quirement of this study. Hence, in order to be
certain that the illusion was present, the perceived
slant of the window was measured. For this
purpose, after every equidistance judgment made
by O, a pair of lights was turned on in an area
on O’s immediate left. This area contained a
black rotatable indicator rod (14X14 X12 inches)
and a gray reference board (to provide a physi-
cally fronto-parallel plane) mounted on a light-
gray surface. The task of O was to adjust the
indicator until it seemed to be slanted with re-
spect to the reference board by the same amount.
that the window had appeared slanted with re-
spect to his frontal plane. The indicator was
horizontal or vertical as required by the hori-
zontal or vertical orientation of the window. A
scale, not seen by OQ, enabled £ to record 0's
slant adjustments in degrees.

IIL. Procedure.

The O’s were 16 men with a stereoacuity of at
least 25.25 seconds of are as determined by the
Diagnostic Series for Macular Stereopsis of the
Keystone Orthoscope. All 0’s made four con-
secutive equidistance judgments for each disk
pair in each experimental condition. The se-
quence of stimulus presentations was systemati-
cally varied between O's.

For each adjustment, O used a small switch
near the viewing position to signal Z to move
the adjustable disk in a particular depth direc-
tion until the movable disk appeared to be at the
distance of (equidistant with) the stationary disk.
After completing each disk adjustment, O was

instructed to note the apparent orientation of the
window, to face toward the area to his left, which
contained the slant apparatus, and to indicate the
amount by which the window appeared slanted.

IV. Results.

A summary of both the physical depth dis-
tance between the two disks judged to be equi-
distant and the apparent slant of the trapezoidal
window as measured by 0’s adjustments of the
rotatable indicator is given in Table 1. The
values of apparent slant for the horizontal orien-
tation of the window are averages of 32 scores,
two from each O, where each score is an average
of the four slant adjustments made with a par-
ticular orientation of the window and a particu-
lar lateral separation of the disks. The values
of apparent slant for the vertical orientation of
the window are averages of 16 scores, one from
each O, where each score is the-average of the
four slant adjustments. A positive angle (slant)
in the “Apparent slant” column of Table 1 indi-
cates that the small end of the window was per-
ceptually more distant than the large end. A
positive angle (slant) in the “Physical Slant”
column of Table 1 would indicate that the small
end of the window was physically more distant
than the large end. Since the small end of the
window was perceptually behind the large end
for all orientations of the window, all values in
the “Apparent slant” columns are positive. Since
the small end of the window was physically in
front of the large end for the horizontal orienta-
tions of the window, the “Physical slant” values

Tanre 1, Average Measurements of Apparent Slant of Window and Physical Positions at which Disks Appeared
Equidistant.

A. Horizontal orientation of window

Direction position Adjusted depth between disks

of small end (em)
Smail lat. Large lat.
Separation Separation
Small end left 25.8 23.3
Small end right 26.9 25.7

Amount of
Apparent slant Physical slant — window illusion
(deg) (deg) (deg)
+45.6 —45.0 +90.6
+406 —45.0 +85.6

B. Vertical orientation of window

Small end top 41
Small end bottom +01

+517 0 +5L7
+35.0 0 +35.0





therefore, that the magnitude of the distorting
effect of the binocular illusion upon the apparent
depth positions of the extraneous objects might
vary as the extraneous objects are directionally
displaced from the'display producing the binocu-
lar illusion, Previous studies? * have employed
stimulus displays in which the depth illusion has
been oriented horizontally with the extraneous
object separated laterally within (or nearly with-
in) the right-left extent of the illusion. There
is little reason not to expect similar results, how-
ever, when the binocular illusion is vertically
oriented with a vertical separation between the
extraneous objects and when the extraneous ob-
jects are located outside the horizontal or vertical
extent of the illusion. These conditions were
investigated in the present study.

II. Apparatus.

A. The Binocular Illusion. The binocular illu-
sion in depth was produced by an Ames trape-
zoidal window (Portable Model, Catalog No.
RTW,), 33.8 cm long, which was illuminated by
& projector invisible to O. The average lumin-
ance of the light gray portions of the window
was 0.35 ft-L. Both horizontal and vertical ori-
entations of the long axis of the window were
used. The window was slanted in depth 45° with
respect to 0’s objective frontal plane when pre-
sented horizontally, but it was parallel to O’s
objective frontal plane when presented vertically.
The window presentations were such as to result
in the following four experimental conditions:

1. A horizontal orientation of the window in
which the large end of the window was on
O’s left and was physically more distant
than the small end.

2. A horizontal orientation of the window in
which the large end of the window was on
O’s right and was physically more distant
than the small end.

38. A vertical orientation of the window in
which the large end of the window was
higher in O’s field of view than the small
end, with the two ends physically equidis-
tant from 0.

4, A vertical orientation of the window in
which the large end of the window was lower
in O’s field of view than’'the small end, with
the two ends physically equidistant from 0.

In all experimental conditions, the large end of
the window was 804 cm from the eyes of O. Any

effect of aniseikonia upon the overall experimental
results for the horizontal orientations of the win-
dow was eliminated by orienting the window at
equal but opposite directions of physical slant
(Conditions 1 and 2). Any tendency to induce
cyclorotation of the eyes when the window was
verticaly positioned was avoided by always plac-
ing the vertical window in a plane parallel to
the objective frontal plane of O (Conditions 3
and 4).

B. The Ewtraneous Objects. The extraneous ob-
jects that were adjusted by O to be at the same
apparent distance (from himself) in the presence
of the binocular illusion were two circular spots
(disks) of light with diameters of 14 inch. The
disks were slightly orange in color and were pro-
duced by plexiglass surfaces transilluminated by
incandescent lamps. By means of spur and rack
gear arrangements, the experimenter (Z), while
invisible to O, could adjust the disks through
approximately 60 cm of depth. The luminance
of the disks was 0.35 ft-L.

One disk of the pair being judged remained
stationary with its center always physically sep-
arated 4 cm from the large end of the window
and at the distance of that end (304 cm from 0),
The path of depth movement of the adjustable
disk was always perpendicular to the objective
frontal plane of O, and for Conditions 1 and 2
was displaced laterally either 4 or 14 cm from
the small end of the window. The disks in Con-
ditions 1, and 2 were at the height of O’s eyes
(slightly below the midline of the window) and
were laterally separated from each other by either
31.9 or 41.9 em. For Conditions 3 and 4, only
one vertical separation of the disks was used.
The center of each disk was vertically separated
4 cm from the end of the window most adjacent
to it. Thus, a constant vertical separation of 41.8
cm occurred between the disks when the window
was oriented vertically.

The 0’s binocularly viewed the window and
disks from a darkened observation position that
contained a chin cup and a pair of eyepieces
whose separation could be adjusted for different
interpupillary distances. Apertures, invisible to
O. which were located between O and the window,
eliminated extraneous light so that only the win-
dow and disks were visible.

C. Slant-Measurement Apparatus. The occur-
rence of a binocular illusion in depth was a re-


are negative or zero, respectively. The magnitude
of the binocular illusion in depth is found by
subtracting the physical from the apparent slant.

The average physical depth between the two
disks when they appeared to be equidistant for
the different conditions of the experiment also is
shown in Table 1. It will be recalled that the
movable disk was always directionally most ad-
jacent to the smal] end of the window. A nega-
tive value in the adjusted depth between the
disks indicates that, when the two disks appeared
equidistant, the movable disk was physically
closer to O than the stationary disk. In each
horizontal condition, the disk pair, in order to
appear equidistant, had to be physically separated
in depth by amounts significantly different from
zero beyond the 0.01 level of confidence with ¢
values of 20.20, 11.12, 20.67, and 13.14 (with df’s
of 15) for the values of —25.8, —23.3, —26.9,
and 25.7, respectively, of Table 1. Clearly,
when the orientation of the window and the sep-
aration of the disks were horizontal, a large error
occurred in adjusting the disks to apparent equi-
distance with each other. This error in adjust-
ment was much less, however, when the orienta-
tion of the window and the separation of the disks
were vertical. With the vertical condition, only
the 4.1-cm difference in depth adjustment was
significant (P< 0.01, ¢= 3.46, df= 15). The
amount of distortion of the equidistance adjust-
ments of the disks with the horizontal orientation
of the window was only slightly different between
the 31.9- and 41.9-cm separations, with neither
of these differences significant at the 0.05 level
(¢ = 1.96 and 0.87, df’s of 15, respectively).

V. Discussion.

The results from the present study demonstrate
that the presence of a binocular illusion in depth
can affect the perceived depth between other ob-
jects even though these objects are extraneous to
the illusion and even though no portion of the
binocular-depth illusion (the window in this case)
is directly involved in the task. It is as though
the perceived space surrounding the (horizontal)
window is distorted as a consequence of the binoc-
ular-window illusion. For example, the disk
directionally near the physically closer, but ap-
parently farther, small end of the window had
to be adjusted closer to O than the other disk in
order for the two disks to appear equidistant. It
is as though the apparent depth between the
disks was distorted in the same direction as that

of the ends of the window, and, therefore, a depth.
adjustment opposite to this distortion had to be
made in order for the disks to appear equidistant.
The difference in the signs between the columns
labeled “Adjusted depth between disks” and
“Amount of window illusion” in Table 1 reflects
this process.

Although the physical difference in depth be-
tween the apparently equidistant disks in Table
1 is large, there is reason to consider that this
difference is not as large as would be expected
from the magnitude of the depth distortion be-
tween the ends of the window. Physically the
small end of the horizontal window was approxi-
mately 24 cm in front of the large end. The
stationary disk was always at the distance of
the large end of the window, and, according to
Table 1, the disk directionally near the small end
of the horizontal window had to be adjusted
approximately 25 cm in front of the other disk
in order for the two disks to appear equidistant.
It follows that, when the two disks appeared equi-
distant, they were physically located in depth
near the ends of the apparently slanted window.
This result is in agreement in direction but not
necessarily in magnitude with the simplified hy-
pothesis* that the binocular disparity between
each disk and its directionaly most adjacent end
of the window will determine the apparent posi-
tion of each disk.

There are several reasons why the slant illu-
sion that occurred with the window might be
expected to be greater than that between the two
disks. First, the Ames trapezoidal window con-
tains two (not one) binocular-depth illusions.
One of these is produced by the trapezoidal shape
of the window and is measured by the 0’s adjust-
ment of the apparent slant of the window. The
second binocular illusion is produced by the
shading at the large end of the window and is
used to simulate thickness in the window. The
directions of these two illusions are opposite in
their effect upon the error occurring in the equi-
distance adjustments of the disks. The presence
of the second illusion would act to reduce the
magnitude of the error in apparent equidistance
from that expected from the first illusion.
Another explanation can be found in what is
called the “adjacency principle”? As applied to
the present experiment, this principle states that.
the apparent depth position of each disk would
be most determined by the binocular disparity


AM 66-24

PROBLEMS IN DEPTH PERCEPTION

Equidistance Judgments in the Vicinity of a Binocular Illusion

Frank L. Agee, Jr.
Walter C. Gogel

Approved by Released by
S Wie vy Sy PU°S.2 C Py? »)
J. Rosert Ditiz, M.D. P. V. Stecex, M.D.
Crier, Crviz AnROMEDICAL Feperar Am Surcron
InsriTuTe
July 1966

FEDERAL AVIATION AGENCY
Office of Aviation Medicine



cue that occurred between it and adjacent parts
of the window. If the adjacency is defined as
perceptual rather than as retinal or physical,’
the magnitude of the error in the equidistance
judgments would be expected to be less than the
magnitude of the depth illusion occurring with
respect to the window. A third possible explan-
ation involves the task set of O. It is possibleTM
that, to some extent at least, the act of perform-
ing the apparent equidistance adjustment of the
disks permitted O to ignore the window and,
thus, to reduce somewhat its error-producing
effects.

From Table 1, it is clear that the magnitude of
the errors in the apparent equidistance judgments
of the disks was less for the vertical than for the
horizontal orientation of the window. This diff-
erence can also be explained by the opposing
effects of the two illusions (size and shading) in
the window. The magnitude of the first. illusion
clearly increases with an increase in the physical
slant of the window (see Table 1) while the
magnitude of the shading illusion does not. It
follows that the capacity of the second illusion
to offset the effect of the first upon the apparent
equidistance adjustments of the disks should be
much greater for the frontoparallel (vertical)
rather than the 45° (horizontal) orientation of
the window. It is likely that, with the vertical
window, the resultant effect of the two depth
illusions was small and that, therefore, the error
found in the equidistance judgments also was
small.

The increase in the horizontal separation of the
disks (from 31.9 to 41.9 cm) with the window
oriented horizontally did not produce a large
change in the adjustment error (Table 1). The

direction of this change, however, is such as to
suggest that the effect (a) extends beyond the
edges of the window, but (b) with slightly de-
creasing effectiveness. The last portion of this
conclusion must be considered as very tentative
pending the use of additional separations.

REFERENCES

1, Anns, A., Jv.: Visual perception and the rotating
trapezoidal window. Psychol. Monogr. 65, No. 7
(Whole No. 324), 1951.

2. Gocer, W. C.: Perception of the relative distance
position of objects as a function of other objects in
the field. J. exp, Psychol. 47: 335-842, 1954.

3. GoceL, W. C.: Relative visual direction as a factor
in relative distance perceptions. Psychol. Monogr. 70,
No. 11 (Whole No. 418), 1956.

4, Goser, W. C., and Harxer, G. S.: The effectiveness
of size cues to relative distance as a function of
lateral visual separation. J. exp. Psychol. 50: 809-
315, 1955.

5, Ivreson, W. H.: The Ames demonstrations in per-
ception. Princeton: Princeton University Press, 1952.

6. Irrerson, W. H.: Visual space perception. New
York: Springer Publishing Company, Ine., 1960.

7. Zeoers, R. T., and Murray, Parrrcta A.: Perception
of distortion. I, An experimental anproach to illu-
sion. ‘Technical Report NAVTRADEVCEN 506-1.
New York: U.S. Naval Training Device Center, 1962.

. Zeoers, R. T. and Matowe, T. B.: Perception of dis-
tortion, An experimental study of distance and per-
spective in the Ames trapezoidal illusion. ‘Technical
Report NAVTRADEVCEN 1215-1. New York: U.S.
Naval Training Device Center, 1964.

9. Goaer, W. C.: The visual perception of size and dis-

tance. Vision Res. 8: 101-120, 1968.

10. Goaer, W. C.: Perception of depth from binocular
disparity. J. ewp. Psychol. 67: 879-386, 1964.

11. Gooer, W. C.: Size cues and the adjacency principle.
Report No. 63-28. Oklahoma City: Civil Aeromedical
Research Institute, 1963.

we

67-3291



FOREWORD

This study was conducted by Frank L. Agee, Jr. (now at the Boeing
Company, Aerospace Division, Seattle, Washington), under the direction of
Walter C. Gogel (now at the Psychology Dept., University of California,
Santa Barbara), and was submitted by Mr. Agee to the University of
Oklahoma in partial fulfillment of the requirements for the MS degree.

The authors wish to thank James C. Hester for his assistance in collect-
ing the data of this study.

Qualified requestors may obtain Aviation Medical Reports from Defense Documentation
Center. The general public may purchase from Clearinghouse for Federal Scientific
and Technical Information, U.S. Dept. of Commerce, Springfield, Va. 22151


PROBLEMS IN DEPTH PERCEPTIONS:

Equidistance Judgments in the Vicinity of a Binocular Illusion

I, Introduction.

Research has clearly indicated that misleading
size cues can alter the apparent depth orientation
of an object in spite of the presence of veridical
cues of binocular disparity~* For example, if
an Ames trapezoidal window? is oriented with
its smaller end closer to the observer (Q), it will
usually appear as though this end were the more
distant. A situation of this type can be called a
binocular illusion in depth since it is a distortion
by other cues (in this case, the cue of relative
size) of the perception that normally would occur
from the cue of binocular disparity. It has been
demonstrated? that the perceptual consequences
of a binocular illusion in depth are not confined
to the stereoscopic display used in producing the
binocular illusion. More specifically, it has been
asserted that the depth position of an extraneous
object in the vicinity of the depth illusion will
be more correctly judged with respect to portions
of the illusion display with which it is direction-
ally close than with respect to portions of the
illusion display from which it is directionally
displaced.* *

PHYSICAL APPARENT
FRONT VIEW TOP VIEW B
12 3
-looof
2
TOP VIEW
aA L2ae
Ak
abe obs

Freure 1, A schematic drawing illustrating the effect of
a binocular illusion in depth upon the apparent depth
location of other objects.

A demonstration of the effect of a binocular-
depth illusion upon the perceived depth of ex-
traneous objects is schematically illustrated in
Figure 1. In Figure 1, two differently sized play-
ing cards (A and B), and three disks (1, 2, and
3) are physically located at the same distance
from O and, according to the stereoscopic (binoc-
ular-disparity) cue, should appear at the same
distance. As a result of the misleading relative
size cue between the two cards, however, Card A
appears in front of (closer to O than) Card B.
The difference between the physical and apparent
distance positions of the card in Figure 1 repre-
sents a binocular illusion in depth. The disks in
Figure 1 are the extraneous objects; ie., they
contain no misleading size cues. The apparent
depth positions of these disks approximate the
mean results obtained in an experiment® in which
a single disk was alternately presented in each
of the three lateral positions and judged as to its
depth position with respect to each card. As is
indicated in Figure 1, Disk 1 correctly appears
at the distance of the left card, but it incorrectly
appears in front of the right card. Similarly,
Disk 3 is seen correctly in depth only with re-
spect to the playing card (Card B) with which
it is most nearly in line of sight. Disk 2, which
is directionally midway between the two cards,
is correctly perceived with respect to neither card
but appears midway between them in depth.

It can be inferred from this and similar dis-
plays that if the disks had been adjusted to ap-
pear equidistant from O, Disk 2 would have had
to be moved physically nearer to O than Disk 1,
ete? It is possible, however, that in adjusting the
disks to apparent equidistance with each other, O
would be able to ignore the playing cards and
consequently the effect of the binocular illusion
upon the equidistance judgment would be reduced.
or eliminated. Also, as is indicated in Figure 1,
the effect of the binocular-depth illusion extends
beyond the immediate vicinity of the illusion-
producing objects (playing cards). It is possible,