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perceived distance of objects in a binocular configuration.
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. perceived size and distance. J. Psychol., 53, 475-489,

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Gogel, W. C. and Harker, G. S. (1955). The effective-
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—18—



fh

tome

a ee eae

Ficuns 35 Apparatus for a study of the interrelation of perceived size and distance.3

@ ‘Figure 3 (reproduced with the permission of the Journal Press) has appeared previously as Figure 2 in Gogel,
1960c. .

12



a

requires that cues be present which can directly
determine perceived absolute distance, Visual
cues of perceived absolute distance can be
divided into the ocular cues such as converg-
ence and accommodation and the so called
“empirical” cues such as the size cue associated
with familiar objects. If perceived absolute
distance is the determiner of perceived relative
distance, it is reasonable to expect that direct
and fairly precise visual cues of perceived
absolute distance must always be available for
the observer in situations in which perceived
relative depth can occur. From this point of
view it would also be expected that a change
in perceived relative distance cannot occur
without concomittant changes in perceived ab-
solute distance. Both of these expectations re-
quire examination.

1. The convergence of the eyes as a cue to per-
ceived absolute distance

The number of cues which can act directly in
the sensing of the distance of an object from
the observer are limited. The most important
of these in situations involving only binocular
cues are the converggnce and accommodation
of the eyes. The problem is whether accom-
modation and convergence per se are indicators
of perceived absolute distance. Accommoda-
tion and convergence differences are not to be
considered since these are possible direct in-
dicators of relative not absolute depth.

The role of convergence and accommodation
in the perception of distance has received con-
siderable experimental attentjon [see Osgood
(1953), Woodworth (1938), ard Woodworth
and Schlosberg (1954) for revfews of this re-
search]. It is not always clear in this experi-
mentation whether 't is percéived relative. jor
perceived absolute distances which is being
studied, and whether accommodation and/con-
vergence differences or accommodation and
convergence per se are the significant variables.

However, a general conclusion which is possible ‘

frém this work is that while convergence is
more effective than accommodation, neither
appears to be a very precise determiner of per-
ceived absolute distance. In some recent ex-
petiments (Gogel, 1961a; 1961b; 1962b), per-
ceived absolute distance was measured by

providing the observer with a visual ruler con-
sisting of a monocularly observed alley. This
acted as a measuring stick against which the
perceived distance of binocular configurations
or of a single binocular object could be judged.
In the experiments by Gogel, only a limited
number of observers demonstrated any relation
between convergence and perceived absolute
distance. This was so whether a single binoc-
ular object or a configuration of binocular ob-
jects was used. Even for the observers who
evidenced some relation between convergence
and perceived absolute distance, the rate of
change of perceived absolute distance with
convergence was usually small and remained
small whether a single binocular object or a
configuration of binocular objects was used.
Furthermore, for these successful observers, the
convergence-perceived distance function dif-
fered depending upon the position of the binoc-
ular objects in the configuration of binocular
objects. Thus, it appears that convergence is
not a cue system which is effective with either
sufficient frequency or precision to be a theo-
retical basis for the perception of relative depth
resulting from a binocular disparity. This gen-
eral inadequacy of convergence is pertinent to
the Luneburg theory of binocular vision (Lune-
burg, 1947, 1948, 1950; Shipley, 1957). How-
ever, the fact that convergence does have some
perceptual consequences with a few observers
is also of significance. For example, the as-
sumption that the addition of a constant amount
of convergence will not affect the perceived
depth in a binocular configuration (Blank,
1957, 1959; Hardy, Rand, Rittler, Blank, and
Boeder, 1953) ‘is neither true nor false. From
the above studies by Gogel, it is true with most
observers but not with all.

2. Familiar size wo cue to perceived absolute
distance ‘

Another of thé factors which has been con-
sidered to be a determiner of perceived abso-
lute distance ig the retinal size of a familiar
object. If this cue operates with reliability
and precision, then in a number of situations
it offers the possibility that absolute distance
perceptions are the necessary antecedents of
perceived relative distance. The possible im-

-~3-



Morgan, M. W., Jr. (1944b). The clinical aspects of
accommodation and convergence. Amer. J. Optom., 21,
801-313.

Ogle, K. N. (1983), Precision and validity of stereoscopic
depth perception from double images. J. Opt. Soc. Amer.,
43, 906-913,

Ogle, K, N, (1959). Theory of stereoscopic vision. In
8. Koch (Ed.), Psychology: A study of a science, Vol. I,
New York: McGraw-Hill, 362-304.

Ohwaki, S. (1954). On the role of accommodation in
the size constancy phenomenon. Tohaku Psychol. Folia,
14, 17-31.

Ohwaki, S. (1955). On the factors determining accom-
modation: Research on size constancy phenomenon, Tohaku
Psychol. Folia, 14, 147-158,

Osgood, C. 'E. (1953). Method and theory in experi-
mental psychology. New York: Oxford University Press.

Rock, I, and Ebenholtz, $. (1959), The relational deter-
mination of perceived size. Psychol. Rev., 66, 387-401.

Rump, E. E, (1961). The relationship between per-
ceived size and perceived distance. Brit, J. Psychol. 52,
111-124.

Schlosberg, H. (1950). A note on depth perception, size
constancy, and related topics. Psychol. Rev., 57, 314-317.

Shipley, T. (1957). Convergence function in binocular
space. I. A note on theory. J. Opt, Soc. Amer., 47, 795-803.

Von Kries, J. (1925). Notes on perception of depth.
In H. V. Helmboltz’s Treatise on Physiological Optics, Vol.
UI (J. P. G, Southall, Ed.), Menasha, Wisconsin: Banta.

Wallach, H. and McKenna, V. V. (1960). On. size-
perception in the absence of cues for distance. Amer. J.
Psychol,, 73, 458-460.

Woodworth, R. $, (1938). Experimental Psychology.
New York: Henry Holt and Co., Inc.

Woodworth, R, S. and Schlosberg, H. (1954). Experi-
mental Psychology. New York: Henry Holt and Co., Inc.

-19~—

FAA AC 62°38


tween Objects f and g. Direct depth cues be-
tween Objects e and g are trivial in specifying
the perceived depth between these two objects.

B. Psychophysical Equations of Perceived
Space

The previous discussion provides evidence for
the importance of adjacency in the perception
of space. It also sets some general require-
ments which psychophysical equations con-
cerned with perceived space must meet. From
the results of the experiment involving familiar
objects and other considerations, it is concluded
that the relational, not the absolute extents of
retinal stimuli are determiners of perceived
space. It follows from this that psychophysical
equations involving perceived extents should
contain terms for retinal extents, but only when
these are in the form of ratios.‘ It is also clear
that these ratios should be between physically
adjacent stimuli. In the previous discussion it
has been assumed that physical (or perhaps
retinal) adjacency has been the important ad-
jacency factor. It is also possible that instead
of either of these, it is perceptual adjacency
which is the important quality, The resolu-
tion of this problem will ‘require the investiga-
tion of situations in which each of these three
forms of adjacency differ. However, for the
purposes of the present discussion, it is suffici-
ent to note that the adjacency principle requires
that large perceived depth intervals are the
summed effect of a series of small perceived
depth intervals. From this point of view, the
perception of large spacial extents is basicadly
a process of perceptual summatidn, Specific-
ally rejected is the notion that thej perception
of small extents is the result of a Process of per-
ceptual subtraction.

It has been found that equations ‘aerived from ;

Equation 2 were able to predict the medi:

depth adjustments for the experiment discus:

with the aid of Figure 3 (Gogel, 1960c). The
psychophysical equations predicted and the
experimental results verified a linear contrac-
tion of perceived depth with respect to physical
depth. This general gliscrepancy between the
perceived and physical world has been noted in

‘other experiments (Gilinsky, 1951). Clearly,

not all systems of depth cues invariably pro-
dice veridical perceptions. This suggests that

experience is not a determiner of the form of all
psychophysical equations of perceived depth.
It might be expected that experience can affect
observer constants and scalar factors associated
with psychophysical equations e.g., factors like
C and S’ in Equation 2. But, experience is not
expected to affect the form of these psycho-
physical equations. Indeed, there seems to be
no reason from the viewpoint of the effect of
experience why the form of Equation 2, for
example, should be as it is. Experience would
be expected to determine the form of a psycho-
physical equation by selectively reinforcing cer-
tain perceptions and not others. Those per-
ceptions would be reinforced which tended to
be in agreement with reality. Thus, if the form
of the psychophysical equation were deter-
mined by experience it would be expected that
the psychophysical equation would predict ver-
idical perceptions. Since this is not the case,
it is suggested that the form of the psychophysi-
cal equation, as distinct from observer constants
and scalar factors, is not the product of
experience,

There is one other aspect regarding psycho-
physical equations of perceived space which
might be mentioned. It is customary to enum-
erate the cues of space perception as those of
binocular disparity, relative size, brightness,
interposition, etc. However, it is possible that
a more parsimonious set of variables might be
established if the common aspects of these cue
systems were investigated. If the perceived
depth resulting from the different cue systems
had the same phenomenal characteristics this
would offer the possibility of some communal-
ity between them. It has sometimes been
thought that binocular disparity produces an
impression of depth, which is qualitatively dif-
ferent from that of other cue systems. There
is evidence against sthjs. Binocular disparity
intervals have been used to measure perceived
intervals developed by other cues such as that
of relative size (Gogel and Harker, 1955). Ap-
parently, this can be done without any feelings

-of ihappropriateness. This suggests that the

quality of the depth experience is independent
of the cue system used. This encourages the
search for factors common to the various cue

4 It will be noted that Equation 2, which contains a ratio
of retinal extents} i.c., A\ o/8, meets this criterion.

-~16—

ee Ae oe



v= val

it ec ORE

ES AOS Si

distance are convergence and the retinal size
of a familiar object. It is asserted that the
absolute retinal size of a familiar object is not
an adequate cue to perceived absolute distance.
Gonvergence per se, in an imprecise manner,
under certain circumstances, with some ob-
servers, can affect perceived absolute distance,
perceived three-dimensional shape, and pos-
sibly perceived size. But, the last two effects,
if and when they occur, are not determined by
the first effect. It seems that, under certain
conditions with certain people, convergence
possibly can have some effect upon the per-
ceptions of relative size and distance. But the
effect is direct and does not involve perceived
absolute distance as a necessary condition. This
is further seen in experiments with a stereo-
scope in which convergence is sometimes found
to affect perceived size and distance differently
(see Woodworth, 1938, pp. 674-676). It should
also be kept in mind that apparently many
people cannot use convergence effectively with
respect to perceived absolute distance and per-
haps perceived absolute size. Convergence is
not a very promising cue for asserting the di-
rect importance of egocentric localization in
the perception of size and distance.

The effect of apparent distance on accom-
modation and convergence has been investi-
gated (Hofstetter, 1942, 1950, 1951; Ittelson
and Ames, 1950; Morgan, 1944a, 1944b; Oh-
waki, 1955), It may be concluded that con-
vergence and possibly accommodation can be
affected by the apparent distance of the fix-
ated object. It has been noted previously tat
a number of studies have een cemed with
the possible relation between convprgence and
perceived size (Gogel, 1962a, 1962b; Heine-
mann et al., 1959; Hermans, 1954; Holway and
Boring, 1941). The pdssible relation between
accommodation and perceived,'size has als¢
been studied (Chalmers, 1952; Heinemann,ét
al., 1959; Holway and Boring, 1941; Ohwaki,
1954), In some of these studies, it is not al-
ways clear whether the terms perceived size,
perceived distance, accommodation, and con-
vergence refer to absglute values of these events

_ or to changes in their magnitudes. But, to the

extent that the accommodation-convergence
omptex affects the perception of relative size
and distance and is in turn affected by per-

ceived absolute distance, to this extent ego-
centric localization can have some effect upon
perceived relative size and distance. However,
the evidence is that a perception of absolute
distance is not a necessary condition for the
perception of either relative size or distance.
At best it is a peripheral and indirect contri-
butor to these perceptions and is not a basis
for their theoretical explanation.

IH. THE ADJACENCY FACTOR IN THE
PERCEPTION OF SIZE AND
DISTANCE

A. The Relational Character of Stimuli

In the previous discussion, the factors which
were considered to be possible cues to absolute
distance are non-relational. These were con-
vergence (or accommodation) per se, rather
than convergence (or accommodative) differ-
ences, and the absolute retinal size of a famil-
iar object rather than the differences in retinal
size between objects or between presentations.
Thus, cues for the direct perception of absolute
distance are absolute in character rather than
being relational. There is considerable experi-
mentation which bears on the problem of the
relational characteristics of stimuli as deter-
miners of perception. This paper has also pre-
sented some evidence relevant to this issue.
For example, it is suggested that the absolute
size @ of a retinal image has no relation to
either absolute or relative perceived size or
distance. This is to be contrasted with rela-
tive retinal size, for example, the relative retinal
size of the width to the height of Object e in
Figure 1. Perceptually, it is immediately clear
even with Object e in isolation that Object e is
higher than it is wide. The size of the width
(or the height) of Object e on the retina is an
absolute retinal siz@#he ratio of the width to
the height jis a relative retinal size. The latter,
not the former, constitutes an adequate per-
ceptual stimulus. It is a fundamental premise
‘of this paper that perceived size and distance

‘ are determined by, the relational characteristi¢s

of the stimuli, It will be the purpose of the
remainder of this paper to discuss a factor
which is important in organizing the relational
characteristics into perceptions of size and dis-
tance, This factor will be called the “adjacency

—8—



ceived relative not perceived absolute distance.
If familiar size is not a cue to perceived rela-
tive distance, it is also not likely to be a cue
to perceived absolute distance. The reverse is
not necessarily the case, however. The demon-
stration that familiar size is not a cue to per-
ceived absolute distance does not remove the
possibility that it can affect the perception of
relative depth.

3. The independence of perceived relative dis-
tance from perceived absolute distance

If perceived relative distance were to involve
the subtraction of two perceived absolute dis-
tances, it is clear that changes in perceived ab-
solute distance would be the necessary antece-
dents of changes in perceived relative distance.
Direct evidence concerning this possibility is
available. In the study of familiar size as a
cue to perceived absolute distance (Gogel et al,
1957), following the presentation of a particu-
lar retinal size of playing card, the other retinal
sizes were presented successively to the same
observers, Under these conditions, throwing
differences occurred as a function of the
changes in retinal size. The results indicate
that perceived relative depth occurred from
the successive presentation of different retinal
sizes even though perceived absolute depth did
not occur from the first presentations. Depth
between the successive objects was perceived
independently of any perception of the dis-
tance of any object from the observer. This
experiment suggests that the perception of
relative depth is immediate rather than’ a con-
sequence of the difference Between two per-
ceptions of the distance of gbiects from the
observer. . }

The physical depth interval (relative depth)
associated with a ‘constant binocular dispirity
varies approximately as the’ square of th¢ dis-
tance of the objects from the observery It is
possible that, in the perception of’ a depth in-
terval from binocular disparity cues, there is
some perceptual process which parallels the
wlation between physical depth and binocular
disparity. It might be expected that the per-
ceived depth between two objects resulting
from a binocular disparity would be some func-
tion of the perceived or estimated distance of
* the objects from the observer (Fry, 1950; Ogle,

1953, 1959; Von. Kries, 1925). Indeed, early
experimental evidence was interpreted as sup-
porting this point of view (Heine, 1900). How-
ever, a more recent experimental test does not.
In an experiment by Gogel (1960a), a ring
of light was located a constant distance behind
a pair of familiar objects (playing cards) with
all of these objects binocularly observed in an
otherwise dark room. The angular (retinal)
size of the playing cards differed for two groups
of observers. Measurements were made of
both the perceived absolute distance to the
playing cards and the perceived depth between
the playing cards and ring. The two groups
did not evidence any difference in the per-
ceived absolute distance of the cards for the
two angular sizes. The perceived depth be-
tween the cards and ring, however, was greater
for the smaller size of the playing cards. It
was concluded that the apparent depth be-
tween the ring and cards associated with a con-
stant binocular disparity could be made to vary
in spite of the fact that both the convergence
and the perceived absolute distance of the
cards were held constant. The importance of
this experiment for the present discussion is
that it indicates that a change in the perception
of the absolute distance to a configuration of
binocular objects is not a necessary condition
for a change in the perception of the depth
between them.

In another study, the perceptions resulting
from a three dimensional configuration were
compared as a function of whether adequate
cues of absolute distance were present or absent
(Gogel, 1958b). The correlations between the
results from the two types of situations again
indigate that perceived absolute distance is not
a determining condition for the three dimen-
sional perceptions resulting from a configura-
tion of binoculagapbjects. It appears from di-
rect test that perceived absolute distance is not
necessary to the perception of the relative
depth between objects for either the binocular
disparity cue or the cue of familiar size.

' if t
B. The Role of Egocentric Localization in
the Perception of Size

1. The size-distance invariance hypothesis

The supposed dependence between perceived
size and perceived absolute distance has found

~5-


A

|
|

portance of this cue system is further enhanced
by the circumstance that there are few (if any)
other non-binocular cues, which might be di-
rect determiners of perceived absolute distance,
independent of perceptions of relative distance.
Neither the relative size cue, nor its amplifica-
tion into the perspective cue, nor the cue in-
volving gradients of retinal size offer this pos-
sibility if size familiarity is not present.

According to the cue of familiar size, famil-
iarity with an object, for example, a playing
card, will result in a particular distance being
associated with a particular retinal size of the
playing card. This means that as a result of
seeing playing cards at different distances, the
observer will come to associate a particular ret-
inal size of the card with a particular distance
so that when only the retinal stimulus is pres-
ent, the appropriate distance will be immedi-
ately perceived. If this hypothesis is correct,
a familiar object in the absence of all other dis-
tance cues should be seen at a distance which
varies inversely with its absolute retinal size
(Ittelson, 1951, 1953; Schlosberg, 1950).

But, before considering familiar size as a cue
to perceived absolute distance, it is necessary to
distinguish between relative and absolute ret-
inal size. Consider the instance in which the
eye is stimulated by a rectangle of light. For
example, consider Object e of Figure 1. The
retinal size, either angular (6,) or linear, of the
width (or height) of this rectangle is an ex-
ample of absolute retinal size. The ratio of the
height to the width of the retinal image of pe
rectangle is an example of relative retinal size.
Relative retinal size is involved when a succes-
sive or simultaneous comparison, of retinal
sizes is possible, while absolute /retinal size
might be measured a’, the number of milli-
meters or the number’of receptér units sub-:
tended on the retina by the stimulus. The e/
of successive stimulation in the above defint-
tion of relative retinal size is designed to apply
to the situation in which a stimulus, momen-
tarily presented on the retina, is followed after
a timé interval by a stimulus of the same shape
(or familiar characteiMstics ) but of different re-

. tinal size. Suppose that, under these condi-

tions, the observer perceives the retinally larger
abject'as being closer than the retinally smaller
object. What may be occurring in this case is

a judgment of relative distance as a conse-
quence of the successive presentation of the dif-
ferent retinal sizes. No judgments of absolute
distance need be considered as having occurred.
This example points out a caution which must
be used in testing whether familiar size is a cue
to perceived absolute distance. To be certain
that absolute distance is being judged, the ob-
server must not be permitted to compare retinal
sizes either simultaneously or succcessively. An
analysis of previous research on this problem in
relation to these criteria is discussed elsewhere
(Gogel, Hartman and Harker, 1957).

To meet the above requirements, different
retinal sizes of a familiar object (a playing
card) were presented to different observers and
the perceived absolute distance of the card was
measured kinesthetically without introducing a
second visual object. The kinesthetic method
of measurement consisted of throwing darts to
the apparent distance of the playing card with-
out knowledge of results. This method proved
to have a precision which was more than ad-
equate for the hypothesis being tested (Gogel,
et al., 1957).

The results from this experiment were that
the average distances thrown by the different
groups of observers did not differ as a conse-
quence of the different groups having been
presented with different retinal sizes of the
playing card. It follows that familiar size is not
a cue to perceived absolute distance. This con-
clusion is also supported by a later study in
which different retinal sizes of playing cards
were used (Gogel, 1960a).

A review of the evidence relevant to familiar
size as a cue to distance is given by Epstein,
Park, and Casey (1961). In a number of pre-
vious studies, it had been concluded that famil-
iar size can determine perceived absolute dis-
tance. In these studi#€ the requirements listed
above for measuring: perceived absolute dis-
tance had not been met (Gogel et al, 1957)
and it is asserted that perceived relative not

_absolute distance was being studied. Also, a

number of experiments have questioned thé
adequacy of familiar size as a cue to perceived
distance (Hochberg and Hochberg, 1952, 1953;
Hochberg and McAlister, 1955; Epstein, 1961).
These experiments, however, involve the pos-
sible relation between familiar size and per-

-4-

If
ti
to
m
st

p
Te

th
ti

He Pp Hae

RA ENO


systems so that, for example, cue systems can
be added together to produce pefceptually pre-
dictable results,

SUMMARY

The concept of egocentric localization has
been a central assumption in attempts to under-
stand our visual perceptions of the three-
dimensional world. This assumption is re-
jected. It is asserted that relative retinal events
are the only events which can be stimuli for
perceptions. These retinal events are organi-
zed by a factor which is termed the adjacency
principle. The adjacency principle states that
the apparent size or position of any object in

the field of view is determined by whatever
size or distance cues occur between it and ad-
jacent objects. This point of view emphasizes
the importance of local perceptual events and
their summation into larger perceived extents
rather than the reverse. It is suggested that
experience can affect the observer constants
and scalar factors in a psychophysical equa-
tion but it probably does not affect the form of
the equation.

The adjacency principle has been applied to
a situation involving perceived movement as
well as to a number of static situations. It
seems that the predictive ability of the princi-
ple is good under both types of circumstances.



distance is relevant here also (Gogel et al.,
1957). The most likely reason for the failure
of this hypothesis is that the retinal size of the
familiar object was not a datum which could be
used in the observer's perception. It is reason-
able to expect that in the past history of the
observers there were many opportunities to as-
sociate the absolute retinal sizes of playing
cards with perceived absolute distances. The
conclusion that such associations did not occur,
therefore, suggests that the absolute size of the
retinal image is not a datum of experience. It
indicates that the absolute size of a retinal
image has no perceptual consequences. But,
the absolute retinal size @ is a possible variable
in Equation 1, ie., according to Equation 1,
$'/D’ is proportional to @. Thus, the conclu-
sion that the absolute retinal size of an image
has no perceptual consequences is in opposition
to the size-distance invariance hypothesis.

2. The convergence of the eyes as a determiner
of perceived size

The judgment of the size of one visible ob-
ject with respect to another visible object has
been investigated in situations in which only
binocular factors aré‘ present. In several of
these studies, situations were used such that
only convergence or convergence differences
were available as possible distance indicators
with binocular disparity absent (Heinemann,
Tulving, and Nachmias, 1959; Hermans, 1954;
Holway and Boring, 1941). The results obtained
from these situations indicate that the ratio of
the perceived sizes of the objacts was not equal
to the ratio of their retinal sizes. Some amount
of size constancy was present, fen when con-
vergence was the only distancd indicator avail-
able. It is possible to explain this size con-
stancy in terms of two successive judgments of
perceived absolute distance.’ From the fize-
distance invariance hypothesis, perceived¥abso-
lute distance should determine the perceived
absolute size associated with a retinal stimulus.

ingreased the perceived absolute size associated
with a constant getinal size would increase
proportionately. If each perceived size were
determined in this way, the comparison of sizes
could also be explained by this process. But,
“ from the previous discussion, perceived abso-

Accordingly, as the perceived absolute distance ‘

lute distance usually will not occur as a func-
tion of convergence alone, and it is unlikely
that absolute retinal size can determine per-
ceived size. Therefore this explanation is
doubtful. However, a direct test of this pos-
sibility has been made. The perceived absolute
size of an object of constant angular size has
been measured using a kinesthetic method, with
convergence the only possible distance indica-
tor (Gogel, 1962a, 1962b). The results indicate
little or no change in perceived absolute size as
a function of convergence. Thus, the partial
size constancy usually found with essentially
only binocular cues present probably involves
perceived relative size, resulting from perceived
relative distance as a consequence of conver-
gence changes, with perceived absolute dis-
tance not a significant factor.

C. The Role of Egocentric Localization in
the Perception of Shape

From the discussion thus far, it appears that
perceived size and perceived relative depth are
not determined by perceived absolute distance
even though, for a limited number of observers,
these perceptions are not invariably independ-
ent of the cue of the convergence of the eyes.
It might be expected that perceived shape,
which can be regarded as a combination of a
perceived frontal size (S’) and of perceived
relative depth (d’) would be similarly inde-
pendent of perceived absolute distance and
convergence. A direct test of this has been
made in relation to the convergence of the
eyes. In these experiments (Gogel, 1958a;
1958c) the perceived three-dimensional shape
of a binocular ‘object was measured under con-
ditions in which only binocular cues were pres-
ent. It was found that the perceived shape
varied somewhat, ag a function of the converg-
ence value to the object. It is concluded from
these résults that ‘convergence can have an ef-
fect upon percejved three-dimensional shape.

' D. Discussion’ ‘
The evidence is that egocentric localization

as it is reflected in perceived absolute distance

is not the determiner of either perceived frontal

size or percéived relative depth. Two of the
major cues for the direct perception of absolute

-7-




ee

ject CD the left end of the object (A or C) is
physically closer to the observer than the right
end (Bor D). All the objects in Figure 2 are
observed binocularly. Figure 2b represents a
top view of the apparent position of the same
window and tube. As before, in distinction to
physical events, perceived events will be indi-
cated by the prime notation. In Figure 2b,
A’B’ represents a top view of the apparent
orientation of the window while C’D’ repre-
sents a top view of the apparent orientation of
the tube. It will be noted by comparing
Figures 2a and 2b that the perception of the
orientation of the window and tube in Figure
2b is indicated as being veridical. It is meant
by this that Figure 2b is drawn as though be-
havioral tests had revealed that the window
and tube were perceived to be where they are.
Suppose, however, that, instead of a normally
shaped window, an Ames trapezoidal window
(Ames, 1951) were used at AB with the small
end at A and the large end at B in Figure 2a.
In this case, as is indicated in Figure 2c, the
small end A would appear to be behind the
large end B even though the reverse was
physically true. What will be the apparent
orientation of the tube CD? Experimentation
on this type of problem has specified that the
apparent orientation of CD will be as shown in
Figure 2c with d's and d’so having the same
magnitude in Figure 2c as in Figure 2b (Gogel,
1956b). It will be noted in Figure 2 that points
A and C are always on the common line-of-
sight L, while B and D are always on another
common line-of-sight Ly. It can be, generalize

that the perceived depth resulting from the
binocular disparity between points (ot objects)
along common lines-of-sight is unaffected by
perceptual distortions occurring elsewhere. For
example, Point C’ in Figure 2c rémains cor-
rectly perceived with respect to Point A’ but
not with respect to Points B’ or D’. It'is a

though the apparent position of Point C with
respect to any other point is determined by its
unchanged relation in apparent depth with re-
spect e Point A: The apparent position of C
is determined only by*tts line-of-sight binocu-
lar disparity with respect to A. More formally
stated, the binocular disparity between any
point (such as Point C or D) and that other
point (such as Point A or B) which has the

}

-~10—

smallest difference in visual direction from the
first point (C or D) will be the binocular dis-
parity most effective in determining the ap-
parent position of the first point (C or D) with
respect to any other points in the field of view
(Gogel, 1956b, p. 1). This principle applies
to both Figures 2b and 2c. However, only in
the case of Figure 2c, ie., only in the case of
a perceptual distortion, does the problem, as to
which of the binocular disparities are perceptu-
ally most effective, become obvious. It is con-
cluded that the effectiveness of a binocular dis-
parity in determining a perception of apparent
position is inversely related to the relative di-
rectional separation between the points (or
objects). As a limiting case, when the two
objects (or points) are along an almost com-
mon line-of-sight the binocular disparity be-
tween these two points is almost completely
dominant in determining their apparent posi-
tion with respect to other points (or objects ).

If this principle is applied in detail to
Figure 2, it will follow that if A’B’ in Figure 2c
is a straight line, C’D’ must have some slight
curvature. Also, using the same principle, ¢’
in Figure 2c will not equal ¢’ in Figure 2b. In
general, Figure 2 can be considered as illustrat-
ing a situation in which the perceived orienta-
tion of a vertical plane, defined in the top view
drawing of Figure 2c by A’B’, differs from its
physical orientation (AB of Figure 2a). Asa
consequence of this perceptual distortion, all
other planes in its vicinity (such as CD), which
otherwise would have been correctly perceived,
will also be distorted in perceptual orientation,
with this distortion occurring in a systematic
manner in agreemerft with the factor of direc-
tional separation discussed above.

The importance of directional separation or
rather of directional adjacency in the percep-
tion of relative depth“tts been clearly demon-
strated for the binocular disparity cue (Gogel,
1954; 1956b). It will be assumed pending
further tests that this‘ holds for all cue systems
and that it can be generalized to the following
statement: The relation between the per-
ceived and the physical position of objects
along a common line-of-sight is unaffected by
distortions in perceived depth occurring else-
where. A corollary is that the apparent posi-
tion of an object in a configuration of objects

tiv
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principle.” The principle of adjacency deter-
mines how the relational characteristics of the
stimuli are organized. It asserts that percep-
tions of relative size and distance are locally
determined, e.g., they are determined by events
which exist in the vicinity of the objects being
judged and do not involve cues extending from
the observer to the objects. This point of view
when expressed in terms of retinal excitation
means that there is a local autonomy on the
retina with regard to perceptual effects, The
perception of the sizes of two objects or of the
depth between them is not determined by the
entire retinal stimulation but rather by excita-
tions usually occurring in the vicinity of the two
retinal images of these objects.

B. Directional Adjacency

The adjacency principle can be divided into
depth and directional adjacency. Experimental
evidence is available with respect to each of
these aspects. A study involving directional
adjacency will be discussed with the aid of
Figure 2.

In Figure 2a, the broken lines L, and Ly
represent two lines of sight originating from
the position of the observer with the observer's
position being located below the figure. The
line AB represents a top view of the physical
position of an object, for example, a window,
while the line CD represents a top view of the
physical position of another object, for example,
a long slender tube passing through the win-
dow, so as to form the angle ¢ with the plane
of the window. For both Object AB and Ob-

PHYSICAL PERCEIVED
NORMAL TRAPEZOIDAL
, , WINDOW | WINDOW
1
L '
. tr ue La
'
Ul
‘ t
oe
d, 4
ol.
: 1
\

Ficune 2. The field effects of a visual distortion.

—9-


FO I aS

expression in what is termed the size-distance
invariance hypothesis, This hypothesis states
that the perceived absolute size (S’) of an ob-
ject of constant retinal size (@) is specified by
its perceived absolute distance (D’). In equa-
tional form, the hypothesis is that

y=KoD (1)

where K and sometimes 9 are constants (Kil-
patrick and Ittelson, 1953).

In Equation 1, D’, a perception of absolute
distance, is the perception by the observer that
an object is at a particular distance from him-
self, In the present paper, the perception of
absolute distance has been contrasted with the
perception of relative distance with the latter
being the perceived distance between objects.
Similarly, S’ which is a perception of absolute
size can be contrasted with the perception of
relative size with the latter being the perceived
ratio of the sizes of two objects, This distinc-
tion can be illustrated by Figure 1. In Figure 1,
6, 9, and 9, refer to the angular or retinal size
of the widths of Objects e, f, and g. The per-
ceived absolute sizes associated with the widths
of Objects e, f, and g atte called S’,, S, and 8’,
where S., S,, and S, are the respective physical
widths. When the sizes of two objects such as
Objects e and f are perceived relative to each
other a perception of relative size or perceived
relative size has occurred. This would be
measured, for example, by adjusting the width
of S, until it appeared equal tq S,. Wheny the
size of a visual object is judged, by using Some
modality other than vision, howéver, a meas-
ure of perceived absolute size S’ t approached,
since a visual comparison between the visual
object and the measiiring devi¢e does not o¢
cur, For example, the kinesthetic modalf
could be used to measure perceived: absatate
size by having the observer adjust a non-visible
distance between his two hands to apparently
equal the width of the object seen in the visual
field.
perceived absolute ‘size and perceived relative
size becomes clearer when the two types of
measures are compared under the condition in

which the perceived absolute size of all objects
in the visual field is, for example, doubled.

This operational distinction between’

Under this condition, the relative size adjust-
ment (the adjustment of one visual size to ap-
parently equal another) would be unchanged,
whereas the kinesthetic adjustment would
double, Thus, a kinesthetic adjustment method
more nearly reflects an absolute judgment than
does the method of adjusting one visual per-
ceived size to that of another.

The experimental evidence relevant to the
size-distance invariance hypothesis has been
reviewed by Kilpatrick and Ittelson (1953) and
by Epstein, Park and Casey (1961). One
method used to test the size-distance invariance
hypothesis has been to correlate the results
from a size constancy adjustment with the re-
sults from a distance fractionation judgment
at a constant distance. Usually the correla-
tions resulting from this process have not been
significantly positive (Carlson, 1960; Gruber,
1954; Jenken and Hyman, 1959; Rump, 1961).
When correlations between perceived size and
perceived distance are determined as a function
of distance, however, positive correlations
though not necessarily a linear relation between
perceived size and perceived distance have
been found to occur (Kuroda, 1961; Gogel, Wist
and Harker, 1962; Rump, 1961). In the study
by Gogel et al., (1962) measurements of per-
ceived absolute size and of perceived absolute
distance were determined with normal observa-
tion and also with decreased and increased in-
terpupillary distances (base magnification). It
was found that although perceived absolute
size increased with increases in perceived ab-
solute distance, the results do not support
Equation 1. The zatio S’/D’ for a constant value
of 8 was found to vary significantly as a func-
tion of both physical distance and base magni-
fication. A positive relation between D’ and
S’ was indicated but the form of the relation
was neither always linear nor necessarily
constant for different viewing conditions. Per-
ceived absolute distance and perceived absolute

‘ size may have a gommunality of determining

events. But the experimental evidence does
not support the hypothesis that the former
necessarily determines the latter.

The previously discussed experiment which
tested the hypothesis that the retinal size of a
familiar object is a cue to perceived absolute

-6—



ae

Ficuar 1, A schematic diagram for considering perceptions of size and distance.

A perceived distance can be enumerated for
each of the physical distances D,, D,, and D,.
The perceived distances associated by the ob-
server with the physical distances D., D,, ang D,
will be labeled D’.,, D’,, and DL respectively.
Egocentric localization is involved in D’,, D’,
and D’, since each is an observer /perception of
the distance of an object from himself. Per-
ceptions of this kind are termed ‘perceptions of
absolute distance or perceived absolute dig-
tances, The perceived depths associated with
the physical distances du, dj, and d,,’ are per-
ceptions of relative distance and will be labeled
du, dq, and d’,,. The explanation of d’., in

terms of egocentric localization is that the ob- -

server arrives at d’x by a process which is simi-
lar or equivalent td” subtracting D’, from D’.
Similarly, d’, would be explained as the con-
sequence of a perceptual subtraction of D’,
from D’,, and d’,, as the consequence of a per-
ceptual subtraction of D’. from D’,. From this

point of view, the perception of relative dis-
tance is a result of the difference between two
perceptions of absolute distance. It follows,
for example, that to the extent that D’, and D’,
are ambiguous or impossible, d’, is ambiguous
or impossible. According to this viewpoint,
perceptions of absolute distance are the basic
perceptual data, the immediate events, which
determine the derived perceptions of relative
distance. Aad

An alternative hypothesis is possible. This
hypothesis is that the perception of relative
distance is the immediate event and that the
“perception of absolute distance, when it oc-
curs, usually requires the perceptual summihg
of perceived relative distances. In this paper,
some experimental evidence relevant to the
two hypotheses will be examined.

The hypothésis that perceived absolute dis-
tance determines perceived relative distance

-2-

aman Ae


ie., the observer adjusted h, j and | such that
d’g, d’y, and d’y each in tum equaled d’,, The
S’ values at D,, D,, and D, were measured by
adjusting the lateral distance between Objects
1 and 2 to duplicate the apparent width of the
rectangles g, i, and k, It was found in agree-
ment with equations derived from Equation 2,
that the value of S’/@ and the amount of bin-
ocular disparity required for the perceptually
equal depth intervals were linearly related.
The experiments concerned with three-
dimensional, perceived shape (Gogel, 1958a;
1958b; 1960b) support the same conclusion,
ie., Equation 2 is in agreement with the ob-
tained results.

It will be considered that the depth adja-
cency factor can be applied to cues in addition
to that of binocular disparity. A statement of
a principle of depth adjacency would then be
as follows: The ratio of retinal extents arising
from physical extents in the depth vicinity of
each other determines the ratio of their per-
ceived extents. This hypothesis asserts that
frontal and depth extents in the same depth
vicinity are perceptually interdependent such
that for any cue to relative distance or per-
ceived size, the specification of one also speci-
fies the other.

D. The Equidistance Tendency

The importance of a relative directional fac-
tor in the organization of visual perceptions has
also been demonstrated in the identification of
what has been called the “equidistance ten-
dency.” If two or more, objects ae simulta-
neously presented jn a visually reduced situa-
tion, such that no cues are/present to indicate
the depth between the objects, they will appear
to the observer to be at the same distance

(equidistant). ‘This is the equidistancp tend-
ency (Gogel, 1956a). This tendency o€curs in
all visual situations but is masked by/the pres-
ence of other distance cues. For example, if
size cues exist between the objects, the effect-
iveness of the equidistance tendency will’ be

@ teduced though probably not completely élimi-

nated. It hgs been demonstrated that the
equidistance tendency can modify the percep-
tual effectiveness of size cues (Gogel and Har-
ker, 1955) and even’ under certain circum-
stances the cue of binocular disparity (Gogel,

-13-

Brune and Inaba, 1954). The equidistance
tendency can modify the perceived depth be-
tween either or both monocularly or binocu-
larly observed objects.

Of importance for the present paper, the
strength of the equidistance tendency has been
found to be inversely related to the directional
separation of objects, The closer the objects
are in visual direction, the stronger is the tend-
ency for them to appear equidistant. This
conclusion is meant to apply to both vertical
and horizontal directional separations even
though direct demonstrations have been made
only with respect to horizontal separations. The
equidistance tendency is another demonstration
that directional adjacency is an important factor
in the organization of the visual world. The
effectiveness of the equidistance tendency in
modifying perceived depth between objects
varies inversely as the magnitude of the direc-
tional separation of the objects from each other.

E. Discussion

These studies in depth adjacency and in di-
rectional adjacency demonstrate that relation-
ships between adjacent objects (or parts of
objects) determine the perceived characteris-
tics of these objects. The observer might wish
to compare the relative position of two direc-
tionally nonadjacent ‘objects independently of
their relation to directionally adjacent objects,
but he cannot. According to the principle of
directional adjacency, the relations between
directionally adjacent objects are dominant in
determining apparent spatial position regardless
of which other relations the observer attempts
to use. Of, the observer might wish to judge
ome depth interval directly with another, dis-
regarding the perceived size (per unit of retinal
size) of nearby objects. But again he cannot
do this. Acédéfding to the principle of depth
adjacency, the value of $’/@ at a particular dis-
tance determines the’ perceived extent associ-
ated with a binocular disparity at that distance,
regardless of ‘the intent of the observer. Con-
sidering these two types of adjacency; and ex-
tending the adjacency concept to the perception
of object size, it can be stated that the per-
ceived depth intervals between objects or the
perceived sizes of objects are determined by
relations with respect to adjacent objects. Thus,


perceived space veridical over a range of stim-
ulus conditions? These questions will be con-
sidered with respect to the binocular disparity
and the size cue to relative depth.

1. The binocular disparity cue to relative depth

There is considerable evidence that the per-
ceived depth resulting from binocular disparity
is not proportional to physical depth. As an
example of this, consider the results from the
study conducted with the apparatus illustrated
in Figure 3. As discussed previously, the ob-
server adjusted Object h behind g, j behind i,
and | behind k until each of the depth intervals
appeared equal to the perceived depth between
Objects e and f. Only the binocular disparity
cue was present between these objects to de-
termine the perceived depth. From the re-
sults of this study, it was evident that perfect
depth constancy was not present. The magni-
tude of the physical depth interval required in
order to produce the constant perceived depth
interval increased linearly with the distance
of the depth interval from the observer (Gogel,
1960c). Perceived depth was not proportional
to physical depth and therefore, the binocular
disparity cue does ‘not necessarily produce
veridical depth perceptions.

2, The size cue to relative depth

From a study discussed in a previous portion
of this paper it has been concluded that the
absolute size of a retinal image has no percept-
ual consequences. Additional evidence fo sup-
port this point of view is pravided by a study
by Wallach and McKénna (1980) in which it
was found that the perceived absolute size of
a retinal stimulus.in a reduced cue situation
had no relationshig’ to the perceived size, of
objects in more usual situgtions. Applying
the conclusion concerning the perceptugl in-
adequacy of the absolute size of a retinal image
to the problem of perceived size, it is expected
that only the ratios of retinal sizes (not their,
absolute sizes) are of importance in determin-
infg the perceived depth resulting from the cue
of relative size. 'n agreement with this, Rock
and Ebenholtz (1959) found that the perceived
sizes of objects were dependent upon the size
of*surrounding objects (also see Gibson, 1959,
pp. 478-479). The conclusion concerning the

importance of ratios of retinal size may be com-
bined with the adjacency principle and applied
to the perception of size. It follows that per-
ceived size like the perceived depth resulting
from a binocular disparity is determined by
ratios of retinal sizes formed between adjacent
objects. The application of this conclusion is
illustrated with the aid of Figure 1. Suppose
in Figure 1 that the size cue is the only cue
present to determine the perceived depth as-
sociated with d. and d,,. The retinal size of
Objects e, f, and g is 6., 6, and 9,, respectively.
From the requirement that relative retinal ex-
tents are the determiners of perception, ratios
of 4s rather than 6s per se are the significant
stimuli. From the requirement that only ad-
jacent stimuli are perceptually compared, the
ratios of retinal sizes which are significant are
those between physically adjacent objects. It
follows that

a
d's =’, only when ae

G e

(3)

It is clear that Equation 3 predicts that the
perceived depth from size cues will not be
veridical throughout the visual field, For ex-
ample, for objects of equal physical size if D, =
10 and D,= 20 feet, D, would have to be 40
feet in order to produce successively equal
ratios of retinal size. In this case, d,=2 du
when d’,,=d’.. According to Equation 3, the
perceived depth from size cues is not propor-
tional to physical depth.

Figure 1 can also be used to illustrate the ap-
plication of the adjacency principle to the per-
ception of the large depth interval d.,. It is
asserted from the adjacency principle that the
perceived extent d’., would be determined by
the two smaller perceived extents d’, and d’,
such that d’,, =ale + d’,. In fact, for a con-
tinuously filled ‘visual field (and perhaps
for any’ visual field) the perceived distance d’.,
would be determined by the perceptual sum-
mation of a large number of smaller intervals.
/However, consider only the case in which the
perception of Object e with respect to Object
g is a consequence of the two intermediate per-
ceptions. This means that the perception of
the depth position of Object e with respect to
Object g is determined by whatever depth cues
are available between Objects e and f and be-

-~15-—


THE VISUAL PERCEPTION OF SIZE AND DISTANCE!

WALTER C. GOGEL

ABSTRACT

The perception of absolute distance has been assumed to be important in the perception
of the size of objects and the depth between them. A different hypothesis is proposed. It
is asserted that perceived relative size and distance are the primary psychological phenomena,

with perceived absolute distance derived from the perceptual summing of

depths. In agreement with this point-of-view, it is stressed that relative, ral
retinal extents, are the determiners of visually

“adjacency princlple” is identified as perceptual

le states that the spparent size or position of any object in the field-of-view is

stance cues occur between it and adjacent objects. Some

This princip|
determined by whatever size or

reeived relative
er than absolute

ceived extents. A principle called the
fy organizing the relative retinal stimuli.

evidence for the adjacency principle is discussed and some consequences of the principle are

considered. §.

I, INTRODUCTION

Egocentric localization either explicitly or
implicitly has been assumed to play a jcentral
role in the perception ,of size' apd distance. It
is the purpose of this paper to question the
validity of this point of view/and to offer an
alternative explanation of the factors important
in perceived size artd distance; This alternative
explanation stresses that the relational fen
acteristics of stimuli are the determiners gf per-
ception. It asserts that the perceptions of size
and distance are determined by events unre-
lated to the observer’s perception of his own‘
ngsition in the visual world. Jt further asserts
that factors are gperative to determine which
of the many relafional characteristics of visual
stimuli are important for particular perceptions.
One such factor, labeled the “adjacency princi-
ple,” is identified and some consequences of
the operation of this factor are discussed.

Ii. EGOCENTRIC LOCALIZATION AND
THE VISUAL PERCEPTION OF SIZE
AND DISTANCE

A. The Role of Egocentric Localization in
the Perception of Relative Distance.

Tie possible role of egocentric localization
in the perception of relative distance can be
considered wi aid of Figure 1. Figure 1
gives a notation for some physical sizes and
distances associated with Objects e, f, and g.

'
i '
i
1 This paper is a modification of a paper presented by the
author Rehile a member of the us. ‘Atay Medical Re-
search Laboratory, Fort Knox, Kentucky) ‘at the sympo-
sium on visual space perception (sponsored by the Armed
Forces and the Committee on Vision of the National
Research Council) Washington, D.C., 27 and 28 March,
1961.

-1-



THE VISUAL PERCEPTION OF SIZE AND DISTANCE

WALTER C. GOGEL, Ph.D.°

* Chief, Sensory Section

62-15

a

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JULY 1962 i



is determined dnly by its line-of-sight relations.
A more general statement is that the effec-
tiveness of a cue system in determining the ap-
parent relations (perceived size or distance)
between objects (or between parts or points of
objects) is inversely related to the magnitude
of the relative directional separation between
the objects (or between parts or points of ob-
jects). This is a statement of a principle of
directional adjacency.

C. Depth Adjacency

In addition to the evidence for directional
adjacency as an organizing factor in deter-
mining apparent position, there is evidence for
a factor of depth adjacency. The evidence
comes from a series of experiments which have
been concerned with the problem of specifying
the factors which permit a binocular disparity
to be interpreted as a depth extent. It was
hypothesized in. these experiments that the per-
ceived size (S’) of objects in a fronto-parallel
plane (perceived frontal extents) in the vicinity
of a binocular disparity determine the perceived
depth associated with the binocular disparity
(Gogel, 1958a; 1958b; 1958c; 1959; 1960a;
1960b; 1960c). It’ is as though the observer
perceives the depth resulting from the binocu-
lar disparity to be a multiple of the width or
height of an adjacent frontal extent. More
precisely, it was hypothesized (Gogel, 1960b )?
that the small perceived depth A d’ resulting
from a small amount of binocular disparity Aa

is : y
iy +
SS Ae ‘y
Ad=o i (2)

where S’ is the perceived size and @ the angu-
lar (retinal) size of a frontally presented gbject
(an object presented in a fronto-parallel plane}
at the same distance as the obje¢ts préducing
the binocular disparity, and C is an individual
constant. Equation 2 can be illustrated with
the aid of Figure 3 which is a schematic pet-
&pective diagram of an observer’s viewing posi-
tion and objects in a field of view. Consider
the rectangle labeled g and the small disc
labeled h located a very short distance behind
y. As in Figure 1, the angular size of the fron-
tal width of g is 8 The perceived depth be-

tween Objects ‘g and h in Figure 3 is A d’a.
The perceived width of Object g would be
labeled S’,. Equation 2 states that A d’,./S’,
= A a,/CO,, or the ratio of the perceived
depth (A d’,,) to the perceived size S’, of the
frontal extent S, is equal to the ratio of the
binocular disparity (A@,,) to the frontal an-
gular size (8,) with 1/C. being a constant of
proportionality. In other words, Equation 2
states that the ratio of perceived extents is pro-
portional to the ratio of retinal extents.

It will be noted that in the discussion of
Equation 2, (see Figure 3) the S’/@ value at
Object g not at Object i or k was used to de-
termine the perceived depth between Object g
and h. Equation 2 specifies that a ratio of
perceived extents is proportional to a ratio of
retinal extents but only when the retinal ex-
tents arise from physical extents in the vicinity
of each other, Aside from the constant C, the
factor which determines A d’y is S,/8, (not
S//0, or S’,/@.), the factor which determines
Ad’, is $//8, (not S,/@, or S,’/%), and the
factor which determines Ad‘n is S,’/6, (not S,’/
@, or S//6,). A depth adjacency effect is oc-
curring. Not all perceived extents interact
equally. In perceiving the depth associated
with a binocular disparity, only perceptions
involving frontal extents in the depth vicinity
of the binocular disparity are important. It is
asserted that this is not an act of conscious
judgment but occurs as a consequence of the
nature of the process by which a perceived
depth results from a binocular disparity.

What is the evidence for the validity of Equa-
tion 2 and thus for the validity of the depth
adjacency factor? In an experiment discussed
previously (Gogel, 1960a) the value of @ was
changed with both the binocular disparity and
S’ essentially constant. It was found in agree-
ment with Equaéion 2 that as @ increased, the
preceived depth between the binocular objects
decreased, Equation 2 has also been applied to
the comparison of depth intervals (Gogel,
1960c), This, also can be illustrated with
Figure 3. A constant binocular disparjty be-
tween Objects e and f was presented and was
duplicated in apparent depth at D,, D,, and D,,

2 The original notation used in Equation 2 has been
changed tg conform with the notation employed in this
paper. In the original studies, A a and E were used
instead of /\d’ and S’, respectively.

~ll-


:

what might be called the adjacency principle
in three-dimensional perception can be stated as

follows: The apparent position or apparent
size of any object in a configuration of objects
is determined by whatever cues or factors
occur between the object and perceptually ad-
jacent objects.

The adjacency principle emphasizes the in-
teraction of local events and their independ-
ence from egocentric localization or other more
remote events. In this process, use is made
of some of our most precise visual abilities.
These are the abilities to determine when ob-
jects are at the same or at a different distance
(and direction) from each other, Some of
these are such cues as zero amount of binocu-
lar disparity, the size cue involving equal ret-
inal extents, the cue of overlay, etc. Thus,
precise cues are available for establishing per-
ceptual adjacency and consequently for de-
termining the interaction of locally perceived
extents. Locally perceived extents then sum-
mate to produce larger perceptual intervals.
These larger perceptual intervals are therefore
derived extents and should tend to decrease
in precision with an increase in the size of the
interval. ’

Directional adjacency has been used success-
fully to predict the perceived path of move-
ment in visually distorted fields. The per-
ceived path of a moving object can be very
different depending upon the arrangement of
the object with respect to the adjacency factor
(Gogel, 1956b). Observers can be made to
see an object as moving through a limited jAre
or as traversing an entire gircle, depending up-
on this factor. Also, it must be/emphasized
that the effect of adjacency on peyception does
not occur by means of a conscious judgment.

In situations as complex as those which have;

been used, e.g., in a situation in’ which object

or parts of objects are moving in different gi-
rections, it is clearly impossible for’ even a
highly sophisticated observer to deduce rather
than perceive a path of movement. It is as-

serteg that adjacency is a principle which or- .

ganizes perception quite independently of the
thought process or tRe set of the observer.

It is also possible that the adjacency princi-
ple can be extended to the temporal as well as
the spatial dimension. In the experiment in-
volving the throwing of darts to the perceived

-14-

absolute distance of playing cards (Gogel et al.,
1957), it was found that the temporal order in
which the different retinal sizes were presented
affected their perceived positions. This sug-
gests that the order of presentation is perceptu-
ally significant. Consider the case in which
the observer is presented with three different
retinal sizes A, B, and C with A. presented first
and C last. According to the adjacency prin-
ciple, the position (or size) of Stimulus A with
respect to Stimulus C is determined by what-
ever cues or factors are operative between Stim-
uli A and B and between Stimuli B and C.
The perception of the distance (or size) of A
with respect to C must occur via the intermedi-
ary perceptions of A with respect to B and B
with respect to C. The adjacency principle as-
serts that the first stimulus (A) cannot be
judged directly with respect to the last stimulus
(C) but must occur by means of the perception
of each of these stimuli with respect to the
intermediate stimulus (B).

IV. IMPLICATIONS

A. The Veridicality of Size and Distance
Cues

The use of the concept of egocentric local-
ization as a primary rather than a derived
quality of spatial perception is congenial to the
hypothesis that spatial perception is veridical.
Suppose, for example, that the convergence or
accommodation of the eyes were potentially
adequate cues to perceived absolute distance.
Through experience, the actualization of this
potential could be adjusted so that perceived
absolute distance and subsequently all per-
ceived distances were veridical. Also, as dis-
cussed previously, if convergence produced ver-
idical perceptions of absolute distance, this
would at least offersthe possibility that the per-
ceived depth associated with a binocular dis-
parity would also be veridical. A parallel dis-
cussion would apply with respect to the
absolute distance cue of familiar size as a de-
terminer of the perceived depth between famil-
iar objects. But; the concept of egocentric
localization as a primary datum of perception
has been rejected in this study. How veridical
then are cues to perceived size and distance?
If egocentric ‘localization is a consequence
rather than a determiner of perceived space, is

awa