The influence of surface complexity on judgments of area


The influence of surface complexity on judgments of area 1

RONALD T. VERRILW2 AND CHRISTOPHER K. GRAEFF3
SYRACUSE UNIVERSITY

Fig. 1. Surface configurations of the
judged cards. The patterns from Group 1
through Group 4 represent an increasing
order of complexity. Each group contained
a series of nine differently sized cards.

cards remained at approximately eye level.
The illumination of the room was
uniformly controlled at an average level.

The Ss were asked to assign numbers
that appeared to be representative of the
area of each card. They were requested not
to think in terms of standard units of
measurement and to use any number,
smaller or larger than one, that seemed to
fit the area of the card. They were
cautioned to judge the area of the card and
not the area of the pattern. All cards of a
specific group were presented three times
for estimation according to a
predetermined random order. Geometric
means of the final two estimates were used
for the analysis of data. The sequence of
group presentations was also random.
Stimulus cards, concealed from the S's
view, were presented one at a time by the
E, who was also concealed from view. No
time limit was imposed for viewing each
card, but most judgments were made
within 1 min. The Ss closed their eyes
during card changes.

Six undergraduate students (three men
and three women) were used. All reported
having 20/20 vision, several w!~J, corrective
lenses. With the exception of one .:: art or
architecture students were not used since
some sources indicate that people visually
trained give visual data that is somewhat
different from that given by untrained Ss
(Thouless, 1932).

The apparent size of squares was
determined as a function of physical area
and of surface complexity using the
method ofmagnitude estimation. Apparent
area increases as a power function of
physical area with a slope of about 0.90.
The judged areas also increased as a
function of complexity of patterns upon
the surface, the most complex surfaces
being judged approximately 30% larger
than the most simple surfaces.

It has been noticed by one of the
authors (C.K.G.) that certain surface
qualities affect the apparent size of
buildings. When cultural mores have
motivated a desire for grandeur in certain
periods of history, such as the Italian
Renaissance, architecture has responded
with, among other things, an increasing
complexity of form and surface. In more
recent times, Louis Sullivan and others
have employed a technique that also
appears to affect apparent size. This
technique involves the compositional
contrasting of small, rather complex and
detailed areas of ornament with larger, less
complex areas. Modern buildings, often
stripped of surface ornamentation, present
a smaller apparent size than is actually the
case. The psychophysical method of
magnitude estimation (Stevens, 1957)
appears to be an appropriate means of
submitting these observations to an
experimental test.

The quantification of size judgments has
revolved mainly around the phenomenon
of size constancy and other size-distance
relationships (Holway & Boring, 1941;
Gilinsky, 1955; and others). The
development of the method of magnitude
estimation led many investigators to
examine the relationship of estimated area
to the physical area of the stimulus
(Ekman & Junge, 1961; Stevens & Guirao,
1963; Teghtsoonian, 1965). The
relationship obeyed Stevens's power law
and yielded exponents that ranged from
0.70 to 1.0, depending upon the
experimental conditions and instructions
(Teghtsoonian, 1965).

The foregoing experiments used simple,
unpatterned stimulus configurations.
Although Gibson (1950) emphasizes the
importance of texture in perception, most
of the published papers dealing with
surface arrays are limited to qualitative

descriptions. Baird (1965) has studied the
estimation of area and distance of
patterned stimuli (black and white
squares). His Os were asked to judge the
physical area of single or multiple black
regions on a white surface viewed with
monocular regard through a reduction
tube. Under these conditions, the results
did not fit a power function well.

The aim of the present experiment was
to relate size estimation as a function of
surface patterning, using the method of
magnitude estimation. Specifically, two
hypotheses were tested: (1) A uniform
pattern does not greatly alter apparent size,
and (2) a contrast of large and small
compositional elements increases apparent
size. It must be pointed out that these are
two-dimensional surface considerations,
not three-dimensional spatial
considerations. The results, therefore,
should not be interpreted as affirming or
denying theories of three-dimensional
space perception.

METHOD AND PROCEDURE
Four groups of nine square cards, having

the following characteristics, were
prepared, as illustrated in Fig. 1:
Group I-no pattern, blank white;
Group 2-uniforrn pattern, white with a
random distribution of black squares of
equal size; Group 3-white, with a random
distribution of black squares, circles, and
triangles, all of approximately equal size;
Group 4-large and small compositional
elements, white, with a random
distribution of black squares, circles, and
triangles of three different sizes. The ratio
of the black pattern to the total area of the
card was constant (20%) for all cards. For
Groups 3 and 4, the number of squares,
circles, and triangles of the same area was
equal for all cards. Each group consisted of
a graduated series of nine cards having
areas of 16, 30, 49, 72, 100, 132, 169,
209, and 256 sq in. The constructed
patterns were photographed and printed
onto Kodak Poly-contrast paper to obtain
uniformly black images on uniformly white
paper. Reproduction ratio was held
constant. The sheets were dry-mounted on
stiff cardboard.

The cards were presented to the Ss
seated 5 ft ± 3 in. from a 30%-40% gray
painted wall, where the cards were
mounted, one at a time. The center of the

D
GROUP I

GROUP m

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GROUP II

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Perception & Psychophysics, 1970, Vol. 7 (5) Copyright 1970, Psychonomic Journals, Inc., Austin, Texas 289



Fig. 2. Subjective mapitude of squares
as a function of physical area with
complexity of the surface patterns as the
parameter. Complexity of the Sllrface
pattern increase. from Group I (no
pattern) through Group 4 (contrasting
large and small elements). Estimated area
increases with surface complexity.

RESULTS AND DISCUSSION
The responses from Runs 2 and 3 were

averaged for each S (geometric mean) and
plotted. The geometric means obtained for
each pattern group are shown in Fig. 2.
Straight lines were fitted by the method of
least squares. The slopes for all groups may
be described as power functions with
exponents of approximately 0.90. The
addition of patterns of varying complexity
does not appear to have an effect upon the
rate of growth of apparent size, but the
differences in the intercepts of the
functions indicates that pattern does
influence the apparent size of the stimulus.
Both hypotheses are verified by the results.
The close correspondence between the
curves for Groups 1 (no pattern) and 2
(uniform pattern) confirms the first
hypothesis: The addition of a uniform
pattern to a surface does not alter its
apparent size. The estimates of Group 4
cards (large and small compositional
elements) were approximately 30% greater

REFERENCES
BAIRD, J. C. Area and distance estimation of

single and multiple stimuli. Vision Research,
1965,5,66Hi78.

BAIRD, J. C. Toward a theory of frontal-sized
judgments. Perception & Psychophysics, 1968,
4.49-53.

EKMAN, G. Two generalized ratio scaling
methods. Journal of Psychology, 1958, 45,
287-295.

EKMAN, G.• BERGSTROM. B., & KVNNAPAS.
T. A comparison between two psychophysical
scaling methods. Report of the Psychological
Laboratory, University of Stockholm. No. 37,
1956.

EKMAN. G., & JUNGE. K. Psychophysical
relations in visual perception of length. area
and volume. Scandinavian Journal of
Psychology, 1961.2,1·10.

GIBSON, J. J. The perception of the visual
world. Boston: Houghton Mifflin, 1950.

GIUNSKY. A. S. The effect of attitude upon the
perception of size. American Journal of
Psychology, 1955,68.173-192.

HOLWAY, A. H., 8t BORING, E. G.
Determinants of apparent visual size with
distance variant. American Journal of
Psychology, 1941.54,21·37.

STEVENS, S. S. On the psychophysical law.
Psychological Review, 1957, 64.153-181.

STEVENS, . S. S.• & GUIRAO, M. Subjective
scaling of length and area in the matching of
length to loudness and brightness. Journal of
Experimental Psychology, 1963, 66, 177-186.

TEGHTSOONIAN, M. The judgment of size.
American Journal of Psychology, 1965, 78,
392-404.

THOULESS, R. H. Individual differences in
phenomenal regression. British Journal of
Psychology, 1932, 22, 216-241.

NOTES
1. This study was supported in part by

Grant GB-8412 from the National Science
Foundation and Grant NINDB-NB-0395Q-07
from the National Institutes of Health. U.S.
Department of Health, Education. and Welfare.

2. Address: Laboratory of Sensory
Communication, Syracuse University, Syracuse.
New York 13210.

3. The second author was a graduate student in
the Syracuse University School of Architecture
when the experiments were performed. He is
curren tly on the architectural staff of
Architecture 2001. 2001 Center Avenue,
Pittsburgh, Pennsylvania.

(Accepted for publication Augu,t 20, 1969.)

CONCLUSIONS
The results support the view that

estimated area is a power function of
physical area. Furthermore, increasing the
amount of complexity (pattern or texture)
of the judged surface tends to increase
estimated area. While a uniform pattern
does not appear to increase the apparent
area of a surface, the contrasting of large
and small compositional elements
significantly increased the apparent area of
the surface. Caution must be observed in
directly translating these results of
t w o- dimensional surfaces to
three-dimensional buildings, but the
observation that ornamentation appears to
affect the apparent size of buildings would
seem to be consonant with the results of
the present study.

than those of Group 1 (no pattern),
confirming the second hypothesis: A
contrast of large and small compositional
elements increases apparent size. The
estimates of Group 3, which had a pattern
of intermediate complexity, fell
approximately midway between the
simplest and most complex patterns used.

The results clearly support the view that
judged area is a power function of physical
area. The value of the exponent falls within
the range of previously obtained slopes,
but it is difficult to make a direct
comparison because a wide variety of
instructions and experimental conditions
had been used. Ekman et at (1956) and
Ekman and Junge (1961), using the
method of ratio estimation, obtained
values of 0.86 and 0.92, respectively, for
estimated area of squares. Stevens and
Guirao (1963), using the method of
magnitude production with a standard,
obtained an exponent of 0.70 for squares,
and Teghtsoonian (1965) obtained a value
of 0.81 for irregular polygons by the
method of magnitude estimation with a
standard.

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290 Perception & Psychophysics, 1970, Vol. 7 (5)