e

PANEL
POSITION
8B

PANEL
POSITION

MIRROR

FLUORESCENT
LIGHT
SOURCE

Ficune 1. A schematic perspective drawing of the apparatus used in the study.

anglés of 45 and 22.5 minutes-of-arc, respec- The physical position of Objects e, f, g, and h
tively. The Stzes of Objects e and f were such was constant throughout the study. Thus, both
as to subtend a visual area equal to that sub- the convergence values of the eyes to the Ob-

tended by Objects g and h, The horizontal jects e, f, g, and h in the binocular configuration

aration between Objects e and f or between —_ and the binocular disparities between these ob-
Objects g and h was 2°57’ of visual angle, jects were invariant throughout this study,

—3-—


,Sponding verbal reports

convergences to the configuration remaining
constant throughout the experiment.

The mean and median results (in centi-
meters) from the cart adjustments to, and the
verbal reports of, the apparent distance of Ob-
jects e, f, g, and h are given in Table 2. The
differences between the median and mean
verbal reports in Table 2 are mostly due to the
results from one O. From Table 2, the binocu-
lar configuration appeared to be more distant
when the panel was more distant or all Os
except one, verbal reports of,
cart adjustments to, Objects e’, f, g’, and h’ al-
ways were greater for the far rather than for
the near position of the panel. In agreement
with the results from the hand adjustments,
both the verbal reports and cart adjustments of
Table 2 indicate that the apparent depth with-
in the binocular configuration was greater when
configuration appeared in a more
distant portion of the alley.

The average cart adjustment to the apparent
distance of the striped panel was 535.1 and
183.5 cm, for the greater and smaller distances
of the panel from O, respéctively, with corre-
(converted to centi-
meters) of 664.5 and 190.0 cm. The apparent

DISCUSSION
As discussed elsewhere (Gogel, 1960a; Gogel,
1960b), Equation 1 should be applied only to

small vaiues of binocular disparity, For larger
values of binocular disparity, such as were used

Equation 1 as a basis is

v-i¢
t=cf ou

_ ‘TABLE 8
AVERAGE CART ADJUSTMENTS TO, AND VERBAL REPORTS
OF, THE APPARENT POSITION OF OBJEETS e, f, g, AND h

Distance “ / Apparent Distance of Objects
Position 7 Er
of j/—Means
Panel Object ¢ Object 'f Object g Object h
Cart | Verbal Cart Verbal Cart Verbal | Cart Verbal
Adjustment | Report | Adjustment | Report | Adjustment | Report | Adjustment | Report
548.6 tm, 3147 04.2, 295.9 288.9 398.8 426.4 302.3 ATS
182.9 cm. 1516 *} 133.9 152.2 136.2 173.7 1717 176.5 187.2
: Medians

sis.e cm. 338.4 221.0 322.6 213.4 423.1 301.0 403.2 301.0
182.9 cm. 153.7 118.1 158.0 118.1 1763 160.0 1798 160.0

*



g
B
e
z
a
F

alley. The red card
was monocularly observed (with the right eye)
and its apparent distance position in the alley
was clearly seen by the interposition of its
bottom edge with the alley floor, By turning a
knob with his right O could move the
cart along the track and consequently could
rove, he red card in distance along the alley
to the apparent depth position of Objects e, f,
g, or h as required.

To measure the values of S’ in the binocular
configuration, a distance indicator using the
kinesthetic modality was located at the position
of O, The device consisted of two vertical rods
which O could grasp, one in each hand, The

left rod was while the right rod
could be moved lat until the ion
between the rods to O to be the same

as a designated frontoparallel distance (width)
in the binocular configuration. The At ad-
justment apparatus was not visible to O during
the width adjustments, An attached scale per-
mitted the experimenter (E) to measure the
lateral distance (S’) which O adjusted between
the rods, A similar device has been used to
Measure perceived size in studies
(Gogel, 1962a; Gogel, 1962b). From the visual
angle (@) of the width being perceptually du-
plicated and the obtained adjustment (S’), the
ratio S’/@ could be computed. ‘

The apparent depth within the binocular
configuration (the appargnt depth from the
rectangles to the half-circles) was also meas-

ured by means of the hand ad it ap-
paratus, The Os kinesthetically ad; the
laterial distance between thé rods it ap-
peared equal to the designated depth interval
in the binocular configuration.

OBSERVERS “4

Ten men gnd six women were used as Os.
Each O had a stereoscopic acuity of at least 18
seconds-of-arc as measured with the Keystone
Multi-Stereo Test. A§ a consequence of a pre-
liminary test, several potential Os were not

used in the iment because they saw some
portion of the binocular configuration imbedded
in the surface of the panel.

PROCEDURE

To determine that O saw the alley as extend-
ing away from himself in distance, a white
(monocularly observed) target, 7.6 em. wide
and 20.3 cm. high, was presented vertically on
the floor of the alley at randomly presented dis-
tances of either 140, 235, 330,

zB
g
g
8

&
g
g,
&
i
Ry
Fe

verbal

white target from himself. During
cedure, the striped panel was located at its
position. Following these adjustments,
white target was removed and the front
was lowered, eliminating the view of the
The binocular stimuli were tumed on
checked to determine that he saw all four ob-
jects of the binocular stimulus (e, f, g, and h)
with each eye. The front curtain was raised
and O was asked to adjust the lateral distance
between the inner edges of the rods of the hand
adjustment apparatus until it seemed to be the
same physical size as the extent between either:

(1) the inner edges of the half-circles (a
judgment of width, S’.) or;

(2) the inner edges of the rectangles (a
judgment of width, S’,.) or;
(3) the depth between the left half-circle
and¢the left rectangle (a judgment of
. depth, d’) or;

(4) the depth between the right half-circle

and ight rectangle (a jud t of
rae ke gle (a judgmen

For a particular position of the panel and a
particular O, all judgements of width (or depth)
were completed before proceeding to the judg-
ments of depth (or width).

Thus, each O used the hand adjustment ap-
paratus to make two width and two depth
judgments for each of the two positions of the
panel. Each O repeated each width or depth
judgment three times. The starting position

E
Bees

B.
°

5


The Alley

As illustrated by Fig. 1, Objects e’, f, g’, and
h’ appeared to be located in an alley which ex-
tended away from O in distance. The floor of
the alley (48 ft. long and 4 ft. wide) consisted
of a checkerboard pattern of light and dark
grey rectangles (8 inches wide and 16 inches
Tong). The alley was illuminated by a series
of overhead fluorescent lights extending the
length of the alley. The sides of the alley were
formed on the right by white curtains and on
i, left by a, wall covered with white cloth

and jects in alley except
Objeat f, g, and h were observed mono-
cularly, This was accomplished by opaquing
the back surface of that portion of the mirror
which was in front of the left eye of O. The
mirror was a first surface mirror which both
reflected and transmitted light. This enabled
O to view Objects e, f, g, and h with both eyes
while viewing the alley with his right eye only.
Care was taken that the left eye of O was in
darkness except for Objects e, f, g, and h.

To remove extraneous light, the viewing posi-
tion of O was enclosed in black velveteen and

‘a small black tube extended from the left eye

of O to the vicinity of the left half of the
mirror, To eliminate the accommodative cue
between objects in the visual field, O viewed

- the entire scene through two pin hole apertures

(.05 cm. in diameter) located very close to his
eyes, When a small black curtain in front $f
the viewing position was lowered; the view to
the monocularly observed alley cut off
without disturbing the ability to see the binoc-
ular stimuli, An adjustable chin rest was lo-
cated at the viewing position of O and a light
adaptation surface, (51 ft.—L.),! which could
be turned on or off by the experimentet (EY.
was located to the left of the viewing position.
To make the constant binocular configuration
appeas in different portions of the monocularly
ol alley at different times, a monocularly
observed panel consifting of diagonal black
and grey stripes was vertically presented at
either 182.9 or 548.6 cm. from, O in the alley.
two alternate positions of the panel are
lustrated as A and B of Fig, 1, It was antici-
pated that the binocular configuration would

appear to O to be closer to himself (in a less
distant portion of the monocularly observed
alley) when the panel was in position A rather
than in position B, Since some amount of
frontoparallel size constancy would be ex-
pected to occur in the alley, the different dis-
tance positions in the alley would be expected
to have different values of S’/8. The process
by which the panel would make the binocular
configuration appear to change in distance posi-
tion in the monocularly observed alley is called
the “equidistance tendency” (Gogel,. 1956).
This is the tendency for objects to appear. equi-
distant unless restricted by the of ef-
fective depth cues. It is clear that, except for
the equidistance tendency, there was no reason
why the binocular configuration would appear
at one distance rather than another in the alley.
The only factor other than the equidistance
tendency available for localizing the binocular
configuration in apparent distance was the
convergence of the eyes required for binocular
fusion, But, it has been demonstrated that this
cue is usually ineffective in establishing a per-
ceived distance (Gogel, 1962b). Thus, the
equidistance tendency would be expected to be
effective between the binocularly observed ob-
jects and the monocularly observed panel with
the result that the binocular configuration
would appear to be at the distance vicinity of
the panel.

Measurements of Apparent Size and Distance

Three types of psychological measurements
were required in this study. It was necessary
to determine (1) that the change in the posi-
tion of the panel’ effective in inducing a
change in the apparent "position of the binocu-
lar configuration (Objects e’, f, g’, and h’),
(2) that concomitant with the change in ap-
parent position of the binocular configuration,
the value of S'/@ associated with the fronto-
paralle] extents of the binocular configuration
also changed, and (3) that the apparent depth
within the binocular configuration changed in
agreement with the change in S’/0.

The measurement of the apparent depth posi-
tion of Objects e’, f, g’, and h’ was accom-
plished by using the track and cart (see Fig. 1).

-4-


repeated. With half the Os, the panel was
presented first at the near position ‘and then at
the far position, With the remaining Os, the
order of presentation was reversed,

RESULTS

Figure 2 contains the average results ex-
pressed in centimeters obtained from the
adjustment of the red card to the apparent dis-
tances of the white et and from the verbal
reports of the distances white target, It
is clear from Fig. 2 that the alley appeared to
extend away from O in distance and that in-
creasing values of cart adjustment or verbal
reports represent increasing values per-
ceived distance.

The mean and median results in centimeters
for the hand adjustments are given in Table 1.
The measurements of perceived depth between
the left and right pairs of binocular objects
have been averaged in the d’ data of Table 1.
For two Os, the. perceived depth within the
binocular configuration was greater than could
be measured with the hand adjustment appara-
tus. These two Os were asked to perceptually
duplicate only 3/3 of the magnitude of each
extent within the binocular configuration and,
therefore, the results from these Os were mul-
tiplied by three to arrive at the values which
would be expected to occur if these Os had
been able to make the apparent duplications

«

‘

directly. Some of the distributions of hand ad-
justments are skewed positively. For each
position of the panel, the width adjustments in
Table 1 are separated into the adjustments
measuring the perceived width between the
half-circles (S’.) and the adjustments measur-
ing the perceived.width between the rectangles
(S’s). The values of width adjustments were
transformed into S’/@ by dividing each value
of S’ in Table 1 by the constant value of @
(2°57’). The S’/@ value for the 548.6 cm, posi-
tion of the panel is 1.30 and 1.53 cm. per degree
for the width between the half-circles and the
rectangles, respectively. For the 182.9 cm.
position of the panel, $’/@ is 1.07 and 1.18 cm.
per. degree for the width between the half-
circles and the rectangles, respectively, The
six distributions of scores whose means are
iven in Table 1 were converted to common
ithms, The differences between the aver-

age logarithms'‘paralleling the mean differences
listed in Table 1 all proved to be statistically
significant using the ¢ test at the .01 level. It is
clear that some amount of frontoparallel size
constancy was present in this experiment. Also,
Table 1 indicates that the perceived depth with-
in the configuration of binocular objects in-
creased as the value of S’/@ increased, The
change in depth between the rectangles and the
half-circles occurred in spite of both the binoc-

TABLE! 1

’ DEPTH AND WIDTH ADJUSTMENT IN CENTIMETERS

AS A FUNCTION oF THE APPARENT

ION OF THE

iv’ CONFIGURATION '

Distance Depth Adjustments Width Adjustments (S’)
Eoeition id Bet. Half-Circles (Sz) | Bet. Rectangles (5'a)
+. Mean Median Mean Median Mean Median
548.6 cm. 68.2 42.1 38.4 37.0 45,3 37.0
. | 182.9em, 378 26.0 315 313 34.8 23.2
. Difference 30.4 16.1 69 57 105 138

-~7-



RES!

AD 429 827

THE PERCEPTION OF DEPTH FROM
BINOCULAR DISPARITY

63-10

Sa,

FEDERAL AVIATION AGENCY
AVIATION MEDICAL SERVICE
AEROMEDICAL RESEARCH DIVISION
CIVIL AEROMEDICAL RESEARCH INSTITUTE
OKLAHOMA CITY, OKLAHOMA

“PEPRODUCED BY
NATIONAL TECHNICAL
INFORMATION SERVICE

‘BS. DEPARTMENT OF COM
‘SPRINGFIELD, VA. maa

MAY 1963
\


+"

KN. AN, Precision and validity of
mage from double images. J. Opt. Soc, Amer., 1!

Soe ame, 188,

Gogel, W. C. The visual perception of size and distance. i
cw td Ree Leb Rap, 1962, Oklahoma City, No. (Boh eres ons Cy of oe, VL, Now Yo
€2-18.(c). McGraw- :

‘ of depth. In \

Lichten, W. and Lurie, S. A new technique for the Halbolt ir Tbeotas “pheiobcieal Sieh al ih !
study of perceived size. Amer. J. Paychol, 1980, 63, PC. Southall, Ed.) Mensha, nook 1h
280-282, 368-400, !

i
5,
L i
‘ 7 .
i
! ‘
' / \ bt
/
‘ ,
e
3
C0
-10- ‘8 UM GOVERNMENT PRINTING OFFICE : 1963 0 - 116-027


¥

In Equation 2, two factors in addition to the
individual constant C are important in the de-
termination of d’. One factor is the value of
binocular disparity «,— a, where a, and are
the convergence values of the eyes to the near
object (e) and the far object (f) producing the
disparity. The other factor is the variation in
S'/@ between the convergence limits « and a,
of the eyes. Equation 2 is designed to apply
to situations in which the convergence value
(@,) to the nearest binocular object in the
binocular configuration specifies the apparent
distance position of this object in the field-of-
view. This does not imply that the convergence
of the eyes is considered to be an effective
distance cue. An object in a binocularly
observed field will appear at the distance of
that object in the field with respect to which
it has. zero amount of binocular disparity.
Geometrically, this is equivalent to stating that
the two binocular objects will appear at the
same distance when the convergence value of
one equals that of the other. In the present
study, the visual field was monocularly ob-
served except for the binocular configuration,
and only the equidistance tendency was avail-
able to perceptually localize the binocular con-
figuration in depth, Therefore, Equation 2° is
not in a form which can be applied directly to
the present study. A consideration of Equa-
tion 2 does serve to illustrate, however, that
Equation 1, while valid for small depth inter-
vals, can be expected to predict the direction
but not necessarily the magnitjlde of the
changes in perceived ‘depth (d’) which oc-
curred as a consequence of the changes in S’/0
in the present study. ,

The present experiment demonstrates that
the perceived depth resulting from a ‘constant
binocular disparity can’ differ depending upon
the portion of the field-of-view inwhich the
binocular configuration appears, This phe-
nomenon is attributed to the different values
of S’/@ in different parts of the visual field.
However, both the perceived absolute distance
of the binScular configuration and the S’/é
values within the configuration changed for the
two positions of the panel. But, from previous
evidence (Gogel, 1960a), it is concluded that
the change in the perceived size per unit of

frontoparallel size (S’/@), not the change in
perceived absolute distance, is the significant
variable,

The present study asserts the importance of
so-called “monocular cues” upon the depth per-
ception resulting from binocular cues. Many
cue systems affect S’ and, through S’/0, affect
the perception of depth from binocular dispar-
ity. Thus, the monocular cues, to the extent that
they determine S$’, also determine the perceived
depth associated with a particular binocular
disparity, This statement is not equivalent to
the truism that a variety of cue systems con-
tributes to the perception of depth, The as-
sertion is that the perceived depth from binocu-
lar disparity is not predictable unless the per-
ceived size per visual angle of frontoparallel
size (S'/@) in the depth vicinity of the dispar-
ity is known, Except in the case of zero
amount of size constancy, the value of S’/6 will
differ for different distances in the visual field.
Unless the values of S’/@ are known, the per-
ceived depth from a binocular disparity in any
specified part of the visual field cannot be pre-
dicted, It is clear from the present study that
the amount of size constancy present and the
magnitude of the perceived depth between bin-
ocular objects are interrelated phenomena and
a theory of binocular vision is incomplete unless
it provides for this interrelation,

REFERENCES
Fr 7, G. A. Visual perception of space. Amer. J. Optom.,
1950) 97, 531-553.
Gogel, W. C. The tendency to see objects i
disaster “tata spun,
~aychol. Monogr., 1986, 70, No. 4,-(whole No. 411).

Gogel, W. C. An observer constant in the perception of
stereoscopic depth. U.S. Army Med. Res, Lab. Rep. 1958,
Fort Knox, No*3#6. (a).

Gogel, W. C., The effect of convergence and angular
size uy the com; value of a hypothetical observer
constant in binocular vison, US, Ano Mea Ree tan
Rep. 1958, Fort Knox, No. 372.(b).

Gogel, W. C. Perceived frontal size as a determiner of
; binocular depth. J. Pryohol., 1960, 50, 119-131.
a).

Gogel, W. C. The of shape from binocular
disparity cues. J. Peychol, 1900, 50, 178-102.(b).

Gogél, W. C. The of a depth interval with
binocular disparity cues. J. Peychol., 1860, 50, 257-260.(c).

Gogel, W. C. determiner of perceived
abecld’ 06.7, Popol teeet Setter of

~9-


600 -
no
a
be 500
uJ
=
Fe
ig 400
oO
2
uw 300;
oO
<
Ee
 200f--
a.
a
Wi
@ 100 @—@ CART ADJUSTMENTS
2 yO-—O VERBAL REPORTS
0 pit po ! J

100 ;200 ,300 400 500 600
, / ten 4
PHYSICAL bistANcE IN; CENTIMETERS.

Ficuma 2, The relation between behavioral and physical distance in the alley.
a

for the Minds for these adjustments (hands to-
gether or hands far apart), was systematically
varied. Following each set of three width or
depth judgements, O adjusted the red card to
the distance of each of the {wo binocular ob-
jects*involved in the particular judgment, ve

ally estimated in feet the distance to each
binocular object, and turned to look at the

light adaption surface which was turned on by
E for approximately 10 sec, After completing
the width and depth judgments for one posi-
tion of the striped panel, O adjusted the red
card to the distance of the panel, and verbally
estimated this distance from himself in feet.
Following this, the striped panel was moved to
the second distance and the judgments were

*


The hypothesis used in the present study to
explain the perceived depth resulting from a
binocular disparity is based upon the demon-
strated ability of O to equate the perceived
depth from a binocular disparity to the per-
ceived size of an adjacent front: extent
(Gogel, 1958a; Gogel, 1958b; Gogel, 1960b).
It is asserted that the perceived depth associ-
ated with a binocular disparity depends upon
the perceived size associated with adjacent
frontoparallel extents (Gogel, 1960a; Gogel,
1960b; Gogel, 1960c). This is an example of
what has been termed the “adjacency principle”
(Gogel, 1962c). The perceived depth interval
which results from a particular binocular dis-
parity is determined by the perceived fronto-
parallel size (S’) at the distance of the objects

producing the binocular disparity. More spe-
cifically (Gogel, 1962c}’,
SY Aa
ada] € (1)

>

where Aa is a small amount of binocular dispar-
ity, Ad’ is the perceived depth interval which
results from Aa, and S’ is a perceived size of a
frontoparallel extent whose retinal size (visual
angle) is 6. The term C is a constant for a
particular O. The ratio S’/@ is the perceived
size per unit of retinal size at the distance of,
the objects producing 4a, As a ratio, $’/0 isi!
independent of any particular frontoparallel
extent and ean be applied to an entire fronto-
parallel plane.
It is evident that S’/@ usually is not constant
throughout the visual field. For example, if
perfect frontoparallel size tis present,
for a constant value of 8, S’ and hence S’/0 will
increase linearly with the physical distance
from O. It is clear, therefore: that according
to Equation 1, a t value of binocular
disparity, will produce different perceived ex-
tents when it is perceived to be in portions of
the visual field having different values of S’/8.
It is the purpose of the present experiment to
test this point of view. Objects. producing a
congfant value of binocular disparity will be
made to appear in portions of a field-of-view
having different values of S’/@, The resulting

perceived depth interval should increase as the
value of $’/9 increases.

APPARATUS
The Binocular Stimuli

A perspective schematic drawing of the
apparatus is given in Fig, 1, A binocular dis-
parity was generated by binocularly viewing a
configuration produced by two pairs of objects.
One pair consisted of two luminous half-circles
(Objects e and f) and the other pair consisted
of two luminous rectangles (Objects g and h).
The four objects (e, f, g, and h) were physi-
cally located to the right of O (see Fig, 1).
Light from these objects passed through a black
tunnel and was reflected from a mirror into the
eyes of O, The result was that O perceived
the objects to be in front of himself instead of
at their actual locations. The perceived posi-
tions of Objects e, f, g, and h are given in Fig. 1
as e’, ?, g’, and h’, respectively.

As is illustrated in Fig, 1, Objects e, f, g, and
h were formed by placing a fluores-
cent source of light (94 ft. —L.) behind ap-
propriate apertures, (cf. Lichten & Lurie 1950),
Care was taken that no light from the portion
of the apparatus producing Objects e, f, g, and
h was visible except that from the objects.
Both Objects g and h (the luminous rectangles)
were vysicalh 277.2 cm. from O while both
Objects e ‘and f (the luminous _half-circles)
were physically 252.0 cm, from O, The half-
circles were always higher in the visual field
(by 30 minutes of vigual angle) than the lu-
minous rectangles. For the average inter-
pupillary distance of the Os used in this study
{6.46 cm.), the binocular disparity between the
/pair of luminous rectatigles and the pair of

/ half-circles was.477 seconds-of-arc. The height

and width of Objects g and h subtended. visual

,

“Originally, (s00 1960b), the terms As’ and E were
in Equation 1 instead of the 4 d’ and S’, respec-

tively, of present study. The associated
Wit the forme? teoas LowSver see dente to tens

the present study.

~2-

=


~@—- ——

THE PERCEPTION OF DEPTH FROM BINOCULAR DISPARITY!

WALTER C. GOGEL, Ph.D.

’

One of the cue systems used in! the percep-
tion of the depth between objects is the cue of
inocular disparity. jpurpose of the pres-
ent study is to demonsteste the factor which
determines the perceived depth interval which
will result from the presence of a icular
binocular disparity for a p observer
(O). As has been pointed out (seg Von Kries
[1925] for example), a constant binocular dis-
parity will not necessarily be perceived by O
as producing the same depth interval at differ-
ent distances from himself, It follows that the
perceived extent associated with the binocular
disparity is Shot determined exclusively by the
magnitude of the. binocular disparity. Some
factor which varies as a function of the distance
from O must be involved in the process of
translating the binocular disparity to a per-

ceived depth extent. Two such factors which
have been considered are (1) the convergence
of the eyes, and (2) the perceived distance
from O of the objects producing the binocular
disparity (see Fry, 1950; Ogle, 1953; Ogle,
1959; Von Kries, 1925). However, evidence is
available agltiinst each of these possibilities
(Gogel, 1962e) and a different explanation will
be used in the present study.



Yo THE PERCEPTION OF DEPTH FROM

BINOCULAR DISPARITY ,

| (OO d, WALTER C. GOGEL, 2bD—

: Chief, Sensory Psychology Section
PSYCHOLOGY BRANCH

63-10

D
e FEDERAL AVIATION AGENCY
AVIATION. MEDICAL SERVICE
AEROMEDICAL RESEARCH DIVISION
CIVIL AEROMEDICAL RESEARCH INSTITUTE
OKLAHOMA CITY, OKLAHOMA,

MAY 1963

N