Copyright 1984 by the
American Psychological Association, Inc.
Journal of Experimental Psychology:
Human Perception and Performance
1984, Vol. 10, No. 5, 713-723
A Limitation of Position Constancy
Hans Wallach and Donna Nitzberg
Swarthmore College
Robert Becklen
Sarah Lawrence College
When the eyes track a moving object, the image of a stationary target shifts on
the retina colinearly with the eye movement. A compensation process called
position constancy prevents this image shift from causing perceived target motion
commensurate with the image shift. The target either appears stationary or seems
to move in the direction opposite to the eye movement, but much less than the
image shift would warrant. Our work is concerned with the question of whether
position constancy operates when the image shift and the eye movement are not
colinear. That can occur when, during the eye movement, the target undergoes a
motion of its own. Evidence is reported that position constancy fails to operate
when the direction of the target motion forms an angle with the direction of the
eye movement.
In 1978, Wallach, Bacon, and Schulman induced motion shifted it simultaneously to
raised the following question: Is the induced the left, resulting in a sloping path, and when
motion that is perceived when the eyes track the pattern and the dot reversed their motions,
the moving surround instead of looking at the dot appeared to move downward at the
the surrounded "target" object really induced same slope angle. Wallach et al. (1978) used
motion, or is the perceived target motion, estimates of that slope angle to measure the
under these conditions, a direct result of the extent of the induced motion relative to the
retinal path of the target image, which reflects, extent of the dot's motion. Estimates of the
of course, the eye movement? Ordinarily, a slope angle were obtained before and after a
compensation process termed position con- period of adaptation that diminished the
stancy takes eye movements into account, extent of the induced motion. Mean slope
thus preventing image displacements caused estimates were steeper after adaptation by an
by eye movements from leading to perceived angle that implied a 15% shortening of the
motion, but position constancy may not take horizontal, induced motion. But this result
effect in the particular arrangement Wallach was obtained only when the subjects' eyes
et al. (1978) used.
tracked the vertical motion of the target;
A large pattern of vertical lines that was when the eyes tracked the horizontal motion
made to move alternately to the right and to of the surround, the apparent slope of the
the left would have caused a centered station- target motion remained unchanged after adary dot to appear to shift left and right in aptation.
induced motion. But the dot was not stationWallach et al. (1978) considered two explaary; rather, it moved upward when the pattern nations for this unexpected result. One asmoved to the right and downward when the sumed that the slope of the motion path
pattern moved to the left. Here, the induced perceived when the eyes tracked the surround
motion manifested itself in a changed motion was not the result of induced motion, but
path of the dot. When the dot moved upward, rather the result of the path of the dot's
retinal image. The authors pointed out that
the motion of the dot's retinal image had
This work was supported by Grant 11089 from the both a vertical and a horizontal component
National Institute of Mental Health to Swarthmore Col- when the surround was tracked. The vertical
lege—Hans Wallach, principal investigator.
component was caused by the untracked verWe are grateful to Eileen Kowler for her generous help tical motion of the dot, and the horizontal
in writing this report.
Requests for reprints should be sent to Hans Wallach, component was caused by the horizontal eye
Department of Psychology, Swarthmore College, Swarth- movements. These two displacements resulted
in an oblique image path. If perceived motion
more, Pennsylvania 19081.
713
714
R. BECKLEN, H. WALLACH, AND D. NITZBERG
corresponded to the retinal motion, it would play the moving surround was placed within
not be altered by adaptation.
stationary edges that were symmetrically loThe other explanation proposed by Wal- cated straight ahead of the subject. This
lach, Bacon, and Schulman (1978) assumed display was used by Wallach, O'Leary, and
that position constancy takes the eye move- McMahon (1982) when they compared the
ment into account, and thus perceived motion effectiveness of three stimulus conditions
does not correspond to the image displace- known to produce perception of motion:
ment. According to this view, induced motion conngurational change that results from obis explained in the following way: Position ject-relative displacement, ocular pursuit, and
constancy would compensate for the shifting image displacement. In the absence of staof the surrounded'object's image when the tionary edges, they found that conngurational
surround is tracked, and thus the surrounded change prevailed when it was in conflict with
object would be represented as stationary. At ocular pursuit. However, when conngurational
that point, the motion of the surround would change was in conflict with image displaceproduce induced motion. In the experiments ment, the two conditions were about equally
by Wallach et al. (1978) this sequence was effective. Adding the stationary edges diminmore complex because the target was also ished the extent of induced motion from
moving. Position constancy would compen- 100% to 75% when conngurational change
sate only for the component of the retinal was in conflict with ocular pursuit and from
path produced by the horizontal eye move- 44% to 25% when it was in conflict with
ments. Induced motion, however, would cause image displacement. Introducing stationary
the perceived target motion to be oblique. vertical edges into the display, then, diminThis view of what happens in Wallach et al.'s ished induced motion. Will induced motion
experiment would not, however, explain why also be diminished when the eyes track the
no adaptation was measured when the eyes horizontal motion of the surround instead of
the moving target, or will the effect then fail
tracked the moving surround.
Recently we discovered another condition to occur as it did in the experiment described
that affected induced motion only when the above? The following experiment provided
eyes tracked the moving target (Wallach & the answer.
Becklen, 1983): Increasing the horizontal
speed of the surrounding vertical line display Method
diminished the extent of the induced motion
Subjects. Fourteen paid undergraduates of Swarthmore
when the observer looked at the target. When College participated.
the eyes tracked the horizontal motion of the
Equipment. The apparatus described in detail by
surround, induced motion was less affected Wallach and Becklen (1983) was used. The horizontally
by the increased speed. The remaining effect moving line pattern and the vertically moving target were
rear-projected on a translucent screen by different lanterns
was found to correspond to reduced tracking whose
beams were shifted by means of tilting mirrors.
that occurred at higher velocities. These re- The height of the moving pattern was 116 cm and
sults supported the hypothesis that the path subtended a visual angle of 98.5°. It was 87 cm (82°)
of the perceived motion of the moving target wide and consisted of 33 vertical gray lines, 0.3 cm wide
resulted from the path of its image on the and 2.6 cm apart. It moved 9.8 cm horizontally. The
target was a light dot of 0.5 cm diameter. It moved 9.6
retina and not from induction.
cm (11°) vertically. Both reciprocating motions were
Experiment 1 was conducted to find further simple harmonic (0.26 cycles/s). Their phase differed by
support for this hypothesis. It describes an- 90°, so that one motion was at its midpoint when the
other instance in which induced motion de- other started. The stationary vertical edges were produced
vertical black screens suspended at each side of the
pends on whether the target rather than the by
display.
moving surround is tracked.
Displays. There were four display conditions. In
Experiment 1
We used the same induced motion display
as did Bacon, Gordon, and Schulman (1982),
called the aligned center display. In this dis-
Condition N (no edges) the screens were omitted so that
the entire moving line pattern was visible. In the other
three conditions, the moving line pattern was partly
hidden by the screen. The edges of the screen were either
60 cm, 30 cm, or IS cm apart, leaving corresponding
openings in which the moving lines were seen and which
subtended visual angles of 62, 33, and 17°. These openings
715
POSITION CONSTANCY
were always centered about the dot. Each of these display
conditions was observed either when the subject's eyes
pursued the vertically moving dot or when they tracked
the surrounding horizontally moving line pattern.
Response measure. When the subjects viewed such a
display, they saw the dot moving on an oval path whose
height depended on the vertical motion of the dot and
whose width represented the extent of the induced motion.
In each condition the subject used a pair of calipers to
give a width and a height estimate of the perceived
motion path. The ratio of the two estimates measured
the extent of the induced motion, because the extent of
the vertical motion of the dot was the same under all
conditions. These width/height ratios have the advantage
that they reduce the variability with which different
subjects represent visual extents.
Procedure. Subjects gave width and height estimates
for each of the eight conditions (two observation conditions
for four display conditions), once in ascending order of
size of the opening, ending with Condition N and again,
after a pause, in the opposite order. The different observation conditions connected with one display condition
were paired and followed each other immediately. The
order of the observation condition within a pair was
different in the ascending and descending order for each
subject. These two orders were counterbalanced, resulting
in four combinations. Two subjects were randomly assigned. The average of the two width/height ratios obtained
in each condition was the score for that condition.
Results
The means of these width/height ratios
obtained in the eight conditions are listed in
Table 1. In the dot pursuit condition, the
ratios depended on the presence or absence
of the stationary vertical screen edges and on
the size of the opening between them. The
difference between the mean width/height
ratios obtained with no edge present and
with the largest opening between the edges
was significant at the .05 level, and the means
listed for the three different openings were
significantly different from each other at the
.001 and .004 levels, respectively. In the line
tracking condition the ratios, with one exception, did not depend on the size of the
opening between the edges. They were the
same for the no-edge condition and the 60cm and 30-cm opening conditions. Moreover,
these ratios were about 1, indicating that the
subjects saw a nearly circular path closely
resembling the path of the dot's retinal image
that had a ratio of 1.02. Only in the case of
the 15-cm opening was the ratio diminished.
This difference was significant, f(39) = 3.08
and p ~ .004.
An ANOVA, which justified these p values,
was performed. To make the distribution of
Table 1
Mean Ratios of Width and Height Estimates
of Oval Motion Paths
Display conditions
Openings (in cm)
Observation
conditions
No edges
60
30
15
Dot pursuit
Line tracking
1.10
1.03
1.01
1.04
0.85
1.02
0.71
0.88
the ratio scores symmetrical about 1, scores
above 1 were transformed according to the
following formula: transformed ratio = 2 —
1/ratio. The ANOVA showed that the ratios
for the dot pursuit and the line tracking
conditions were the same in the absence of
the edges. In the presence of the edges, the
two observation conditions yielded significantly different mean estimates, F(3, 39) =
12.59 and p - .000007. The interaction was
also highly significant, F(3, 39) = 7.10 and
p » .00064; in other words, the difference
between the slopes of the mean width/height
ratios for the dot pursuit and for the line
tracking conditions was highly significant.
The ratios that were obtained at the 30-cm
opening showed that in the line-tracking condition the perceived path matched the path
of the dot's retinal image, whereas in the dotpursuit condition, the visible stationary edges
diminished the induced motion by 23%, a
difference that was significant, f(30) = 5.50.
At the narrowest opening of 15 cm, the
difference between the width/height ratios in
the two viewing conditions was still highly
significant, with t(39) = 3.74 and p = .0006.
The stationary edges provided configurational information about the dot's motion
that contradicted the configurational change
between the dot and the moving line pattern,
the cause of the induced motion. This accounts for the diminished induced motion.
The same result would have been obtained
if, in the line tracking condition, the horizontal component of the dot's apparent motion
path had also been induced motion, that is,
caused by the configurational change between
the dot and the moving line pattern. Because
it did not happen, we conclude that in the
line tracking condition the perceived motion
716
R. BECKLEN, H. WALLACH, AND D. NITZBERG
path was not caused by induced motion but
corresponded to the dot's image path.
Narrowing the opening to 15 cm caused
the width/height ratio to drop significantly in
the line tracking condition also. We propose
the following explanation: The horizontal
tracking movements of the eyes, which cause
the horizontal component of the dot's image
path, also cause a horizontal image displacement of the vertical edges of the opening.
Thus, the moving dot and the vertical edges
shifted on the retinas in a fixed configuration,
within which the dot moved vertically. The
vertical motion that resulted from this configurational change combined with the circular retinal image motion and resulted in a
narrowing of the perceived path. There are
other instances where an image path and a
configurational change combine to result in
a single perceived motion path. An example
can be found in the experiments of Wallach,
O'Leary, and McMahon (1982): In the fixation condition, the perceived sloping path of
the vertically moving dot results from the
combination of its image path and the induction effect caused by the laterally moving
lines.
Experiment 2
two motion patterns is spontaneously reported. It results from the configurational
change between the dots (Wallach, 1963).
According to unpublished findings by Wallach
and O'Leary, when the subject is instructed
to track the horizontally moving dot, its
apparent path is more nearly horizontal, and
only the vertically moving dot is still seen to
move obliquely. Is this oblique path still the
result of the configurational change between
the dots, as is the case when the subject views
the display without tracking one of the dots,
or is it evoked directly by the sloping path of
the dot's retinal image that results when the
horizontally moving dot is pursued?
We tried to answer this question by altering
the configurational change in which the nontracked white dot was involved, so that configurational change would tend to cause a
perceived motion different from the motion
that its image path would evoke. A third, red
dot was added to the display. This dot also
moved horizontally, but always in the direction opposite to the motion of the tracked
green dot. The configurational change between
the red dot and the vertically moving white
dot would also be oblique but with the opposite slope. The combination of the two
configurational changes should give the white
dot a vertical motion. If, in the two-dot
display, the perceived oblique path of the
white dot was due to configurational conditions, introducing the moving red dot should
cause the white dot to appear to move vertically. If this perceived oblique path was due
to the path of the white dot's retinal image,
introducing the red dot, and with it another
configurational change, should alter the white
dot's motion only in a minor way. It should
still be oblique.
In this experiment we omitted the line
pattern that caused induced motion in the
dot pursuit condition and had the eyes track
instead a horizontally moving green dot. A
simple arrangement resulted where a white
dot moved vertically and a green dot horizontally, with their paths forming a cross.
The 90° phase difference was omitted because
more is known about the condition where
the reciprocating motions of the dots are in
phase. When the green dot was tracked, the
resultant of the two displacements of the
white dot's image was, therefore, a sloping Method
straight line instead of a circular path.
Subjects. Subjects were 19 paid undergraduates.
This arrangement of crossing motion paths
Equipment. The device used in Experiment 1 was
can give rise to the perception of two simulmodified to provide three moving dots. The path of the
taneous motions, which Johansson (1950) beam
of one lantern remained unaltered. It still shifted
has considered the result of vector analysis. in the horizontal plane, but it now projected a dot and
If they are not instructed to track one of the passed through an orange-red filter. After the beam from
dots, many subjects report two simultaneous the other lantern had been reflected by the moving mirror
motions. The dots seem to approach and that caused it to move in a vertical plane, the beam was
in two. A stationary beam splitter reflected half of
pass each other on an oblique path and also split
it upward. The part of the beam that passed through the
to move as a group in a direction perpendic- beam splitter was reflected toward the screen by a solid
ular to that path. Often only the first of the mirror where it projected, as before, the vertically moving
POSITION CONSTANCY
717
white dot. The part of the beam that was reflected Table 2
upward was reflected by a slanting mirror that turned Mean Tilt Estimates for the Apparent Path
the plane in which it moved to horizontal and, at the of the Vertically Moving White Dot
same time, directed it toward the screen. It passed
through a green filter and provided the other horizontally
Condition
M tilt estimate
moving dot. The vertical path of the white dot was 10.4
cm long. The green and the red dot moved horizontally
A
over a distance of 10.7 cm and 10.0 cm, respectively.
Two dots (w-G)
-33.7°
The centers of their paths coincided with the points at
-21.1°
Three dots (w-G-r)
which they crossed the white dot's path. These points
were just above and just below the centers of the white
B
Two dots (W-g)
-8.4°
dot's path.
-.01°
Three dots (W-G-r)
Procedure, Subjects gave estimates of the tilt angle of
the apparent path of the vertically moving white dot
under four conditions. Under two conditions, they tracked Note. A = motion given as image displacement. B = motion
the white dot, either in the presence of only the green given by ocular pursuit. N = 19.
dot (W-g) or of both the green and the red dot (W-g-r).
In the other two conditions, they tracked the green dot,
either in the absence of the red dot (w-G) or in its
presence (w-G-r). The motion speed was the same under estimate was -.01°) because the configuraall conditions, namely 0.30 cps. The conditions in which tional effect of the red dot should cancel the
the green dot was tracked were critical and were tested effect of the green dot. The differences befirst. Half the subjects were first presented with the w-G
condition and then with the w-G-r condition, and for the tween the mean tilt estimates of -8.4° and
other half his sequence was reversed. The white dot of -.01° was highly significant (p < .001).
tracking conditions (W-g and W-g-r) followed, also with
When the subject tracked the horizontally
reversed order for half the subjects. The same tilt esti- moving green dot and when the red dot was
mation method was used that had been employed in the
previous studies cited; the subject adjusted the orientation absent (w-G), the mean tilt estimate for the
of a 57-cm long, white, test rod that was perpendicularly white dot's path was -^33.7°. This large deattached to a horizontal shaft so that it could be given viation from the objective motion of the
any desired direction in a vertical plane. This rod was white dot observed when the green dot was
visible against a square black surface and was located on
tracked suggested that the white dot's apparthe subject's left with its rotation plane forming a right
angle with the screen. When it was time to set the rod, ent motion resulted from its image path. The
the subject turned to the left to face it, and the experi- mean tilt of -33.7° of the apparent motion
menter turned on a table lamp to illuminate it. The of the white dot did fall short of the expected
distance from the rod to the subject's eyes was approxi- value of 45.8°. Even if we take into account
mately 75 cm. The subject made two settings, one from
a vertical and the other from a horizontal starting position, the fact that tilt estimates for diagonal direcwith their average serving as the estimation score. For tions are as much as 5° too steep, the reobvious reasons, only the one with the horizontal starting maining shortfall of 7° was still significant at
position was used in the W-g and W-g-r conditions.
the .01 level. Perhaps subjects tracked the
green dot less than accurately because they
had to pay attention to the white dot's mo1
tion.
The averages of the angles that the rod
settings formed with the vertical were the
individual scores. The mean tilt estimates are
1
An experiment that is an analogue to our noncritical
listed in Table 2. Clockwise deviations were condition
(w-G) was conducted by Festinger, Sedgwick,
given positive signs. When the white dot was and Holtzman (1976). They varied the orientation of the
tracked and only the green dot was present motion path of the target spot that corresponded to our
in the W-g condition, the mean tilt estimate white dot between 60° and 120°, whereas ours was 90°
of the apparent path of the white dot was and the motion speeds between 0.125 and 1.0 cps. Their
resembled ours: The perceived motion direction of
-8.4°. This deviation from the vertical direc- results
the nontracked dot was very different from the objective
tion of the objective motion of the white dot directions of that dot and was quite close to the direction
was the result of the configurational change of the dot's image path. Festinger et al. assumed that the
between the white dot and the green dot. As perceived motion direction of the nontracked dot resulted
its image path. They did not consider the possibility
predicted, adding the red dot in the W-g-r from
that object-relative dispacements may be a stimulus concondition caused the apparent path of the dition in such arrangements, and they did not manipulate
white dot to become vertical, (the mean tilt it as we did in our critical condition and in Experiment 3.
Results
718
R. BECKLEN, H. WALLACH, AND D. NITZBERG
The critical result for our hypothesis was
the mean tilt estimate of the path of the
white dot in the presence of both horizontally
moving dots when one of them was tracked
(w-G-r). If the perceived path of the white
dot depended on configurational change rather
than on its retinal path, its apparent path
should be vertical when all three dots were
present because its object-relative relation to
the red dot on the one hand and to the green
dot on the other balanced each other, as
happened when the white dot was tracked.
But the path of the white dot was still tilted
with an angle of 21.1°, and this angle was
significantly different from 0° with f(18) =
8.95 and p < .0001. This finding makes sense
only if the perceived motion path is based at
least in part on the oblique path of its retinal
image. Here, the shortfall of the perceived
tilt compared to the presumed tilt of the
image path of 45.8° was even greater than in
the w-G condition. When two dots with
different motions of their own were present,
tracking the green dot may have been even
less complete than in the w-G condition and
may have resulted in an even steeper image
path of the white dot. But we did not measure
eye movements and do not know how complete pursuit movements were.
In our next experiment we made the task
of pursuing a dot while observing the path
of another dot easier by having a line pattern
that filled the subject's visual field undergo
the same horizontal motion as the tracked
dot. We knew-from the experiments by Wallach and Becklen (1983) that under these
circumstances tracking is accurate at the
speed used in the present experiments. These
authors measured ocular pursuit of the line
pattern at three speeds with the afterimage
method and found an appreciable shortfall
in pursuit only at the highest speed of 1.39
cps and none at 0.26 cps, the latter comparable to our speed (corrected for observation
distance) of 0.21 cps. Adding the line pattern
had still another purpose. The configurational
change between the target dot and the pattern,
which would have caused complete induced
motion of the dot if it were tracked, is so
effective that it would obscure the much
weaker configurational change between the
target dot and a tracked dot, which had
remained an issue in Experiment 2.
Experiment 3
This experiment employed the display used
by Wallach, Bacon, and Schulman (1978), a
pattern of vertical lines in reciprocating horizontal motion centered on a light dot that
moved up and down. The two motions were
in phase. When the dot was tracked, the
relative displacement between it and the lines
resulted in a horizontal induced motion component, which caused the perceived motion
of the dot to be oblique. The same tilted path
was perceived when the lines were tracked,
but here it could have been the result of the
dot's oblique image path, the resultant of the
dot's vertical motion and of the horizontal
image shift caused by the eye movement. Or
here, too, the apparent tilted path of the dot
could have resulted from induction taking
place after position constancy had compensated for the horizontal component of the
dot's image motion.
In order to obtain different predictions
from the two explanations, we changed the
direction of the tracking eye movements and
with it the dot's image path. Instead of having
the subject track the line pattern horizontally,
they tracked an obliquely moving point of
such a slope that it shortened the vertical
component of the dot's image path and therefore increased its tilt. Thus, if the apparent
motion of the dot depended on its image
path, it should now be more horizontal than
when the eye movements were horizontal. If,
on the other hand, position constancy prevailed, the apparent motion of the dot should
remain unaltered.
Method
Subjects. Subjects were 16 paid undergraduates.
Displays. The excursion of the horizontally moving
line pattern was 9.2 cm (13° of visual angle), and a light
dot, which served as target, moved up and down over a
distance of 16.4 cm (23°). Therefore the tilt angle of its
image path was arctan 9.2/16.4 = 29.3° when the eyes
tracked the lines horizontally through the full excursion
of 9.2 cm. A dark spot that moved horizontally with the
line pattern helped guide the line-tracking eye movements.
A second light dot was provided for tracking to produce
oblique eye movements. The path of this obliquely
moving dot formed an angle of 38.8° with the horizontal.
This path can be considered to be the resultant of two
components, of a horizontal motion component of 9.2
cm, which caused the eyes to keep up with the line
pattern, and a vertical component of 7.4 em. This vertical
component shortened the vertical component of the
719
POSITION CONSTANCY
image path of the target dot by the equivalent of 7.4 cm
so that it now corresponded to a vertical motion of the
target dot of 16.4 - 7.4 = 9.0 cm. When this vertical
component was added to the horizontal image motion
component, which was caused by the horizontal tracking
motion of the eye (9.2 cm), the resultant image motion
path formed a tilt angle of arctan 9.2/9.0 = 45.6". That
would be the direction of the apparent motion of the
target dot that results from the image path of the target
dot when the obliquely moving dot is tracked.
Equipment. The apparatus used in Experiment 1 and
2 was slightly modified. The lantern, whose beam was
made to shift horizontally, projected the line pattern
slide. As before, the other lantern projected a light dot.
Its beam was shifted up and down and then encountered
a beam splitter. One portion that was reflected toward
the screen passed through a dove prism, which gave its
path the 38.8° tilt. The other portion eventually encountered a vertical mirror, which reflected it toward the
screen; it carried the vertically moving target dot, whose
greater excursion was caused by the longer traveling
distance of its beam portion. The dark dot was produced
by placing a blank slide with a single dot image in the
first projector next to the line pattern slide.
The line pattern was 89 cm high and 60 cm wide (96°
and 74° of visual angle). The obliquely moving dot and
the dark dot were each 3 mm across. The target dot
was, of course, 1.8 times larger. The motion speed was
0.17cps.
Procedure. In the control condition, the dark horizontally moving dot was visible, in addition to the line
pattern and the target dot, but the obliquely moving dot
was absent. The subject was asked to track the dark dot
and to give tilt estimates for the apparent path of the
target dot as was done in Experiment 2. The experimental
condition resembled the control condition except that
the dark dot was absent and the obliquely moving dot
was visible and was to be tracked. As before, two tilt
estimates were given for each apparent motion path, one
where the starting position of the test rod was horizontal
and the other where it was vertical. The average of the
two settings became a subject's tilt estimation score.
Starting positions and control and experimental conditions
were fully counterbalanced across subjects.
Results
The mean tilt estimates and their standard
deviations are given in Table 3, which also
lists the tilt angles of the image paths of the
target dot under the two tracking conditions,
when it is assumed that tracking is accurate.
The mean tilt estimate for the control condition, where the horizontally moving dark
dot was tracked, was 30.19° and was in good
agreement with the tilt angle of the target
dot's image path, which amounted to 29.3°.
A mean tilt estimate of about the same value
should also be expected under the assumption
that position constancy operated and that the
tilt of the path was due to induction. This
Table 3
Mean Tilt Estimates for the Apparent Path of a
Moving Dot During Eye Movements in
Different Directions
Tracking eye movements
Estimated and actual tilt
Mean tilt estimates
SD
Tilts of image paths
Horizontal
Oblique
30.19°
5.97°
29.3°
42.93°
4.57°
45.6°
condition, however, can serve as control for
the oblique tracking condition because the
assumption that position constancy operates
would predict the results to be the same in
both the oblique and the horizontal tracking
condition.
The mean tilt estimate for the oblique
tracking condition was 42.93°, again in good
agreement with the 45.6° tilt of the image
path. The difference of 2.67° is accounted
for by the overrating of slopes of diagonal
directions mentioned earlier; this difference
was, however, marginally significant, with
t(\5)= 2.34 and p < .05. The important
comparison is the one between the mean tilt
estimate of 42.93° and the one obtained
under the control condition. The difference
between these two means was 12.74° and
was highly significant, with t(\5) = 6.78 and
p < .0001. This result indicates that the mean
tilt estimate of 42.93° cannot have resulted
from position constancy and induction. Direct
perception of the image path must have taken
place, and position constancy has failed.
Experiment 4
In our final experiment, another strategy
was used to make tracking more accurate.
Instead of having the eyes track a reciprocating motion, we made the tracked motion
path circular, which involves a uniform eye
movement. Another of Johansson's (1950)
motion pattern that often yields vector analysis was employed. In this arrangement, one
dot moves on a circular path, and another
dot next to it moves up and down. The latter
dot's reciprocating motion is simple harmonic
and reverses direction when the circling dot
passes through its highest and lowest point.
Because the circular motion path can be the
720
R. BECKLEN, H. WALLACH, AND D. NITZBERG
kinematic resultant of two straight simple
harmonic reciprocating motions, one vertical
and the other horizontal, which are combined
with a 90° phase shift, the circling dot's
progress in the vertical dimension is always
the same as that of the other dot. When the
perceived dot motions agree with vector analysis, the dots appear to move horizontally
toward each other and apart and, at the same
time, move together up and down. Tracking
one of the dots causes the perceived motion
of that dot to be veridical, as happens in the
crossing motion path arrangement. Subjects
usually report circular motion when the circling dot is tracked. The issue is how the
motion of the other dot is perceived when
the circular path is tracked. Because tracking
the circular path accurately amounts to moving the eyes up and down in concert with the
vertically moving dot, the latter is implicitly
pursued too. The horizontal components of
the circular eye movements, however, cause
horizontal displacements of the image of the
vertically moving dot. If position constancy
operates and compensates for these image
displacements, the vertical motion of that dot
should be correctly perceived. If position
constancy does not operate, the horizontal
image displacement of the dot results in a
horizontal component of its perceived motion,
which combines with the dot's perceived vertical motion and results in a circular path.
That is what usually happened.
Method
Subjects and equipment. Subjects were 37 paid undergraduates.
The moving dots were 2.1-volt light emitting diodes
(LEDs) attached to a mechanical device that was described
in Wallach, Becklen, and Nitzberg (in press). The diameter
of the circular path of the LED on the right was 9 cm,
and the length of the vertical path of the LED on the
left was also 9 cm. The latter's distance from the nearest
point of the circular path was 8 cm. Observation was in
total darkness. The subjects wore goggles with neutral
density filters, which obscured small spots of stray light.
A transparent mirror in front of the display concealed it
when the room was illuminated and, together with the
goggles, made the LEDs dimmer. The observation distance
was 4.6 m. To facilitate tracking, the motion speed was
slower than in the experiment by Wallach et al. (1984);
the LED completed its circular path in 3.7 s.
Procedure. The experimental gfoup contained 18
subjects who were instructed to track the circular path.
Initially, the vertically 'moving LED was disconnected,
and subjects practiced tracking the other LED. After 30
s the room light was turned on, and the subject had to
draw the motion path they had seen. Then the vertically
moving LED on the left of the circling LED was also lit.
The room was darkened and the subject was instructed
to track the dot on the right and to draw the path of
both dots when, after 20 s, the room was lit again. The
19 subjects of the control group first practiced tracking
the vertically moving LED for 30 s. After its perceived
path was drawn, both LEDs were lit, and the subject was
instructed to follow the left dot with his or her eyes and
then draw the path of both dots.
Results
There were large individual differences with
regard to the onset of autokinetic movement.
A few subjects who saw strong autokinetic
motion drew a zigzag line after they had
tracked the vertically moving dot, and they
drew a corkscrew spiral after tracking the
circling LED. Fourteen of the 18 experimental
subjects drew two circles after observing both
LEDs and tracking the one on the right.
Thus, in their case there was clearly no
compensation for the horizontal displacement
of the image of the vertically moving dot,
which was caused by the horizontal component of the circular eye movements that the
tracking of the circular path entailed. Three
subjects drew interlacing spirals, the outcome
of an addition of autokinetic motion to circular Sr elliptic dot motions. Because it was
not possible to state with assurance that the
primary dot motion was circular and not
elliptical, these 3 subjects were not counted.
A fourth subject drew two horizontal ellipses,
a result that was also counted as uninterpretable.
Among the 19 control subjects were 2
whose drawing showed strong autokinetic
motion components that made them uninterpretable. A third subject's drawing was also
uninterpretable. All of the remaining 16 subjects drew a straight vertical motion path on
the left. This means that configurational
change between the vertically moving dot and
the circling dot had no effect on how the
vertically moving dot was perceived. This
result made it clear that in the experimental
condition, too, the perception of the vertical
dot motion did not result from configurational
change between the dots. In both cases, the
vertical motion of the dot on the left was
given by eye movements, in the control condition by direct tracking, and in the experi-
POSITION CONSTANCY
mental condition by the vertical component
of the circular tracking. If configurational
change had been effective in the experimental
condition, it would have been effective in the
control condition also. Thus, the perceived
circular motion of the vertically moving dot,
which was reported for the experimental condition, resulted from the horizontal displacement of its image.
Even if no instructions are given to track
the vertically moving dot, its motion path is
drawn as straight and vertical. Wallach et al.
(1984) presented our motion pattern to 44
subjects without the instruction to track one
of the dots and obtained drawings. Seven
drawings were uninterpretable and 10 subjects
drew two circles, the result of tracking the
path of the circular dot, as we now know. All
remaining 27 subjects represented the left
dot's vertical path as straight and vertical, as
did the majority of our control subjects.
Summary and Discussion
The experiments here reported argue that
position constancy or the compensation for
target image displacement caused by pursuit
eye movements has a limitation. It does not
operate when the direction of the displacement of the retinal image of the target is
different from the direction of the eye movement. This happens when, during pursuit,
the target is not stationary but moves objectively in a direction different from that of the
motion of the tracked point.
Our first experiment investigated the induced motion of a target that, while it was
subject to induction, moved perpendicularly
to its induced motion. Because the induced
motion was caused by a pattern of parallel
straight lines, the perceived target motion was
the result of a combination of motions,
namely, the target's own objective motion
and the induced motion.2 The shape or the
slope of the resultant motion path could serve
here as a measure of the induced motion.
This arrangement had been used previously
to measure the effect of two factors that
diminish induced motion, adaptation and
increase of the motion speed. The two experiments had this in common: When, instead
of the target, the moving line pattern was
tracked, induced motion was not diminished.
721
Tracking the line pattern resulted in two
simultaneous image dispacements of the target, one due to the relative displacement
between the lines and the target and the other
due to the target's objective motion. The
resulting image path resembled the motion
path that was perceived when, prior to adaptation or at low speeds, the target was
tracked.3 We explained the failure of adaptation and of speed-up to cause diminished
induced motion in the line-tracking condition
by claiming that the perceived target motion
depended here directly on the target's image
path and not on induced motion. This explanation found support in our Experiment 1,
where a third factor that diminished induced
motion also failed to do so in the linetracking condition.
The assumption that an image path that is
the resultant of two image displacements
gives rise directly to the target's perceived
motion implied that the component of the
image path that was caused by line-tracking
was perceptually effective and that position
constancy did not operate. This failure of
position constancy seemed to be connected
with the fact that the image displacement
produced by eye movements was here a component of an image path, which was simultaneously representing an objective target
motion. Our remaining experiments were
designed to show that perceived motion depended here on the target motion as it was
given on the retina. These conditions occur
when a target moves while the eyes are engaged in pursuing a differently moving point.
To confirm the hypothesis that, under these
conditions, position constancy is not operating
we had to show that the perceived target
motion is more similar to the target's image
path than to the objective target motion. We
also had to show that the perceived target
motion did not result from configurational
change between the target and the tracked
2
A detailed explanation of induction by a pattern of
parallel lines has been previously given several times.
See, for example, Wallach, O'Leary, and McMahon (1982),
page 2, column 2.
3
Wallach, O'Leary, and McMahon (1982) found induction to be complete in the dot tracking condition,
causing a slope of the tracked dot's apparent path that
would be the same as the slope of its image path.
722
R. BECKLEN, H. WALLACH, AND D. NITZBERG
point but from the target's image path. The
three remaining experiments employed different strategies to deal with this issue. The
relation between the target motion and the
motion of the tracked point was also different
in the three experiments.
In Experiment 2, the perceived target motion differed significantly from the objective
target motion and had a direction that approached the target's presumed image path
halfway. In Experiments 3 and 4, the perceived
target motions did not only differ greatly
from the objective target motions, as perceived
under the control conditions, but also were
in close agreement with the presumed image
paths.
In all our experiments, the motion of the
target and the pursuit eye movements were
meant to have different directions. Therefore,
our results left open the question whether
position constancy failed because the target
moved during pursuit movement instead of
being stationary or because the target and the
tracked point moved in different directions.
Experiments are in progress where the target
does move during the eye movements but
where its motion and the motion of the
tracked point are colinear. Our results show
that position constancy operates under these
conditions. It appears that position constancy
fails only when the target motion forms an
angle with the motion of the tracked point,
that is, when it would have to compensate
for a component of the given image path and
when vector analysis of the image path would
have to take place.
This limitation of position constancy applies only to image displacements that are
caused by pursuit eye movements. Saccadic
eye movements function differently. Mack
(1970) had a target move vertically during a
flash-induced horizontal saccade. When the
extent of that vertical target motion was
above a certain threshold value and was
perceived, it was perceived as vertical, not as
oblique, as was the displacement of the target
image. This result was confirmed and expanded by Whipple and Wallach (1978). They
used voluntary saccades that were vertical,
horizontal, or oblique and target motion during the saccades in those three directions.
There were six combinations of eye movements and target motions where directions
differed. Target motions with extents above
certain threshold values were correctly reported, although the retinal paths of the
target images were very different. Hansen
(1979) reported still another instance of position constancy under conditions where the
motion of the target formed an angle with
the motion of the tracked point. In his Experiment 2 the subject used a hammer to
stike a target whose path formed various
angles with a pursuit eye movement when
they heard a brief tone. They performed this
task accurately at a variety of speeds of the
tracked point.
Does this mean that vector analysis takes
place in connection with saccades and in
Hansen's experiment? We think not. There
is a level of visual processing where the effect
of eye position and of eye movements on the
relation between the whole visual field and
the eyes is taken into account and where the
environment is represented as it is related to
the observer's head. At that processing level,
individual motion paths are represented as
they are oriented in relation to the head,
provided the head does not move at the time,
because they are part of the representation
of the whole visual field that is corrected for
the effect of eye movements.
Evidence for the existence of such a processing level comes from the work by Wallach
and Bacon (1977) on adaptation in the constancy of visual direction. This constancy
renders the perceived environment immobile
during head turning or nodding. It can be
rapidly altered by an arrangement where the
environment is made to move in a regular
fashion, depending on the rotation of the
head. Perception of the environmental motion
gradually diminishes during exposure to such
conditions. Wallach and Bacon found that
this adaptation could be obtained under two
different conditions. In one condition a mark
that the subject had to track during the head
movement moved objectively dependent on
the head rotation; apart from this mark, the
visual field was at rest and underwent the
normal relative displacements that resulted
from the head movements. Only the eye
movements (EMs) the subject made were
different from the EMs that are ordinarily
made when the eyes rest on a stationary
point during head rotation. Adaptation con-
723
POSITION CONSTANCY
sisted here in a changed evaluation of EMs.
In the other adaptation condition, the subject
fixated a stationary mark, but the rest of the
visual field was made to move dependent on
the head rotation. In this case, adaptation
consisted in a changed relation between the
whole visual field and the head (field adaptation). Both adaptation conditions yielded
identical results: After exposure, real motions
of the environment during and dependent on
head turning appeared diminished, and the
stationary environment seemed to move during head turning. In other respects, though,
the two adaptations had different manifestations, both connected with tests of visual
direction given while the head was turned to
the side. Pointing to a target straight ahead,
which required an eye movement into that
position, was altered after EM adaptation but
not after field adaptation, whereas setting a
target in the straight ahead position was
altered after field adaptation but not after
EM adaptation. Because field adaptation was
produced by an exposure during which the
subject looked at a stationary mark during
head turning and therefore the eyes performed
normal compensating movements, Wallach
and Bacon concluded that field adaptation
takes place at a processing level where compensation for eye movements has already
taken place and where the visual field is
represented as it is related to the head. Field
adaptation alters that relation.
There is also evidence of a close relation
between saccadic eye movements and the
processing level at which field adaptation
takes place. Another experiment required the
subject to make one saccade during every
head movement cycle. Particularly strong field
adaptation was obtained in this case. Its
effect, measured by setting a target in the
straight ahead direction, was doubled compared to the effect of an exposure with fixation
of a stationary mark. Thus, saccades seemed
to be initiated from the processing level where
field adaptation takes place and where the
effect of eye position and of eye movements
on the representation of the whole visual
field has already been taken into account.
This may be the reason why position con-
stancy is complete in connection with saccades. Position constancy in connection with
pursuit movement apparently operates independently, involving a compensation process
that matches up individual image displacements with simultaneous tracking movements.
The motor responses used by Hansen (1979)
may also be directed from a processing level
where the representation of the whole visual
field is corrected for the effect of eye position,
but there is no supporting evidence as there
is in the case of saccades.
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Received February 3, 1984
Revision received May 26, 1984