International Journal of Brain and Cognitive Sciences 2017, 6(2): 34-41
DOI: 10.5923/j.ijbcs.20170602.03
A Preference for Longer Shape but a Limit to
Preferred Contour Complexity
Jay Friedenberg
Psychology Department Manhattan College, New York, U.S.A.
Abstract Most shapes in natural and constructed environments are elongated. Although the effect of elongation on
recognition has been investigated, nobody has yet studied how it may affect perceived aesthetics. In two experiments we
presented random polygons of varying length to undergraduates who judged their perceived beauty. Ratings increased
linearly with an increase in the shape’s axes of elongation. In experiment 2 however participants preferred elongated shapes
with fewer sides, suggesting that preference for elongation is only partly explained by a preference for increased boundary
contour. The results are discussed in terms of hedonic processing fluency.
Keywords Aesthetics, Beauty, Axis, Elongation, Shape, Polygon
1. Introduction
One of the most salient properties of an object is its axis.
An axis in general terms is a line that passes through an
object and which minimizes the distances between opposing
boundary contours. Axes capture important information.
They can specify an object’s orientation and the relationship
between its parts, both of which are crucial for judging
orientation and for recognition [1, 2] (Boutsen, 2001;
Sekuler, 1996). Axes for two-dimensional shapes can be
classified into several basic types. An elongation axis is the
single longest line that can fit through an object, sometimes
also referred to as a principle axis. A symmetry axis specifies
the line about which the whole or part of an object is
reflected. A medial axis or shape skeleton results from a
grassfire transformation and is formed from the boundaries
where “fire” travelling inward from outer contours meets [3]
(Blum, 1973). It is possible for one or more of these axes to
coincide. For instance, the medial can also be the symmetry
axis.
Recent research shows that shape axes have a neural basis
and are thus functionally significant. Hung (2012) used In an
adaptive shape sampling technique neurons in the
inferotemporal cortex (area IT) of the macaque monkey wer
found to code for both medial axis and surface characteristics
[4]. Neurons in this part of the mammalian brain can thus
represent both internal object structure and surface features,
both of which are necessary for object perception. Lescroart
and Biederman (2013) In another study line drawings of
* Corresponding author:
[email protected] (Jay Friedenberg)
Published online at http://journal.sapub.org/ijbcs
Copyright © 2017 Scientific & Academic Publishing. All Rights Reserved
novel geometrical shapes were shown to human observers
[5]. Using an fMRI-based voxel categorization method they
found evidence of medial axis structure representation in
area V3 of the visual system. They propose that medial axes
are used to specify the relative position of an object’s parts.
Other psychophysical evidence points to the importance of
axes in shape perception. Kovacs and Julesz (1994)
Researchers measured contrast sensitivity for a target in
different areas enclosed by a border [6]. Local sensitivity
was enhanced within a boundary even when the distance
between these areas and the border was large. In other work
using a reverse mapping procedure they found that maxima
in contrast sensitivity maps for bounded shapes fell along the
medial axis [7] (Kovacs, Feher, & Julesz, 1998). These
researchers propose that the visual system extracts shape
“skeletons” as an intermediate-level representation of an
object. This representation forms a structurally simple shape
description that can be used to specify object location. The
skeleton could then be operated upon by higher-level
perceptual operations, for example to group parts or to match
the object against a stored memory representation.
Firestone and Scholl (2014) Investigators in one study
presented shapes to participants on a touch-sensitive tablet
and asked them to tap the shape anywhere they wanted [8].
The tap locations across subjects formed the shape’s
medial-axis skeleton. Predicted changes conforming to an
axis interpretation held across different shape variations,
when the shape borders were perturbed and under conditions
of amodal completion. They argue that shape skeletons allow
for shape constancy across alterations in orientation and
perspective and note that this solution as been used in
computer vision models to accomplish the same ends.
Despite the research cited above there has been very little
work investigating the role that axes might play in perceived
International Journal of Brain and Cognitive Sciences 2017, 6(2): 34-41
35
shape aesthetics. Friedenber (2012) The current author had
observers rate right triangles at different axis lengths defined
by the ratio of the two sides forming the right angle [9]. He
found that an increase in this ratio produced a decrease in
judgments of perceived beauty and concluded that
compactness, not elongation was preferred. It was
hypothesized that compact shapes are preferred because they
are perceptually stable, i.e., less likely to bend or break.
Right triangles however are typically seen in more compact
forms and so familiarity may explain these results.
To determine if this is the case one would need to use
random polygons that observers cannot interpret as
meaningful. In the current study we utilize random polygons
rather than familiar geometric shapes. The number of sides
for a given condition is kept constant. In experiment 1 the
shapes we use have eight sides. In experiment 2 they have
more. But in each case the orientation of the shapes and the
location of the vertices is determined randomly. By using a
rectangular template of different lengths we can vary how
long these shapes are, effectively increasing their elongation.
In addition to compactness there is an alternate and
competing prediction for the judged beauty of elongated
shape. According to the hedonic processing fluency account,
stimuli that are more easily processed are judged as more
pleasing and beautiful [10] (Winkielman et. al., 2003).
Fluency here refers to the relative speed or ease of mental
operations, either at the perceptual or cognitive level.
Fluency can occur through repeated exposure to a stimulus,
what is deemed the mere exposure effect [11] (Bornstein,
1989). Since the visual system is receptive to processing
shape axes and has experience in doing so (most shapes both
natural and manmade have an axis), it follows that shapes
with an axis might be judged more beautiful than those
without. It is unknown, however if there is a limit to this.
Preference may peak for shapes at some maximum length
and then drop off after this.
If compactness determines perceived beauty then we
would expect to replicate the results obtained with right
triangles and find a decrease in preference as shapes get
longer. If processing fluency determines liking then we may
see the opposite effect in which shapes that are longer would
be more preferred. Should this be the case, the ease with
which the axis is identified should be positively correlated
with beauty judgments. The axes on more elongated shapes
should be more easily identified and therefore more beautiful.
However there may be a limit to this effect, with beauty
ratings dropping at extremely high or low axis lengths.
Average age was approximately 20 years.
2. Experiment 1
Figure 1. The dimensions of the rectangular template used to construct a
100 mm elongated polygon
2.1. Method
Figure 1 shows an example of how a polygon for the 100
mm case was constructed. To generate the upper contour
three points between 1 and 100 were randomly determined.
Next, three values between 1 and 30 were randomly
determined. These constituted the paired x and y values for
the upper vertices. This same procedure was then applied to
2.1.1. Participants
Sixteen undergraduates participated to fulfill a course
requirement. There were ten females and six males in the
group. All vision was normal or corrected to normal.
2.1.2. Stimuli
To eliminate familiarity we used random polygons at
different axis lengths. We employed five axis lengths
running from 70-190 mm in 30 mm increments (70 mm, 100
mm, 130 mm, 160 mm, 190 mm). These values were chosen
because they spanned a wide range of values, the smallest
being easily visible, the longest being about as long as could
be presented on the computer monitor without getting close
to the edge of the screen. Viewing distance was on average
about 45 cm. At this distance the lengths in increasing order
corresponded to the following visual angles: 76°, 96°, 111°,
121° and 129°.
The polygons were created using rectangular templates
whose longer sides equaled the five lengths. Locations
parallel to the elongation axis were randomly determined for
each longer side. Next, locations perpendicular to the axis at
these sites were randomly determined. These positions were
the x and y coordinate points for the polygon’s longer sides.
Following this end points were determined by randomly
selecting sites along the smaller sides of the rectangular
template. In a final step, each of these points was connected
with a straight line to form the polygon’s vertices.
The smaller side of each rectangle was determined to be
70 mm so that the smallest rectangle formed a square. This
was the limiting case in which there was no elongation. This
smaller side of the rectangle was also made just long enough
so that an internal space could be inserted preventing the two
longer sides from touching. The minor axis of the polygons
will at its shortest be equal to 10 mm, the width of the
internal space, or at its longest be equal to 70 mm, the length
of the smaller side of the rectangular template.
36
Jay Friedenberg: A Preference for Longer Shape but a Limit to Preferred Contour Complexity
the bottom contour with a different set of random values. The
left and right endpoints in this example were each chosen as
independent random values between 1 and 70. All of the
resulting points were then connected with straight lines to
form the vertices and the rectangular frame was deleted. The
original shapes were horizontal when constructed.
Orientations were then randomized during presentation.
The construction produced octagons. We decided to use
eight-sided figures because they are a relatively simple shape
and because they allow comparison with other work with
octagons [12] (Friedenberg & Bertamini, 2015). All of the
polygons were centered in the middle of the computer screen.
They appeared as black lines against a white background.
Figure 2 shows examples for each of the five length
conditions.
patterns within each block was randomized. Each polygon
was presented at a different random orientation on every trial
and appeared on the screen for as long as a participant
needed to respond.
A 1-7 rating scale was used with a 1 labeled as “Very Ugly”
and a 7 labeled as “Very Beautiful”. Participants were
instructed that they could use any number in between these
two extremes to indicate their response, including a 4 that
corresponded to neutral. They were additionally told that
there was no right or wrong answer and to judge the beauty
of the patterns in their own way. Reaction times were also
recorded. Following the experiment participants completed a
debrief form and answered several questions regarding
themselves and the stimuli.
2.1.4. Results and Discussion
The data were first screened for outliers. Any trials more
than three standard deviations away from the mean, those
longer than 16 seconds, were discarded. These
constituted .007 percent of the data. A simple regression was
next performed with axis length as the predictor and the
ratings response as the dependent variable. The regression
was run on the data averaged across subjects. Each data point
in the scatterplot thus corresponds to this average. There was
a significant fit F(4, 78) = 6.45, p < .01 with an R-square
value of .076 and a Pearson correlation coefficient of .28.
The slope for this analysis was .27 with an intercept value of
2.78. Effect size based on Cohen’s method was .082. Beauty
ratings increased linearly with an increase in axis length as
shown in Figure 3. The means and standard deviations for
beauty ratings for axis length are provided in Table 1.
Figure 2. Examples of polygons from each of the elongation conditions in
experiment 1
2.1.3. Procedure
Ten polygons were generated for each of the five axis
conditions yielding a total of 50 unique patterns. These
constituted a single block of trials. There were four blocks in
the experiment for a total of 200 trials. Presentation order of
Figure 3. The scatterplot and fitted regression line for mean beauty ratings
and axis length in experiment 1
It is surprising that the results we obtain here are the
opposite of those for elongated right triangles where there
was a preference for less elongated shapes [9] (Friedenberg
2012). The explanation might be due to familiarity. Right
triangles are more often presented as compact versions, with
elongation not usually exceeding an aspect ratio of 3:1.
International Journal of Brain and Cognitive Sciences 2017, 6(2): 34-41
When familiarity is removed as we did in this study,
preference changes and longer shapes are preferred. It is
unclear whether compactness is still useful as an explanatory
construct. It may useful as a predictor for other types of
shapes taking familiarity into account.
Table 1. Means and Standard Deviations for Beauty Ratings by Axis
Length in Experiment 1
Axis Length (mm)
70
100
130
160
190
Mean
3.28
3.52
3.65
4.00
4.27
Standard Deviation
1.54
1.55
1.49
1.73
1.83
3. Experiment 2
Previous research shows that observers prefer random
octagons with greater perimeter lengths and with a greater
number of concavities, suggesting beauty judgments may be
driven by object complexity [12] (Friedenberg & Bertamini,
2015). The results of experiment 1 also suggest a complexity
preference because elongated polygons on average have
longer contours and hence may be considered more complex.
In the next experiment we create elongated polygons with an
37
increased number of sides. If viewers prefer complex shapes
then ratings will be higher for those with more sides.
3.1. Method
3.1.1. Participants
Twenty-three undergraduate college students participated
to satisfy a course requirement. There were four males and
19 females in total. Vision was normal or corrected to normal.
Average age of the participants was 19.6 years.
3.1.2. Stimuli
Method of construction was the same as in the previous
experiment. There were three side number conditions
corresponding to polygons with 16, 24 and 32 sides
respectively. Shapes with 16 sides had 16 randomly
generated locations parallel to the axis, those with 24 sides
had 24 locations, and so on. We connected the endpoints on
the short sides of each rectangle to close the figure. The
dimensions of the template were the same as before. Figure 4
shows examples for each condition.
Figure 4. Examples of polygons from each of the elongation and number of side conditions in experiment 2
38
Jay Friedenberg: A Preference for Longer Shape but a Limit to Preferred Contour Complexity
Figure 5. Scatterplot and fit regression lines for mean beauty ratings split by number of sides in experiment 2
3.1.3. Procedure
Five examples were created for each of the five axis length
conditions and for each of the three side number conditions
yielding a total of 75 unique patterns. These constituted a
single block of trials. There were four blocks in the
experiment with a total of 300 trials. Presentation order of
polygons within each block was randomized. On each trial
the shapes were presented at a different randomly
determined orientation. As before, the polygons were
centered in the middle of the computer screen. They
appeared as black lines against a white background. The
template and construction lines were removed prior to the
experiment. Viewing distance was about 45 cm.
Each pattern appeared on the screen for as long as a
participant needed to respond. The 1-7 rating scale from
experiment 1 was used again. Participants were not given
any special instructions regarding responding and were told
that they should judge the aesthetics of the forms in their own
way. Response times were gathered. At the end of the
experiment participants completed a debrief form containing
a series of questions about themselves and the stimuli.
3.1.4. Results and Discussion
We considered responses more than three standard
deviations from the mean (those that took longer than 17
seconds) to be outliers and removed them from any
subsequent analysis. The amount of removed data was .006
percent of the total. We performed a linear models regression
for the response data with axis length cast as a continuous
variable, number of sides as a categorical variable and their
interaction as the three factors. The regression analysis was
run on the data averaged across subjects. There was a
significant main effect for axis length, F(4, 88) = 38.36,
p < .01 and number of sides, F(2, 66) = 81.98, p < .01. Their
interaction did not attain significance. Tables 2 and 3 show
the means and standard deviations for these effects, Table 4
shows the intercepts and slopes. As in the previous
experiment ratings increased linearly with an increase in axis
length, replicating this finding. The main effects means for
number of sides showed that beauty judgments were highest
for the 16-sided shapes, second highest for 24-sided shapes
and lowest for 32-sided shapes. Figure 5 shows the axis
length scatterplot with the corresponding regression lines.
Table 2. Means and Standard Deviations for Beauty Ratings by Axis
Length in Experiment 2
Axis Length (mm)
70
100
130
160
190
Mean
2.92
3.00
3.19
3.32
3.43
Standard Deviation
1.67
1.62
1.67
1.70
1.76
Table 3. Means and Standard Deviations for Beauty Ratings by Number of
Sides in Experiment 2
Number of Sides
16
24
32
Mean
3.40
3.15
2.96
Standard Deviation
1.75
1.66
1.65
We replicated our previous finding that observers prefer
more elongated polygons. However, the result for number of
sides runs contrary to a complexity prediction. Shapes with
more sides were considered less beautiful. The results thus
show there is a limit to preference for contour complexity.
The Friedenberg and Bertamini (2015), Our previous work
showed a complexity preference used eight-sided figures that
International Journal of Brain and Cognitive Sciences 2017, 6(2): 34-41
were radial and lacked any main axis, these polygons being
much simpler [12]. In the current experiment we used up to
four times this many sides with a salient main axis.
Table 4. Intercept and Slope Values for Beauty Ratings in the Axis Length
Regression for Number of Sides in Experiment 2
Number of Sides
16
24
32
Intercept
2.85
2.69
2.48
Slope
0.34
0.29
0.24
It is possible participants prefer contours of a moderate
level of complexity and that the stimuli in this experiment
exceeded that amount. There is a well-known preference
across many types of pattern for moderate complexity with
an inverted U-shaped preference function [13] (Nadal, 2007).
It is interesting to note that in our data there was no
interaction between axis length and number of sides. The
39
slopes for these functions were quite similar. This suggest
that the effect of sides is additive to elongation, the
differences between them being characterized by intercepts,
not slopes.
4. General Discussion
We tested aesthetic preference for elongated shape and in
two experiments found observers judge longer shapes to be
more beautiful. In experiment 1 this was found using
octagons and in experiment 2 it was replicated using shapes
with 16-, 24- and 32-sides. To provide the reader with a more
concrete sense of what shapes were preferred we show the
most beautiful and least beautiful polygons for each
experiment in Figure 6. For experiment 2 these are shown by
number of sides.
Figure 6. Examples of the least and most beautiful shapes in both experiments
40
Jay Friedenberg: A Preference for Longer Shape but a Limit to Preferred Contour Complexity
Most shapes that we encounter have an axis. The visual
system seems to be set up to process axes because they are
useful in recognizing objects and in guiding action toward
them [14] (Kimia, 2003). Shapes with a prominent axis
appear to automatically activate neural receptors in area IT in
monkey and area V3 in human cortex [4, 5] (Hung, 2012;
Lescroart & Biederman, 2013). This automatic activation
may then produce an associated hedonic response as
explained by processing fluency theory [10] (Winkielman
et. al., 2003). In this view shapes with longer axes would
produce even more neural activation and so elevate aesthetic
judgment further.
Processing fluency may also account for our second major
finding that shapes with more sides were less preferred. A
shape with more sides contains more contour and is therefore
more complex. More complex shapes may take longer to
process, reducing processing fluency and the corresponding
hedonic response. The results of the second experiment
might therefore demonstrate a sort of “streamlining” effect
where longer objects are preferred but only if they are
relatively simple, without too many external details. It is
speculative at this point, but shapes with increased
aerodynamic or hydrodynamic properties may be judged
beautiful because of their perceived dynamism or ability to
move through a surrounding medium. However, it is possible
to construct more streamlined shapes with a greater number
of sides, depending upon how they are angled, so the current
data do not address this conjecture.
We do not claim that processing fluency is the single or
only theoretical account of our data. It is merely plausible. In
this study we seek to demonstrate the effect, not provide a
definitive explanation. If axis-based and aesthetic brain areas
were concurrently activated in response to presentation of
our stimuli, it would provide additional support for this
theoretical account. Future work could explore whether this
axis effect extends to familiar objects and whether it
correlates with other perceptual processes. Lawson (2004)
for example, found that extending the axis of familiar objects
aided orientation-based judgments but not object
recognition.
A complexity interpretation is supported by the
experiment 2 ratings data where we see an overall drop in
perceived beauty with an increase in number of sides.
Participants preferred 16-sided polygons to 24-sided ones
and 24-sided polygons to 32-sided ones. More complex
shapes could be more aesthetically ambiguous and require
greater visual exploration prior to passing judgment.
Friedenberg and Bertamini (2015), Our former work
showed a complexity preference for octagonal shapes with
increased contour [12]. The results of experiment 1 can be
explained in the same way, with increased liking for more
elongated shapes that contain more contour. However, there
seems to be a limit to contour complexity because in
experiment 2 the pattern reverses, with participants
preferring fewer sided shapes containing less overall contour.
The shift occurs for our polygons somewhere between 8
sides and 16 sides. So like the proverbial tale of Goldilocks,
we appear to like contours that are complex, but not too
complex.
5. Conclusions
An elongated axis is a prominent property of most objects.
Recent evidence suggests that the extraction of an axis may
be one of the steps necessary to form a structural description
of a shape so that it can be recognized. However, no studies
to date have investigated the aesthetic properties of
elongation. If fast automatic processes like axis extraction
are judged aesthetic as might be predicted according to
processing fluency theory, then objects with prominent axes
ought to be considered more beautiful.
This hypothesis was tested in two experiments. In
experiment 1, polygons with random contours at five
increasing elongations were presented to undergraduates.
Longer shapes were consistently judged as more beautiful,
with a strong linear effect of elongation length, thus
supporting the processing fluency account. In experiment 2
these lengths were used again but with a varying number of
sides. Shapes with longer axes have greater contour so if
increased boundary contour is responsible for the effect then
increasing the number of sides ought to enhance beauty
judgments.
Surprisingly the results showed the opposite of this.
Shapes with a greater number of sides were judged less
rather than more beautiful. It is not clear why we obtained
this effect. Complexity may play a role. Shapes with a large
number of sides may be considered too complex. Shapes
with more sides have more boundary contour but the
orientation of the lines may detract from the overall
orientation of the shape reducing how streamlined it appears,
which perhaps may also detract from its appearance. This
idea couldbe tested in future work.
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