600

500

400

300

200

100

Figure 8.

100 200 300 400 500

St_Se
OF Ge

(Data from Ittelson, 1951b, Experiment II), The relation between perceived
relative distance d’, and differences between perceived sizes per unit of retinal
sizes (S,/0, — S’,/6,) for different sizes of moving objects with d’,, measured
by using a comparison field. The terms d’,, S’, and S’, are in centimeters. The
terms 6, and 6, are visual angles expressed in radians.

—~20—


order to calculate $’/@ for this study, it was
assumed that S’ was 8.9 cm, (the height of a
normal-sized playing card). The average data
are very close to the line representing 1/K, = 1.
The filled circular data points in Figure 3 give
the average results from a control group of Os
in an experiment by Epstein (1961, Experiment
I) when playing cards of different angular sizes
were presented successively with measurements
taken of both apparent size and apparent dis-
tance. In spite of the factor of familiar size,
the cards were not always perceived to be of
the same size. Nevertheless, the data reason-
ably fit the line representing 1/K,=1 in Fig-
ure 3, From the viewpoint of the present paper
the results from both of these studies are inter-
preted to mean that the cards were perceived
to be located at those distance positions in the
comparison field at which the comparison and
experimental objects had equal values of S’/@
and that, as might be expected, perceptions of
size in the comparison field were essentially
veridical. When the perceived size S$’ of the
playing card in the experimental field differed
from that expected from familiar size, the per-
ception was in agreement with the S’/@ value,
not in agreement with familiar size. The un-
filled circular data points in Figure 3 are the
average results from the study by Epstein
(1963) in which figures of different kinds of
coins with different assumed sizes but with
constant retinal sizes were presented singly
to different groups of Os. Pinhole viewing was
used to eliminate accommodation as a distance
cue. Both the sizes and the distances of the
coins were judged, The judged size of the
coins was close to that of normal-size coins of
the particular denominations. The average data
lie near the solid line representing 1/K, = 1 in
Figure 3.

Equation 1, with a value of 1/K,=1, also
can be approximately satisfied when non-
familiar objects are used in the “thereness—
thatness” type of apparatus. This is indicated
by the results obtained with non-familiar ob-
jects in the study by Ittelson (1951c) and also
by Figure 4, The data points of Figure 4 are the
average results from an experiment in which
different discs of different colors and different
angular sizes were presented one at a time to

the same group of Os with observer judgments
made of both the sizes and distances of the
discs (Epstein, 1961, Experiment II).

It seems that the data of both Figures 3 and
4 are in agreement with Equation 1 since
essentially the data points seem to lie on a
straight line passing through the origin. But,
the data do more than satisfy Equation 1 in
general. Specifically, the data lie close to the
line specified by 1/K:=1. These results would
be expected if, as this paper asserts, the Os (re-
gardless of their intentions) were matching
S’/@ values between the experimental object
and objects in a veridically perceived compari-
son field instead of judging the absolute dis-
tances of the experimental object. Either this
interpretation or Equation 1 is adequate for all
the results shown in Figures 3 and 4, The
interpretation that the standard objects were
perceived at absolute distances, consistent with
normal-sized objects of the particular retinal
sizes, is appropriate to the triangular and open
circle data points of Figure 3, but is not relevant
to the remaining data of Figure 3, or to the
data of Figure 4.

If the use of comparison fields is not an ap-
propriate method of testing Equations 1 and 2,
and if Equations 1 and 2 are not valid, methods
of measuring perceived depth from size cues
which do not use comparison fields should give
results in disagreement with these equations.
Results from several studies pertinent to this
problem are shown in Figures 5, 6, and 7, In
Figure 5, the D’ values are the average dart
throwing and verbal reports in centimeters
from the study by Gogel, et al., (1957) in
which playing cards of different retinal sizes
were presented one at a time to four different
groups of 20 Os. The S’ values used in com-
puting S’/@ in Figure 5 are assumed to be the
height of an ordinary playing card (8.9 cm).
The line labeled 1/K,=1 again represents
Equation 1 with 1/K, equal to unity. The re-
sults from cards at different distances but sub-
tending the same visual angle are averaged in
Figure 5. The curves labeled “first presenta-
tions” give the average results from the first
presentations of the cards. These results are
concemed with perceived absolute distance.
The results from all presentations of the cards

-14-


with respect to a binocularly observed, com-
parison field. The experimental object would
appear equidistant with that object in the com-
parison field with respect to which its binocular
disparity was zero. Clearly, this result would
have no bearing on the possible relation be-
tween convergence and perceived distance.
Similarly, an experimental object with a par-
ticular value of S’/@ will appear equidistant
with that object in the comparison field which
has the same value of S’/@. This result has no
bearing upon whether familiar size is a cue
to perceived absolute distance or, more gen-
erally, no bearing upon the validity of the size-
distance invariance hypothesis (Equation 1).
Equation 1 as it applies to size cues may be
correct. But, such a conclusion cannot be made
with confidence on the basis of evidence result-
ing from the use of comparison fields. Futher-
more, there is some evidence which indicates
that, contrary to Equations 1 (and 2), the
perceived distance resulting from size cues is
not a linear function of S’/@. An hypothesis
which might be called the ratio hypothesis is
tentatively suggested (Equation 6) as meet-
ing certain requirements of the operation of
the size cue to relative depth.

If, as seems likely, the perceptual effect of
relative values of $’/@ can occur between the
experimental and comparison field, even though
the two fields are not presented simultaneously,
the specification of comparison fields becomes
more general. A comparison field is any visual
field which O has observed prior to, or simul-
taneously with, the observation of the experi-
mental object. It is also possible that a visual
field which occurs following the presentation
of the experimental object might affect the
perceptions associated with the experimental
object. This more general definition of com-
parison fields calls attention to the possibility
that the occurrence of visual fields prior to the
particular experiment can effect the perception
of the distance or the size of the experimental
object even though no comparison fields are
presented in thé experimental situation, As
mentioned previously, however, it seems reason-
able that the magnitude of the interaction be-
tween the experimental field and the compari-
son field (as defined either in the specific or

more general sense) would be a decreasing
function of the time intervals between their
occurrences.

The importance of $’/0 is not limited to the
specification of the size cue to relative depth.
It has been demonstrated in several studies
(Gogel, 1960; Gogel, 1964a) that the perceived
depth from binocular disparity varies as a func-
tion of the $’/6 values in the perceptual vicinity
of the objects producing the disparity, There-
fore, the concept of S’/@ may be the concept
which relates the binocular disparity and size
cue systems. If so, it is likely that the prev-
alent distinction between these two systems
as primary and secondary cues is inappropriate
since both cue systems are subject to the op-
eration of a common factor.

REFERENCES

Adelson, D. The relational influence of size on judgments
of distance. J. gen. Psychol., 1963, 69, 319-333.

Baird, J. C. Retinal and assumed size cues as deter-
minants of size and distance perception. J. exp. Psychol.,
1963, 66, 155-162.

Carr, H. A. An introduction to space perception. New
York: Longmans, Green, 1935.

Epstein, W. The known-size-apparent-distance hypothesis.
‘Amer, J. Psychol., 1961, 74, 333-346.

Epstein, W. The influence of assumed size on apparent
distance. Amer. J. Psychol., 1963, 76, 257-265,

Epstein, W. Effective difference in influence of relative
size on perceived relative distance. Percept, mot. Skills,
1964, 18, 383-384.

Epstein, W., & Baratz, S. S. Relative size in iso-
lation as a stimulus for relative perceived distance.
J. exp. Psychol., 1964, 67, 507-513.

Epstein, W., Park, J., & Casey, A. The current status
‘of the size-distance hypotheses. Psychol. Bull., 1961,
58, 491-514.

Gogel, W. C. Perception of the relative distance position
of objects as a function of other objects in the field.
J. exp. Psychol., 1954, 47, 335-342.

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

Gogel, W. GC. The tendency to see objects as equidistant
and its inverse relation to lateral separation. Psychol.
Monogr., 1956, 70, No. 4 (Whole No. 411). (b)

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

Gogel, W. C. Convergence as a cue to absolute distance.
J. Psychol., 1961, 52, 287-301.

—24—


object being considered, When S’,/6> S’./6.,
Object f is perceived to be more distant than
Object e. When S’,/0, = S’,/8., Objects e and f
are perceived to be equidistant and when
’/4. < $’,/8., Object f is perceived to be less
distant than Object e. It is asserted that the per-
ceived depth d’. is a function of the values of
S’/@ for the two objects. To apply the con-
cept of S’/@ to the relative size cue, consider a
situation in which the similarity of shape of the
two non-familiar objects results, for example,
in the perception that S’, = S’,. Thus, that ob-
ject in the pair of objects which has the smallest
value of @ will have the largest value of S’/0
and will appear to be the more distant object.
To apply the concept of S’/@ to the familiar
size cue consider a situation in which, for
example, two objects (¢ and f) are of the same
shape and retinal size (@,= 9) and are per-
ceived to be a matchbox and a playing card,
respectively, Since experience indicates that
a playing card is larger than a matchbox,
S’, > S’, and thus S’,/6, > S’./@,. Therefore, the
playing card (f) will be perceived to be more
distant than the matchbox (e). Familiar size
and similarity of shape are merely different
methods of determining values of perceived
size (S’), Other factors such as assumptions
(Hastorf, 1950) and sometimes, but not always,
special experience (Smith, 1952a; Epstein, 1961)
are also determiners of perceived size, There-
fore, the familiar size cue and the relative size
cue are never in opposition, It is the inequality
in the perceived sizes of the objects regardless
of the manner in which this inequality is pro-
duced which together with the retinal sizes re-
sults in a perceived depth, The concept that
the relative values of S’/0 for the several objects
determine the resulting perceived depth be-
tween the objects subsumes both the relative
and familiar size cues into one system.

When Object e¢ is of different shape than
Object f, the concept of the relative size cue
does not apply. If the objects are also familiar
objects, however, the concept of the familiar
size cue does apply. It has been asserted that
relative depth judgments using the familiar
size cue can be made under such conditions
(Ittelson, 1951c; Ittelson, 1953). This asser-
tion would also be made from the viewpoint

taken in the present paper that variations in
$’/0 between objects is the significant variable
in the perception of relative depth from size
cues, Two objects which differ in S’/@, in the
absence of other distance indicators, will be
perceived at different distances, But, the con-
cept of S’/0 is not only applicable to situations
in which the familiar objects are of the same
or similar shape. The concept of S’/@ as the
significant variable in the size cue to relative
depth will apply to irregularly shaped objects
such as trees and animals as well as to geo-
metric figures such as playing cards or circles.
The application of $’/@ to differently or irreg-
ularly shaped objects is illustrated in Figure 2.
Figure 2 illustrates three apparent frontoparallel
planes labeled e’, f’, and g’ located at different
physical distances from O. A man is pictured
as located in Plane e’, a horse and tree in
Plane f’, and a house in Plane g’. It will be
assumed that no distance cue other than that
of size is available to determine the apparent
depth between these planes and objects, Ac-
cording to the concept that $’/@ is the signifi-
cant variable in the size cue, the objects in the
different apparent frontoparallel planes are in
different apparent frontoparallel planes because
they have different values of S’/@, Also, the
objects in the same apparent frontoparallel
plane (and all portions of an object in the same
apparent frontoparallel plane) are in the same
apparent frontoparallel plane because they
have the same value of S’/0. For example,
suppose that two marks made on the trunk of
the tree in Plane f’ are separated by one degree
of visual angle and are perceived to be sep-
arated by one foot. In this case, the S’/@ value
is one foot per degree. A separation of one-
half degree of visual angle anywhere else on
the tree, or on the horse, or anywhere in Plane
f should appear to be six inches in length,
giving thereby the same value of S’/9. It fol-
lows that a constant value of S’/@ applies to an
entire apparent frontoparallel plane including
all the objects and interspaces within this plane
regardless of their irregularity, Figure 2 is
drawn to represent a situation in which the S’/@
values associated with the several apparent
frontoparallel planes is greatest for g’ and least
for e’. Hence, g’ and e’ appear respectively

-~5—



ef

Figure 9. (Data from Epstein and Baratz, 1064). The relation between perceived relative

distance d’,, and differences between perceived sizes per unit of retinal sizes
(81/0, — S“,/6,) for pairs of coins with the perceived extents measured by using
a comparison field. The terms d’,, S’, and S’, are in centimeters. The terms
6, and 6, are visual angles expressed in radians.

—21-

100



Retinal Size Ratios as Size Cues to Relative
Distance

Based upon the conclusions that perceptually
significant cues (a) involve relative rather
than absolute retinal size and (b) occur be-
tween adjacent rather than displaced objects,
it has been suggested (Gogel, 1963, p, 116)
that “ratios of 4s rather than 9s per se” are the
retinal stimuli for the relative size cue to rela-
tive depth, According to this point-of-view,
two perceived depth intervals d’. and dp
would be perceived as equal, using the rela-
tive size cue with non-familiar objects, only
when the ratios of the retinal sizes between
each pair of objects were equal. That is, as-
suming that S’, = S’, = S’,= $4,

d= da only when 4./6, = 9,/Os. (4)

Equation 4 can be contrasted with Equation 2,

with the latter stating that if S’.= S’,= S’,=S’,
d.=d', only when
1/6, — 1/0, = 1/0, — 1/4. (5)

The pairs (e and f) of retinal stimuli in-
volved in the data points labeled 1, 2, and 4
in Figure 10 produced a constant ratio of
retinal sizes 9./0, and, as shown on the ordinate,
resulted in a nearly constant value of perceived
depth d’., It was concluded by Epstein (1964)
that the results from this study support the
hypothesis that the perceived depth between
the pairs of objects was determined by the
ratio of their retinal sizes, Within the limita-
tions involved in the use of comparison fields
for the measurement of depth between non-
familiar objects, this conclusion supports Equa-
tion 4, An equation relating d’ and size cues
probably should satisfy at least the following
conditions: (1) The requirement that S’/@
is the significant variable in the size cue to rel-
ative depth; (2) The requirement that d’ is
zero, positive, or negative when S’./0. is equal
to, less than, or greater than S’,/@,, respectively;
(3) The probability that ratios of 9s rather than
49s per se are the perceptually significant stimuli;
(4) The probability that D’ is a negatively ac-

celerated function of S’/@. An example of one
of the simplest equations satisfying these re-
quirements is

Ss Silt
4

T 9/8,

(6)

where T is an observer constant. Equation 4,
for example, can be derived directly from Equa-
tion 6. It is obvious, however, that additional
research will be required, and preferably by
methods other than those using comparison
fields, before the psychophysical function of
the size cue to relative depth can be specified
with confidence.

Conciupinc Remarks

It is concluded that both perceived size S’
and retinal size 6 are involved in both the rela-
tive (retinal) size cue and the familiar size cue
to relative depth. Furthermore, it is asserted
that these two factors are the only factors in-
volved in the size cue to relative depth. When
the two factors S’ and @ are expressed as the
ratio S’/@ they can be shown to be applicable
to any objects regardless of the shape or com-
plexity of the objects. It is clear that, from
this point-of-view, size cues to relative depth
occur, for example, between a rock and a tree
as well as between two playing cards or other
symmetrical objects. The $’/0 value of each of
the two (or more) objects must be considered
in predicting the perceived depth which will
occur between them, It remains to specify the
exact relation which occurs between perceived
depth and the relative values of S’/8. The
evidence that the size-distance invariance hy-
pothesis in its usual form can specify this re-
lationship at first appears conclusive. How-
ever, much of the evidence for this conclusion
was obtained by using comparison fields for
the measurement of perceived distance. It is
asserted that the use of a comparison field in-
troduces an artifact in the measurement of per-
ceived depth from the size cue. An analogous
case would be an attempt to measure the effect
of the convergence of the eyes on perceived
distance by measuring the perceived position
of a binocularly observed, experimental object

—~23-



are given in the curves labeled “all presenta-
tions”, These latter results represent relative
distance judgments as a function of the succes-
sive presentation of the cards to the same group
of Os. It seems that none of the data curves of
Figure 5 fit Equation 1. They either seem to
be non-linear, or if extrapolated would not pass
through the origin as Equation 1 requires,

In a study by Over (1963), 4 Os made 90
verbal judgments of the size and distance of
diamond-shaped figures (squares) of different
physical sizes presented successively at yarious
distances under reduced viewing conditions,
ie., with no size or distance cues present ex-
cept the size cue between successive presenta-
tions, Following this, the same Os repeated
the judgments under unrestricted viewing con-
ditions, i.e., conditions in which many size and
distance cues were available. Since the same
Os were used for the successive presentations,
the judged distances in the reduced cue situa-
tion probably were not perceived absolute dis-
tances. However, the differences between pairs
of distance judgments can be interpreted as
representing perceived relative distances. No
perceptual scale was available under the re-
duced cue conditions and it is, therefore,
unlikely that the magnitude of any single per-
ceived relative distance was meaningful, How-
ever, changes in perceived relative distance as
a function of changes in relative retinal size
would be meaningful data. The results from
the reduced and the unrestricted viewing con-
ditions are given by the open and filled-in data
points, respectively, of Figure 6, The solid line
curve of Figure 6 again represents Equation 1
with 1/K, equal to unity. The judgments made
in the reduced cue conditions clearly are not
in agreement with Equation 1. As shown by
the dashed line curve, judgments made in the
reduced cue conditions appear to determine a
curvelinear rather than a linear function, The
judgments made under the unrestricted view-
ing conditions involved many cue systems in
addition to that of size. The data from the
unrestricted viewing conditions, as expected,
are close to the curve labeled 1/K,=1. The
unrestricted viewing data are not pertinent

when considering the function involved in per-
ceived size as a cue to distance. However, judg-
ments from the unrestricted viewing conditions
do demonstrate that the method of judging size
and distance used in the study was valid and
reliable. It follows that the curvelinearity of
the “reduced viewing” function cannot be attri-
buted to a non-linear scale inherent in the
method ‘of measurement and, therefore, the
results from the reduced viewing conditions
represent valid evidence against Equation 1
(and 2).

Average data from a study by Baird (1963)
are presented in Figure 7, The curve labeled
“Experiment II” concerns the verbal reports of
the distance of a rectangular figure designated
as the size of a 12 inch ruler. Different retinal
sizes of this figure were presented to different
groups under reduced conditions of observa-
tion, with ten Os in each group. It will be
noted that the curve labeled “Experiment II”
differs considerably from the first presentation
curves of Figure 5 and is essentially in agree-
ment with Equation 1, with 1/K,=1. The
curve in Figure 7 labeled “Experiment I” refers
to the average results from another experiment
by Baird in which different assumed sizes were
induced in a triangle of constant retinal size
by first showing rectangles of differing angular
size with each rectangle designated as being
12 inches wide. Only the results obtained un-
der objective instructions were used in Figure 7.
Size judgments were made by using a compari-
son triangle, and distance judgments were
made verbally. Most likely, the curve labeled
“Experiment I” of Figure 7 represents relative
judgments of size and distance. Since the dis-
tance judgments for the middle and small
retinal sizes were greater than the distance to
the comparison object it is likely that the com-
parison field could not completely determine
the distance judgments. Obviously the “Ex-
periment I” curve does not fit Equation 1.
Also, the “Experiment II” curve is essentially
linear while the “Experiment I” curve is not.
Experiments I and II by Baird are considered
to measure perceived relative and perceived
absolute distance, respectively. However, if

—18~—


non-familiar objects as a consequence of the
presence of a comparison field is as follows:
It is very difficult to eliminate all extraneous
factors (factors other than the cue system be-
ing studied) which can relate the depth posi-
tion of one or more of the experimental objects
with respect to the comparison field. It has
been found, for example, that the accommoda-
tive differences between the experimental and
comparison fields by itself sometimes can de-
termine the apparent depth position of the
experimental object (Gogel, 1961). Also, even
when the difficult task of completely eliminat-
ing extraneous cues is accomplished, factors
such as the equidistance tendency (Gogel,
1956b) probably would result in some localiza-
tion of the experimental objects with respect
to the comparison field. Assume that one of
the discs, or squares, or ink blots as a conse-
quence of extraneous factors will appear to be
located somewhere in depth with respect to the
comparison field. It follows that the S’/@ value
associated with this apparently equidistant por-
tion of the comparison field will become the
8’/6 value of the object. In other words, the
disc, or square, or ink blot will acquire a per-
ceived size, Then, as a result of shape identity,
the other disc, ot square, etc., (either simul-
taneously or successively presented) will ac-
quire the same perceived size. Each of the
pair of squares, etc., will thus acquire an S’/@
value and, therefore, a specific perceived rela-
tive depth. Consequently, the perceived rela-
tive depth measured between non-familiar ob-
jects using a comparison field is probably not
independent of the comparison field. If the
above explanation is correct, however, the per-
ceived depth which is measured, in this case,
probably is less contaminated by the measuring
(comparison) field than is likely in the case of
familiar objects.

Possible Relations Between Perceived Distance
and S'/6

An Application of the Size-Distance Invariance
Hypothesis

A conclusion of this paper is that the per-
ceived relative depth between objects resulting

from size cues is some function of the S’/@
values of the objects, It is asserted that the
variable S’/@ applies to both relative and fa-
miliar size cues so that these seemingly dif-
ferent types of size cues involve the same basic
process. The task remains, however, of deter-
mining the specific relation between d’ and
values of S’/@. One suggestion for this relation
comes from the size-distance invariance hy-
pothesis (cf., Kilpatrick & Ittelson, 1953) of
which perceived size as a cue to distance is a
particular case (Epstein, Park, & Casey, 1961).
The size-distance invariance hypothesis can
be expressed (Kilpatrick & Ittelson, 1953;
Gogel, 1964b) as
1s

D=e>: a)
where K, is a constant for a particular observer
or situation, Equation (1) states that a par-
ticular value of retinal size (@) and a particular
value of perceived size (S’) determines a par-
ticular perceived absolute distance (D’). Also,
according to Equation (1),

(2)

where d’,=D’,— D’.. From the previous dis-
cussion, the use of a comparison field, for the
measurement of the perceived distance of
familiar experimental objects, results in appar-
ent equidistance adjustments as determined by
equal values of S’/@ of the experimental and
comparison objects, A review of the available
evidence will demonstrate that when a com-
parison field is used the resulting data are in
agreement with Equation 1, However, it will
also be asserted that such agreement would
occur whether Equation 1 is valid or not,
Suppose that a double-sized playing card
(17.8 om, high) is presented at 304 cm. in an
experimental field and its apparent distance
measured with a comparison field, The double-
sized card usually will appear to be 8.9 cm.
high (its normal height) and will subtend a
visual angle of .058 radians. It follows that
the S’/@ value of the playing card is 152 cm./
radian, The comparison field is a full cue

~10-


behind and in front of f’. It is asserted that the
different values of S’/@ between the different
objects in the different planes will determine
the perceived depth between these objects (or
between the planes). In a situation in which
the size cue to relative depth is the only dis-
tance cue present, it is hypothesized that all
the perceived depths within this visual field
are immediately specified by specifying the
S’/0 values of the different objects.

The Size Cue to Absolute Distance

In the discussion involving Figure 1, the per-
ceived distance D’ of an object from O was
called a perceived absolute distance to dis-
tinguish it from the perceived depth between
objects d’ (perceived relative distance), The
size cue considered above is the size cue to
perceived relative distance, not the size cue
to perceived absolute distance. It is usually
assumed (at least implicitly) that the rea-
son why familiar size is a cue to perceived
relative distance is because it is a cue to per-
ceived absolute distance. It is supposed that
experience will result in perceived absolute
distances being associated with retinal sizes of
a familiar object such that for any particular
retinal size an appropriate absolute distance
will be perceived (Ittelson, 1951c). From this
point-of-view, a perceived relative distance is
merely the difference between two perceptions
of absolute distance, If this point-of-view is
correct, the psychophysics of familiar size as a
cue to relative distance is specified when the
psychophysics of familiar size as a cue to ab-
solute distance is known, Evidence relevant
to this point-of-view will be examined in this
portion of the paper.

A number of studies involving the so-called
“thereness — thatness” type of apparatus have
been interpreted as supporting the notion that
the retinal size of a familiar object can deter-
mine a perceived absolute distance (Ittelson,
195lc; Hastorf, 1950; Ittelson & Ames, 1950;
Epstein, 1963). In these studies the objects
with the familiar (or assumed) size (the ex-
perimental objects) were presented in a vis-
ually reduced (experimental) field. The per-
ceived distance of the experimental object was

measured by comparing the apparent position
of the experimental object with respect to that
of a comparison object presented in a com-
parison field, The comparison object was either
part of a visually well-structured field or was
itself a familiar object, In either case, visual
size comparisons could occur between the ex-
perimental object and objects in the comparison
field. It has been asserted (Gogel, et al., 1957)
that the measures obtained under these con-
ditions have not been demonstrated to be meas-
ures of perceived absolute distance. The same
assertion has been made recently (Adelson,
1963) in a study in which interactions between
the experimental and comparison fields have
been reported.

The kind of judgment which may occur when
the “thereness — thatness” type of apparatus is
used can be analyzed with the aid of Figure 2.
Suppose that by means of appropriately placed
mirrors, a playing card is made to appear in
the visual field illustrated in Figure 2, with no
cues present to localize the card in distance
except its familiar size. The visual field illus-
trated in Figure 2 corresponds to the compari-
son field in the “thereness — thatness” apparatus
while the playing card corresponds to the
experimental object, The playing card will
have a perceived size S’ as determined by its
familiar characteristics and also will have a
retinal size 6, Thus, the playing card will have
a particular value of S’/@ as will every object
in the perceptually well-structured comparison
field. If, as this paper asserts, S’/@ is the sig-
nificant variable in the size cue to relative
depth, the playing card will appear in that
apparent frontoparallel plane in the comparison
field which has the same value of S’/@ as does
the playing card. All that is required of O for
this perception to occur is a null comparison
(a judgment of equality) of the S’/@ values of
objects in the comparison field with respect to
the S’/@ value of the playing card, Entirely
incidental to this process is the question of how
far the playing card appeared to be from O.
No judgment of perceived absolute distance is
required, The physical distance from O to the
position of the plane (or to the position of
objects in the plane) at which the card appears

-7-



I"

obs.

Figure 2. A schematic perspective drawing useful in considering the changes in perceived
size per unit of retinal size for frontoparallel objects in different portions of the
visual field,

—~6—


the curve for perceived absolute distance is
linear, the curve for perceived relative distance
according to Equation 1 should be linear also.
Although the curves in Figure 7 are consider-
ably different from those in Figure 5, both
Figures 5 and 7 can be interpreted as indicat-
ing that perceptions of relative distance from
size cues are not always explainable in terms
of differences between perceptions of absolute
distance,

In Figures 5, 6, and 7 only the “Experiment
II” curve of Figure 7 supports Equation 1.
The curves in Figures 5, 6, and 7 which do not
support Equation 1, also do not support Equa-
tion 2, However, there are several studies
which directly have measured d’ rather than D’
as a function of size cues. An experiment which
can be applied here is the experiment by
Ittelson (1951b, Experiment IT) in which three
playing cards of different physical sizes were
moved, one at a timé, a constant distance to-
ward and away from O, in a visually reduced
experimental field. Using a comparison field,
five Os judged the nearest and farthest positions
of the movement for each of the physical sizes
of the card. Physical distance between these
judgments can be taken: as d’, @s can be cal-
culated from the physical sizes and the physical
distances of the near (e) and far (f) positions,
and S’ can be assumed to be the size of a nor-
mal playing card. The results from plotting
the average values of d’ against differences
in S’/0 are shown by the curve containing data
points in Figure 8. The straight line labeled
1/K, = 1 again represents the results expected if
1/K, in Equation 2 were unity. The data curve
of Figure 8, although linear with a slope of
approximately unity, does not pass through zero
as Equation 2 requires. Either the data do not
support Equation 2 or the discrepancy is a
consequence of interactions between the ex-
perimental and comparison fields. In the study
by Epstein and Baratz (1964, Experiment II)
a comparison field was used to measure the
perceived depth between pairs of simultane-
ously presented coins with each coin subtend-
ing one of three possible retinal sizes. Thirty-
two Os adjusted two nonsense-form comparison

figures to duplicate the apparent distance be-
tween each of the pairs of coins, The radial
difference between the adjustments in the com-
parison field for each pair of coins was con-
sidered to be the perceived depth d’ between
the pairs of coins, Figure 9 shows the obtained
relation between d’. and S’,/@,—S’./@., with
each data point being the average result from
a particular pair of coins. The values of S’
used in determining $’/@ in Figure 9 were ob-
tained from the average apparent sizes of
monocularly observed coins obtained under sim-
ilar conditions in a previous study by Epstein
(1963, Table II). From Figure 9 it is clear
that the perceived depth between coins (as
measured in the comparison field) and the
algebraic difference between values of S’/@ are
related (r= .90) and in general satisfy Equa-
tion 2 with 1/K,=1 (although there is pos-
sibly some tendency for the relation to be non-
linear for large differences in S’/@). Again,
these results can be interpreted either as valid
evidence for Equation 2 (and 1) or, as an
artifact resulting from the use of a comparison
field, In a recent study, Epstein (1964),
using a comparison field, had 18 Os adjust
nonsense-form comparison figures to duplicate
the apparent depth between simultaneously
presented pairs of non- familiar, luminous
squares of different retinal sizes presented in
a dark experimental field. The radial difference
between the adjustments in the comparison
field for each pair of squares was considered
to be the perceived depth (d’) between the
pairs of squares. Since the squares were non-
familiar objects, the physical sizes of the
squares cannot be considered to represent their
perceived sizes. Therefore, S’ is unknown and
the value of K, in Equation 2 cannot be de-
termined from the data of this experiment.
However, d’ can be plotted as a function of
1/6,—1/@, as shown in Figure 10. If, as is
reasonable, it is assumed that S’ is a constant
throughout this experiment, a linear curve
fitted to the data of Figure 10 should pass
through the origin if Equation 2 is valid. It
follows that the data of Figure 10 do not sup-
port Equation 2.

—19-



It was pointed out in the study by Gogel,
et al., (1957) and also in the study by Baird
(1963) that, since size comparisons can occur
over time, it is difficult to measure perceived
absolute distance uncontaminated by successive
size comparisons. Probably, the time separa-
tion between the previous visual experience and
the judgments in the test situation should be
as long as possible. It is, however, important
to determine the limiting conditions under
which judgments of absolute distance can occur
to further examine if indeed perceived absolute
distance can provide a basis for the explanation
of perceived relative distance (Gogel,- 1963).
The study by Gogel, et al., (1957) directly in-
dicates, that the perceived relative distance
resulting from size comparisons can occur in-
dependently of perceived absolute distance.
If this conclusion is correct, it follows that the
psychophysics of perceived relative distance
needs to be re-examined,

The Measurement of Perceived Relative
Distance with a Comparison Field

It is probable that the “thereness — thatness”
apparatus does not measure the perceived ab-
solute distance of familiar objects. It is equally
unlikely that it measures the perceived relative
distance of familiar objects. Consider the case
in which two familiar objects are viewed
monocularly in a Visually reduced experimental
field with the perceived depth between the two
objects measured by the physical distance be-
tween their apparent positions in a full-cue
comparison field. Each of the familiar objects.
in the experimental field would subsequently
appear at the distance of that portion of the
comparison field which has the same value of
S’/0 as the familiar object. Again, only appar-
ent equidistance judgments would be required
by O. It follows that the physical distance
between the positions of the objects in the
comparison field which appeared equidistant to
the familiar objects in the experimental field
would not be a valid measure of the perceived
distance between the experimental objects, Ac-
cording to this point-of-view O has matched
S’/@ values between each experimental object
and portions of the comparison field. The per-

ceived depth between the two experimental
objects has not been represented in O's per-
formance and consequently has not been
measured.

Attempts to measure the perceived relative
depth between two non-familiar objects by
means of a comparison visual field also intro-
duces problems, Suppose, in the previous exam-
ple, that two luminous squares of different
retinal size are used instead of the familiar
objects, Under these conditions, the retinally
smaller square will appear to be the more dis-
tant square, But, what will be the perceived
depth between the squares? . The squares by
themselves provide no scale or metric by means
of which such judgments can be made, An O,
if asked to make a relative depth judgment
without the comparison field present, may do
so. But it is doubtful whether such a judg-
ment can be meaningful. However, Epstein
and Baratz (1964) have found that Os can
adjust two objects in a comparison field to the
apparent radial distance of each of the two
simultaneously presented, experimental squares
of different retinal size. The distance between
the two adjustments was interpreted to be a
measure of the perceived depth between the
squares, Evidently, the comparison field intro-
duced a metric which was not in the original
perception, Perhaps even more difficult to
understand is the finding that non-familiar ex-
perimental objects such as ink blots, diamond
shaped figures (Ittelson, 1951c) or discs (Ep-
stein, 1961, Experiment II) presented singly
will have an apparent localization with respect
to the comparison field which changes system-
atically as a function of their retinal size.
In this latter case, however, it has been found
(Epstein, 1961, Experiment III) that the sys-
tematic change is considerably reduced when
different groups of Os are used with the dif-
ferent retinal sizes. When the same Os are
used with different retinal sizes, it seems that
a perception of relative not absolute distance
is being measured as a consequence of the
successive presentations, A possible explana-
tion of how a perception of relative distance
can result from a retinal size difference be-
tween successively or simultaneously presented

-9-



Gogel, W. C. The visual perception of size and distance.
Vision Res., 1963, 3, 101-120.

Gogel, W. C. The perception of depth from binocular
isparity. J. exp. Psychol., 1964, 67, 379-386. (a)

Gogel, W. C. Visual perception of spatial extent. J. opt.
Soc. Amer., 1964, 54, 411-416, (b)

Gogel, W. C., & Harker, G. S. ‘The effectiveness of size
cues to relative distance as a function of lateral visual
separation. J. exp. Psychol. 1955, 50, 309-315.

Gogel, W. C., Hartman, B. O., & Harker, G. S. The
retinal size of a familiar object as a determiner of ap-
parent distance. Psychol. Monogr., 1957, 71, No. 13
(Whole No. 442).

Hastorf, A. H. The influence of suggestion on the rela-
tionship between stimulus size and perceived distance.
J. Psychol., 1950, 29, 195-217.

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

Hochberg, C. B., & Hochberg, J. E. Familiar size and
subception in perceived depth. J. Psychol. 1953, 36,
341-345.

Hochberg, J. E., & McAlister, E. Relative size vs. fa-
miliar size in the ion of represented depth. Amer.
J. Psychol., 1955, 68, 294-296,

Ittelson, W. H. The constancies in perceptual theory.
Psychol. Rev., 1951, 58, 285-294, (a)

Ittelson, W. H. Size as a cue to distance: Radial motion.
Amer, J. Psychol., 1951, 64, 188-202. (b)

Ittelson, W. H. Size as a cue to distance: Static localiza-
tion. Amer. J. Psychol., 1951, 64, 54-67. (c)

Ittelson, W. H. A note on “familiar size and the percep-
tion of depth”. J. Psychol., 1953, 35, 235-240.

Ittelson, W. H. Visual space perception. New York:
Springer, 1960.

Ittelson, W. H. & Ames, A., Jr. Accommodation, conver-
gence and their relation to apparent distance. J. Psychol.,
1950, 30, 43-67.

Kilpatrick, F. P. The nature of perception: Some visual

lemonstrations. In F, P. Kilpatrick (Ed.) Explorations
in transactional psychology. New York: New York
Univer. Press, 1961,

Kilpatrick, F. P., & Ittelson, W. H. The size-distance in-
variance hypothesis. Psychol. Rev., 1953, 60, 223-231.

Over, R. Size and distance-estimates of a single stimulus
under different viewing conditions. Amer. J. Psychol.,
1963, 76, 459-457.

Smith, W. M. Sensitivity to apparent movement in depth
as a function of “property of movement”. J. exp.
Psychol., 1951, 42, 143-152.

Smith, W. M. Past experience and the perception of
visual size. Amer. J. Psychol., 1952, 65, 389-403, (a)

Smith, W. M. Sensitivity to apparent movement in depth
as a function of stimulus dimensionality. J. exp. Psychol.,
1952, 43, 149-155. (b)

Smith, W. M. Effect of monocular and binocular vision,
brightness, and apparent size on the sensitivity to ap-
parent movement in depth. J. exp. Psychol., 1955, 49,
357-362.

Updegraff, R. The visual perception of distance in young
children and adults: A comparative study. Univer.
Iowa Stud. Child. Welf., 1930, 4, No. 4.



AM 64-13

THE SIZE CUE TO VISUALLY
PERCEIVED DISTANCE

WALTER C, GOGEL, Ph.D.
Chief, Spatial Perception Section
PSYCHOLOGY BRANCH

Approved by Released by .
Shembey R Sehr Y ft Whee
STantey R. Mounier, M.D. M. S. Wurre, M.D,

Director, CARI Frpenat Ain SuRcEON

FEDERAL AVIATION AGENCY
Office of Aviation Medicine
Civil Aeromedical Research Institute
Oklahoma City, Oklahoma
January 1964



600 7

500 +

400 -

300 7

200

100

Figure 3.

e PLAYING CARDS
(EPSTEIN)

© COINS (EPSTEIN)

4 PLAYING CARDS
(ITTELSON)

0 100 200 300 400 500 600

s'/@

(Data from Ittelson, 1951c, Experiment Il; Epstein, 1961, Experiment I; and
Epstein, 1963). The relation between perceived distance (D’) and perceived
size per unit of retinal size (S’/e) of playing cards and coins, determined by
using a comparison field, The terms D’ and S’ are in centimeters and @ (visual
angle) is in radians. :

~12-


situation such that the objects comprising the
comparison field will be perceived to be their
physical size, Therefore, an object, for exam-
ple, a square, 8.9 cm. high, at 152 cm. in the
comparison field will appear to be 8.9 cm. high,
will subtend a visual angle of .058 radians, and
will have an S’/@ of 152 cm./radian. Since the
square and the playing card have equal $’/@
values, the playing card will appear to be at the
same distance position as the square in the
comparison field. As is the practice when using
comparison fields, the 152 cm. distance of the
square from O would be taken to be a meas-
ure of the perceived absolute distance of the
playing card, Actually the playing card in the
experimental field might have been perceived
by O at any or no absolute distance without
changing the measured result. The unwar-
ranted conclusion would be made that the
double-sized playing card physically located at
304 cm. actually appeared to O to be 152 cm.
from himself. From the results of such meas-
urements, the unwarranted conclusion would
be drawn that familiar objects of particular
retinal sizes will be perceived to be at distances
which normal-sized objects of that familiar
category would have to occupy in order to
produce the particular retinal sizes, This is
also the conclusion which would be predicted
from Equations 1 or 2 when 1/K,=1. There-
fore, the use of comparison fields should result
in Equations 1 or 2 being satisfied regardless
of the validity of these equations.

In Equation 1, measurements of S’, D’, and @
should reflect the perceived size, the perceived
distance, and the visual angle, respectively, of
the experimental object. However, according
to the point-of-view of this paper, when the
“thereness—thatness” apparatus is used, the ex-
perimental object will appear equidistant with
that object in the comparison field which has
the same value of $’/@ as does the experimental
object. Furthermore, the rationale of using
comparison fields requires that the physical
distance of this apparently equidistant object
in the. comparison field be taken as the per-
ceived distance of the experimental object.
Therefore, S’ and 6 refer to events in both the
comparison and experimental fields while D’
is measured by D in the comparison field.

Equation 1 can be put in the form

Ss is 3

D KD (3)
where S/D = @ in radians. But if D’ is assumed
to be measured by D in the comparison field,
it follows from Equation 3 that the only re-
quirement in order for 1/K, to equal unity in
Equations 1 and 2, is that S’ is proportional to
S in the comparison field. This condition might
be termed the condition of veridicality of per-
ceived size in the comparison field, i.e., perfect
size constancy in the comparison field. It fol-
lows that, if perfect size constancy occurs in
the comparison field, and if the judgmental
process involves only the comparison of S’/@
values between experimental and comparison
objects, the data obtained from using the com-
parison field should have the slope 1/K,=1,
when D’ is plotted against S’/@ with 6 expressed
in radians, If this reasoning is correct, the
results from using a comparison field are likely
to measure the amount of size constancy in
the comparison field rather than the perceived
absolute distance of the experimental object,
It will be noted that a value of 1/K,=1 in
Equations 1 and 2 would also be expected if
the familiar object would be perceived at a
distance which a normal-sized object of that
particular category would have to occupy to
subtend the particular retinal size, ie., if the
retinal size of a familiar object were a veridical
cue to perceived absolute distance,

Figure 3 shows the relation between D’ and
S’/@ from three experiments in which a
“thereness—thatness” type of apparatus was
used. The solid line in Figure 3 represents the
results which would be expected if the data
fitted Equation 1 exactly and if 1/K, were unity.
However, any series of data points which de-
scribe a linear function passing through the
origin of Figure 3 would satisfy Equation 1
with the slope of the function determining
1/K,. The triangular data points in Figure 3
represent the average results from successively
presenting three different retinal sizes of a play-
ing card to the same group of observers in a
study by Ittelson (1951lc, Experiment II). In

~l-—



can be measured as is done with the “thereness
— thatness” apparatus, But, if the point-of-
view expressed in this paper is correct, this
measure has nothing to do with O’s task and
does not represent a perception of the absolute
distance of the card. Similar comments apply
when the method of measuring apparent dis-
tance involves adjusting the comparison object
or the experimental object to apparent equi-
distance with each other. It is suggested that
the results from the “thereness — thatness”
apparatus demonstrate that experimental and
comparison objects with the same $’/@ values
appear equidistant but it is further suggested
that the use of the “thereness — thatness”
apparatus does not result in measures of per-
ceived absolute distance. A similar type of
objection has been stated previously (Gogel,
et al., 1957) by noting that the measurement
of the perceived absolute distance of a familiar
object requires that a test situation be used in
which only the familiar object is presented
visually to O. A second requirement for the
measurement of perceived absolute distance is
not specific to the “thereness — thatness” type
of apparatus. It is asserted that if different
retinal sizes of the familiar object are used these
must be presented to different Os. Comparisons
can occur between successive presentations of
different retinal sizes of the same or different
familiar objects with the result that observer
judgments which are actually judgments of
relative distance may be interpreted by the
experimenter (E) as being judgments of ab-
solute distance.

From the point-of-view of the above criteria,
there have been few adequate tests of whether
familiar size is a cue to absolute distance, The
study by Gogel, et al., (1957) was designed to
meet the above requirements, Kinesthetic
judgments and verbal reports were used to
measure the perceived absolute distance to
singly presented playing cards in visually re-
duced situations using different groups of Os
for the first presentations of the different retinal
sizes, Only the responses to the first presenta-
tions were considered to represent perceived.
absolute distances. Response changes as a
function of successive presentations were con-

sidered to measure perceived relative distance,
The results from this study indicate that the
retinal size of a familiar object in isolation is
not an effective cue to perceived absolute
distance and also that the perception of rela-
tive depth which occurred between successive
presentations of the cards occurred independ-
ently of any perception of absolute distance.
A recent study by Epstein (1963), using fig-
ures of coins of three different denominations
but constant retinal size as familiar objects and
with a different group of Os viewing each coin,
seems to support the point-of-view that familiar
size is a cue to perceived absolute distance.
However, since the judgments were made using
a “thereness — thatness” type of apparatus, the
experimental results do not necessarily meas-
ure perceived absolute distance but, instead,
probably indicate the ability of Os to perceive
that experimental and comparison objects which
have the same value of S’/@ are equidistant.

A recent study by Baird (1963, Experiment
II) meets the criteria discussed above. Three
groups, with ten Os in each group, made verbal
estimates of the distance of a luminous rec-
tangular strip, with each group presented with
a different retinal size. The Os were informed
that the figure was the same size as a 12 inch
ruler, The figure which was in a darkened
room was always physically at the same dis-
tance (25 feet) and was observed monocularly
through a reduction tube originating in a
lighted observer compartment, The different
groups gave average results which were close
to the physical distances at which a 12 inch
ruler would have to be placed to subtend the
particular visual angles. This study supports
the point-of-view that the retinal size of a
familiar object can be a determiner of perceived
absolute distance. It was noted, however, that
the inter-subject variabilities for the distance
estimates were large (standard deviations of
5.6, 7.3, and 42.6 feet associated with the mean
distance estimates of 14.3, 24.0, and 48.2 feet
respectively) It is unlikely that the perception
of absolute distance from familiar or assumed.
size occurs with sufficient precision to provide
an explanation for the perception of relative
depth from familiar or assumed size.

—8—


755

50 +

25 4

eu

on
on

ea

Figure 10.

25 50 75

(Data from Epstein, 1964), The relation between perceived relative distance
and differences between reciprocals of retinal sizes for pairs of squares, with
the perceived depth measured by using a comparison field. The value of
S’ of the squares is assumed to be constant throughout the experiment. The
term d’, is in centimeters. The terms 0, and 6, are visual angles expressed
in radians.

—-22—

1
100


The Familiar Size Cue to Relative Distance

Familiar size as a cue to relative distance can
also be considered with the aid of Figure 1.
Suppose that Objects e and f are presented
simultaneously and are monocularly viewed
with the remainder of the field-of-view totally
dark. Suppose also that Objects e and f are
familiar objects, for example, two playing cards.
Since 8, > @,, Object e will be perceived as less
distant than Object f (Ittelson, 1951c; Gogel,
1956a; Gogel & Harker, 1955), In this example,
however, it is not necessary to resort to familiar
size to explain the resulting perceived depth.
An explanation in terms of relative size would
be equally plausible (Hochberg & Hochberg,
1952; Hochberg & Hochberg, 1953; Hochberg
& McAlister, 1955). Suppose, however, that
Object f appears to be a similarly shaped but
physically smaller object than a playing card,
for example, a matchbox, with Object e contin-
uing to be seen as a playing card. In this latter
example, Object f might appear to be less dis-
tant than Object e even though 4. > 6. Accord-
ing to the usual explanation of the familiar size
cue, each of the objects (the matchbox and
the playing card) should appear at a distance
position which a normal-sized object of that
particular category would have to occupy to
produce that particular retinal size (Ittelson,
1951c). In the latter example since the objects
are of similar shape and 0. > , Object f should
appear behind Object e according to the rela-
tive size cue but in front of Object e (for some
values of 9, > 9,) according to the familiar size
cue, Thus, it has been argued (Ittelson, 1960,
p. 71; Epstein & Baratz, 1964) that the relative
size cue and the familiar size cue in such situa-
tions are in opposition to each other,

The question as to whether the cue of
familiar size has been demonstrated to be dis-
tinct from the cue of relative size has been
answered in the affirmative by Ittelson (1951c)
and in the negative by Hochberg and Hochberg
(1952; 1953) and by Hochberg and McAlister
(1955). A recent experiment by Epstein and
Baratz (1964, Experiment II) is pertinent to
this issue. In the experiment by Epstein and
Baratz, perceived depth was measured between
objects representing a dime, a quarter, and a

half dollar presented in pairs. Each coin sub-
tended three possible retinal sizes such that
the relative and familiar size cues could be
placed in agreement or in opposition, The
results of the study indicate that the per-
ceived depth between the pairs of coins when
the two cue systems were in opposition was
always in agreement with the familiar, not the
relative size cue. It seems reasonable to con-
clude that the familiar size cue to relative depth
cannot be subsumed under the relative size
cue to relative depth.

Specification of the Significant Variable in the
Size Cue to Relative Distance

From the previous discussion, it follows that
in the perception of relative depth which re-
rsults from the cues of relative and familiar
size, the important variables are the relative
values of S’ and 9. In both the relative and
familiar size cue, 8 is determined by the phy-
sical size and physical distance of the stimulus
objects. In the relative size cue, relative values
of S’ are determined by the perception that the
identically shaped objects are identical or sim-
ilar in size. In the familiar size cue, values of
S’ are determined by the size associated with
each of the familiar objects, A difference in
apparent size by itself does not determine a
perceived relative distance. For example, in
the case of the relative size cue, two identically
shaped objects of different retinal sizes appear
to be at different distances because they appear
to be the same size. Also, perceived depth
from the size cue is not determined solely by
the relative retinal sizes of the objects. For
example, as shown by Epstein and Baratz
(1964) two objects of the same retinal size
will appear to be at different distances be-
cause they appear to be of different sizes. It
follows from such considerations that S’ and @
considered jointly determine the perceived rel-
ative depth resulting from the size cue for
both relative and familiar size. The point-of-
view of this paper is that the significant vari-
able in the size cue to relative depth is the
relative values of S’/@ for each of the objects
being considered.

The term S’/6 is the perceived size per unit
of retinal size of the particular frontoparallel

—4-


800

600

D' 400

200

“FIRST PRES.

ALL PRESENTATIONS
VERBAL REPORTS

FIRST PRESENTATIONS
VERBAL REPORTS

THROWING ?

SCORES wy Je
e

a

PRESENTATIONS
THROWING
SCORES

T q
ce) 200 400 600

s'/@

Figure 5. (Data from Gogel, et al, 1957). The relation between verbal and throwing

measures of perceived distance (D’) and values of perceived size per unit of
retinal size (S’/0) for both the initial and successive presentation of playing
cards, The value of S’ is assumed to be constant for all the presentations. The
terms D’ and S’ are in centimeters with the value of S’ set equal to 8.9 cm.,
the height of a normal-sized playing card. ‘The term @ (visual angle) is in
radians.

-I15-—



1600 5

D' 800 +

ie) 400 800 1200 1600
s'/8

Figure 7. (Data from Baird, 1963). The relation between perceived distance (D’) and
perceived size per unit of retinal size (S‘/@) as obtained from size and dis-
tance estimates (Experiment I) or distance estimates (Experiment II) of tri-
angular or rectangular figures. The terms S’ and D’ are in centimeters and @
(visual angle) is in radians.

-17-



The relative size cue to relative depth will
be effective when the objects (e, f, and g of
Figure 1) are presented successively, as well
as simultaneously to the same O (Carr, 1935,
pp. 260-261; Gogel, Hartman, & Harker, 1957;
Over, 1963). The variability in the resulting
perceived depth (d’), however, might be ex-
pected to increase as the time interval between
the presentation of the two objects increased.
The perception of a change in depth as a func-
tion of a continuous change in visual angle has
also been demonstrated for a single non-familiar
or familiar object (Ittelson, 1951b; Smith, 1951;
Smith, 1952b; Smith, 1955; cf., Ittelson, 1960,
p. 71). ‘The evidence is clear, Objects of the
same shape with visual angles which differ
either successively (as in the case of the same
object of different retinal sizes presented at
different times to the same O) or simulta-
neously (as in the case of presenting two
similar objects of different retinal size at the
same time) or continuously (as in the case of
the object whose visual angle changes while
O is observing it) will result in a perception of
relative depth.

Relative values of S’ as well as 9 are necessary
in order for the relative size cue to result in
a perceived distance. There is evidence
(Hochberg & McAlister, 1955) that two simul-
taneously presented rectangles or two simulta-
neously presented circles of different retinal
sizes can produce an apparent depth but, that
the simultaneous presentation of a rectangle
and circle of different retinal sizes does not.
Clearly, some perception (S’. and S’,) of the
relative sizes of the objects (e and f) is neces-
sary. Neither S’. nor S’, must necessarily be
perceived as being a particular size but some
perception of the relation between the sizes is
necessary. Also, while a difference in shape
between two objects tends to destroy the per-
ception of relative depth, it is not necessary
that the two objects be identical in all char-
acteristics except that of retinal size. It has
been found, for example, that a depth percep-
tion can occur as the result of the simultaneous
presentation of two squares of identical shape
but different color (Epstein & Baratz, 1964,
Experiment I). It is also unnecessary to as-

sume that S’, must equal S’; in order for the
relative size cue to result in a perception of
relative depth, This can be shown by the
results from a portion of a study by Over
(1963) in which the perceived sizes and per-
ceived distances of successively presented,
diamond-shaped squares of various retinal sizes
were measured under visually reduced condi-
tions, The present author concludes that the
results from this study by Over indicate that
perceived distance can vary between presenta-
tions as a function of the changes in retinal
size (see the dashed line curve of Figure 6)
even though the perceived sizes of the squares
were not always equal in the different
presentations.

In summary the experimental evidence is in
agreement with the following description of
the essential processes involved in the relative
size cue to relative distance: (1) The relative
size which is referred to is a relative retinal
size’ and is a difference (or equality) in retinal
sizes occurring from the simultaneous or suc-
cessive presentation of similar objects. If the
retinal sizes are different, a perception of depth
between the objects will occur with the object
having the retinally smaller size appearing more
distant. If the retinal sizes are the same, the
objects will appear equidistant. (2) Relative
retinal size, by itself, is not sufficient to pro-
duce a perception of relative depth, Some sim-
ilarity of shape between the objects must be
present, and (3) must result in some percep-
tion of the relative sizes of the objects, with
the usual perception being that of size equality,
It is clear that relative values of S’ as well as
relative values of @ are involved in the relative
size cue to relative depth.
+The expression “relative size judgments” (Gogel, et al.,
1957) or “relative size” (Baird, 1963) has sometimes
been used to refer to the perception of the relative sizes
of objects presented either simultaneously or successively,
regardless of whether the perceived size occurred between
similarly shaped objects or not. Instead, the expression
“elative size’ cue” in this paper follows the meaning used
by Hochberg and McAlister (1955), ie., the relative size
cue as used in this paper is the relative depth cue which

occurs from observing two (or more) similarly or iden-
tically shaped objects of different retinal size.

-~3-





Figure 1. A schematic perspective drawing useful in considering terms involved in the
operation of size as a cue to distance. This figure has appeared previously as
Figure 1 in Gogel (1964b).

ence in the retinal sizes of the rectangles.
Under these conditions, neither rectangle by
itself would be perceived as having a unique
size. However, the rectangles are assumed by
O to be of the same size, and therefore, S’. = S’,.
Tf D, is greater than, equal to, or less than D.,
and S, = S,, it follows that 6, is less than, equal
to, or greater than 9@., respectively. When
S’.=S',, and 9,> 6, Rectangle f is perceived
as more distant than Rectangle e (d's is posi-
tive). When S’.=S’, and 9, < 0, Rectangle f
is perceived as less distant than Rectangle e
(for consistency, d’z should be considered as
negative) and when S’,=S’, and 0.= 6, the
two rectangles are perceived to be at the same
distance (d’x is zero).

There is evidence that the simultaneous
visual presentation of two similar but non-
familiar objects such as Rectangles e and f in
Figure 1, in the absence of other depth cues,
will result in a perceived depth d’x. The term
non-familiar is used here to indicate that there

are no familiar characteristics associated with
the objects which would specify a perceived
size. For example, although rectangles are
shapes which are frequently encountered, there
is no unique size which would normally be
associated with them. It is reported (Kil-
patrick, 1961) that a simultaneously presented
series of lines of different retinal sizes whose
centers are all at the same height will appear
at different distances, The same phenomenon
has been quantitatively demonstrated, for exam-
ple, for a series of trapezoids (Gogel, 1954),
for a pair of squares (Epstein & Baratz, 1964,
Experiment I) and for a pair of discs (Upde-
graff, 1930; Carr, 1935, pp, 262-263), ete., (cf.,
Ittelson, 1960, p. 70). Similarly, two balloons
of different visual angle but of the same
brightness will appear at different distances
with the perceived depth between them chang-
ing with continuous variation in the size of
one (Kilpatrick, 1961),

—~2-


250

250

200
{50
D'
100
50
ie) 1 T q T U 1
ie) 50 100 150 200
s'/@.

Figure 4, (Data from Epstein, 1961, Experiment Il). ‘The relation between perceived
distance (D’) and perceived size per unit of retinal size (S’/@) of colored discs,
with §’ and D’ measured by using a comparison field. The terms D’ and S’
are in centimeters and @ (visual angle) is in radians.

~123-



Figure 6.

300 600 900
s'/@

(Data from Over, 1963). The relation between perceived distance (D’) and
perceived size per unit of retinal size ($//é) as obtained from verbal estimates
distance of diamond-shaped figures. The terms D’ and $” are

of the size anc
in centimeters and 6 (visual angle) is in radians.

~16—

1200