Depth Cues Changes Circle Size Judgment Measured by Psychophysical Scaling

Abstract

The aim of our study was to investigate whether different circle sizes, in conditions of pure size judgment and in a simple contextual judgment with an interfering depth suggesting background, produce different size perceptions. We used the magnitude estimation to obtain the apparent size of circles under two different experimental conditions: with a neutral black background and with a convergent gradient to generate an artificial horizon to evoke depth cues. Twenty-two subjects with normal or corrected-to-normal visual acuity (mean age = 21.3 yrs; SD = 1.6) were tested. The procedure consisted of two gray circles at luminance of 40 cd/m2, separated 10 degrees of visual angle apart from each other. On the left side was always present the reference circle (visual angle of 1.1 degree) in which was assigned an arbitrary value of 50 was assigned. The subjects' task was to judge the size of the circles appearing in the right side of the monitor screen assigning a number proportional to the perceived altered size, relative to the reference circle. Seven different sizes (0.6, 0.8, 1.0, 1.1, 1.3, 1.4, 1.5 degrees) were presented in each condition. Our results have shown a high correlation for circle size and depth conditions (R = 0.987 and R = 0.997) between the logs of the stimuli and the subjective magnitude estimated values. The exponents obtained by the Power Law were 0.79 and 1.09, respectively to each condition. Additionally, a gender effect was observed in which males had showed an expansive perception of size with no dependence on the background. We concluded that in the induced depth condition, the perception of the circle sizes were judged subjectively closer to their respective physical size than in the condition of free visual cues. Our data reinforces the integrative manner of perceptual system when working with the sensory information.

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The Open Psychology Journal, 2014, 7, 45-49 45
1874-3501/14 2014 Bentham Open
Open Access
Depth Cues Changes Circle Size Judgment Measured by Psychophysical
Scaling
Marcelo Fernandes Costa*,¹,², Balázs Vince Nagy¹ and Adsson Magalhães²
¹Departamento de Psicologia Experimental, Instituto de Psicologia, Universidade de São Paulo, São Paulo, Brasil
²Núcleo de Neurociências e Comportamento e Núcleo de Neurociências Aplicada, Universidade de São Paulo, São
Paulo, Brasil
Abstract: The aim of our study was to investigate whether different circle sizes, in conditions of pure size judgment and
in a simple contextual judgment with an interfering depth suggesting background, produce different size perceptions. We
used the magnitude estimation to obtain the apparent size of circles under two different experimental conditions: with a
neutral black background and with a convergent gradient to generate an artificial horizon to evoke depth cues. Twenty-
two subjects with normal or corrected-to-normal visual acuity (mean age = 21.3 yrs; SD = 1.6) were tested. The procedure
consisted of two gray circles at luminance of 40 cd/m2, separated 10 degrees of visual angle apart from each other. On the
left side was always present the reference circle (visual angle of 1.1 degree) in which was assigned an arbitrary value of
50 was assigned. The subjects' task was to judge the size of the circles appearing in the right side of the monitor screen
assigning a number proportional to the perceived altered size, relative to the reference circle. Seven different sizes
(0.6, 0.8, 1.0, 1.1, 1.3, 1.4, 1.5 degrees) were presented in each condition. Our results have shown a high correlation for
circle size and depth conditions (R = 0.987 and R = 0.997) between the logs of the stimuli and the subjective magnitude
estimated values. The exponents obtained by the Power Law were 0.79 and 1.09, respectively to each condition.
Additionally, a gender effect was observed in which males had showed an expansive perception of size with no
dependence on the background. We concluded that in the induced depth condition, the perception of the circle sizes were
judged subjectively closer to their respective physical size than in the condition of free visual cues. Our data reinforces the
integrative manner of perceptual system when working with the sensory information.
Keywords: Depth perception, magnitude estimation, size judgment, p psychophysical scaling, spatial vision.
INTRODUCTION
The human visual system can take viewing distance into
account when judging apparent size. It is interesting to note
that the shape and the size of objects are judged
independently but both are also under influence of the
distance presented [1, 2].
Studies investigating the environmental, physiological
and mental functions related to these perceptual variances
were performed generating two opposite hypothesis. The
moon size illusion is one of the many phenomena related
with the apparent size changes in different surrounding
contextual seeing situations [3]. In this illusion, the size of
the moon appears bigger when it is viewed near the horizon
and smaller when it is at the top of the sky. Previous
explorations were based on the retinal images and spatial
code interactions and led the authors suppose that spatial
coding mechanisms modulate the retina output [4] and in the
absence of contextual references the retinal circuity had less
*Address correspondence to this author to the Departamento de Psicologia
Experimental, Instituto de Psicologia USP, Av. Prof. Mello Moraes, 1721,
05338-030, Butantã, São Paulo, SP, Brasil; Tel: +55 11 3091 1918;
E-mail: costamf@usp.br
information to compare spatially and the output to the visual
cortex were biased. On the other hand, other study found that
environmental size is determined prior to the mental scaling
suggesting that the subjective size of moon is built up in
higher perceptual levels [5].
Interesting results were obtained in a study where the
relative sizes of objects were judged in different high
positions. As a main result, the horizon is a strong reference
in judging the relative sizes of the objects supporting the
second hypothesis presented [6]. Also a previous study
shows that background texture could modulate the size
perception for motion stimuli [7].
In visual arts, the inductions of depth and of the relative
distances are based not only on backgrounds inducing depth
but also in size changes of the painting elements among
other pictorial cues [8]. These findings suggest that the sizes
are based on the input computation of spatial cues and could
be explained in terms of spatial circuitry presented in lower
levels of sensation mechanisms.
Despite the absence of a consensual mechanism
supporting the size judgment, some interesting results could
be added as important information to this issue. Subjective
scaling of white circle sizes in a black background was

46 The Open Psychology Journal, 2014, Volume 7 Costa et al.
performed by Stevens [9]. He found a Power Law exponent
of 0.7 for a square size, suggesting a not very good size
perception which, in this case, meant a perceptual change of
3.5 times when the physical size changed 6 times. However,
there are no studies calculating the magnitude perceived in
contextual conditions.
Since the measurements previously performed have
shown an underestimation of the size without visual cues, we
aimed to measure the Power Law exponents under depth
induced by a convergent background. We hypothesized that
small changes in the perceptual magnitude (Power Law
exponent) with the background present could be more related
to a simple circuitry processing at lower levels of visual
system. Instead, bigger changes in the perceived size would
suggest a more perceptual, higher level, visual processing.
METHODS
Subjects
We evaluated 53 volunteers with a mean age of
21.3 years (SD = 3.1 yrs; 28 females), recruited among the
students of the University of São Paulo. Inclusion criteria
were best-corrected visual acuity of 20/20 or better measured
monocularly at 4 meters using an ETDRS chart - tumbling E
(Xenonio, Sao Paulo, Brazil), refraction of ≤ 3.0 diopters
considering the spheric equivalent of astigmatism values,
absence of ophthalmological diseases and absence of known
neurological and systemic diseases.
All subjects gave a signed informed consent to participate
in the experiment. All were naive to the specific
experimental question. This study is also in accordance with
the ethical standards laid down in the 1964 Declaration of
Helsinki and was approved by the local Ethical Committee
(CEPH-IPUSP 240.412; 26/11/2012).
Equipment and Procedures
The stimuli were generated by the software MatLab
version 7.8.0 (R2009a, The MathWorks Inc., USA) installed
in a PC computer. The stimulus consisted of two circles with
gray , luminance of 40 cd.m-2; separated 10 degrees apart
from each other. On the left side was the reference circle
(visual angle of 1.1 degree of visual angle at 50 cm)
presented in a LED screen. Seven different circle sizes
(0.6, 0.8, 1.0, 1.1, 1.3, 1.4, 1.5 degrees of visual angle) were
presented.
We used the Direct Magnitude Estimation (DME) to
assess the subjective magnitude related to the differences
between the circle sizes. The DME method was developed
by SS Stevens [9, 10], in which numbers are directly
addressed to the subjective magnitude regarding a stimulus
presented. The relation between the subjective magnitude
and the physical manipulation of the stimulus can be
expressed by the Power Law function:
 = Kn (Eq.1)
This means that the magnitude estimated  grows as the
physical  raised to a power of n.
Direct Magnitude Scaling (DME) is a very simple
procedure and consists of arbitrarily associating a number to
a particular dimension, in our case, the circle size. The
subject task was to judge the next dimensions relating then to
the first dimension, adjusting the number to match their
impression. If the first dimension was numbered as 10 and
the second dimension appears to have three times more
sensation, the subject have to give a corresponding number,
in this case 30. For more detailed explanation regarding the
method see [9, 11].
A preliminary training session was performed for each
subject to guarantee that they had understood the procedure
and would be able to perform it. The preliminary training
consisted of a DME procedure in a task of judging the line
length in a series of ten lines. As expected by the study of
Stevens & Harris [11], all subject performed these judgments
satisfactorily which means a Power Law exponent of 1.0
(data not presented in this paper). The line length judgment
is a simple task that can be performed for any subject and the
exponent obtained must be around 1.0. This previous
training is recommended when the subjects were not
experienced in that psychophysical task or when the
dimension under judgment is more abstract.
In the test session, the reference (modulus) circle was
chosen as the gray circle with size of 1.1 degree and it
always appears in the left side of the screen. To make the
ratio judgment possible, an arbitrary number of 50 was
associated to the reference size. The subjects were instructed
to look at the center of the screen and compare the circle size
presented in the right side of the screen with the modulus
circle by giving a number corresponding to the magnitude of
their impression of the circle size difference. The subjects
were instructed to be as precise as they can which means that
they could use fractions or decimal numbers. The circle sizes
were randomly presented and the geometric mean of two
presentations was used as the subject judged values.
The subjects randomly performed the circle size
judgment in two different conditions: free background
condition in which the background of the screen was totally
black (Fig. 1A) and in the condition of a convergent lines
texture gradient to induce the depth perception (Fig. 1B).
In the depth perception condition, the subjects were
instructed to make the circle size judgment and not a
distance or depth perception judgment that could appear in
some situations.
Statistical Analysis
Statistical analysis was performed with the software
Statistica (v11. StatSoft Inc. Tulsa, USA). Statistical
differences were verified by a Repeated Measurements
ANOVA considering the dependent variables the
background condition and the gender and the independent
variable the Power Law exponents. A Pearson-Moment
Correlation was used to verify the relationship between
magnitude estimation values and the physical circle size.
RESULTS
All subjects performed the two conditions satisfactorily.
For the circle size judgment free of background we measured
an exponent of 0.79 with a significant positive correlation
(r = 0.974; p < 0.001). In the condition with the textured
background the exponent measured was 1.09 (r = 0.999;
p < 0.001). The power functions and the correlation
coefficients are shown in Fig. (2).

Depth Cues Changes Circle Size Judgment Measured by Psychophysical Scaling The Open Psychology Journal, 2014, Volume 7 47
Gender differences in circle size scaling were analyzed.
Significant differences were found between genders for the
scaling exponents (F = 16.7, p = 0.002). We also found
differences when comparing the exponents obtained with
different background conditions. In the no background
condition the exponent of magnitude scaling of males was
1.67 and females was 1.21. Similar result was found with
background condition, in which the exponent measured for
males, 1.33 is significantly different from those of females,
0.86. The statistical significance comparing the background
conditions was F = 29.85, p < 0.001 (Fig. 3). However, no
interaction effect was observed between gender and
background condition.
Intra-subject variability was evaluated by a Pearson-
moment correlation coefficient obtained for each gender
between the judgments in those background conditions. The
correlation coefficients are presented in Table 1.
DISCUSSION
Contextual information as the background texture could
induce the perception of depth in pictorial images. The
relative size of objects also induces depth perception. Thus, a
reasonable question is whether the texture could influence
the size judgment by inserting a depth cue in the visual
context. We have investigated the effect of the background
texture in the relative size of circles measuring their
subjective magnitude for two conditions – with and without
depth cues in the background. Our results show a significant
change in the circle size judgment approaching the
perceptual size to the physical size with a little
Fig. (2). Psychometric functions of the power law obtained for the two viewing conditions. Without background the exponent
was 0.79 with a high correlation coefficient (r = 0.965) and with background inducing depth the circle sizes judged follow a
magnitude of 1.09 (r = 0.997).
Fig. (1). Screen view from the subjects’ point of view showing the
stimulus conditions without (A) and with background (B). The left
circle was the modulus and was associated with a reference number
of 50. The subject’s task was to give a number representing the
magnitude of the size change in the right circle.

48 The Open Psychology Journal, 2014, Volume 7 Costa et al.
overestimation, evidenced by a change in the exponent value
from 0.79 to 1.09. The exponent of 0.79 obtained in the
background free condition means that the physical size of the
circle increases, for example, 6 times and the perceived
circle size increases about 4.1 times. In the depth induced
background the exponent goes to 1.09 which means an
increase of 7 times in the perceptual size at a 6 time increase
in the physical size meaning a very close approach between
the physical and the perceptual sizes.
An interesting study found that the width and the height
of a cylinder with depicted texture demonstrates an illusory
shrinkage with the change of a depth cue [12]. This result is,
in some sense, in line with our study since it showed that
depth cues may determine the size of 3D elements. In our
study, we found that the depth cue changes the perceptual
size of circles in an improving fashion , approaching the
perceptual size to the physical size. One explanation for our
results is that the background texture creates a slant. Studies
found that the slants induce depth perception [13]. Another
explanation based on the literature [14] could be that the
sizes of objects intercepting the horizon line are jugdeg with
overestimation. Since all of our stimuli intercepted the
horizontal line of our texture background an increase in the
perceptual size could explain the improvement in circle size
judgment at the background condition.
The importance of the depth cues in size perception was
investigated by Farran et al. [15]. In that study, the authors
performed a same-different measurement for size judgment
with no background and with three different depth cue
conditions: height in the visual field, linear perspective, and
texture gradient. They found that texture gradient had an
effect on increasing the accuracy of size judgment. That
result is in line with ours.
The difference in the size judgment with background
texture means an increase of three times in the perceptual
size which could be considered a huge change for a
relatively complex contextual scene. That amount of
perceptual change could not be related only to the retinal size
of the image and, of course, to the retinal circuitry, but it is
Table 1. Pearson correlation coefficient for intrasubject viriiability.
Male
Female
No Background
r = 0.997
r = 0.997
P < 0.001
P < 0.001
No Background
r = 0.996
r = 0.998
P < 0.001
P < 0.001
Fig. (3). Gender differences found for both stimulus conditions. Males showed an higher expansive perception with no background (A) than
with background (C) Females also had an expansive size perception without background (B) but, differing from males in the background
condition, they showed a compressive perception (D).

Depth Cues Changes Circle Size Judgment Measured by Psychophysical Scaling The Open Psychology Journal, 2014, Volume 7 49
much more related to the perceptual process based on mental
sizes. The study of Bennett & Warren [5] manipulating
retinal and environmental images sizes suggests that environ-
mental size is determined prior to mental scaling. Based on
this study, our more complex scene composed by a back-
ground texture feeds the perceptual systems with enough
information to recalculate the size of the circles, making
circle size comparisons more reliable.
Gender differences that we found are strongly supportive
for differences in the underlining mechanisms of size
perception in males and females. Males showed an expansive
perception of size with no dependence on the background.
However, the expansiveness of males was reduced in the
presence of the background. We could interpret that result as
a correction for a smaller size. Females had a quite different
effect. They also had an expansive perception with no back-
ground, similar to males, but showed a slightly compressive
effect with background. These results suggest a strong power
of the contextual stimulus adjusting the perceptual size close
to the physical size which is an evidence of a more common
and probably basic mechanism of apprehending sizes in
contextual situations. Studies had reported invariance to
spatial stimuli both for spatial frequency [16] and for spatial
judgment of quantity [17]. However, independence of size
and distance judgment had also been found [18]. Our results
suggest that males maintain the invariance in judgment of
size, even with the reduction in the expansive perception.
Females, on the other hand, change from expansive to
slightly compressive perception of sizes in the presence of
depth texture in the background. The differences between
males and females in judging sizes in contextual conditions
could reflect adaptive and evolutionary differences showed
by innumerous studies but not intended to be discussed here.
Visual art is a complex environment in which our brain
extracts information to represent a vivid deepness of many
attributes of the real world. In this sense, the study of visual
arts could be a way to understand our mental structure about
visual perception. Our results show a strong change in
perceptual size based only on a textured background adding
depth information. Color mode changes by depth cues [19]
and by color perception integrating depth and form vision
[20] are rich grounds in which visual perception could lean.
CONCLUSION
Perceptual sizes are changed by the introduction of a
textured background inducing depth perception. Our scaling
measurements found a two-fold change from an underesti-
mated size perception to a size perception almost equaling
the physical size. Gender differences were also observed in
which males showed more expansive judgment of size
perception than females. Males also had invariance in size
judgment while females exhibited a change to a compressive
perception with background.
CONFLICTS OF INTERESTS
The authors confirm that this article content has no
conflict of interest.
ACKNOWLEDGEMENTS
I would like to thank Dora Fix Ventura for all the
theoretical discussions and insights during the entire work
and for the CNPq (401153/2009-6) and FAPESP
(2013/04049-4) for the financial support. M.F.C. is a CNPq
level 2 Fellow Researcher.
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Received: October 09, 2013 Revised: June 13, 2014 Accepted: June 16, 2014
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