NASA Technical Reports Server (NTRS) 19970010712: Time-to-Passage Judgments in Nonconstant Optical Flow Fields

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Perception & Psychophysics #
1995, 57(6), 817-825
Time-to-passage judgments
in nonconstant optical flow fields
MARYK.KAISER and HEIKO HECHT
NASA Ames Research Center, Moffett Field, California
The time until an approaching object will pass an observer (time topassage, or TrP) isoptically spec-
ified by a global flow field even in the absence of local expansion or size cues. Kaiser and Mowafy
(1993) have demonstrated that observers are infact sensitive tothis global flow information. The present
studies investigate two factors that are usually ignored inwork related to q_I'P: (1) non-constant mo-
tion functions and (2) concomitant eye rotation. Non-constant velocities violate an assumption of
some q'TP derivations, and eye rotations may complicate heading extraction. Such factors have prac-
tical significance, for example, in the case of a pilot accelerating an aircraft or executing a roll. In our
studies, a flow field of constant-sized stars was presented monocularly on a large screen, q'l'P judg-
ments had to be made on the basis of one target star. The flow field varied inits acceleration pattern
and its roll component. Observers did not appear toutilize acceleration information. Inparticular, "l_Ps
with decelerating motion were consistently underestimated, q_rPjudgments were fairly robust with re-
spect to roll, even when roll axis and track vector were decoupled. However, substantial decoupling
between heading and track vector led to a decrement inperformance, inboth the presence and the ab-
sence of roll.
As an observer moves through the environment, the (Perrone & Stone, 1994; Royden, Banks, & Crowell,
temporal ranges of objects are specified by optical vari- 1992; Warren &Hannon, 1990).
ables. Specifically, the time until an object passes the ob- Most empirical research on observers' sensitivity totau
information has focused onthe situation of collision rather
server's eye plane (i.e., the plane perpendicular to the ob-
server's motion vector) is approximated by the function than passage, although Schiffand Oldak (1990) have con-
global tau (_-g= 0/0), where 0isthe angle between the ob- sidered both collision and passage cases, and Bootsma
ject and the heading vector, land/} the temporal derivative and Oudejans (1993) have examined performance from a
of this angle). Examination of the derivation of rgreveals variety of vantage points. In the case of direct approach,
that the relative observer-object velocity isassumed tobe the optical variable local tau (?l) approximates time to col-
constant inorder for rgto be an accurate estimate of time to lision (TTC). 2Local tau operates on the angular expanse
passage (TTP) (Kaiser & Mowafy, 1993; Lee, 1976; Tre- of the approaching object and the rate of change of that ex-
silian, 1991). In addition to the mathematical assumptions panse; that is, local tau operates on the local expansion of
the object image. For the case of passage (i.e., wherein the
underlying zg, pragmatic assumptions concerning ob-
servers' competencies must be made. Notably, one must object passes the observer's eye plane some distance from
assume that the observer can register both the angle (or the heading vector), local tau information is degraded
retinal distance) between the object and the observer's since expansion isbounded by the visual angle achieved at
track vector, and the rate of change of this angle (or dis- closest approach, and because changes in the object's an-
tance). The difficulty of extracting these parameters may gular extent reflect observer-relative rotation as well as
be increased if the concomitant motion resulting from approach. In such passage situations, global tau is the ap-
head rotations is added to the visual stimulus; ithas been propriate optical variable. Global tau operates on the ex-
shown that such motions affect the precision of heading pansion of the angle (or distance) between an object and
estimates, particularly in the absence of efferent signals the observer's track vector; itrequires aglobal analysis of
the flow field (to establish both the track vector and the ob-
ject's position relative to it). The mathematical derivations
of local and global tau are formally equivalent, but the
The authors would like to thank Larry Beck and Felix Shung of Ster-
ling Software for their excellent programming support. We also thank functional utility of the two information sources assume
Mike Braunstein, William Schiff, James Tresilian, and an anonymous different perceptual competencies (Kaiser & Mowafy,
reviewer for their extremely helpful comments and suggestions. Heiko 1993).
Hecht's work was supported by apostdoctoral fellowship from the Na-
The effect ofnonconstant velocity on TTP and TTC has
tional Research Council. This research was funded by NASA RTOP
538-04-11. Portions of this research were presented atthe 35th meeting been considered previously (Lee & Reddish, 1981;Tresil-
of the Psychonomic Society and the 1994 meeting of the Association for ian, 1993, 1994). Essentially, all analyses of the issue
Research in Vision and Ophthalmology. Correspondence concerning agree that tau-based strategies assume constant velocity.
this article should be addressed to M. K.Kaiser, Mail Stop 262-2, NASA
Thus, the utilization of atan-based strategy inthe presence
Ames Research Center, Moffett Field, CA 94035-1000 (e-mail:
of acceleration (positive or negative) will result in sys-
moose(_eos.arc.nasa.gov).
817 Copyright 1995 Psychonomic Society, Inc.
818 KAISER AND HECHT
tematic errors in judgment. However, surprisingly little the final experiment, we examined the impact on judg-
empirical data on performance exist) The most notewor- ments when the roll axis was decoupled from the track
thy studies were performed by Lee and his colleagues, ex- vector.
amining intercept timing behavior in birds (Lee & Red-
dish, 1981) and humans (Lee, Young, Reddish, Lough, & EXPERIMENT 1
Clayton, 1983). The findings of these studies suggest that Acceleration and Deceleration
TTC judgments are consistent with an assumption of con-
stant approach velocities, even when acceleration was pre- The first experiment assessed the accuracy of ob-
sent. However, Tresilian (1993) argues that these studies servers' TTP judgments under constant linear decelera-
may not have been sufficiently sensitive to discriminate tion and acceleration conditions as opposed to zero accel-
between timing based on a constant velocity assumption eration (constant velocity). Since the target stimulus
and nonconstant velocity strategies. maintained aconstant projected size, no local (i.e., within-
Similarly, there is relatively little information concern- object) tau information was available. Likewise, binocu-
ing the effect of concomitant head rotation on tau-based lar and accommodative cues to proximity were absent
judgments. Unlike acceleration, the presence of a z-axis from the display. Thus, the optical information specifying
rotation (i.e., rolling about the line-of-sight axis) does not TTP was limited to those contained in the global flow (see
violate the underlying assumptions of the tau derivation. Tresilian, 1991, for a discussion of potential global vari-
However, such a rotation adds an extraneous motion com- ables in addition to r[0]). Owing to the inconclusive find-
ponent to the optic flow, which must somehow be removed ings concerning the impact of acceleration on TTC judg-
to recover accurate heading (and hence TTP) information. ments, we held no firm hypothesis concerning passage
There is an extensive analytic literature suggesting how judgments in the presence of nonconstant velocity flow
the parsing of rotational and translational components fields: observers might be sensitive to acceleration infor-
might be accomplished (see Perrone & Stone, 1994, for a mation and adjust their TTP estimates accordingly, or they
review), but these models largely deal with y-axis rota- might make TTP estimates that ignore the constant accel-
tions (i.e., rotations about the vertical axis that are associ- eration of the flow field presented to them.
ated with gaze fixation). Perrone (1992) does briefly con-
sider the likely impact of roll on his detector/template Method
model, but only to suggest that large field roll detectors Observers. Eight male observers were recruited by an on-site or-
might interfere with the outputs of the other detector types ganization and paid for their participation. Most attended local col-
(see also Simpson, 1988, for a discussion of how con- leges and universities. They ranged in age from 20 to 44 years and
had normal or corrected-to-normal vision.
comitant roll would be expected to affect perfect and im-
Apparatus and Stimuli. The stimuli were generated on aSilicon
perfect filter models). There have been two empirical
Graphics Onyx RE 2workstation with a resolution of 1,280 x 1,024
studies of the impact of roll on TTC judgments: Simpson
pixels and arefresh rate of 60 Hz (noninterlaced). The animation up-
(1988) reported that stimulus roll degraded TTC discrim- date rate was 60 ffames,'sec. The display was routed via an Electro-
inations; Freeman, Harris, and Tyler (1994) found that home R(;B rear-projection system toalarge screen (244 × 183cm).
TTC estimates were unaffected by the addition of z-axis The observer was seated 300 cm away from the screen inaheight-
rotations. There were, however, important differences in adjustable chair tocenter his line of sight atthecenter of thedisplay
the two sets of studies. Freeman et al.'s stimuli consisted screen; the display subtended 44.2° visual angle horizontally x
33.9°vertically.
of an annular pattern of constant-sized dots; Simpson's The stimulus displays depicted acloud of single-pixel white dots
stimuli were expanding forms (crosses). The rotational ("stars") that were randomly positioned inavirtual 3-D viewing vol-
velocity in the Freeman et al. study was less than 6°/see; ume (see Figure 1).One three-pixel red dot served asthe target. Nei-
Simpson's stimuli rotated at 45°/sec. Thus, as in the case therthe target nor background dot size varied as afunction of de-
picted distance. The depth ofthevolume was constructed sothatthe
ofnonconstant velocity, findings concerning the impact of
observer's eye-point did not traverse more than 50% of the volume
roll on TTC judgments are inconclusive.
atthepoint atwhich thetarget passed theeye plane. The depth ofthe
All previous studies on nonconstant velocity and con-
volume was assigned the arbitrary scale of 1,000 graphical units
comitant roll have examined TTC situations; none have (gu). Average eye-point translation was 60 gu/sec. The track vector
considered passage events. Because the findings of these was always centered on the display. A total of 800 dots was used;
studies are inconclusive, and since local and global tau dots that exited the viewing volume were not replaced. During pilot
variables assume different perceptual competencies, an testing, it was determined thatthethinning out of stars intheview-
ing volume as the observer moved forward was less distracting than
examination of the impact of acceleration and roll for TTP
thecoming-into-existence of new stars, which would have been nec-
judgments is required. The studies we report investigate
essary to keep the number of visible stars constant throughout the
how observers' global TTP judgments are affected by the trial.
presence of acceleration and observer head rotation. Our Design. A three-fhctor, within-observer design was used. The
stimuli were constructed so that no local tau information first factor, acceleration, had five levels: two decelerating, one con-
was available to observers. In the first experiment, we ex- stant velocity, and two accelerating. In constant-velocity trials, the
amined the effect of a constant linear acceleration/decel- eye point translated at60 gu/sec; acceleration trials started with a
translation rateof 25gWsec and accelerated by 10or 15gu/sec2; de-
eration on TTP estimates. In the second experiment, we
celeration trials started with atranslation rateof 100 or 130 gu/sec
examined the effect of introducing a constant-velocity z- and decelerated by 10or 15gWsec2.Thc second factor, initial target
axis rotation (i.e., roll) about the observer's track vector. In depth, had three levels. Itwas set at660, 490, and 320 guin front of
EFFECTOSFACCELERATIOANNDROLL 819
6sac to Pass 11 sac to Pass
at 60 gu/ssc at 60 gu/sec
Figure I.Schematic of the simulated viewing volume used in Experiments 1and 2.Targets were positioned in
the rear and center portion of thevolume. Their positions differed indepth aswell asinX-displacement. The dot-
tedline originating atthe eyepoint represents thetrack vector. The field of view (FOV) in Experiment I subtended
44.2° horizontally × 33.9° vertically. The circular aperture (used in Experiment 2) reduced the FOV to 33.7° in
diameter.
the eye point foracceleration and constant-velocity trials; 490, 320, The other distractor group consisted of acceleration trials with ex-
and 260 gufordecelerating stimuli. Thus, overall TTPs ranged from treme target offsets (100 or 134 gu); these targets remained onthe
3to 11sec. The final factor was target offset; four lateral distances screen as briefly as the shortest decelerating experimental trials.
between target and track vector (15,30, 45, and 60gu)were chosen. Since thetarget was offset from thetrack vector inalltrials, italways
Varying lateral offset partially decorrelates target distance and ini- exited the screen before itpassed theobserver. Extrapolation times
tial angular offset (Kaiser & Mowafy, 1993). The resulting stimulus ranged from 0.5 to 3.5 sec.
display times and velocities are shown inTable 1. Procedure. The observers were seated inadarkroom 3m from
The 60 experimental stimuli described in Table 1were supple- the large screen display such thattheir line of sight was centered on
mented by 18distractor trials, which were included to decorrelate the screen. The viewing situation was likened to aspace ship pilot
the time when the target was visible onthe screen (i.e., display time) flying through astar field. Itwas explained thatthe target star and
with the type of motion. One distractor group consisted of deceler- thewhite stars would notmove withrespect toone another (i.e., they
ating trials with minimal lateral offset (6 or 10gu), resulting inon- allwere fixed stars), andthatthe target would always goout of sight
screen times typical ofthe longest experimental acceleration trials. before itpassed theobserver. The observers were instructed to click
Table 1
Stimulus Parameters [or Experiment 1
Acceleration Display Time inSeconds Initial Velocity Exit Velocity (gu/sec) Mean Displayed
(gu/sec2) Range M (gu/sec) Range M Velocity Change
-15 1.03-4.98 2.34 100or 40.3-84.5 64.9 -35.1%
3.03-4.77 3.84 130" 58.5-84.5 72.4 -44.3%
-10 1.02-3.35 2.15 100or 66.5-89.8 78.5 -21.5%
2.82-4.10 3.45 130" 89.t_101.8 95.5 -26.5%
0 2.6(_10.32 6.46 60 60.0 0
10 3.62-8.92 6.50 25 61.2-114.2 90.0 +260%
15 3.18-7.58 5.60 25 72.7-138.7 109.0 +336%
*This higher initial velocity was required for the most distant deceleration targets (490 gu), to ensure that the flow
field would not stop (orreverse direction) inthecaseof TTP overestimation.
820 KAISERANDHECHT
theleftbuttoonfathree-bumttoonusaetthepoininttimethatthe
comparisons between constant motion and the four levels
targeptasstehdeieryeplane.
The experimenter also informed the of acceleration. Constant-motion TTP judgment bias was
observers that distributing their attention would make iteasier tode-
significantly different from that for decelerations of 10
termine the point of passage---that is,they were told that the target
should not be tracked. An eye patch was worn over the observer's gu/sec 2[F( 1,7) - 5.96, p < .05] and 15 gu/sec 2[F( 1,7) =
less preferred eye toprevent interference from inconsistent binocu- 18.46, p < .005], but did not differ significantly from that
lar depth cues. The display sequence continucd until the observer in the two accelerated motion conditions.
clicked amouse button to indicate the passage point. Following the The precision of observers' judgments, as assessed by
observer's TTPjudgment, amenu appeared, and the observer used a absolute error, is shown by solid bars in Figure 2. There
mouse cursor to classify the stimulus motion of_he trial into one of
was asignificant effect for acceleration [F(4, 28) - 30.92,
three categories: (1) the star field slowed down, (2) the star field
p < .001]; errors were smallest for acceleration trials, and
sped up, or (3) the star field moved ataconstant rate. After the ob-
server had categorized the stimulus motion, feedback on his TTP largest for deceleration trials. This trend likely reflects the
judgment was given (i.e., how early or late the response was in mil- fact that greater TTP judgment variability is associated
liseconds). The next trial started automatically, after a4-sec pause. with longer extrapolation times; acceleration trials had the
Each observer received 15-20practice trials with feedback (selected shortest extrapolations, constant-velocity trials had ex-
from the set of distractors) before the experimental trials were trapolation times of intermediate length, and deceleration
started.
trials the longest. To control for this confound, the data
On each trial, observers had the option of indicating that their re-
were reanalyzed with extrapolation time as a covariant. 4
sponse was in error and should be discarded (e.g., the response but-
ton was pressed accidentally). They eliminated 5.4% of the trials This analysis of covariance revealed no significant effect
with this process. Trials in which observers responded more than for acceleration but a significant effect for extrapolation
3sec after the actual TTP were also excluded; these trials accounted time [F(1,398) = 98.52, p < .0001 ], thus confirming that
for 0.6% of all cases. Thus, atotal of 6% of the experimental trials the ANOVA-based acceleration finding was an artifact of
were omitted from the analyses.
extrapolation time. Deceleration trials also had, on the av-
erage, shorter on-screen times. However, no significant
Results
correlation was noted for display time and absolute error.
Observers' ability to compensate for nonconstant ap-
Our second analysis to assess whether observers took
proach velocities in the TTP judgments was assessed in
acceleration into account involved fitting their judgment
three ways. First, the bias (i.e., constant error) and the pre-
data to aconstant velocity extrapolation (CVE) model strat-
cision (i.e., absolute error) of TTPjudgments for constant
egy. According to the CVE model, observers simply base
and nonconstant motion trials were compared. If ob-
their judgments on aconstant extrapolation of the target's
servers fail to take velocity changes into account, decel-
velocity when it exits the screen. (A second constant-
eration and acceleration trials should demonstrate consis-
velocity model, based on average visible velocity, did not
tent biases: positive errors (i.e., early responses) for
fit as well as the final velocity model and was subse-
deceleration; negative errors (i.e., late responses) for ac-
quently abandoned.) We then compared the fit of the ob-
celeration. No particular trend is predicted for absolute
servers' judgments with the actual TTPs (which factors in
error, except that longer extrapolations tend to produce
the constant acceleration) and with hypothetical TTP val-
more variable judgments. Second, the fits of observers'
ues resulting from the CVE model. The observers' judg-
TTPjudgment data to models that do and do not consider
ments correlated significantly more highly with the CVE
acceleration were compared. Finally, the correlation be-
model's predictions than with actual TTPs [t(7) = 2.97,
tween TTP judgment error (defined as judged TTP minus
p < .05]; correlations were higher for the CVE model than
actual TTP) and a variable defined as the product of ac-
celeration rate and extrapolation time was examined.
These three convergent measures were used since it is
800-
difficult to use any single assessment to determine whether
acceleration influenced judgments. This difficulty is caused A !_ Constant Error
by the limited sensitivity of any particular assessment; re- I Absolute Error
E
sults expected from constant-velocity and acceleration-
based strategies are often difficult to distinguish (Tresilian, 40o
v
1993). In the present experiment, for example, the correla- 1111
tion between actual TTP (i.e., factoring in acceleration) and
passage times based on an extrapolation of final velocity ILl
°
was .886. This high correlation of the models' predictions
limits the sensitivity of competitive model fitting and in-
creases the necessity for convergent measures.
The constant errors of TTP judgments were fairly sim- -15 -10 0 10 15
ilar on constant-motion and acceleration trials; observers Acceleration (gu/s_ 2)
responded significantly earlier when the motion deceler-
Figure 2.Average absolute andconstant time-to-passage errors
ated. The average bias errors for TTP judgments are
for the three motion conditions in Experiment 1.For the signed
shown with striped bars in Figure 2. A repeated measures constant errors, positive values indicate early responses; negative
analysis of variance (ANOVA) was used to conduct planned values indicate late responses. Error bars depict _+ISE.
EFFECTS OF ACCELERATION AND ROLL 821
Table 2 misclassify any of the accelerating stimuli; t(7) = 1.25 for
FitofJudgment DatatoActualTTPandConstant Velocity deceleration trials].
Extrapolation (CVE) Model,andCorrelation of ActualTTP
andTTP BasedonCVE Model inExperiment 1
Discussion
Correlation
Passage events containing decelerating motions are not
JudgedTTPwithactualTTP 0.639 judged as accurately as those with constant velocity.
JudgedTTPwithTTPbasedonCVEmodel 0.719
Whereas TTPjudgments for acceleration trials showed no
ActualTTPwithTTPbasedonCVEmodel 0.886
significant bias, the short extrapolation times for these
stimuli make the observation of bias unlikely; the corre-
lation between actual TTP and TTP assuming an extrapo-
for actual TTPs for 7 of the 8observers' data). The aver-
lation of exit velocity was extremely high (r = .98) for ac-
age correlation coefficients are shown in Table 2. A re- celerating trials. For both accelerating and decelerating
gression analysis revealed the same effect; adding an ac-
motions, observers' responses can be adequately modeled
celeration factor toa simple constant-extrapolation model
with astrategy based onfinal screen exit velocity (i.e., one
did not explain a significant proportion of additional vari-
that does not require the monitoring of target accelera-
ance inobservers' judgments.
tion). It remains to be investigated whether observers will
Our final method to assess whether observers adjusted
shift to different strategies if the acceleration is more ex-
their TTP judgments for acceleration was to examine the
treme than the range we tested. Our results are consistent
correlation between a TTP error defined as (judged
with findings obtained with a TTC paradigm (Lee et al.,
TTP - actual TTP) and avariable which was the product
1983). However, the question of whether the acceleration
of acceleration rate and extrapolation time (e.g., 15gu/sec 2
values used in their study were detectable (Tresilian,
*750 msec). If observers did not consider acceleration,
1993) can also be applied to the present case. Observers
judged - actual error magnitude would increase as a mul-
may not have produced accurate TTP judgments because
tiple of these two factors. 5 Separate correlations were
they did not accurately perceive the acceleration. In fact,
computed for each observer. All correlation coefficients
observers correctly classified the trials as accelerating,
were positive, six of the eight significantly so; the average
constant, or decelerating only about half of the time, de-
coefficient value was .382. These positive correlations
spite the fact that the resultant velocity changes inthe dis-
further support the CVE model.
plays were reasonably large (as shown in Table 1). In any
Observers' categorization of stimulus motions was
case, the observers' TTP judgments do not reflect sensi-
used to address the question of whether observers were
tivity to acceleration in this context.
even aware of the acceleration (and if such an awareness
led to less biased TTP judgments). The observers reported EXPERIMENT 2
acompelling sense of being in amoving star field, but said Track-Coincident Roll
it was difficult to judge whether the star field speed
increased or decreased. This reported uncertainty is sup-
The impact of z-axis rotation (i.e., roll about the line of
ported by the classification data shown in Table 3.The ob-
sight) on TTP judgments was assessed inthis experiment.
servers demonstrated a bias toward classifying velocities
In previous studies of the effect of roll on TTC discrimi-
as constant; 41.2% of the accelerating stimuli and 68.4%
nations and judgments (Freeman et al., 1994; Simpson,
of the decelerating stimuli were identified as such.
1988), roll was centered on the object's approach axis. For
Pearson's adjusted coefficient of contingency between
simplicity and comparability, we duplicated this condition
stimulus motion type and observer classification was
using a TTP paradigm; that is, the observer's rotational
0.316. (A sensitivity analysis--which does not consider
axis and track vector were coincident. However, the align-
categorization bias--yielded d' values of 1.0, 1.55, and ment of rotational axis with track vector resulted inan in-
0.75 for constant velocity, acceleration, and deceleration,
teresting property in the optic flow field; the focus of ex-
respectively.) pansion (from translational motion) was likewise the point
Explicit awareness of the target's acceleration did not
of zero rotational displacement. Thus, the 2-D image ve-
significantly decrease TTPjudgment bias: [t(5) = - 0.88
locities traced a vortex whose center saliently specified
for acceleration trials--the reduced degrees of freedom
the observer's track vector. Since the use of global tau re-
resulted from the exclusion of two observers who did not
quires extraction of the object's displacement from the
track vector over time, heading-coincident roll might have
Table3 two opposing effects: it could facilitate performance be-
PercentofTrialsJudged asConstant, SpeedingUp,or cause itmakes the track vector more salient; alternatively,
SlowingDownforEachMotion Condition
roll could interfere with performance because the target
Stimulus
continuously changes its observer-relative orientation.
Judgment ConstantMotion Acceleration Deceleration
"Constant" 86.8 41.2 68.4 Method
"Spedup" 5.5 56.1 11.4 Observers. Thesame 8observers who participated inExperi-
"Sloweddown" 7.7 2.7 20.3 ment 1weretested inthis experiment. Halfofthemparticipated in
Total 100 100 100
Experiment 2first;theotherhalfbegan withExperiment 1.
822 KAISER AND HECHT
Apparatus and Stimuli. The same apparatus and virtual view- was virtually indistinguishable from performance in the
ing volume were used as in Experiment 1 The constant velocity no-roll condition. However, it should be noted that roll
stimuli from Experiment 1were modified byadding varying rates of
was always about the track vector. This coincidence of roll
z-axis rotation (roll). The simulated roll created aflow field such as
axis and track vector could be responsible for the robust-
that seen by a pilot whose airplane rotates around its longitudinal
axis while flying straight ahead. That is,heading and track vectors ness of TTP judgments across different degrees of roll.
coincided. Inorder toequate screen exit times fbrall target orienta- Since roll increased the local image velocities of the sim-
tions resulting from roll, a largeboard with acircular aperture was ulated stars as afunction of distance to the axis of rotation
putbetween the screen andtheobserver approximately 150cm away (and, coincidentally, the focus of expansion), it created a
from the observer. Itsdiameter (33.7°)was slightly less than the vi-
spiral effect, which was likened by some observers to
sual angle subtended bythe vertical extent of the screen. The board
"water going down a drain pipe" (i.e., a vortex). This ef-
was painted matte black toavoid light reflections.
fect could have made the orientation of the track vector
Design. A three-factor (roll, initial target depth, target offset)
within-observer design was used. An equal number of clockwise, more salient (especially for high degrees of roll) and thus
counter-clockwise, and zero-roll trials werc created. Velocity was have offset any negative effects that roll might have had on
constant at 60 gu/sec in all trials. Roll ranged from -45°/see to extracting the target's position with respect to the track
45°/sec in 15°steps. During pilot testing, 45"/see was determined to vector.
be the largest roll that would not bear the risk of inducing motion
There was some evidence that a moderate rate of
sickness. Even small degrees of roll (e.g., 10°/see) conveyed avery
compelling sense of ego rotation. Initial target depth ranged from roll (15 ° 30°/sec) produced a bias in observers' judg-
360 to 440 gu insteps of 20gu. On alltrials, the eye-point transla- ments; TTP judgments were significantly earlier in these
tion rate was 60gu/sec. Three lateral target offset distances between conditions. If this effect is reliable (it was not replicated in
target and track vector (15, 20, 25gu) were used, with offset ran- the next experiment), it could result from a confusion of
domly to the left or right of the track vector. The crossing of these the target's rotational and expansional motion compo-
factors resulted inatotal of 105trials. Overall TTPs ranged from 3.6
nents, aconfusion that is less likely to occur when the ro-
to4.8 sec. Extrapolation times ranged from 0.4 to 1.0sec. Target dis-
play time ranged from 2.9 to 4.4 sec (mean = 3.5 sec) in allcondi- tational motion becomes more coherent at higher angular
tions. velocities.
Procedure. The same procedure was used as in Experiment 1.In To test the possibility that the coincidence of track vec-
addition, observers were asked toalert the experimenter ifthey felt tor and roll axis aided observer performance, these axes
nauseous. In that case, abreak would be taken. Other than making were decoupled in Experiment 3. Also, longer extrapola-
TTP judgments, observers did not evaluate the stimuli. Feedback
tion times were added to the design to ensure that effects
about accuracy (in milliseconds) was given following each trial.
were not being suppressed by restricted error ranges.
Results
EXPERIMENT 3
In their debriefings, the observers reported a com-
Decoupling of Track Vector and Roll Axis
pelling sense of motion and of rotation. As in the first ex-
periment, observers' judgments were assessed in terms of
Experiment 2 was replicated with a critical modifica-
bias (constant error) and precision (absolute error), in
tion: The observer's roll axis and track vector were de-
contrast to acceleration, it would be predicted that roll
coupled (i.e., a lateral motion component was added). The
would more likely affect observers' precision (i.e., the ro-
simulated flow field now corresponded to a pilot rolling
tational motion would add noise to observers' judgments)
his craft while deflected by a strong crosswind. That is, the
than add a systematic bias. Analyses of absolute error
aircraft was rolling about its heading axis while moving
demonstrated no significant effect for roll. The introduc-
tion of moderate rates of rotation (15°or 30°/sec) about the
track vector resulted in the least precise TTP judgments,
but this trend was not statistically significant. Average ab-
solute error rates for each roll magnitude are indicated by
solid bars in Figure 3.
The striped bars in Figure 3 show the average constant
errors plotted by roll magnitude. Here, there was a small
yet significant effect for roll [F(3,21) = 3.72, p < .05];
trend analyses indicated the quadratic effect accounted for
96% of the variance. Thus, performance was least biased Ii!
in the absence of roll and at the highest roll rate (45°/sec).
Across all roll conditions, the trend was for observers to
underestimate TTP [M -- 126 msec; t(7) = 5.21,p < .005]. O'
0 15 30 45
Discussion
Roll (degrees/sec)
The precision of TTPjudgrnents was fairly robust to the
presence of roll. Moderate roll rates (15°and 30°/sec) pro- Figure 3.Average absolute and constant time-to-passage errors
in Experiment 2asafunction of roll magnitude. Data have been
duced some bias in TTP estimates and a trend toward less collapsed across clockwise and counterclockwise roll within each
precision, but performance at the highest roll rate (45°/sec) category of roll magnitude. Error bars depict _+1SE.
EFFECTS OF ACCELERATION AND ROLL 823
along a track vector that deviated 0% 7.5 °, or 15° from the
heading axis. The viewing geometry was modified to ac- (a)
commodate this decoupling, resulting in a deeper and E 800,
wider viewing volume and longer extrapolation times.
z
Method tu
Observers. Eight male observers were paid fortheir participation, a.
They ranged inage from 18to36years and had normal orcorrected- I_ 400.
to-normal vision• They had not participated in Experiment 1or 2.
O Roll=25°/uc
Apparatus and Stimuli. The same apparatus, including the cir- _ 200-
cular viewing aperture, was used asin Experiment 2.The virtual 3-D mO • Roll=0OImlc
viewing volume that accommodated the cloud ofsingle-pixel white .la
dots ("stars") was enlarged considerably and filled with 3,000 ran- _ 0 I i t
0 7.5 15
domly positioned stars. This was necessary because decoupling
tracking and heading results in an oblique translation through the Crab angle In degrees
viewing volume. The volume was extended and shaped like acone,
growing wider as afunction of distance from the initial eye point• _" 1000
The depth of the volume was enlarged to 1,500 gu; eye-point trans- 8 (b)
lation rate was again 60gu/sec. The targets were placed proportion- _ 800-
ally farther back inthe volume, resulting in longer trials (on-screen m
times as well as extrapolation times). Overall TTPs ranged from 3to
11sec. Extrapolation times ranged from 0.5 to 3.5 sec. As before, 600
one three-pixel red dot served asthe target. ILl
Design. Afour-factor (crab angle, initial target depth, lateral tar- 4OO
get offset, and roll), within-observer design was used. The first fac- _sOlle c
tor, crab angle, describes the angle between the track vector (direc- m
tion of simulated observer motion) and roll axis (observer heading). _ 2011
Inthe presence of crosswind, crab angle differs from 0°. In the pre- _ . _" • Roll=,0°llec
vious experiments, crab angle was always 0°(i.e., heading and track tO 0
vector were coincident). Here, three crab angles were selected (0°,
7.5°,or 15°);thus, the observer was going straight through the star
Crab angle In degrees
field orangled toward theright. Initial target depths ranged from 260
to380 in steps of 30gu. Lateral target offsets from the track vector Figure 4. Average absolute (a) and constant (b) time-to-
were 20guto the left of the observer; 20, 30, and 40gu tothe right. passage errors in Experiment 3 as a function of roll and crab
Roll about the heading axis was 0°or25°/sec. The roll rate of25°/sec angle. Error bars depict -+1SE.
was chosen since it fell within the range of rates (15°-30°/see) for
which some bias was noted in Experiment 2.
Procedure. The same monocular viewing conditions and proce- above and beyond the contribution of extrapolation time
dure were used as in Experiment 2.Itwas explained that the target
[F(2,860) = 8.69, p < .0005]. Extrapolation time was also
would sometimes, but not always, move at an angle with respect to
asignificant factor [F(1,860) = 523.87, p < .0001 ];errors
the observer. Observers were asked to factor this into their judg-
increased with extrapolation time. (See note 4.)
ments about the target's intersection with theeye plane. They clicked
amouse button to indicate their TTP judgments. Feedback concern- Similarly, TTP judgments showed no bias effect of roll,
ing judgment accuracy (in milliseconds) was given after each trial. but did show a significant effect of crab angle in both roll
conditions. Figure 4B shows that average constant TTP er-
Results rors were almost identical for the roll and no-roll condi-
The precision of TTP judgments was not affected by tions, but that they were significantly larger for the large-
roll. However, a large decoupling of track and heading crab-angle condition. A repeated measures ANOVA
axes led to increased absolute error, in both the presence confirmed this effect for crab angle [F(2,14) = 16.31, p <
and absence of roll. Figure 4A shows that average ab- .0002]. As in Experiment 2, there was atrend to underes-
solute error was significantly larger for the more extreme timate TTPs, but this trend was only significant for the
crab angle (15°). Arepeated measures ANOVA confirmed large crab angle It(7) = 6.79,p < .001].
this impression, revealing a significant effect of crab angle
[F(2,14) = 19.24,p < .0001]. Discussion
Introducing crab angle into a given set of stimuli in- The more extreme (15 °) decoupling of heading from
creased extrapolation times, because the target moved track vector decreased the precision of observers' TTP
obliquely to the observer's heading (as opposed to paral- judgments and introduced a significant bias toward un-
lel to heading for a crab angle of 0°). Thus, overall in- derestimating TTP. Roll about the direction of heading
creased extrapolation times might account for larger er- does not affect performance. Observer judgments proved
rors in the large-crab-angle condition. However, an to be robust to potential detrimental effects of roll; the
analysis of covariance, with extrapolation time as the co- judgment bias noted for moderate roll rates in Experi-
variate, revealed that crab angle had a significant effect ment 2 was not replicated here.
824 KAISER AND HECHT
GENERAL DISCUSSION z-axis rotation may enhance it. Rather, it is the introduc-
tion of motion components that disrupt the optical speci-
Our findings suggest that observers do not factor ac- fication of motion direction (e.g., substantial crab angles)
celeration into their TTP estimations. As in the TTC stud-
that will degrade temporal range estimation.
ies reported by Lee and his colleagues, judgments ap-
peared to reflect a constant-velocity strategy. In our study,
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EFFECTOSFACCELERATIOANNDROLL 825
NOTES 4. Analysis of covariance treats all data points as independent, an as-
sumption violated byour data inthis and the third experiment. Thus, theef-
I.Tau derivations can be performed with either apolar coordinate sys- fect size we report for these analyses are likely inflated (but stillclearly sig-
nificant); further, the null finding for acceleration in Experiment 1isvalid.
tem (reflecting visual angle) or aEuclidean system (reflecting retinal dis-
tance). The former utilizes the law' of small angles approximation (i.e., 5.That is, the larger the acceleration magnitude and the longer the pe-
tan 0- 0); the latter approximates the retinal surface with aplane. riod for which it is ignored, the greater the resultant error magnitude
2. The taxonomy of tau-based variables that we utilize in this paper (negative for deceleration, indicative of underestimating TTP; positive
for acceleration, reflecting TTP overestimation).
was set forth by Yresilian (1991).
3. There isan extensive literature on sensitivity to visual motion ac- 6. The term "heading" as used in the heading extraction literature isa
celeration (e.g., Calderone & Kaiser, 1989; McKee, 1981; Runeson, misnomer. Technically, heading is the direction in which a vehicle (or
1974: Schmcrler, 1976) and the ability tofactor velocity changc into mo- body) isfacing; the direction inwhich itismoving isits track. For most
terrestrial locomotion, the two are coincident (hence the tendency for
tion tracking and extrapolation tasks (e.g., Gottsdanker, 1952; Gotts-
danker, Frick, & Lockard, 1961; Jagacinski, Johnson, & Miller, 1983: heading to be used tomean the direction ofmotion). We differentiate be-
Rosenbaum, 1975). tlowever, these studies deal with motions orthogo- tween the two terms, using track for direction of motion, and heading for
nal to the line of sight, rather than toward the observer. While the phe- direction of forward gaze.
nomena are likely related, one cannot generalize from exocentric motion
analyses land the generally poor competencies reported) to egocentric (Manuscript received July 27, 1094;
revision accepted for publication January 30, 1995.)
approack"passage cases.