that such an explanationcannot account for our collision-avoidance data: A largeapproaching object that projects a relatively large visualangle, but that is assumed to be the same virtual size as asmaller object, should appear at a relatively smaller distancefrom the viewpoint at every point in time. However, theapparent change in the large object's distance (velocity) alsoshould appear smaller by the same proportion. Accordingly,the larger object should appear relatively closer but slower,and apparent time-to-contact should remain the same fordifferent-sized objects (assuming perceived time-to-contact

is based on perceived distance and perceived velocity). W ewould thus expect the same launch times for all objects,which is inconsistent with ou r data. W e acknowledge thatthis explanation assumes that apparent size and apparentdistance are coupled. Such an assumption may not alwaysbe valid, as demonstrated by the m oon illusion: Althoughthe zenith and horizon moons project the same visual angle,the moon appears larger and closer, instead of farther (for asummary, see Hershenson, 1989). In any case, our analysessuggest that the apparent size-distance couplings consid-ered here cannot adequately accoun t for size-arrival effects.

Finally, we acknowledge that projected size, change inprojected size, and rate of expansion were a ll relatively lessfor the sm aller objects, and thus we cannot tease apart theireffects. We prefer to consider explanations of our data interms of projected relative size because it is more closelytied to apparent distance, whereas changes in projected sizeor rate of expansion are more closely tied to apparentvelocity (see also Bootsma & Oudejans, 1993).

Effective Information Varies Overth e Viewing Period

Thus far, it seems that tau and pictorial relative sizeinformation cannot adequately explain size-arrival effects.Our previous explanations were based on the assumptionthat such information was used by observers over the entireviewing period. It is possible, however, that the visualinformation that determined performance varied over time.For example, during the initial part of the trial, the smallerobject may have appeared farther due to pictorial size in-formation. Then, as time progressed and time-to-contactbecame smaller, tau may have become more influential;participants may have realized that the small object was notas far as originally perceived. This would be consistent withthe results of our optical analyses of Experiments 1-3: Ifeither tau or optical size alone w as used by participants, thenlaunch times would have occurred when such informationreached the same value for large and small objects. Analy-ses indicated, how ever, that although the ratio of optical sizefor large to small objects decreased dramatically from 8.0 atthe trial's start to 3.7 at launch time, it did not reach 1. Inaddition, although the ratio of time-to-contact for large tosmall objects began at 1, it increased to 2.1 at launch time;even so, it was closer to a ratio of 1 than was the ratio foroptical size. Thu s, it is plausible that both pictorial size and

tau contributed to performance but that the influence of eachvaried over the course of the trial. Such an explanationmaintains both pictorial relative size and tau as viablesources of information that contribute to size-arrival effects(see also DeLucia, 199la, 1991b) and that vary in effec-tiveness throughout the task.

6 Apparent size-distance relationships also can occur when dif-ferent-sized objects are presented successively (Epstein, 1961),and when objects are dissimilar in shape (Epstein & Franklin,1965; for a relevant study on time-to-arrival, see also Caird &Hancock, 1992).


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Conclusion

The results of the present experiments extend DeLucia's(1989, 1991a, 1991b) findings that size-arrival effects canoccur under a wide range of display and passive task con-ditions. We show that such effects can also occur withactive collision-avoidance tasks and when different-sizedobjects are shown successively rather than simultaneously.The previous results obtained with passive tasks were ex-tended in the present study with an active task that could beconsidered closer to ordinary perceptual conditions (e.g.,see Gibson, 1979). Further study must be done beforesize-arrival effects can be explained adequately. Neitherpictorial size (on the basis of an assumption of equal-sizedvirtual objects) nor tau alone can explain our results if it isassumed that such information was used continuously overthe course of the trial. Alternatively, observers may haveused pictorial size in the early part of the trial, until taureached a certain value and then increasingly influenced

performance.Previous studies in which action, or judged arrival time,was correlated with geometric time-to-contact informationsuch as tau, have been taken to indicate that observers gearperformance to such information. This argument is basedpartly on the observation that such a strategy is relativelysimple and economical, that is, it is not necessary to per-ceive either distance or velocity in order to perceive time-to-contact (Lee, Young, Reddish, Lough, & Clayton, 1983;see also Savelsbergh, Whiting, & Bootsma, 1991; Tresilian,1991). However, it also has been suggested that, undercertain conditions, visual information other than tau may beused to guide timing judgments or actions (Cavallo &Laurent, 1988; DeLucia, 1991a; Schiff & Oldak, 1990;

Tresilian, 1991, 1994). The results of the present study areconsistent with this assertion: Pictorial relative size as wellas tau may contribute to the jumping tasks we studied. Inaddition, our optical analyses suggest that observers mayhave used elevation angle to adjust altitude prior to thejump, because elevation angle may provide useable infor-mation about height. If relative size is indeed used incollision-avoidance tasks, it becomes critical to measure thelimits and relative strengths of both pictorial and motion-based depth information when considering models of depthand arrival-time perception (DeLucia, 1991a, 1991b, 1992).

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Received April 9, 1992Revision received January 12, 1994

Accepted January 12, 1994 •

Pictorial and Motion-based Depth Information During Active Control of Self-motion- Size-Arrival...

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