Computational aesthetics and applications

Abstract

Abstract Computational aesthetics, which bridges science and art, is emerging as a new interdisciplinary field. This paper concentrates on two main aspects of computational aesthetics: aesthetic measurement and quantification, generative art, and then proposes a design generation framework. On aesthetic measurement and quantification, we review different types of features used in measurement, the currently used evaluation methods, and their applications. On generative art, we focus on both fractal art and abstract paintings modeled on well-known artists’ styles. In general, computational aesthetics exploits computational methods for aesthetic expressions. In other words, it enables computer to appraise beauty and ugliness and also automatically generate aesthetic images. Computational aesthetics has been widely applied to many areas, such as photography, fine art, Chinese hand-writing, web design, graphic design, and industrial design. We finally propose a design generation methodology, utilizing techniques from both aesthetic measurements and generative art.

Full text

R E V I E W Open Access
Computational aesthetics and applications
Yihang Bo
1
, Jinhui Yu
2
and Kang Zhang
3*
Abstract
Computational aesthetics, which bridges science and art, is emerging as a new interdisciplinary field. This paper
concentrates on two main aspects of computational aesthetics: aesthetic measurement and quantification, generative
art, and then proposes a design generation framework. On aesthetic measurement and quantification, we review
different types of features used in measurement, the currently used evaluation methods, and their applications. On
generative art, we focus on both fractal art and abstract paintings modeled on well-known artists’styles. In general,
computational aesthetics exploits computational methods for aesthetic expressions. In other words, it enables
computer to appraise beauty and ugliness and also automatically generate aesthetic images. Computational
aesthetics has been widely applied to many areas, such as photography, fine art, Chinese hand-writing, web
design, graphic design, and industrial design. We finally propose a design generation methodology, utilizing
techniques from both aesthetic measurements and generative art.
Keywords: Computational aesthetics, Aesthetic measurement, Generative art, Fractal art, Abstract painting
Background
The term “aesthetic”originated in Greek “aisthitiki”means
perception through sensation. In Cambridge Dictionary,
aesthetic is “related to the enjoyment or study of beauty”,
or “an aesthetical object or a work of art is one that throws
great beauty”. Aesthetics is subjective to a great extent,
since there is no standard to judge beauty and ugliness.
People from various domains may have totally different
understandings to an art work, influenced by their back-
grounds, experiences, genders or other uncertain factors.
With the rapid advances of digital technology, com-
puters may play useful roles in aesthetic evaluation, such
as aesthetic computing, making aesthetics decision, and
simulating human to understand and deduce aesthetics
[1]. One can use scientific approaches to measure the
aesthetics of art works.
Relating to digital technology and visual art, two inter-
disciplinary areas emerge: computational aesthetics and
aesthetic computing. Both areas focus on bridging fine
art, design, computer science, cognitive science and phil-
osophy. Specifically, computational aesthetics aims to
solve the problems of how computers could generate
various visual aesthetic expressions or evaluate aesthetics
of various visual expressions automatically. For example,
automatic generation of abstract paintings in different
styles, such as those of Malevich or Kandinsky and aes-
thetic assessment of photo, calligraphy, painting, or other
forms of art works. On the other hand, aesthetic computing
aims to answer the questions of how traditional visual art
theory and techniques could aid in beautifying the products
of modern technology or enhance their usability. This
paper will concentrate on the former, i.e., computational
aesthetics.
The first quantitative aesthetic theory was proposed in
“Aesthetic Measure”by Birkhoff in 1933 [2], which is con-
sidered the origin of computational aesthetics. Birkhoff
proposed a simple formula for aesthetic measurement:
M¼O=Cð1Þ
where Ois the order of the object to be measured, Cis
the complexity of the object, and Mis the aesthetic meas-
urement of the object. This implies that orderly and simple
objects appear to be more beautiful than chaotic and/or
complex objects. Often regarded as two opposite aspects,
order plays a positive role in aesthetics while complexity
often plays a negative role.
Birkhoff assumed that order properties, such as
symmetry, contrast, rhythm, were elements, could bring
comfortable and harmonious feelings. These properties
apply to shape and composition at a high level, and also
* Correspondence: kzhang@utdallas.edu
3
Department of Computer Science, The University of Texas at Dallas,
Richardson, TX 75080, USA
Full list of author information is available at the end of the article
Visual Computing for Industry,
Bi
o
m
ed
i
c
in
e
a
n
d
Ar
t
© The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and
reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
the Creative Commons license, and indicate if changes were made.
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6
https://doi.org/10.1186/s42492-018-0006-1

color and texture at a low level. Color perception is one of
the most important factors for aesthetics, and color har-
mony [3] is frequently used to evaluate aesthetics.
On the other hand, fractal theory is another major
element of aesthetics since similar objects could be
perceived more easily. In 1967, Mandelbrot proposed the
self-similarity of Britain coast [4], and in 1975, he created
the fractal theory and studied the property and application
of fractals. Spehar et al. [5] compares between fractals and
human aesthetics to enable fractal theory to be a measure-
ment of order.
According to Birkhoff, complexity is another vital fac-
tor to quantify aesthetics. People prefer simple and neat
objects to complicated and burdensome ones. The more
effort human visual processing system makes in viewing
an object, the more complex the object is. For example,
one could measure a photograph’s complexity by count-
ing the number of objects, colors or edges in it.
This paper concentrates on two main aspects of com-
putational aesthetics (as shown in Fig. 1). Section “Aes-
thetic Measurements”describes the aesthetic criteria
and measurements, and reviews their applications. Sec-
tion “Generative Art”discusses generative art, including
fractal art and abstract painting modeled on well-known
artists’styles. Section “Computational Aesthetics for De-
sign Generation”proposes a design generation method-
ology, combining the techniques in Sections “Aesthetic
Measurements and Generative Art”. Section “Conclu-
sions”concludes the paper.
Methods
Aesthetic measurements
How to simulate the human visual system and brain to
measure and quantify aesthetics is a great challenge. It,
however, becomes possible with the rapid development of
artificial intelligence, machine learning, pattern recogni-
tion, and computer vision. This section will first discuss
various possible aesthetic criteria to be used for measure-
ments, and then consider evaluation approaches using the
criteria. We will then sample a few application domains.
Criteria
Similar to most computer vision and pattern recognition
algorithms, aesthetic measurements need to consider an
object’s features and their descriptions. This subsection
will discuss composition criteria at a high level and image
attributes at a low level.
Composition Photographers always apply certain rules to
make their photos appealing, including Rules of Thirds,
Golden Ratio (Visual Weight Balance), focus, ISO speed
rating, geometric composition and shutter speed [6]. Stud-
ies show that the photographic compositions conformed to
human visual stimulation can give high aesthetic quality.
Rule of thirds As an important guideline for
photographic composition,“Rule of Thirds”means
dividing a photo into 3 × 3 equal grids, as shown in
Fig. 2. The four intersection points by the four dividing
Fig. 1 Structure of this paper
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 2 of 19

lines are preferred places for the photo’s main object.
Placing the foreground object at an intersection point or
on a dividing line would make the composition more
interesting and aesthetic than placing it in the center.
Bhattacharya et al. [7] define a relative foreground position
to measure the coincidence of the foreground and the
strong focal points. They use the following equation to
characterize a 4-dimensional feature vector (F):
F¼1
HWx0−s1
kk
2;x0−s2
kk
2;x0−s3
kk
2;x0−s4
kk
2

ð2Þ
where Hand Ware the frame’s height and width
respectively, x
0
is the foreground object center, and
s
i
(i= 1,2,3,4) represents one of the four red crosses
as shown in Fig. 2.
Dhar et al. uses a similar approach to compute the
minimal distance between the center of mass of the
predicted saliency mask and the four red crosses [8].
If the foreground centers at or near one of the strong focal
points, the photo would become more attractive. Figure 3
shows an example with the foreground centered at two
different positions in the same frame with the same
background [8]InFig.3a, the foreground is in the middle
of the frame, while in Figure 3b, the visual attention moves
to the bottom-left focal point. Figure 3b appears more
comfortable and harmonious than Fig. 3a.However,this
measurement is only applicable to photographs with a sin-
gle foreground object. Additionally, Zhou et al. [9]con-
siders that the Rule of Thirds in saliency regions is
generated by computing the average hue, saturation and
value of the inner third regions, similar to the work of
Datta et al. [10] and Wong et al. [11].
Golden Ratio Golden Ratio, first proposed by Ancient
Greek mathematicians, is also called golden mean or
golden section [12]. For example, two line segments a and
b are in golden ratio if (a + b)/a = a/b = (1 + √5)/2 ≈1.618.
The art work “TheMonaLisa”(Fig. 4) is a perfect
example of golden ratio, whether one measures the length
and width of the painting or draws a rectangle around the
object’s face. In photography, we often use visual weight
balance or aspect ratio. Zhou et al. [9]andDattaetal.
[10] consider that the image size and aspect ratio are
crucial factors affecting photographs’aesthetics. In their
opinion, approximating the golden ratios, 4:3 and 16:9,
can make viewers pleasing and comfortable. Obrador
et al. [13] also uses photograph composition features,
such as Rule of Thirds, the golden mean and the golden
triangles based on edges instead of regions [14].
Focus, focal length and low depth of field In
photography, focus aims to adjust the distance and clarity
of the frame to emphasize the foreground or salient object.
Low depth of field results in the salient region or object
always in sharp focus while the background is blurred.
Dhar et al. [8] trains an SVM classifier on Daubechies
wavelet [15] based features to calculate the blurring
amount [10]. Their experiments show that low depth of
field photographs receive high evaluation and rating.
Fig. 2 Rules of Thirds
Fig. 3 An example of foreground in the middle (a) and (b) in the one third position [3]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 3 of 19

Imaging features Image aesthetic features could be
categorized as low-level or high-level, saliency-based,
category-based, object-based, composition-based, and
information theory-based. Low-level features include color,
luminance, edges, and sharpness. They describe an image
objectively and intuitively with relatively low time and space
complexity. High level features include regions and contents.
Color Color is one of the most important low-level fea-
tures [16,17]. In computational aesthetics, we usually
measure color in terms of colorfulness, color harmony,
and apposing colors.
Colorfulness [10,13,18–21] is decided by average
Chroma and the spread of Chroma distribution,
computed by brightness and saturation in a 1D form.
Specifically, average Chroma presents the average
distance of color to neutral axis.
Hasler and Suesstrunk [17] propose an approach for
measuring colorfulness, via an image’s color pixel
distribution in the CIELab color space. Colorfulness
(CFN) is a linear combination of color variance and
Chroma magnitude:
CFN ¼σab þ0:37∙μab ð3Þ
where σab ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ2
aþσ2
b
q, represents the trigonometric
length of the standard deviation in ab space, and μ
ab
represents the distance of the center of gravity in the
ab space to the neutral axis.
The experiment by Obrador et al. [18] shows that a
colorful image could receive a high rating in image
appeal even though the image’s content is not attractive
at all.
As another important factor for image quality, color
harmony is a color combination harmonious to human
eyes and sensation. In general, color harmony studies
which colors are suitable for simultaneous occurrence.
This theory is based on the color wheel, on which the
purity and saturation increase along the radius from the
center outward. In other words, the color in the center
of the circle has the lowest purity and saturation.
Lu et al. [22] divide current color harmony models into
two types: empirical-based [23–25] and learning-based
[26–29]. The former, defined by designers or artists, ap-
pears to be subjective, while the latter behaves rationally
and objectively. Most of the learning models focus on
tuning the parameters on training the sample data. To
make the two distinct models benefit each other, Lu et al.
[22] proposes a Bayesian framework to build color
harmony. Photos with harmonious colors appear
comfortable to human and are usually rated with high
aesthetic scores.
Opponent color theory, on the other hand, states that
human eyes could perceive light in three opposing
components, i.e., light vs. dark, red vs. green, and blue vs.
yellow. One could not sense the mixtures of red and
green, or blue and yellow. Therefore, in reality, there is
no such a color perceivable by human that is reddish
green, or bluish yellow. Opposing colors can create
maximum contrast and stability of an image. Photos or
images with opposing colors are more appealing than
those without. In addition, complementary colors
occurring simultaneously in a photo can also enhance
the foreground saliency.
Dhar et al. [8] trains a classifier to calculate and predict
complementary colors, useful for aesthetic assessment.
Ke et al. [30] uses color contrast as one of their
aesthetic assessment criteria. They believe that
foreground and background should have
complementary colors to highlight prominent subjects.
Luminance and exposure In addition to color,
illuminance and exposure are two other important
Fig. 4 Golden Ratio example on “The Mona Lisa”
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 4 of 19

factors for photograph aesthetic assessment.
Researchers use overexposure and underexposure to
penalize the overall image appeal by calculating the
luminance distribution. For example, Obrador and
Moroney [18] use average luminance histogram and
standard deviation to measure penalization. The
more luminance values, the less penalty is imposed.
Wong and Low [11] consider that a professional
photograph should be well exposed. Obrador et al.
[13] uses luminance to compute the contrast of a
region.
Edges Researchers have also proposed to use edge
spatial distribution [11,30] to measure the simplicity of
photos and images. A simple photo should have a salient
foreground and concise background. Figure 5a gives an
example by an amateur photographer with noisy
background and obscure foreground. The edge spatial
distribution appears rambling. On the other hand, Fig. 5b
shows an edge map of a professional photograph. The
foreground contour stands out clearly with few edges in the
background. Ke et al. [30] proposes two different methods
to measure the compactness of the spatial distribution of
edges. A compact and clear distribution of edges in a
photograph makes the photograph visually aesthetic.
Sharpness As a feature to measure contrast, sharpness
can be calculated by color, luminance, focus or edges.
Obrador et al. [18] measures sharpness by contrasting
edges. High contrast edges usually generate high
sharpness. Wong et al. [11] extends Fourier transform
[30] to compute sharpness.
Regions Apart from the low-level features mentioned
above, regions and contents may be considered high level
features. An appealing image does not mean all of its
regions to be aesthetic. Hence, researchers attempt to
estimate regions’rather than the entire image’saesthetics.
Usually, regions are segmented before aesthetic assessment.
Obrador et al. [18] develop a region-based image evalu-
ation framework, which includes measurements of sharp-
ness, contrast and colorfulness. All of these region
features are composed to render an appealing map. Ex-
posure, size and homogeneity measurements of the ap-
pealing map are then applied. Zhou et al. [9] propose to
use salient region detection for photograph aesthetic
measurement. Wong et al. [11] use Itti’s visual saliency
model [31] to obtain the salient locations of a photo-
graph, and then compute the exposure, sharpness and
texture details of these salient regions. Their approach
also analyzes the position, distribution and the number
of salient locations to obtain other evaluation results.
Similarly, Obrador et al. [13] generates contrast regions,
rather than salient regions, by analyzing five low-level
features, including sharpness or focus, luminance,
chroma, relevance and saliency. The approach generates
five segmentation maps to aid aesthetic measurement.
Contents The contents of a photograph always make
great contributions to human aesthetic judgment.
Different types of objects would give viewers different
visual experiences. People are the most common
target in photography. Dhar et al. [8] estimate whether
there are people in a photograph by a face detection
method [32].Ifthedetectedfaceareaislargerthan
25% of the whole image, it is considered a portrait
depiction. Meanwhile, the presence of faces [18,20,33]
is another key factor that impacts the photograph’s
appeal. Based on the face detection result, one may
calculate the aesthetic score by assessing the size, color,
and expression of the face [34]. Except the average
luminance, contrast, color and size of the face, Obrador
et al. [18] detect smile [35] with a probability, if the face
region is over 3.6%.
Fig. 5 Examples of different edge distributions [30]: (a) an amateur photo, (b) a professional photo
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 5 of 19

Another approach trains a SVM classifier to judge
the presence of animals in photographs [8]. It also
divides the content into indoor and outdoor scenes,
and proposes 15 attributes to describe various
general scene types. For outdoor scenes, it uses sky-
illumination attributes to measure the lighting, which
effect the perception of photographs. Photos taken
in a sunny day give a clear sky, while those taken in
a cloudy day give a dark sky. Obviously, photos with
a clear sky appear aesthetic.
Overall evaluation
After selecting and measuring appropriate features, com-
bining their aesthetic scores to make overall evaluation
is the next step. There are two types of evaluation
methods: binary classification and rating. A binary
method classifies photos into beautiful and unbeautiful.
A rating method scores photos according to their appeal,
typically from 1 to 10.
User studies Obrador et al. [18] conduct user surveys to
help selecting appropriate features. They give image ap-
peal six ratings: excellent, very good, good, fair, poor and
very poor. For example, excellent photos require higher
sharpness, while very good ones need not be in perfect
focus. The results of user surveys could also provide reli-
able basis for feature selection. Users are asked to list and
sort the features used in their aesthetic measurement. The
selected features can be used for automatic aesthetic
quantification.
Classifiers Support Vector Machine (SVM) is one of
the most popular methods for binary classification [8].
Based on aesthetic features, one may train SVM classi-
fiers on a labeled training data and classify photos into
professional and amateur, or appealing and unappealing.
Zhou et al. [9] choose the liv-SVM algorithm, and use
the standard RBF kernel to perform classification. The
n-fold cross-validation runs 10 times per feature by and
filters out top 27 features. Then a greedy algorithm is
used to find the top 15 features among the 27 to build a
SVM classifier. Although SVM is a strong binary classi-
fier, it performs poorly when many irrelevant features
exist. CART (Classification and Regression Tree) [36]is
a tree-based and fast approach, which can help analyzing
the influence of various features.
Probabilistic methods [30,37] are also commonly used
for classification. Given a set of aesthetic quality metrics,
researchers usually create a weighted linear combination
of metrics. Ke et al. [30] propose a Naïve Bayes classifier
using the following equation:
q¼Pprjq1;q2;……;qn
ðÞ
Pamjq1;q2;……;qn
ðÞ
¼Pq
1;q2;……;qnjprðÞPprðÞ
Pq
1;q2;……;qnjamðÞPamðÞ ð4Þ
However, one cannot ensure the independence of the
features. If any features are interrelated, they would be
inoperative.
Example applications
Apart from photographs and images as discussed above,
computational aesthetics has been applied to other fields,
such as paintings, handwritings, and webpages, as summa-
rized below.
Paintings The aesthetics of digital or digitized paintings
is subjective, varied due to different painters, types of
paintings, drawing techniques, etc.. Li et al. [38,39]
build an aesthetic visual quality assessment model,
which includes two steps. Step one is a questionnaire.
Participants are asked to list at least two factors that
affect the aesthetics of paintings. These factors are then
grouped into color, composition, content, texture/brush-
stroke, shape, feeling of motion, balance, style, mood,
originality, and unity. Step two is a rating survey. The
assessment model uses the survey data to perform train-
ing and testing.
One could consider aesthetic visual assessment of paint-
ings a machine learning problem. Using the prior survey re-
sults and knowledge, one could generate features to
represent the given image both globally and locally. Global
features include color distribution, brightness, blurring, and
edge distribution. Local features include segment shape and
color, contrast between segments, and focus regions. Given
the global and local features, one could use Naïve Bayes
classifier to classify paintings into high-quality and
low-quality categories. Assumed independent from each
other, the features are given equal weights.
Different types of features may, however, carry unequal
weights in an aesthetic assessment. AdaBoost [40] assigns
different weights adaptively. It performs better than Naïve
Bayes classifier, but both perform distinctly better than the
random chance approach, as shown in Fig. 6.
Aiming to discover whether white space in Chinese ink
paintingsisnotsimplyablankbackground space but rather
meaningful for aesthetic perception, Fan et al. [41]exam-
ines the effect of white space on perceiving Chinese paint-
ings. Applying a computational saliency model to analyze
the influence of white space on viewers’visual information
processing, the authors conducted an eye-tracking experi-
ment. Taking paintings of a well-known artist Wu Guanz-
honginacasestudy,theycollectusers’subjective aesthetic
ratings. Their results (Fig. 7) show that white space is not
just a silent background: it is intentionally designed to
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 6 of 19

convey certain information and has a significant effect on
viewers’aesthetic experience.
Fan et al. [42] further quantifies white space using a
quadtree decomposition approach, as shown in Fig. 8,in
computing the visual complexity of Chinese ink
paintings. By conducting regression analysis, they valid-
ate the influences of white space, stroke thickness, and
color richness on perceived complexity. Their findings
indicate that all above three factors influence the com-
plexity of abstract paintings. In contrast, mere white
Fig. 7 Calculated saliency result of “Twin Swallows”(a) and heat map of eye movements on Wu Guanzhong’s“Twin Swallows”(b)
Fig. 6 Comparison of Naïve Bayes and AdaBoost methods [0]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 7 of 19

space influences the complexity of representational
paintings.
Chinese handwriting Due to the special structure of
Chinese handwritings, one should design features differ-
ent from those for photos or paintings. Sun et al. [43]
propose two types of features based on the balance be-
tween feature generality and sophistication, i.e., global
features and component layout features.
Global features Global features refer to three aesthetic
aspects: alignment and stability, distribution of white
space, gap between strokes. As shown in Fig. 9, Sun
et al. [43] use the rectangularity of convex hull, slope
and intersection of axis, and center of gravity to
measure alignment and stability. A larger rectangularity
value of the convex hull represents more regular and
stable handwriting. Slope and intersection of axis
divides a character into two subsets. A symmetrical and
balanced character should have an approximately
Fig. 8 aAn example of a quadtree decomposition on “A Big Manor”.bThe quadtree decomposition result of white space in “A Big Manor”
Fig. 9 Global features of Chinese handwritings [43]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 8 of 19

perpendicular axis. The center of gravity is inside the
bounding-box of the character, which could describe
the stability of handwriting from the perspective of
physics.
Write Space Ratio (WSR) is a common aesthetic rule in
calligraphy, representing the crowdness of characters.
Sun et al. [43] use convexity, ratio of axis cutting
convex hull, ratio of pixel distribution in quadrants
and elastic mesh layout to evaluate the distribution
of white space.
The orientation and position of a character stroke
also influence the aesthetics of handwriting. With
Chinese characters, there are four types of strokes
projected to 0
o
,45
o
,90
o
and 135
o
rotated X-axis
respectively. Sun et al. [43] use the variance of each
pixel’s projection and maximum gap proportion to
measure the gap between strokes.
Component layout features Apart from the above
global features, layout features divide every Chinese
character into several components, each constructed by
a set of strokes. As shown in Fig. 10, a component
feature vector is constructed by the horizontal overlap,
vertical overlap, area overlap and distance between
points from two different components.
Similar to paintings, no public Chinese handwriting
datasets are available for aesthetic evaluation. Sun
et al. [43] build a dataset for this purpose based on
the agreement in aesthetic judgments of various
people. They compute the Chinese Character
aesthetic score by
S¼100 pgþ50 pmþ0pb
which could give an average human evaluation score.
Variables p
g
,p
m
, and p
b
are probabilities for good,
medium and bad respectively.
To evaluate the aforementioned features, the authors
construct a back propagation neural network, and show
that their approach gives a comparable performance with
human ratings.
Web pages Researchers have also attempted to study
the relationships between webpages’computational aes-
thetic analysis and users’aesthetic judgment [44]. Thirty
web pages are selected from different types of network
sources with various visual effects. The participants
include six women and 16 men with normal vision and
non-color blindness, who are tested independently. Each
participant labels a page component on a 7-point scale
for repelling to appealing, complicated to simple, unpro-
fessional to professional, and dull to captivating.
For computational aesthetic analysis, Zheng et al. [44]
compute the aesthetics based on low-level image statistics
including color, intensity and texture, regions of minimum
entropy decomposition. They also evaluate the quad-tree
on aesthetic dimensions, including symmetry, balance,
and equilibrium, as shown in Fig. 11. They find that the
human subjective ratings and computational analysis on
several aforementioned aspects are highly correlated.
Logo designs The last application example is the evalu-
ation of logos [45,46], exampled in Fig. 12. The authors
select features, such as balance, contrast and harmony
based on design principles. To obtain reliable training
Fig. 10 Examples of component layout [43]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 9 of 19

data, they also collect human ratings of the above fea-
tures. Using a supervised machine-learning method to
train a statistical linear regression model to perform the
evaluation, they are able to obtain a high correlation of
0.85.
Generative art
Digital art becomes increasingly expressive and humanized.
With the emergence and development of computational
aesthetics, advanced artificial intelligence technology could
help to generate interesting and unique art works.
Levels of automation complexity
Machine intelligence is the key to computer-generated
abstract paintings. We may classify computer-generated
abstract paintings into four levels based on their computa-
tional complexity rather than their visual complexity [47].
Level 1 needs full human participation using an existing
painting software or platform. First, software producer
prepares various visual components either generated
manually or automatically. Users can select visual compo-
nents or draw them using the digital brush provided by
the software. Of course, they can change visual attributes
as needed.
The best representative of Level 2 is fractal art, origi-
nated in late 1980s [48]. Fractals require users to provide
various attributes, styles and mathematical formulas as
inputs. Then a programmed computer can generate re-
sults automatically. In other words, at Level 2, results
are usually generated based on mathematical formulas
Fig. 11 Quad-tree decomposition of a web page [44]
Fig. 12 Examples of black and white logos [45]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 10 of 19

parameterized with certain degrees of randomness. The
next section will discuss fractal art further.
Methods at Level 3 are often heuristics-based using
knowledge-based machine intelligence. There are two
general approaches in producing abstract paintings at this
level: generative and transformational. Using the genera-
tive method, one encodes artists’styles into computational
rules or algorithms. One of the pioneering works by Noll
[49] makes a subjective comparison of Mondrian’s“Com-
position with Lines”with computer-generated images. On
the other hand, a transformational method attempts to
transform digital images into abstract paintings using
image processing techniques. For example, a transform-
ational method can mimic brush strokes or textures and
apply them on an input image to transform it into an
abstract picture [50]. The best representative of transform-
ational methods is the so-called non-photorealistic render-
ing [51], which is out of the scope for this paper.
Level 4 is an AI-powered and promising direction for
approaches in generating highly creative artistic and
design forms. For instance, such an approach detects
specific styles from existing paintings and give an object-
ive aesthetic evaluation automatically, or the results will
be adaptive to audiences’emotional and cultural back-
ground. The current advances in deep learning and arti-
ficial intelligence have created tremendous opportunities
for breakthroughs at this level.
Fractal art
Fractal geometry, coined by mathematician Benoit Man-
delbrot (1924–2010) in 1975, studies the properties and
behavior of fractals and describes many situations that
cannot be explained easily by classical geometry. Fractals
have been applied to computer-generated art and used to
model weather, plants, fluid flow, planetary orbits, music,
etc. Different from traditional art, fractal art realizes the
unity of math and art aesthetics. A curve is the simplest
and classical expression in fractal art, which can be gener-
ated recursively or iteratively by a computer program.
We can easily discover four characteristics of fractal
art works:
a) Self-similar: enlarge the local part of a geometry
object, if the local part is similar to the entire
object, we call it self-similar.
b) Infinitely fine: It has fine structure at any small
scale.
c) Irregularity: one cannot describe many fractal
objects using simple geometric figures.
d) Fractional dimension: generated based on fractal
theory, fractional dimension is an index for
characterizing fractal patterns or sets by quantifying
their complexity.
Singh [52] believes that there is a conversation between
him and his computer when he creates his images. In other
words, when he talks to his computer, the computer func-
tions would be the translator. He builds on elements library
and uses types of string fractals as compositional elements
but not the main subject in the image. Figure 13 shows an
example of combined result used in the Unfractal series.
Seeley uses fractals as the beginning of his art works
[53], making them look less like computer-generated. A
number of fractal software may be used to create this
type of artworks, such as Fractal Studio, Fractal Explorer,
Apophysis, ChaosPro, and XaoS. As shown in Fig. 14,
named Yellow Dreamer, Sheeley creates the base image
using Fractal Studio, and then transforms it with Filter
Forge filters, Topaz Adjust 5, and AKVIS Enhancer.
Modeling abstract painting of well-known styles
According to Arnheim [54], abstract art uses a visual
language of shape, form, color and line to create a com-
position which may exist with a degree of independence
from visual references in the world. It is thus clear that a
large variety of styles of abstract paintings exist. Accord-
ingly, style analysis is an essential step in generative art,
which involves analyzing basic components, background
color, component colors and their layout. The compo-
nents may be independent from each other or
dependent with certain rules among them. Geometrical
components could be easily modeled by computers
while interweaved irregular shapes could be modeled
using a layered approach.
Style analysis
Abstract paintings may be divided into two classes, i.e.
geometric abstraction and lyrical abstraction. Here we
begin with the pioneer of abstract paintings, Wassily
Kandisky, to analyze the style of his abstract paintings
during his Bauhaus years (1922–1933), such as
Fig. 13 An example of combined result [52]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 11 of 19

“composition VIII”(1923), “black circles”(1924), “Yellow
Red Blue”(1925), “several circles”(1926), “Hard But
Soft”(1927) and “thirteen rectangles”(1930).
We take “Composition VIII”shown in Fig. 15 as an
example. According to Kandinsky himself, three primary
forms occur frequently: sharp angles in yellow, circles in
deeper colors, lines and curves in yellow and deeper
colors respectively. He also proposed three pairs of con-
trast forms:
1) The contrast color pair: yellow vs. blue. For
example, a yellow circle is always nested inside a
blue circle, or vice versa.
2) A straight line is intersected with a curve line.
Several straight lines are intersected with a curve
line or individual lines and curves. Some lines are in
one color, while others are in segmented colors.
3) Circle(s) with triangle(s). One circle overlaps one
triangle, multiple circles overlap one triangle, or
several abreast half circles.
Piet Mondrian is another well-known abstract artist,
whose style is based on geometric and figurative shapes.
While his art forms are drastically different from Kan-
dinsky’s, he took black vertical and horizontal lines as
the principal elements and used primary colors red, yel-
low, blue to fill some of the grids, as modeled in Fig. 16.
Russian artist Kazimir Malevich is the originator of
avant-garde movement, and his most famous work
“Black Square”in 1913 represents the birth of suprema-
cism. He used different types of basic supremacist ele-
ments, such as quads, ovals, crosses, triangles, circles,
straight lines and semi-crescent shapes. As noted by Tao
et al. [55] in Fig. 17, his works are frequently colored
boldly and opaque geometric figures above a white or
light colored background. In addition, a large quad de-
termines the orientation of other subsidiary shapes.
Prolific artist Joan Miro developed a unique style in
1920s. He arranged isolate and detailed elements in de-
liberate compositions. During his middle age, his art
works were known as organic abstraction, featuring de-
formed objects as shown in Fig. 18. Xiong and Zhang
[56] call these abstract pictorial elements according to
their shapes and appearances. It is easy to find that the
colors of Miro’s works are always trenchant and bright.
He enjoys using a few specific colors, such as red, yel-
low, blue, black, and white.
Zheng et al. [57] attempt to analyze Jackson Pollock’s
style, who is an influential modern American painter. He
draws his paintings by dripping and pouring on canvases
instead of traditional painting methods, as shown in
Fig. 19. His approach is considered revolutionary for cre-
ating aesthetics, as analyzed by Taylor et al. [58] for its
visual forms characterized by fractals [5]. Carefully
Fig. 14 Yellow Dreamer [53]
Fig. 15 Kandinsky’s“Composition VIII”Fig. 16 Computer generated Mondrian’s abstract painting example
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 12 of 19

analyzed Pollock’s various paintings, Zheng et al. [57]
divide Pollock’s dripping style into four independent
layers, i.e. background layer, irregular shape layer, line
layer and paint drop layer from bottom up. The
elements on each layer are positioned randomly.
Rule-based modeling
After analyzing the styles of various types of abstract
paintings, researchers use different approaches to generate
abstract images that mimic the original artists’styles. The
components of an abstract painting are usually interre-
lated. In fact, their spatial arrangements on canvas follow
certain rules. For instance, in “Composition VIII”by Kan-
dinsky, full circles with contrasting colors are often sur-
rounded by shades with gradual changing colors and grid
forms are always filled with interleaving colors.
Rule-based approach usually follows five steps:
Step 1: Choose a specific style for automatic
generation of the styled images;
Step 2: Generate the background;
Step 3: Decide the composition and prepare basic
components;
Step 4: Position the components based on the
designed composition following the analytical rules;
Step 5: Add texture and decoration, such as worn
signs or pepper noise, if necessary.
Zhang and Yu [59] select four abstract paintings of Kan-
dinsky from his Bauhaus period, including “Composition
VIII”,“Black and Violet”,“On White II”,and“Several Cir-
cles”, to generate the artist’s style of images automatically.
Based on their analysis of the paintings and reading of
Kandinsky’s abstract art theories, they summarize a set of
rules, for example, thin vertical and horizontal lines build
the foundations and intersected by angled lines; dark
boundaries are filled with light color; red and black always
occur together to create a salient effect.
Zhang and Yu [59] parameterize various attributes of the
artist’s typical components, such as boundary color, fill
Fig. 17 Malevich’s abstract painting example
Fig. 18 Miro’s“Ciphers and Constellations in Love with a Woman”
Fig. 19 A computer generated image of Pollock’s“Number 8”[57]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 13 of 19

color, size, and location. They then use the above analytical
rules to color and position the components, while random-
izing other attributes. Example abstract images automatic-
ally generated using this approach are shown in Fig. 20.
Tao et al. [55] attempt to automatically generate Male-
vich style of abstract paintings. They first decide the
color and decorations of the background, then prepare
the basic components with complexities and flexibilities.
Different from the generation approach of Zhang and
Yu for Kandinsky style [59], they define a bounding box
for each component to avoid overlaps among compo-
nents, and evenly distribute components on canvas.
Figure 21 gives three computer-generated results for
“Mixed Shape Style”.
Layered approach
With non-geometrical styles, one could observe the art-
ist’s painting process and follow the process with layers
of structures and components.
A typical example is Pollock’s drip style that is quite
different from those of Kandinsky and Malevich. It is
difficult or even impossible to come up with rules or ob-
serve regular patterns. Based on careful analysis, Zheng
et al. [57] divide the structures of Pollock’s drip paintings
into four independent layers, including background
layer, irregular layer, line layer and paint drop layer from
bottom up as shown in Fig. 22. The background layer
covers the entire canvas and sets the fundamental tone
of each painting. The irregular shape layer includes
Fig. 20 Kandinsky’s styles automatically generated: “Composition VIII”(top left), “Several Circles”(top right), “On White II”(bottom left), “Black and
Violet”(bottom right) [59]
Fig. 21 Computer generated Malevich’s“Mixed Shapes Style”[55]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 14 of 19

ellipses and polygons of random sizes. The line layer is
composed of curve lines of varied lengths and widths.
The top layer has all the paint drops of varied sizes.
Paint drops are filled in different colors and randomly
positioned on canvas. The generation order is bottom
up as illustrated in Fig. 22.
Also using a layered approach, Xiong and Zhang [56]
propose a process modeling approach to generating
Miro’s style of abstract paintings, in the following steps:
Step 1: Structured drawing;
Step 2: Adaptive coloring;
Step 3: Space filling;
Step 4: Noise injection.
Figure 23 shows an example of computer modeled
image of “Ciphers and Constellations in Love with a
Woman”and an example of generated “Poetess”, both of
Miro’s well-known “Constellation”series. Of course, one
could obtain varied and restructured versions of the
same style by resetting or randomizing different parame-
ters and attributes.
In summary, using the aforementioned generative
methods, it is entirely feasibly that more diversified, person-
alized and innovative images could be generated as desired.
Neural nets approaches
To simulate human aesthetics in depth, Gatys et al. [60,
61] proposed an image transformation approach, using a
Deep Neural Network (DNN) approach. Briefly, DNN is a
network constructed by layers of many small computa-
tional units. In each layer, the units are considered image
filters which extract certain features from the input image.
A DNN processes the visual information in a feed-forward
manner hierarchically. Then, the output of the network is
a feature map. Such an approach captures the texture in-
formation and obtains a multi-scale representation of the
input image. Figure 24 shows an example that combines
the content of a photo of Andreas Praefcke in the style of
painting “The Starry Night”by Vincent van Gogh (1889).
Discussion
Computational aesthetics for design generation
Utilizing techniques of aesthetic measurements and gen-
erative art discussed above, we propose an automatic or
semi-automatic design generation framework, initially
presented as a poster at VINCI’2017 [62]. In Fig. 25,
rectangular boxes are manual operations and oval and
diamond boxes are automatic or semi-automatic.
Information elicitation
Design information and requirements are collected, in-
cluding sample design images partially meeting the
requirements.
Rule specification and refinement
Based on the collected information and requirements,
designers use their knowledge and experience to specify
design rules, such as the logical and spatial relationships
among objects, in the first round of the design process.
The rules may be specified in an established formalism,
such as Shape Grammar [63].
During subsequent rounds of the design, given a se-
lected subset of all the generated designs, rules are auto-
matically adjusted via machine learning approaches.
Designers could then refine the adjusted rules.
Design generation
Given the set of design rules, and/or supervised learning
based on the sample designs, the design generation system
(e.g. shape grammar interpreter [64,65])) automatically
generates a large number of designs, while applying a set
of aesthetic rules and guidelines pre-coded in the system.
Deep learning algorithms, e.g., Convolutional Neural Net-
work (CNN), can extract styles from design samples [61],
such as distortion, texture, and rendering. The design
Fig. 22 Layered approach for modeling Pollock’s drip style [57]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 15 of 19

rules could be responsible in generating a variety of basic
designs and deep learning methods help enrich the design
with the extracted design styles. In this way, each design
both satisfies the design principles and has the distinct
artistic style. Moreover, the framework also considers the
designer’s preferences that could be modeled by personal-
ized recommendation methods, e.g., collaborative filtering
and content-based filtering. This step gives priority to the
styles preferred by the designer. Some of the generated
designs may not have been thought of or imagined by
designers. This saves much of designers’time, and
enhances their creativity and imagination.
Design selection
This step is the same as in the traditional design process,
except that the design choices presented are automatic-
ally generated. In digital forms, they are easily modifi-
able, selectable and printable.
Rules learning and modification
When a designer discards many designs, he/she must have
used unwritten guidelines and constraints. The design
generation system is equipped with an AI tool, such as a
constraint solver, that can extract the constraints used by
the designers, or deep learning techniques that can learn
from elicited sample designs (dashed arrows). The rules
involve fundamental visual elements. Deep learning
methods, e.g., CNN and Deep Belief Network (DBN),
could detect shapes or contours from the design samples.
Based on the extracted objects, this step could formulate
new elements. Deep learning methods, e.g., Sparse Auto-
Encoder, could learn color features from the samples to
modify the existing coloring rules or generate new rules.
According to the new elements, more concrete rules could
be automatically learnt. These automatically-modified
design rules may or may not be further refined before
another round of automatic design generation.
Satisfied?
It may be undesirable to judge whether a design is satis-
factory solely by the designer’s own subjective assess-
ment. The selected designs are inspected by the designer
and quantitatively measured for their aesthetics possibly
via their complexity [45] in a semi-automatic fashion.
Quantitative aesthetic measurement methods usually in-
clude two steps: aesthetic feature evaluation and decision.
In the aesthetic feature evaluation, we select the features,
whichrepresenttheworkbestforthespecificdesignappli-
cation. One example is to objectively evaluate color and
shape convexity in logo aesthetic measurement [10]. For
advertisement designs, one also needs to consider saliency
[9]andcompositionintheaestheticmeasurement.Inthe
decision step, there are two types of methods: binary classi-
fication and rating. We obtain positive or negative results
by a binary classification method or a soft result providing
a score ranking, which can facilitate the designer in object-
ively selecting designs.
By combining the judgements of the human designer
and an automated approach, the design generation system
could deliver a result improved over the previous round.
If one or more designs meet the requirements, they
are adopted, before further refinement and final design
application. This final adaption and application process
would feedback to the first step, i.e. information elicit-
ation, to help enhance the generation system. This
Fig. 23 Generated images of Miro’s“Ciphers and Constellations in
Love with a Woman”(top) and “Poetess”(bottom) [56]
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 16 of 19

iterative process could continue as many times as neces-
sary until a satisfactory design is generated.
Conclusions
This paper has introduced the current state-of-the-art of
computational aesthetics. It includes two main parts:
aesthetic measurement and generative art. Researchers
attempt to automate the assessment of aesthetics using
different features in an image. Numerous measurement
approaches have been used on paintings, photographs,
Chinese handwritings, webpages, and logo designs. They
are also applicable to film snapshots, advertisements and
costume designs in the same principle.
Generative art includes fractal art and abstract paintings
generated from existing art styles, both of which can gener-
ate distinctive art works although they use totally different
methods. Fractal art transforms mathematic formula into
visual elements and abstract image generation models on
the basic elements of the existing abstract painting styles.
Given the techniques in aesthetic measurements and
generative art, one may generate aesthetic designs auto-
matically or semi-automatically, as presented in the last
section. With further development of artificial intelligence
and machine learning, computational aesthetics will
become easily accessible and significantly influence and
change our daily life. A realistic application example
would be automatic design generation as discussed above.
Fig. 24 Example that combines the content of a photo with a well-known artwork
Fig. 25 Design generation methodology
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 17 of 19

Acknowledgments
The work is partially supported by National NSFC project (Grant number
61772463) and National NSFC project (Grant number 61572348).
Authors’contribution
YB wrote the first draft with most of the data. JY provided additional data
and discussions. KZ added further discussions, Design Generation Framework
and proofread the manuscript. All authors read and approved the final
manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’sNote
Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
Author details
1
Department of Fine Art, Beijing Film Academy, Beijing 100088, China.
2
The
State Key Lab. of CAD&CG, Zhejiang University, Hangzhou 310058, China.
3
Department of Computer Science, The University of Texas at Dallas,
Richardson, TX 75080, USA.
Received: 6 January 2018 Accepted: 10 May 2018
References
1. Hoenig F. Defining computational aesthetics. In: Computational
aesthetics’05 proceedings of the first eurographics conference on
computational aesthetics in graphics, visualization and imaging. Girona:
Eurographics Association; 2005. p. 13–8.
2. Birkhoff GD. Aesthetic measure. Cambridge: Harvard University Press; 1933.
3. Nemcsics A. The coloroid color system. Color Res Appl. 1980;5:113–20.
4. Mandelbrot B. How long is the coast of Britain? Statistical self-similarity and
fractional dimension. Science. 1967;156:636–8.
5. Spehar B, Clifford CWG, Newell BR, Taylor RP. Chaos and graphics: universal
aesthetic of fractals. Comput Graph. 2003;27:813–20.
6. Aber JS, Marzolff I, Ries JB. Photographic composition. In: Aber JS, Marzolff I,
Ries JB, editors. Small-format aerial photography: principles, techniques and
geoscience applications. Amsterdam: Elsevier; 2010.
7. Bhattacharya S, Sukthankar R, Shah M. A framework for photo-quality
assessment and enhancement based on visual aesthetics. In: Proceedings
of the 18th ACM international conference on multimedia. Firenze: ACM;
2010. p. 271–80.
8. Dhar S, Ordonez V, Berg TL. High level describable attributes for predicting
aesthetics and interestingness. In: CVPR 2011. Colorado Springs: IEEE; 2011.
p. 1657–64.
9. Zhou YM, Tan YL, Li GY. Computational aesthetic measurement of
photographs based on multi-features with saliency. In: Huang DS,
Bevilacqua V, Premaratne P, editors. Intelligent computing theory. Cham:
Springer; 2014. p. 357–66.
10. Datta R, Joshi D, Li J, Wang JZ. Studying aesthetics in photographic images
using a computational approach. In: Leonardis A, Bischof H, Pinz A, editors.
Computer vision –ECCV 2006. Berlin Heidelberg: Springer; 2006. p. 288–301.
11. Wong LK, Low KL. Saliency-enhanced image aesthetics class prediction. In:
Proceedings of the 16th IEEE international conference on image processing.
Cairo: IEEE; 2009. p. 993–6.
12. Livio M. The golden ratio: the story of PHI, the world’s most astonishing
number. New York: Broadway Books. 2003;51:18–21.
13. Obrador P, Saad MA, Suryanarayan P, Oliver N. Towards category-based
aesthetic models of photographs. In: Schoeffmann K, Merialdo B,
Hauptmann AG, Ngo CW, Andreopoulos Y, Breiteneder C, editors. Advances
in multimedia modeling. Berlin, Heidelberg: Springer-Verlag; 2012. p. 63–76.
14. Obrador P, Schmidt-Hackenberg L, Oliver N. The role of image composition
in image aesthetics. In: Proceedings of 2010 IEEE international conference
on image processing. Hong Kong, China: IEEE; 2010. p. 3185–8.
15. Daubechies I. Ten lectures on wavelets. Philadelphia: SIAM; 1992.
16. Matsuda Y. Color design. Tokyo: Asakura Shoten; 1995.
17. Hasler D, Suesstrunk SE. Measuring colorfulness in natural images. In:
Proceedings volume 5007, human vision and electronic imaging VIII. Santa
Clara: SPIE; 2003. p. 87–95.
18. Obrador P, Moroney N. Low level features for image appeal measurement.
In: Proceedings volume 7242, image quality and system performance VI.
San Jose: SPIE; 2009. p. 72420T-1-12.
19. Tong HH, Li MJ, Zhang HJ, He JR, Zhang CS. Classification of digital photos
taken by photographers or home users. In: Proceedings of the 5th Pacific
rim conference on advances in multimedia information processing. Tokyo:
Springer-Verlag; 2004. p. 198–205.
20. Jiang W, Loui AC, Cerosaletti CD. Automatic aesthetic value assessment in
photographic images. In: Proceedings of 2010 IEEE international
conference on multimedia and expo. Suntec City: IEEE; 2010. p. 920–5.
21. Winkler S. Visual fidelity and perceived quality: toward comprehensive
metrics. In: Proceedings volume 4299, human vision and electronic
imaging VI. San Jose: SPIE; 2001. p. 114–25.
22. Lu P, Peng XJ, Li RF, Wang XJ. Towards aesthetics of image: a Bayesian framework
for color harmony modeling. Signal Processing Image Commun. 2015;39:487–98.
23. Itten J. The art of color: the subjective experience and objective rationale of
color. Hoboken: John Wiley & Sons; 1997.
24. Moon P, Spencer DE. Geometric formulation of classical color harmony. J
Opt Soc Am. 1944;34:46–59.
25. Hård A, Sivik L. A theory of colors in combination—a descriptive model
related to the NCS color-order system. Color Res Appl. 2001;26:4–28.
26. Tang XO, Luo W, Wang XG. Content-based photo quality assessment. IEEE
Trans Multimed. 2013;15:1930–43.
27. Chamaret C, Urban F. No-reference harmony-guided quality assessment. In:
Proceedings of 2013 IEEE conference on computer vision and pattern
recognition workshops. Portland: IEEE; 2013. p. 961–7.
28. Tang Z, Miao ZJ, Wan YL, Wang ZF. Color harmonization for images. J
Electron Imaging. 2011;20:023001.
29. Nishiyama M, Okabe T, Sato I, Sato Y. Aesthetic quality classification of
photographs based on color harmony. In: Proceedings of 2011 IEEE
conference on computer vision and pattern recognition (CVPR). Colorado
Springs: IEEE; 2011. p. 33–40.
30. Ke Y, Tang XO, Jing F. The design of high-level features for photo quality
assessment. In: Proceedings of 2006 IEEE computer society conference on
computer vision and pattern recognition. New York: IEEE; 2006. p. 419–26.
31. Itti L, Koch C, Niebur E. A model of saliency-based visual attention for rapid
scene analysis. IEEE Trans Pattern Anal Mach Intell. 1998;20:1254–9.
32. Viola P, Jones MJ. Robust real-time object detection. Int J Comput Vis.
2002;57:137–54.
33. You JY, Perkis A, Hannuksela MM, Gabbouj M. Perceptual quality
assessment based on visual attention analysis. In: Proceedings of the
17th ACM international conference on multimedia. Beijing: ACM;
2009. p. 561–4.
34. Ravì F, Battiato S. A novel computational tool for aesthetic scoring of digital
photography. In: European conference on colour in graphics, imaging, and
vision. Amsterdam: CGIV; 2012. p. 349–54.
35. Chen XW, Huang T. Facial expression recognition: a clustering-based
approach. Pattern Recogn Lett. 2003;24:1295–302.
36. Trendowicz A, Jeffery R. Classification and regression trees. In: Trendowicz A,
Jeffery R, editors. Software project effort estimation. Cham: Springer; 2014.
37. Zhang LM, Gao Y, Zhang C, Zhang HW, Tian Q, Zimmermann R. Perception-
guided multimodal feature fusion for photo aesthetics assessment. In:
Proceedings of the 22nd ACM international conference on multimedia.
Orlando: ACM; 2014. p. 237–46.
38. Li CC, Loui AC, Chen TH. Towards aesthetics: a photo quality assessment
and photo selection system. In: Proceedings of the 18th ACM international
conference on multimedia. Firenze: ACM; 2010. p. 827–30.
39. Li CC, Gallagher A, Loui AC, Chen T. Aesthetic quality assessment of
consumer photos with faces. In: Proceedings of 2010 IEEE international
conference on image processing. Hong Kong, China: IEEE; 2010. p.
3221–4.
40. Li C, Chen T. Aesthetic visual quality assessment of paintings. IEEE J Sel Top
Signal Process. 2009;3:236–52.
41. Fan ZB, Zhang K, Zheng XS. Evaluation and analysis of white space in Wu
Guanzhong’s Chinese paintings. Leonardo: MIT Press; 2016.
42. Fan ZB, Li YN, Yu JH, Zhang K. Visual complexity of Chinese ink paintings. In:
Proceedings of ACM symposium on applied perception. Cottbus: ACM;
2017. p. 9. 1–8.
43. Sun RJ, Lian ZH, Tang YM, Xiao JG. Aesthetic visual quality evaluation of
Chinese handwritings. In: Proceedings of the 24th international conference
on artificial intelligence. Buenos Aires: AAAI Press; 2015. p. 2510–6.
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 18 of 19

44. Zheng XS, Chakraborty I, Lin JJW, Rauschenberger R. Correlating low-level
image statistics with users - rapid aesthetic and affective judgments of web
pages. In: Proceedings of the 27th international conference on human
factors in computing systems. Boston: ACM; 2009. p. 1–10.
45. Zhang JJ, Yu JH, Zhang K, Zheng XS, Zhang JS. Computational aesthetic
evaluation of logos. ACM Trans Appl Percept. 2017;14:20.
46. Li YN, Zhang K, Li DJ. Rule-based automatic generation of logo designs.
Leonardo. 2017;50:177–81.
47. Zhang K, Harrell S, Ji X. Computational aesthetics: on the complexity of
computer-generated paintings. Leonardo. 2012;45:243–8.
48. Mandelbrot BB. The fractal geometry of nature. San Francisco: W. H.
Freeman and Company; 1982.
49. Noll AM. Human or machine: a subjective comparison of Piet Mondrian’s
“composition with lines”(1917) and a computer-generated picture. Psychol
Rec. 1966;16:1–10.
50. Haeberli P. Paint by numbers: abstract image representations. ACM
SIGGRAPH Comput Graph. 1990;24:207–14.
51. Green S, Curtis C, Gooch AA, Gooch B, Hertzmann A, Salesin D, et al.
SIGGRAPH 99 full day course: non-photorealistic rendering. 2018. http://
www.mrl.nyu.edu/publications/npr-course1999/, Accessed June 2018.
52. Singh G. Stringing the fractals. IEEE Comput Graph Appl. 2005;25:4–5.
53. Singh G. Transforming fractals. IEEE Comput Graph Appl. 2014;34:4–5.
54. Arnheim R. Visual thinking. Berkeley: University of California Press; 1969.
55. Tao WY, Liu YX, Zhang K. Automatically generating abstract paintings in
Malevich style. In: Proceedings of IEEE/ACS 13th international conference
on computer and information science. Taiyuan: IEEE; 2015. p. 201–5.
56. Xiong L, Zhang K. Generation of Miro's surrealism. In: Proceedings of the
9th international symposium on visual information communication and
interaction. Dallas: ACM; 2016. p. 130–7.
57. Zheng Y, Nie XC, Meng ZP, Feng W, Zhang K. Layered modeling and
generation of Pollock's drip style. Vis Comput. 2015;31:589–600.
58. Pollock TR. Mondrian and nature: recent scientific investigations. In Orsucci FF,
Sala N editors, Chaos Complexity Res Compend. Nova Science Publishers, Inc.
2011;1(17):229–41.
59. Zhang K, Yu JH. Generation of kandinsky art. Leonardo. 2016;49:48–55.
60. Gatys LA, Ecker AS, Bethge M. A neural algorithm of artistic style. arXiv
preprint. 2015;arXiv:1508.06576v2.
61. Gatys LA, Ecker AS, Bethge M. Image style transfer using convolutional
neural networks. In: Proceedings of 2016 IEEE conference on computer
vision and pattern recognition. Las Vegas: IEEE; 2016. p. 2414–23.
62. Zhang K, Bo YH, Yang Y. Towards a design generation methodology. In:
Proceedings of the 10th international symposium on visual information
communication and interaction. Bangkok: ACM; 2017. p. 71–2.
63. Brown K. Grammatical design. IEEE Exp. 1997;12:27–33.
64. Trescak T, Esteva M, Rodriguez I. General shape grammar interpreter for
intelligent designs generations. In: Proceedings of sixth international
conference on computer graphics, imaging and visualization. Tianjin: IEEE;
2009. p. 235–40.
65. Wang XY, Zhang K. Enhancements to a shape grammar interpreter. In:
Proceedings of the 3rd international workshop on interactive and spatial
computing. Richardson: ACM; 2018. p. 8–14.
Bo et al. Visual Computing for Industry, Biomedicine and Art (2018) 1:6 Page 19 of 19