seemed to be the same as the apparent right-left
extent of the object. This adjustment was com-
pleted twice for each of the objects of the pair.
This total process, except for the ten minutes in
the dark, was repeated for each pair of familiar
objects.

Ill. Results.

The angular sizes (0) of the five familiar ob-
jects are given in Table 1 together with the
simulated sizes (S) and distances (D) of the
objects.

Taste 1, Average Perceived Size 8’ and Perceived Dis-
tance D’ resulting from Objects of Visual Angle
@ and Simulated Width and Distance 8 and D.

@ (rad) D (cm) S (em) D’ (cm) 8’ (cm)
Crest 0428 299 12.8 159 10.3
Drops 0428 284 10.0 126 91
Tape 0578 128 TA 86 78
50¢ 0845 87 3.0 81 53
Key 4.0855 63 54 66 78

The simulated sizes are the widths (left-to-
right extents) of the real objects when oriented
as in the transparencies, and the simulated dis-
tances are the distances from 0 at which the ob-
jects would have to be placed to subtend the par-
ticular angular size (@ in rad. = S/D). The
value of D’ is the average reported distance,
converted to centimeters, at which O perceived
the object to be from himself. The value of 8S’
is the average reported size (width) of the ob-
ject, as determined by using the hand adjustment
apparatus. From Table 1, 8 and 8’ are similar
except in the case of the half dollar and key.
However, D and D’ are only similar for the

smaller values of D. As D increases, D-D’ in-
creases until at a D of approximately 3 meters,
D’ is only about half the value of D.

The relation between average values of S’/0
and average values of the reported depth (d’)
between the objects of a pair is given in Table 2
under “Obtained Values.” The average values
of 8’/@ for each object are shown in the outer
column and upper row. The average values of
d’ are given to the right or below the object
names, with each value of d’ being the average
reported depth between the pair of objects com-
prising that column and row. Each value of d’
is the average of 20 scores, oné from each O,
with each score being the average perceived
depth between the two objects with their right-
left positions systematically reversed. Table 2
is arranged to allow examination of the validity
of the hypothesis that the perceived depth be-
tween the objects is determined by the magnitude
of the difference of the 8’/@ values of the ob-
jects. The objects are arranged in the left half
of Table 2 so that the value of S’/@ increases
from left to right and from top to bottom. If
the above hypothesis is correct, all the values of
d’ within the left half of Table 2 should be posi-
tive and should decrease from left to right and
from bottom to top. Nine of the ten values of
d’ are positive, and the tendency for these values
to change in the expected directions is clear.
The data in the left portion of Table 2 can be
summarized as follows: (1) In general, the fa-
miliar object appearing to be more distant had
the greater value of S’/0; (2) the greater the

Taste 2, Average Values of Perceived Distance @’ (in Centimeters) between Objects Whose Average Values of Per-
ceived Size 8’ (in Centimeters) Per Unit of Visual Angle 9 (in Radians) are Shown in the Column and Row
Headings. The Physical Size § (in Centimeters) and Visual Angle 9 (in Radians) of the Familiar Object and the
Physical Depth d (in Centimeters) between the Objects Simulated in the Experiment are Shown in the Right

Portion of the Table.

Obtained Values

8/9 88 134152
8'/9 Object Key ‘Tape 50¢ Drops
o
134 Tape 26
Pa
152 5O¢ 22 6
a
221 Drops 65 87 46
a

239 Crest 89 7 68 385

Simulated Values

S/O 63 87 128 234

8/6 Object Key 50¢ Tape Drops
a
87 50¢ ot
a
128 Tape 65 41
a
234 Drops 171 “47 106
ad

209 Crest 236 212 im 65





drops, a half dollar, a small Scotch Tape dis-
penser, a door key, and a small tube of Crest
toothpaste. All of the objects were photographed
with their largest side frontally oriented with
respect to the camera. The objects were photo-
graphed against a black background so that only
the image of the object was transparent. The
transparencies were mounted in front of light
boxes consisting of diffusing surfaces homo-
geneously transilluminated by flourescent lamps.
The luminances of the sources were adjusted to
match the relative luminances of the real objects
from which the transparencies were made. The
relative luminances of the real objects were
measured while using a diffuse white illumina-
tion at a constant distance from all the objects.
When mounted on the light sources, the values
of the most luminous parts of the transparencies
were 1.2, 1.0, 0.6, and 0.6 ft.-L for the half dollar,
tube of toothpaste, box of cough drops, and key,
respectively. The most luminous area of the
tape was too small to be measured with the
available photometer. The stimuli were always
presented in pairs in a frontoparallel plane 1.33
meters from 0’s eye with the centers of the two
images of each pair always separated by 23.3 em.
(10°) and centered with respect to the median
plane of the right eye. A +.75 diopter lens
“ mounted in the right eyepiece optically placed
the photographs at an infinite accommodative
distance from 0. The observation was always
monocular (right eye only). Considerable care
was taken to eliminate all extraneous illumina-
tion so that the stimuli appeared to O to be real
objects presented in an otherwise totally dark
visual field. A head and chin rest were located
at the observation position, with the observation.
position enclosed in black cloth so as to eliminate
any extraneous light. Communication between
the experimenter (Z) and O occurred by means
of speakers and microphones. A continuous
masking noise was presented to O except when
£ was communicating with him. A shutter po-
sitioned in front of the viewing aperture per-
mitted Z to change the stimuli without being
observed by O. A contact relay on the head
rest insured that O’s head was properly posi-
tioned for the observation. A light adaptation
surface”, located to O’s left, was designed to
provide a homogeneous visual field with a bright-
ness of 15 ft.-L, which was activated only when

O’s head was appropriately placed in the adapta-
tion apparatus.

A hand adjustment apparatus was used by O
to indicate the perceived size (S’) of the stimulus
objects. The apparatus consisted of two vertical
square rods (1% in. thick) located at the level of
O’s waist. The left rod was fixed, and the right
rod could be moved laterally. A meter stick
was attached to the right rod to measure the
amount of separation of the inner edges of the
rods. Verbal reports were used to measure the
perceived distance to the objects and the per-
ceived depth between them.

Procedure. Twenty men served as Os. All
Os were between the ages of 18 and 35 years
and had at least 20/20 acuity with their right
eye as measured at both the near and far points
using the Bausch and Lomb Orthorater. The
five stimuli were presented in pairs, with each
stimulus equally often on the right and left. The
resulting 20 pairs were presented in a balanced
Latin Square: design? with a different sequence
of pairs used with each O.

The instructions to O emphasized that apparent
judgments were to be made with respect to both
size and distance. A previous study had indi-
cated that when instructed to make judgments
of the apparent size of a familiar object in an
otherwise dark visual field, some Os made angular
size judgments, possibly with respect to an arbi-
trary distance.’ Since apparent size judgments
were required in the present experiment, this
problem was avoided by showing O a simple
diagram which illustrated the difference between
judgments of apparent and angular size. After
the instructions, O sat for ten minutes in the
totally dark observation booth, looked into the
light adaptation surface for 30 seconds, and
then positioned his head in the observation posi-
tion. Following this, the shutter was raised re-
vealing the pair of familiar objects.

According to a balanced order, for each pair
of objects, O reported in feet or inches, or in
some combination of both, the apparent distance
of one of the two objects from himself. O indi-
cated which, if either object appeared to be more
distant and reported the perceived depth between
the objects (again in feet or inches or a combi-
nation of both). Following this, 0, using the
hand adjustment apparatus, adjusted the dis-
tance between the rods until this lateral distance


difference between values of S’/6, the greater,
in general; was the perceived depth between the
familiar objects.

The right portion of Table 2 specifies the
physical (simulated) size per unit of retinal size
8’/8, and the physical (simulated) depth d be-
tween real objects which would be required when
using actual objects (not photographs) in order
to produce the visual angles of the stimuli. It
is clear from Table 2 that, although the S’/@
and S/6 values were reasonably similar, the d’
values were often considerably smaller than the
d values, particularly at the larger values of d.

The left portion of Table 2 indicates the im-
portance of relative values of S’/@ in determining
the perceived depth between two familiar objects.
It will be noted, however, that the form of the
relation between relative values of S’/@ and d’
has not been specified. One possible expression
of this relation can be obtained from the size-
distance invariance hypothesis? which states that

S’=KoD’ (1)
where D’ is the perceived distance to the familiar
object of retinal size (visual angle) @ and per-
ceived size S’ and K is an observer constant.
It follows from Equation 1 that

1 s’ s’
@y=—( -t 2
mH E(4-F) @)
where e and f refer to the two objects whose
separation in depth is being judged and

d’=D’;—D’.2 In order to test Equation 2,
the average perceived depth (d’) between the
two objects of a pair was determined and re-
lated to the average (algebraic) difference be-
tween the S’/@ values for the two objects of the
same pair with the smaller value of S’/@ always
subtracted from the larger. The Pearson pro-
duct-movement correlation coefficient between.
8’:/0:—S’-/0e and det is .81, which is significant
beyond the .01 level (¢=3.91). Values of » were
also computed for the data from each O. The
average value of 7 (.54) was significant at the
.01 level (t=7.24). But, it should be pointed
out that large individual differences sometimes

occurred in the 7 values (o,=.33) with a range
of r from —.42 to 94.

IV. Discussion.
The results from this experiment clearly sup-
port the view that in the absence of other depth

cues, the occurrence of different values of 8’/0
between two objects is a sufficient condition for
the perception of depth between the objects with
the object having the larger value of S’/6 being
perceived as the more distant object. It follows
from this experiment that it is neither the dif-
ference in perceived size nor in retinal size which
defines the significant variable in the size cue to
depth, but rather the change in perceived size
per unit of retinal size (visual angle) between
the objects. The size cue to relative distance
occurs, therefore, between irregularly as well as
regularly shaped familiar objects. It is probable
that it occurs between any objects which have
perceived sizes regardless of their shape or
complexity.

It appears from the significant correlation co-
efficient between d’ and differences in S’/6 that
Equation 2 is at least consistent with the obtained
results. This does not mean, however, that the
perceived distances D’ and d’ are necessarily
veridical, i.e., are similar to D and d. The per-
ceptions of depth tend to be correct only for the
smallest values of D and d with the perceptual
error (defined by D-D’ or d-d’) increasing with
increases in D and d. Clearly A in Equations 1
and 2 is not unity.

It will be recalled that D’ and d’ were deter-
mined by separate judgments. Nevertheless, the
perceptual errors in D’ and d’ are closely re-
lated. This can be seen by comparing the average
obtained d’ with the d’ values obtained by sub-
tracting the-appropriate values of D’ from each
other. It appears that Os on the average are
consistent in their judgments. For example, if
one object of a pair were perceived to be at 5
feet and the other at 3 feet, the perceived depth
between them as directly indicated by a separate
report would tend to be 2 feet.

The results from this experiment lend support
to the notion that the use of a comparison field
or comparison objects can invalidate the result-
ing measurement of the perceived distance to
objects or the perceived depth between them.
If each object is perceptually localized in the
comparison field by 8’/6 differences occurring
between the experimental objects and the objects
in the comparison field, it would be clear that
the perceived depth in the comparison field is
determining, not measuring, the perceived dis-
tance to or between the experimental objects.

Generalizing the results from the present ex-


AM 67-20

PERCEIVED DEPTH BETWEEN FAMILIAR OBJECTS

Walter C. Gogel
and
Henry W. Mertens

Approved by Released by
e
Billi PU age mo
J. Roserr Ditxz, M.D. P. V. Srecen, M.D.
Cuter, Civin AEROMEDICAL Feperay Arr SuRGEON
Insrirure

August 1967

FEDERAL AVIATION ADMINISTRATION
Office of Aviation Medicine



periment, it follows that familiar size is a ubi-
quitous cue to exocentric depth. It occurs be-
tween any objects or any parts of objects of any
size or shape whenever these objects have per-
ceived sizes. Usually this cue system is studied
in the laboratory as occurring between different
visual angles of geometrically-regular familiar
objects of the same shape. Probably, regularly-

shaped similar objects are used because of the
difficulty in specifying or comparing the visual
angle 6 of irregularly or differently shaped ob-
jects. The concept that 8’/@ is the significant
factor in the familiar size cue to exocentric dis-
tance both avoids this problem and asserts that
the size cue to exocentric depth can occur between
objects in a wide variety of situations.

REFERENCES

1, Epwarps, A. L.: Experimental Design in Psycho-
logical Research. New York, Rinehart and Com-
pany, 1960.

Epstein, W., & Baratz, 8. 8.: Relative size in iso-

lation as a stimulus for relative perceived distance.

J. exp. Psychol., 67, 507-513, 1964,

3. Gocer, W. C.: Size cue to visually perceived dis-
tance. Psychol. Bull., 62 :217-285, 1964.

4, Gocer, W. ©.: The measurement of perceived size
and distance. In Contributions to Sensory Physiol-
ogy, 1968, W. D. Neff, Editor (to be published).

5. Goer, W. C. & Mertens, H. W.: Problems in depth
perception: Perceived size and distance of familiar
objects, Federal Aviation Agency Report AM 66-22,
1966.

BR

6. Hocusere, C. B. & Hocuerc, J. E.: Familiar size
and the perception of depth. J. Psychol., 34:107-114,
1952.

7. Hocuserc, C. B., & Hocusere, J, E.: Familiar size
and subception in perceived depth. J. Psychol.,
36 1341-345, 1953.

8. Hocuere, J. E. & McAtister, E,: Relative size vs.
familiar size in the perception of represented depth.
Amer. J. Psychol., 68 :294-296, 1955.

9, Kiuparricx, F. P. & Irrerson, W. H.: The size-
distance invariance hypothesis. Psychol. Rev.,
60 :223-231, 1953,

10, Mertens, H. W.: A homogeneous field for light
adaptation, Federal Aviation Agency Report No.
AM 66-38, 1966.



Qualified requesters 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


Perceived Depth Between Familiar Objects*

I. Introduction.

If two luminous rectangles of the same shape
but with different retinal sizes are viewed mono-
cularly in an otherwise dark room, the retinally
smaller rectangle will be perceived to be the more
distant rectangle. This is an example of the
relative size cue to the perceived depth between
objects, with the perceived depth between objects
being termed a perception of exocentric distance.*
The rectangles in this case are nonfamiliar ob-
jects in the sense that there is no reason why
they should be perceived as having one size
rather than another. If the rectangles are pat-
terned, however, so as to appear as familiar ob-
jects, for example, as playing cards, they will
have a perceived size which, it would be expected,
would be the same as the physical size of a play-
ing card, and again the card with the smaller
retinal size would appear to be the more distant.
This is an example of the familiar size cue to
perceived exocentric depth. The similarity of
these two cases raises the question as to whether
the exocentric distance cue of familiar size can
be subsumed under that of relative size.”
This is answered in the affirmative in a study by
Hochberg and Hochberg* in which it was found
that the perceived depth between different kinds
of similarly shaped familiar objects was deter-
mined by the retinal, not the assumed, sizes of
the objects. Epstein and Baratz? (Experiment
IZ), however, came to a different conclusion. In
this latter experiment the perceived depth was
measured between objects representing a dime,
a quarter, and a half dollar, presented in pairs.
Each coin subtended three possible retinal sizes
so that the relative and familiar size cues could
be placed in agreement or in opposition. The
results of this study indicate that the perceived
depth between the pairs of coins when the two
cue systems were in opposition was in agreement

*The authors wish to thank John J. Coyle Jr, for
his assistance in analyzing the data of this study. Dr.
Gogel is now at the Department of Psychology, Uni-
versity of California, Santa Barbara, California.

with familiar, not relative, size. Recently, it has
been asserted after reviewing the evidence’, that
the familiar size cue cannot be subsumed under
the relative size cue but that both can be sub-
sumed under the concept of perceived size S’ per
unit of retinal size (visual angle) 6 of the object.
Specifically, it has been asserted that in the ab-
sence of other distance cues, two objects which
have the same values of $’/6, will appear equi-
distant. If the two objects have different values
of §’/0, the object with the largest value of
8’/6 will appear to be the more distant object.

An advantage in defining the size cue to exo-
centric distance in terms of the S’/@ values of
the several objects is that the ratio S’/@ can be
applied to objects of irregular as well as of regu-
lar shape.* For example, suppose that an ir-
regularly shaped object such as a door key is
presented in a plane frontoparallel to the ob-
server (O). According to the above discussion,
since all parts of the key appear to O to be equi-
distant, all parts of the key should have the
same value of S’/@. If the perceived size of any
portion of the key and the 6 value of this same
portion of the key are known, the value of 8’/6
for all the key is determined. It follows from
this definition of the size cue to exocentric dis-
tance, that this cue will occur between any fa-
miliar objects regardless of their irregularity and
differences in shape and indeed between any ob-
jects for which S’/6 values can be specified. The
purpose of the present experiment is to test the
hypothesis that the perceived depth between two
familiar objects of different retinal and perceived
sizes will differ when the 8’/6 values of the ob-
jects differ, with the object having the larger
8’/9 appearing to be the more distant object of
the pair.

Il. Method.

Apparatus. Five photographic positive color
transparencies of familiar objects (centered in
314 X 4 inch slides) were used as stimuli. The
familiar objects were a box of Luden’s cough