of the present paper, this result represents a
modification by the equidistance tendency of the
depth perception resulting from size cues alone
or from size and binocular disparity cues to-
gether.

A well-known demonstration that can be used
to illustrate the capability of the equidistance
tendency to modify the perceived depth normally
resulting from size cues occurs with the Ames
monocular distorted room. This room, while
nonrectangular in shape, provides retinal stimuli
equivalent to that of a rectangular room and is
perceived as rectangular. Two windows usually
are located on the far wall of the room with the
left window more distant and proportionately
larger than the right. Since the two windows
have the same retinal size and shape, they are
perceived to have the same size and to be at the
same distance. If a familiar object (for exam-
ple, a face) is presented directly behind each
window, the two faces will appear to be of differ-
ent sizes. The usual explanation for the ap-
parent difference in the size of the faces is that
the familiarity that would indicate that the two
faces are the same size is in conflict with the as-
sumption that the room is rectangular (Ittelson
and Kilpatrick, 1961). This conflict need not
have occurred, however. The observer (in agree-
ment with the known sizes) might have per-
ceived the faces to be of the same size and, there-
fore (in agreement with their differences in
retinal size), might have perceived them to be
at different distances behind the windows. The
perceptual conflict is a consequence of the faces
appearing at the distances of the apparently, but
not physically, equidistant windows. Clearly,
the equidistance tendency is the factor that deter-
mines that each face will appear at the distance
of its directionally adjacent (framing) window.
Thus, the conflict appears only because the equi-
distance tendency is effective in modifying the
normal depth perception that would occur as a
result of the different retinal sizes (the relative
size cue) between the two faces.

It is interesting to note that, according to the
above interpretation, the distorted room is en-
tirely unnecessary in producing the conflict. A
rectangular room with rectangular windows and
with two faces presented at different distances
behind the windows would produce a retinal
stimulus identical to that of the distorted room
with the faces directly behind the windows.

Hence, both the display involving the rectangu-
lar room and the display involving the distorted
room must be perceived as identical. With
either the distorted or rectangular room, if all
distance cues as to the depth between the faces
are absent except the cue of familiar size, the
equidistance tendency would result in faces of ap-
parently different sizes appearing at the distance
of the apparently equally distant windows. It is
the modification of the perceived depth between
the faces by the equidistance tendency, with re-
spect to the windows, that is necessary for the
perception that the two faces are of different
size.

V. Other Instances of the Effects of the Equi-
distance Tendency.

Visual conditions in which the equidistance
tendency would have some perceptual effect occur
frequently. Therefore, it would be expected that
phenomena which can be attributed to this tend-
ency would have been noted either explicitly or
implicitly in a variety of situations. This is indeed
the case, as the following instances demonstrate.
Judd has reported (1898) that white threads
presented against a black background and located
at different distances from an observer seemed to
be equidistant when viewed monocularly, where-
as when viewed binocularly, they were clearly per-
ceived to be at different distances. In discussing
the apparent depth between diplopic images and
a binocularly fixated object, Judd states, “And
we may assert it as a general principle that in
monocular vision objects tend toward a single
plane, the plane determined by binocular factors”
(1898, p. 293). Katz (1935, pp. 71-74) notes that
the apparent location and orientation of film color
is at least partially determined by the location
and orientation of the aperture through which it
is viewed. Simon (1936) discusses some of the
early observations on perceived distortions which
relate to his own experiments (mentioned above)
and, it would seem, also relate to the equidistance
tendency. In an experiment concerned with the
cue of motion perspective, Gibson and Carel
(1952) report that a stationary display of lights
in a reduced-cue situation are perceived as oc-
cupying a frontoparallel plane. The results from
a number of experiments concerning the percep-
tion of slant (Beck and Gibson, 1955; Bergman
and Gibson, 1959; Clark, 1953; Clark, Smith and
Rabe, 1955, 1956a, 1956b; Gibson, 1950b; Gibson



REFERENCES

1. Beck, J., and Gibson, J. J. The Relation of Apparent
Shape to Apparent Slant in the Perception of Objects.
J. Exp. Psychol., 1955, 50, 125-133.

Bergman, R., and Gibson, J. J. The Negative After-
effect of the Perception of a Surface Slanted in the
Third Dimension. Amer. J. Psychol. 1959, 72,
364-373.

Boring, E. G. The Moon Illusion. Amer. J. Physics,
1948, 11, 55-60.

. Clark, C. W. Exposure Time and the Perception of
Slant. Paper Read at Canadian Psychological Asso-
ciation, 1953.

Clark, ©. W., Smith, A. H,, and Rabe, Ausma. Ret-
inal Gradient of Outline as a Stimulus for Slant.
Canad. J. Psychol., 1955, 9, 247-253.

Clark, C. W., Smith, A. H., and Rabe; Ausma. Retinal
Gradients of Outline Distortion and Binocular Dis-
parity as Stimuli for’ Slant. Canad. J. Psychol.,
1956a, 10, 77-81.

. Clark, C. W., Smith, A. H., and Rabe, Ausma. The
Interaction of Surface Texture, Outline Gradient,
and Ground in the Perception of Slant. Canad. J.
Psychol., 1956b, 10, 1-8.

Epstein, W., and Park, J, Examination of Gibson’s
Psychophysical Hypothesis. Psychol. Bull, 1964, 62,
180-196.

Epstein, W., Park, J., and Casey, A. The Current
Status of the Size-Distance Hypothesis. Psychol.
Bull, 1961, 58, 491-514.

Gibson, J. J. The Perception of the Visual World.
Boston: Houghton Mifflin, 1950a.

Gibson, J. J. The Perception of Visual Surfaces.
Amer. J, Psychol., 1950b, 63, 367-384.

Gibson, J. J., and Carel, W. Does Motion Perspective
Independently Produce the Impression of a Receding
Surface? J, Exp. Psychol., 1952, 44, 16-18.

Gibson, J. J., and Gibson, Eleanor J. Continuous
Perspective Transformations and the Perception of
Rigid Motion. J. Exp. Psychol., 1957, 54, 129-138.

Gogel, W. C. The Tendency to See Objects as Equi-
distant and Its Inverse Relation to Lateral Sepa-
ration, Psychol. Monogr., 1956a, 70, No. 4 (Whole No.
411). (Also see AMRL Report No. 146, same title,
1954).

Gogel, W. ©. Relative Visual Direction as a Fac-
tor in Relative Distance Perception. Psychol.
Monogr., 1956b, 70, No. 418, 1-19.

Gogel, W. ©. The Visual Perception of Size and
Distance. Vision Res., 1963, 3, 101-120.

Gogel, W. ©. The Perception of Depth from Binocular
Disparity. J. Exp. Psychol. 1964a, 67, 379-886.
Gogel, W. C. Size Cue to Visually Perceived Distance.
Psychol. Bull. 1964b, 62, 217-235.

Gogel, W. C., Brune, R. L., and Inaba, K. A Modifi-
cation of a Stereopsis Adjustment by the Equidist-
ance Tendency. AMRL Report 157, 1954, 1-11,

o

”

2

10.

11,

12,

13.

14,

15.

16.

17.

18.

19.

12

20, Gogel, W. C., and Harker, G. S. The Effectiveness of
Size Cues to Relative Distance as a Function of
Lateral Visual Separation. J. Exp. Psychol., 1955,
50, 309-815.

Gruber, H. E., and Clark, W. C. Perception of Slanted
Surfaces. Percept. Mot. Skills, 1956, 6, 97-106.

. Gruber, H. E., King, W., and Link, S. Moon Illusion:
An Event in Imaginary Space. Science, 1963, 139,
750-752,

Harker, G. S. Apparent Frontoparallel Plane, Ster-
eoscopic Correspondence, and Induced Cyclotorsion
of the Eyes. Percept. Mot. Skill, 1962, 14, 75-87.
Hartman, A, M. Effect of Reduction on the Relation-
ship Between Apparent Size and Distance. Amer. J.
Psychol., 1964, 77, 353-366,

Howard, I. P,, and Templeton, W. B, The Effect of
Steady Fixation on the Judgment of Relative Depth.
Quart. J. Exp. Psychol. 1964, 16, 193-203.

Ittelson, W. H., and Kilpatrick, F. P. The Monocu-
lar and Binocular Distorted Rooms. In Explorations
in Transactional Psychology. (F. P. Kilpatrick, Ed.)
New York University Press, 1961.

Judd, C. M. An Optical Illusion. Psychol. Rev.,
1898, 5, 286-294.

Katz, D. The World of Colour.
Paul, 1935,

. Kaufman, L., and Rock, I. The Moon Iilusion.
Scient. Amer., 1962a, 207, 120-130.

Kaufman, L., and Rock, I. The Moon Illusion. I.
Explanation of This Phenomenon was Sought
Through the Use of Artificial Moons Seen on the
Sky. Science, 1962b, 136, 953-961.

King, W. L., and Gruber, H. E. Moon Illusion and
Emmert's Law. Science, 1962, 135, 1125-1126,
Kohler, W., and Emory, D. A. Figural After-effects
in the Third Dimension of Visual Space. Amer. J.
Psychol., 1947, 60, 159-201.

McDonald, R. P., and O'Hara, Patricia T. Size-
distance Invariance and Perceptual Constancy.
Amer, J. Psychol., 1964, 77, 276-280.

Natsoulas, T. On Homogeneous Retinal Stimulation
and the Perception of Depth, Psychol, Bull. 1963,
60, 385-890.

Price, G. R. An Emmert’s Law of Apparent Sizes.
Psychol. Ree., 1961, 11, 145-151.

Rock, I., and Kaufman, L. The Moon Illusion, II.
Moon’s Apparent Size is a Function of the Presence
or Absence of Terrain, Science, 1962, 136, 1023-1031.

Rock, L, and McDermott, W. The Perception of
Visual Angle. Acta Psychol., 1964, 22, 119-184.
Roelofs, C. O. Convergence and Depth Perception.
Acta Psychol., 1960, 17, No. 3, 193-217.

Roelofs, C. O. Equidistance Tendency, Acta Psy-
chol., 1961, 18, 368-382.

21,

23.

24,

25.

26.

27.

28, London: Kegan

30.

31.

32.

34.

35.

36.

37.

38.

39.


mined by its perceived distance. This conclusion
partially results from observing the size of the
horizon moon when the terrain between the ob-
server and the moon is modified. There is no
reason, however, for expecting terrain modifica-
tions to affect the apparent distance of the moon
unless there is some factor that makes the moon
appear at some particular distance; ie, at the
distance of some portion of the terrain, It is as-
serted that this factor is the equidistance tend-
ency. Since the horizon or objects on the hori-
zon are usually directionally closest to the moon,
the moon usually tends to appear at the horizon
distance. Thus, either the explanation in terms
of S’/0 or the explanation in terms of the size-
distance invariance hypothesis requires the op-
eration of the equidistance tendency. The ex-
planation in terms of S’/@ can be classified as a
type of explanation which Rock and Kaufman
call “the context effect,” and which they reject as
necessary for understanding the illusion, This re-
jection seems to be on the basis of the previously
mentioned effect of terrain modifications on the
perceived size of the moon illusion, and also be-
cause the moon illusion occurs over water or de-
sert where there are no other objects of particular
perceived sizes (Kaufman and Rock, 1962a;
Rock and Kaufman, 1962). But it is not unreason-
able that terrain modifications could change the
value of S’/@ in the visual field at the apparent-
distance position of the moon, and it is difficult
to imagine a visual field containing no values of
8’/6 while still maintaining the perceived dis-
tances required for the size-distance invariance
explanation. Regardless of whether perceived
distance or S’/@ is the appropriate explanation,
however, the moon illusion, like Emmert’s law,
requires the equidistance tendency as a part of its
explanation.

VII. Possible Explanations of the Equidis-
tance Tendency.

The requirements that must be met by any
attempt to explain the equidistance tendency are
specified by the range of phenomena demon-
strating the tendency. From the point of view
of the present paper, any explanation must en-
compass the following phenomena.

A. The equidistance tendency occurs between
any visual inhomogenities (between any contours
or parts of a figure or surface).

B. The strength or effectiveness of the equi-
distance tendency is inversely related to direc-
tional separation ( in any orientation).

C. The equidistance tendency occurs between
objects viewed monocularly or between objects
viewed binocularly or between objects some of
which are viewed monocularly and some binocu-
larly.

D. The presence of strong depth cues can re-
duce or eliminate the effectiveness of the equi-
distance tendency.

E. Under certain conditions, the equidistance
tendency can modify depth perceptions resulting
from cue systems such as binocular disparity and
relative or familiar size.

F. The equidistance tendency can act as a re-
sultant effect occurring between one object and
a complex visual field.

Roelofs (1960, 1961) presents an explanation
of the process by which monocularly observed
objects appear at approximately the same ap-
parent distance as binoeularly observed objects.
This explanation asserts that the monocularly
presented image in the one eye fuses binocularly
with an unstimulated but corresponding area in
the other eye. Since the resulting fusional process
will tend to be with respect. to corresponding
points, the monocularly observed object will tend
to appear at the same apparent distance as the bi-
nocularly observed fixated object. It is difficult,
however, for the present writer to see how this
explanation can be applied to cases in which
the equidistance tendency occurs between objects
either completely monocularly or completely bino-
cularly observed.

Bergman and Gibson (1959) describe the re-
sults of their study as indicating the occurrence
of a negative after-effect. The tendency for the
slanted surface to appear in a frontoparallel
plane is attributed to a perceptual shift toward
a norm and is called normalization. The effect
of the normalization is assumed to persist over
time and results, for example, in subsequently
presented frontoparallel surfaces appearing tilted
in the opposite direction. It is possible, there-
fore, that the concept of normalization might
provide a basis for understanding the equidis-
tance tendency. There are several reasons, how-
ever, for considering this to be unlikely. One
difficulty in applying the concept of normaliza-
tion to the equidistance tendency is that normal-



size of an afterimage is directly proportional to
its perceived distance from the observer. Accord-
ing to this assertion, Emmert’s law is a special
case of the size-distance invariance hypothesis
(Epstein, Park and Casey, 1961; Price, 1961) and
thus would be subject to the evidence for and
against this hypothesis. The second possible an-
swer to the problem of how the perceived size of
the afterimage is determined can be considered by
returning to the example of an afterimage ap-
pearing at the distance of a directionally adjacent
(or directionally identical) vertical surface. It
has been asserted (Gogel, 1964) that the per-
ceived size of objects is determined by the per-
ceived size (S’) per unit of visual angle (6) of
objects in its apparent depth vicinity. Suppose,
for example, that the visual angle (6,4) of the
height of the afterimage is half as large as the
visual angle (9n) of the height of the vertical
surface and that the perceived size (8’p) of the
height of this surface is 6 feet. Under these con-
ditions, the afterimage would have a perceived
height (84) of 3 feet; i.e., 8’,/0, = S’a/On. The
contributions of the equistance tendency in this
example would be to make the afterimage appear
at the depth vicinity of the surface and thus de-
termine that the §’/@ value of the surface would
become that of the afterimage. It is very difficult
to provide an instance in which the perceived size
of an afterimage cannot be attributed to the action
of relative values of S’/@ with respect to the sur-
rounding environment rather than to its perceived
distance from the observer. The S’/6 values of
perceptually adjacent objects will determine the
perceived size of the afterimage without the need
to involve the concept of perceived distance from
the observer. For the statement of Emmert’s law
in terms of either perceived or physical distance
or in terms of the S’/0 values of objects in its per-
ceptual depth vicinity, however, the equidistance
tendency is a necessary postulate.

C. Application to the Moon Illusion —Conclu-
sions that apply to the perceived sizes of after-
images should also apply to the perceived
size of the moon and hence to the moon illusion
(King and Gruber, 1962; Kaufman & Rock,
1962b). The perceived size of the moon should
be capable of being systematically changed by
making it via the equidistance tendency appear
at the distance of objects with different values
of S’/6. For example, the following demonstra-
tion should be possible. Suppose a “moon”

[this might be an optically generated dise of
light as in the experiments by Kaufman and
Rock (1962b) and Rock and Kaufman (1962) ]
is presented along a line of sight directly
above a rectangular object, for example, a playing
card 11 feet from the observer. No other objects
except the playing card and moon are visible, and
all cues to a perceived depth between the moon
and card are removed. In this case, according to
the equidistance tendency, the moon usually would
appear at the distance of the playing card. Since
the moon appears at the distance of the card
and subtends about one-half the width of a
playing card when the card is at 11 feet, the
moon would appear to be about 1 inch in di-
ameter. Suppose, however, that, without changing
its physical size or distance, the rectangular ob-
ject is made to appear as a window, with conse-
quently about a 12-fold increase in S’/6. Under
these conditions, the moon (still appearing at the
distance of the rectangular object) would appear
to be about 1 foot in diameter. Thus, the moon
could be made to have any perceived size depend-
ing upon the joint operation of the equidistance
tendency and the concept that the moon will
assume the §’/9 value of objects with which it
appears equidistant.’ The moon illusion is the
observation that the moon at the horizon usually
looks larger than it does when it is at the zenith.
But it is clear from the above discussion that the
horizon (or zenith) moon can be made to look
any size by making it appear at the distance of
objects with various values of 8’/6. It follows
that the direction of the moon illusion is a hap-
penstance of the particular visual conditions
usually experienced, since the appropriate manip-
ulation of the visual conditions should make it
disappear or cause its reversal.

The above explanation of the moon illusion is
consistent with the results of the recent research
on the moon illusion by Kaufman and Rock
(1962a, 1962b), King and Gruber (1962) and
Rock and Kaufman (1962) in which evidence
is presented against the angle-of-regard hypoth-
esis of the moon illusion summerized by Boring
(1943). Unlike the S’/@ aspect of the explanation
asserted in the present paper, however, Rock and
Kaufman (1962) use the size-distance invariance
type of explanation; ie., it is concluded that, in
general, the perceived size of the moon is deter-
‘Boring (1943, p. 57) provides an illustration of this phenom-

enon when he notes that the apparent size of the horizon
moon shrinks when viewed between the thumb and forefinger.


the distance to a tall distant object, such as a
water tower, whose base is obscured by inter-
vening hills. The tower appears at the distance
of the highest hill until this hilltop is reached,
at which time it appears at the distance of the
next highest elevation. Other examples of the
action of this tendency in normal situations are
possible. It is clear that the moon illusion is

iL

only one of many real-life situations in which
the equidistance tendency is involved. It is evi-
dent from the present paper that the range of
phenomena that can be classified: under the equi-
distance tendency is large and that the perceptual
consequences of the equidistance tendency must
be considered in a variety of both experimental
and naturally occurring situations.



AM 65-11

THE EQUIDISTANCE TENDENCY AND
ITS CONSEQUENCES

Problems in Depth Perception

Walter C. Gogel, Ph. D.

Approved by Released by
Stembey A Mrnehben Wd Whe
Srantey R. Mouter, M.D. M. S. Wurre, M.D.

Director, CARI Feperat Arr Surceon

April 1965

FEDERAL AVIATION AGENCY

Office of Aviation Medicine
Civil Aeromedical Research Institute
Oklahoma City, Oklahoma



NOTES


AL

42,

43.

44,

45,

. Roelofs, C, O., and Zeeman, W. P, C. Apparent Size

and Apparent Distance in Binocular and Monocular
Vision, Ophthal., 1957, 133, 188-204.

Simon, M. Uber egozentrische Lokalisation. Phychol.
Forsch., 1936, 27, 113-131.

Smith, A. H. Gradients of Outline Convergence and
Distortion as Stimuli for Slant. Canad, J. Psychol.,
1956, 10, 211-218,

Smith, A. H. Outline Convergence versus Closure in
the Perception of Slant. Percept. Mot. Skills, 1959,
9, 259-266,

Smith, A. H. Judgments of Slant with Constant
Outline Convergence and Variable Surface Texture
Gradient. Percept. Mot. Skills, 1964a, 18, 869-875.
Smith, A. H. Delay of Response in the Perception
of Slant and Shape. Canad. J. Psychol., 1964b, 18,
235-244.

13

46, Smith, A. H. Relation of Slant and Shape Judgments
in Reduced Viewing. Canad. J. Psychol. 1964¢, 18,
224-284,

Smith, O. W., and Smith, Patricia C. Interaction
of the Effects of Cues Involved in Judgments of
Curvature, Amer, J. Psychol, 1957, 70, 361-375.
Smith, Patricia C., and Smith, 0. W. Veridical
Perceptions of Cylindricality: A Problem of Depth
Discrimination and Object Identification. J. Exp.
Psychol., 1961, 62, 145-152.

Stavrianos, Bertha K. The Relation of Shape Per-
ception to Explicit Judgments of Inclination. Arch.
of Psychol., No. 296, 1945.

Werner, H. Dynamies in Binocular Depth Perception.
Psychol. Monogr., 1987, 49, No. 2 (Whole No. 218).
Werner, H. Binocular Depth Contrast and the
Conditions of the Binocular Field. Amer. J. Psychol.,
1988, 51, 489-497.

47.

48.

49.

50.

Bl.



ization is sometimes difficult to define. Why, for
example, is a frontoparallel plane more repre-
sentative of a norm than a plane slanted in depth
at 45°? Also, it is not obvious why the effective-
ness of a normalization would be inversely related
to directional separation as is required by the
equidistance tendency. Furthermore, since the
equidistance tendency can occur in visual fields
containing a large number of different objects
at different distances, an explanation in terms of
normalization would require the concept of a
large number of competing normalization tend-
encies, The range of phenomena involved in the
equidistance tendency is such that an explanation
of the tendency in terms of any simple concept of
normalization is not apt to be successful.
Several of the discussions of the equidistance
tendency (Gogel, 1956a; Roelofs and Zeeman,
1957) suggest that the tendency can be treated
as a factor possessing both magnitude and direc-
tion. It would seem reasonable, thereforé, that
the equidistance tendency can be additive or sub-
tractive with respect to other cue tendencies in
the perceptual localization of an object in
apparent depth (Gogel, Brune and Inaba, 1954).
Also, equidistance tendencies can subtract or add
in determining a final equidistance vector. Thus,
in the present paper, it is assumed that the equi-
distance tendency adds a depth factor to any
visual field containing more than a single point
of light, and that as a depth factor it enters
quantitatively in competition or agreement with
other depth factors in the determination of a
final apparent position of an object in depth.

VIII. Some Unsolved Aspects of the Equi-
distance Tendency.

It has been reported that the tendency for
surfaces slanted in depth to appear in a frontal
orientation changes with increasing time of ob-
servation (Bergman and Gibson, 1959; Clark,
1953; Simon, 1936; Smith, 1964). It is therefore
possible that the strength of the equidistance
tendency changes with observation time. In the
absence of opposing cue systems, the effect of the
equidistance tendency may be rapid. This is
suggested by the ability of the equidistance tend-
ency to determine the perceived path of move-
ment of an object attached to the rotating trape-
zoidal window with the entire display viewed
monocularly (Gogel, 1956). The rapidly chang-
ing directional alignments in the study with the

10

rotating window required that the effect. of the
equidistance tendency be rapid in order for it to
determine apparent depth. Without opposing
cues or tendencies, any amount of equidistance
tendency seems to be quickly effective. When other
cues of depth are present, possibly the relative ef-
fectiveness of the equidistance tendency (relative
to that of other cues) increases within some in-
terval of observation time. Additional research
is required to clarify the temporal characteristics
of the equidistance phenomena both for simul-
taneous and successive presentations.

Additional aspects of the equidistance tend-
ency should be considered. The notion that the
equidistance tendency between two objects is a
vector of a particular magnitude would suggest
that increasing the number of objects at a con-
stant distance would increase the strength of the
equidistance tendency toward this distance. In
a similar fashion, the strength of the equidis-
tance tendency between objects might increase
with an increase in their visual area. Also, the
meaning of the term directional separation re-
quires clarification. Is the significant directional
separation to be defined physically, retinally, or
perceptually? In most experimental situations,
a distinction between the three types of defiini-
tions would not need to be made. It is possible,
however, to construct experimental situations in
which the three types of directional separation
are not identical.

IX. Concluding Remarks.

The equidistance tendency may be expected to
modify the perception of depth in any situation
in which cues to depth are either partially or
completely reduced. The effect of the equidis-
tance tendency on any object will depend upon
the adequacy of the specific cues that relate this
object to the remainder of the visual field. Depth
relations in the remainder of the visual field
may be clearly perceived. Unless the depth cues
relating a particular object to the rest of the
visual field are effective, however, the equidis-
tance tendency will modify or determine the ap-
parent depth position of this object. TIllustra-
tions have been given of the distortion in per-
ceived depth that can occur in experimental situ-
ations as a result of the equidistance tendency.
The equidistance tendency might also be ex-
pected to influence perceptions in real-life situ-
tions. Consider, for example, the perception of


in the apparent tilt of the grid. The equidistance
tendency also would be expected to act in the
direction of reducing the apparent tilt by tending
to make all parts of the grid appear at the same
distance. Harker found that only some of the re-
duction in perceived tilt could be attributed to
cyclorotation with the remainder attributed to the
action of the equidistance tendency. Simon
(1936), in a series of experiments, found that a
binocularly observed outline circle physically
slanted in depth would change its apparent orien-
tation under reduced conditions of observation.
Simon suggests that the perceived orientation
(and perceived distance) of such objects would be
along an ellipsoid with the observer at a focal
point. Clearly the observations upon which this
conclusion is based are very similar to those ex-
pected from the equidistance tendency and
probably represent a modification by the equidis-
tance tendency of judgments involving stereo-
scopic cues. It is clear from these experiments
that, under certain conditions, stereoscopic judg-
ments can be modified by the equidistance tend-
ency.

Several studies concerned with after-effects
also may support (at least inferentially) the no-
tion that the equidistance tendency can modify
stereoscopic judgments. Kohler and Emory
(1947), Bergman and Gibson (1959), and How-
ard and Templeton (1964) found that the prior
presentation of inspection figures physically ar-
ranged in depth and viewed binocularly affected
the perceived depth involved in subsequently
presented test figures. Kohler and Emory re-
late their results to satiation theory. Bergman
and Gibson describe their results as a negative
after-effect. A physically slanted textured sur-
face with either steady or moving fixation ap-
peared less slanted with continued observation.
A subsequently presented surface in the same
locality had an error in perceived slant that was
opposite to that found with the original pres-
entation. Howard and Templeton explain their
results by assuming that the inspection stimulus
appeared less three-dimensional than it actually
was (the equidistance tendency) and conse-
quently that the subsequent stimuli appeared dis-
torted in depth in a direction opposite to that
of the distortion in the inspection display. Since
at least some of the effects found in these studies
are attributable to the equidistance tendency, it
is not only likely that the equidistance tendency,

under certain conditions, can modify stereo-
scopic judgments, but also that equidistance
effects occurring in one presentation can extend
to other presentations.

B. Modifications of Judgments Involving Size
Cues.—The equidistance tendency may be effective
even under circumstances in which it opposes
the size cue to relative distance (Gogel, 1956a,
Exper. III). An experiment by Gogel and
Harker (1955) supports the same conclusion.
It was found that the perceived depth between
two playing cards of different retinal size in-
creased with an increase in their lateral separa-
tion. Under the conditions of the experiment,
the size cue would have tended to make the cards
appear at different distances, while the equidis-
tance tendency would have made them appear
equidistant. The increase in the perceived depth
with increased lateral separation of the cards
could therefore be attributed either to an in-
crease in the strength of the size cue with in-
creased directional separation or to a decrease in
the strength of the equidistance tendency with
increased directional separation. In a later ex-
periment (Gogel, 1956a, Exper. IV) using the
larger lateral separation, an additional object
was introduced so that the perceptual effect of
the equidistance tendency resulting from this
additional object would oppose the perceived
depth normally occurring between the cards.
The additional object clearly modified the depth
perception that occurred between the cards. It
appears likely, therefore, that the increase in ap-
parent depth with increased lateral separation
that occurred in the previous experiment (Gogel
and Harker, 1955) was a consequence of a de-
crease of the strength of the equidistance tend-
ency and not the result: of an increase in the
strength of the size cues. It seems that, even
though opposed by the size cues that occur from
familiar objects, the equidistance tendency can
modify the resulting depth perception.

In the study by Bergman and Gibson (1959),
the inspection figure consisted of a textured sur-
face (burlap) viewed through an aperture in
order to eliminate any perception of the edges
of the surface. The texture of the slanted sur-
face provided a gradient of size changes (size
cues) for the perception of slant. There was a
tendency for this surface when viewed either
monocularly or binocularly to appear frontal
with continued observation. From the viewpoint


For this demonstration, two playing cards were
used that appeared at different distances as a
consequence of a difference in retinal size (Gogel,
1956b, pp. 4-6). A small disc was successively
placed directionally closer to either the appar-
ently nearer or the apparently farther card or
midway between the cards in direction. Both the
cards and dise were viewed (with the right eye
only) under conditions in which depth cues
other than the relative size of the playing cards
were reduced or eliminated. The average results
indicate that the disc appeared closer in depth
to the card to which it was directionally closer
and appeared approximately midway between the
cards in depth when it was midway between
them in direction. In a further experiment
(Gogel, 1956b, pp. 7-14), the apparent path of
movement of a monocularly observed dise at-
tached to a monocularly observed rotating trape-
zoidal window was analyzed using the general-
ization that the strength of the equidistance tend-
ency would vary as a function of the changing
directional orientation of the dise with respect to
the various parts of the window. This latter ex-
periment not only demonstrates that binocular
observation of some of the objects is not a neces-
sary condition in order for the equidistance tend-
ency to be effective, but it also supports the con-
cept that the equidistance tendency applies to
parts of objects as well as to objects per se. All
objects, contours, and all parts of objects in the
visual field both exert and are subject to a visual
equidistance effect with respect to all other ob-
jects, contours, and parts of objects, with the
strength of this equidistance tendency between
any two visual inhomogeneities being inversely
related to their difference in visual direction. It
follows, for example, that all parts of a figure
slanted in depth would tend to appear in the
frontoparallel plane in the absence of strong
cues to slant.

III. A Simple Method of Demonstrating the
Equidistance Tendency.

The equidistance tendency can be demonstrated
very simply by using a scene in which many
objects and surfaces are visible. The only ap-
paratus required is a luminous figure; for ex-
ample, a dise of light and a partially reflecting,
partially transmitting mirror to reflect the image
of the dise into one eye only, while observing
the scene binocularly. According to the equidis-

tance tendency, the distance position of the dise
will appear to be near objects in the binocularly
viewed scene to which the disc is directionally
adjacent, which can be demonstrated by rotating
the mirror to move the disc to the directional
vicinity of different objects in the scene. Some of
the conditions that will contribute to the success
of the demonstration are as follows. First, no por-
tion of the surface generating the disc should be
visible except the disc itself. Second, all cues as
to the physical distance position of the dise (such
as its accommodative value) should be removed.
For example, the purpose of using only one eye
in the observation of the disc is to prevent stereo-
scopic cues with respect to the binocularly viewed
scene from determining the perceived distance
position of the disc. Third, the binocularly
viewed objects or contours in the scene that are
physically at different distances should appear at
different distances. Fourth, the directional adjust-
ment of the disc should be such that the disc is
directionally adjacent to only one object at a time
in the binocularly viewed scene. The last condi-
tion is useful in avoiding the complication in-
volved in predicting where the disc will appear
in depth when several objects that are at different:
apparent distances are all in the directional vi-
cinity of the dise and thus make approximately
equal equidistance contributions to its perceived
distance position.

IV. Modifications by the Equidistance Tend-
ency of Judgments Involving Depth Cues.

A. Modifications of Judgments Involving Stereo-
scopic Cues—It was noted that the equidis-
tance tendency sometimes can modify depth per-
ceptions even in situations in which stereoscopic
cues to the apparent depth of the objects are
available. This has been demonstrated in a study
by Gogel, Brune, and Inaba (1954) in which the
equidistance tendency was shown to affect a depth
perception involving stereoscopic cues. The condi-
tions of the experiment were such that the
strength of the equidistance tendency was at a
maximum relative to that of the stereoscopic cue.
That the equidistance tendency can modify a
stereoscopic judgment under other viewing con-
ditions is suggested by an experiment by Harker
(1962) in which a binocularly observed grid was
oriented at various stereoscopic slants. The slant
of the grid in depth would be expected to induce
cyclorotation of the eyes, resulting in a reduction



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