color image segmentation using neuro-fuzzy system in a novel optimized color space
TRANSCRIPT
ORIGINAL ARTICLE
Color image segmentation using neuro-fuzzy system in a noveloptimized color space
B. Somayeh Mousavi • Fazlollah Soleymani •
Navid Razmjooy
Received: 12 April 2012 / Accepted: 19 July 2012
� Springer-Verlag London Limited 2012
Abstract Segmentation is one of the most important pre-
processing steps toward pattern recognition and image
understanding. It is often used to partition an image into
separate regions, which ideally correspond to different real-
world objects. In this paper, novel color image segmenta-
tion is proposed and implemented using fuzzy inference
system in optimized color space. This system, which is
designed by neuro-adaptive learning technique, applies a
sample image as an input and can reveal the likelihood of
being a special color for each pixel through the image. The
intensity of each pixel shows this likelihood in the gray-
level output image. After choosing threshold value, a bin-
ary image is obtained, which can be applied as a mask to
segment desired color in input image. Besides using fuzzy
systems, optimizing color space for segmentation is
another feature of proposed method. This optimizing is
implemented by genetic algorithms and influence on sys-
tem accuracy. Two applications of developed method are
discussed, and still it could be applicable in wide range of
color image segmentation or object detection purposes.
Keywords Image segmentation � Color space � Fuzzy
inference system � Genetic algorithm
1 Introduction
Segmentation is a process that partitions an image into
regions [1]. Image segmentation is an essential but critical
component in low-level vision, image analysis, pattern
recognition and now robotic system. One of the most useful
applications of the color image segmentation is object
detection. Simple segmentation by color thresholding may
be insufficient in this case.
Not until recently, color image segmentation has
attracted more and more attention mainly due to reasons
such as the ones below:
• Color image provides far more information than gray-
scale images, and segmentations are more reliable.
• Computational power of available computers has
rapidly increased in recent years, being able even for
PCs to process color images.
• Handling of huge image databases, which are mainly
formed by color images, as the Internet.
• Outbreak of digital cameras, 3G mobile phones and
video sets in everyday life.
• Improvement in sensing capabilities of intelligent
systems and machines.
Common approaches for color image segmentation are
clustering algorithms such as K-means [2] or mixture of
principal components [3]. However, these algorithms do
not take spatial information into account. Some progress
has been made on this issue; still, much experimentation
needs to be done [4]. In general, color segmentation
methods could be classified as [5, 6]:
B. Somayeh Mousavi
Department of Electrical Engineering,
Hatef Higher Education Institute, Zahedan, Iran
e-mail: [email protected]
F. Soleymani (&)
Department of Mathematics, Zahedan Branch,
Islamic Azad University, Zahedan, Iran
e-mail: [email protected]
N. Razmjooy
Young Researchers Club, Majlesi Branch,
Islamic Azad University, Isfahan, Iran
e-mail: [email protected]
123
Neural Comput & Applic
DOI 10.1007/s00521-012-1102-3
1. Histogram thresholding (mode method) and color
space clustering: Histogram thresholding is one of
the widely used techniques for monochrome image
segmentation [7]. It assumes that images are composed
of regions with different gray-level ranges; the histo-
gram of an image can be separated into a number of
peaks (modes), each corresponding to one region, and
there exists a threshold value corresponding to valley
between the two adjacent peaks. As for color images,
the situation is different from monochrome image
because of multi-features. Multiple histogram-based
thresholding divided the color space by thresholding
each component histogram. There is some limitation
when dividing multiple dimensions because threshold-
ing is a technique for gray scale images. For example,
the shape of the cluster is rectangle [8].
2. Region-based approaches: Region-based approaches,
including region growing, region splitting, region
merging and their combinations, attempt to group
pixels into homogeneous regions. The region-based
approach is widely used in color image segmentation
because it considers the color information and spatial
details at the same time [9].
3. Edge detection: In a monochrome image, edge is
defined as a discontinuity in the gray level and can be
detected only when there is a difference of the
brightness between two regions. However, in color
images, the information about edge is much richer than
that in monochrome case. For example, edges between
two objects with the same brightness but different hue
can be detected in color images [10]. Accordingly, in a
color image, an edge should be defined by a discon-
tinuity in a three-dimensional color space. It should be
emphasized here that edge detection cannot segment
an image by itself. It can only provide useful
information about the region boundaries for the higher
level systems, or it can be combined with other
approaches, for example, region based approaches
[11], to complete the segmentation tasks.
4. Fuzzy techniques: The segmentation approaches men-
tioned above take crisp decisions about regions.
Nevertheless, the regions in an image are not always
crisply defined, and uncertainty can arise within each
level of image analysis and pattern recognition. Fuzzy
set theory provides a mechanism to represent and
manipulate uncertainty and ambiguity. Fuzzy opera-
tors, properties, mathematics and inference rules (IF–
THEN rules) have found considerable applications in
image segmentation [12].
5. Neural networks approaches: Artificial neural networks
(ANN) are widely applied for pattern recognition. Their
extended parallel processing capability and nonlinear
characteristics are used for classification and clustering.
ANN explore many competing hypotheses simulta-
neously through parallel nets instead of performing a
program of instructions sequentially; hence, ANN can
be feasible for parallel processing. Neural networks are
composed of many computational elements connected
by links with variable weights. The complete network,
therefore, represents a very complex set of interdepen-
dencies which may incorporate any degree of nonlin-
earity, allowing very general function to be modelled.
Training times are usually very long, but after training,
the classification using ANN is rapid [13].
In this paper, a novel method is described that can
segment special color or object with special color in an
input color image. Using accurately designed fuzzy infer-
ence system (FIS), acceptable results are obtained. FIS is
supposed to successfully overcome the complexity and
uncertainty problems. Fuzzy set theory provides a mecha-
nism to represent and manipulate uncertainty and ambi-
guity. In fact, fuzzy operators, properties, mathematics and
inference rules (IF–THEN rules) have found considerable
applications in image segmentation [14]. Moreover,
another unique feature of proposed system is introducing a
color space as the optimum color space in segmentation
purpose. This novel optimizing color space method is
developed based on genetic algorithms (GAs). GAs are
robust to computation, readily implemented with parallel
processing and powerful for global optimization. To show
efficiency of designed algorithm, it is applied to skin and
potato color segmentation. Results improve the robustness
of algorithm, especially in optimum color space.
The remainder of this paper is organized as follows:
After a brief description of FIS and GAs concepts in this
section, in Sect. 2, steps of algorithm designing are dis-
cussed. Section 3 develops two applications of proposed
systems including skin color segmentation and also potato
color segmentation. Some experimental results are shown
in Sect. 4, and the paper is concluded in Sect. 5.
1.1 Fuzzy inference system
Fuzzy sets theory provides a framework to materialize the
fuzzy rule-based (or inference) systems that have been
applied to many disciplines such as control systems,
decision-making and pattern recognition [15]. The fuzzy
rule-based system consists of a fuzzification interface, a
rule base, a database, a decision-making unit and finally a
defuzzification interface [16]. These five functional blocks
are described as follows:
• A rule base containing a number of fuzzy IF–THEN
rules.
• A database that defines the membership functions (MF)
of the fuzzy sets.
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• A fuzzification interface that transforms the input crisp
values to input fuzzy values.
• A decision-making unit that performs the inference
operation on the rules and producing the fuzzy results.
• A defuzzification interface that transforms the fuzzy
results of the decision-making unit to the crisp output
value.
In order to perform the inference operation in the fuzzy
rule-based system, the crisp inputs are firstly converted to
the fuzzy values by comparing the input crisp values with
the database membership functions. Then, IF–THEN fuzzy
rules are applied on the input fuzzy values to make con-
sequence of each rule, as the output fuzzy values. The
outputs obtained for each rule are aggregated into a single
output fuzzy value, using a fuzzy aggregation operator.
Finally, defuzzification is utilized to convert the output
fuzzy value to the real-world value as the output.
Sugeno type is one the commonly used fuzzy inference
method that is employed in this study as well. The Sugeno
fuzzy model was proposed by Takagi, Sugeno and Kang in
an effort to formalize a system approach to generating fuzzy
rules from an input–output data set. Sugeno fuzzy model is
also known as Sugeno–Takagi model. A typical fuzzy rule
in a Sugeno fuzzy model has the following format:
IF x is A and y is B THEN z ¼ f ðx; yÞ;
where A, B are fuzzy sets in the antecedent; Z = f(x, y) is a
crisp function in the consequent. Usually, f(x, y) is a poly-
nomial in the input variables x and y, but it can be any other
functions that can appropriately describe the output of the
system within the fuzzy region specified by the antecedent of
the rule. When f(x, y) is a first-order polynomial, we have the
first-order Sugeno fuzzy model. When f is a constant, we
then have the zero-order Sugeno fuzzy model, which can be
viewed either as a special case of the Mamdani FIS where
each rule’s consequent is specified by a fuzzy singleton or a
special case of Tsukamoto’s fuzzy model where each rule’s
consequent is specified by a membership function of a step
function centred at the constant. Moreover, a zero-order
Sugeno fuzzy model is functionally equivalent to a radial
basis function network under certain minor constraints.
Figure 1 depicts an example of Sugeno fuzzy model.
1.2 Canonical genetic algorithm
Genetic algorithms are adaptive algorithms for finding the
global optimum solution for an optimization problem. The
canonical genetic algorithm is developed by binary represen-
tation of individual solutions, simple problem-independent
crossover and mutation operators, and a proportional selection
rule [17]. The population members are strings or chromosomes,
which as originally conceived are binary representations of
solution vectors. CGA undertakes to select subsets of solutions
from a population, called parents, to combine them to produce
new solutions called children (or offspring). Rules of combi-
nation to yield children are based on the genetic notion of
crossover, which consists of interchanging solution values of
particular variables, together with occasional operations such
as random value changes, called mutations. Children produced
by the mating of parents and that pass a survivability test are
then available to be chosen as parents of the next generation.
The choice of parents to be matched in each generation is based
on a biased random sampling scheme, which in some cases is
implemented in parallel over separate subpopulations whose
best members are periodically exchanged or shared. The main
concepts of GA are as follows:
• Initialization: In the initialization, the first thing to do is
to decide the coding structure. Coding for a solution,
termed a chromosome in GA literature, is usually
described as a string of symbols from {0, 1}. These
components of the chromosome are then labelled as
genes. The number of bits that must be used to describe
the parameters is problem dependent.
• Selection: CGA uses proportional selection; the popu-
lation of the next generation is determined by n
independent random experiments; the probability that
individual xi is selected from the tuple (x1, x2, …, xm)
to be a member of the next generation at each
experiment is given by:
Pfxi is selectedg ¼ f ðxiÞPmj¼1 f ðxiÞ
[ 0: ð1Þ
This process is also called roulette wheel parent selection
and may be viewed as a roulette wheel where each member
Fig. 1 An example of Sugeno fuzzy system
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123
of the population is represented by a slice that is directly
proportional to the member’s fitness. A selection step is
then a spin of the wheel, which in the long run tends to
eliminate the least fit population members.
• Crossover: Crossover is an important random operator
in CGA, and the function of the crossover operator is to
generate new or ‘child’ chromosomes from two ‘par-
ent’ chromosomes by combining the information
extracted from the parents. The method of crossover
used in CGA is the one-point crossover. By this
method, for a chromosome of a length l, a random
number c between 1 and l is first generated. The first
child chromosome is formed by appending the last l-c
elements of the first parent chromosome to the first c
elements of the second parent chromosome. The second
child chromosome is formed by appending the last l-c
elements of the second parent chromosome to the first c
elements of the first parent chromosome. Typically, the
probability for crossover ranges from 0.6 to 0.95.
• Mutation: Mutation is another important component in
CGA, though it is usually conceived as a background
operator. It operates independently on each individual
by probabilistically perturbing each bit string. A usual
way to mutate used in CGA is to generate a random
number t between 1 and l and then make a random
change in the tth element of the string with probability
Pm [ (0, 1). Typically, the probability for bit mutation
ranges from 0.001 to 0.01.
2 Proposed method
There are two critical issues for color image segmentation:
1. What color space should be adopted?
2. What segmentation method should be utilized?
Here, optimized HIS color space and Fuzzy technique
for segmentation are applied. The proposed system is a
Sugeno-type fuzzy inference system. This system is used as
a classifier to segment special color in an input image. A
training set of desired color is needed to design and after
that, the system could be applied in any arbitrary image to
segment the special color. More details are in following
sub-sections.
2.1 Color space selection
What we commonly call color is actually our perception of
light waves from a thin band of frequencies within the
electromagnetic spectrum. This region of visible light
ranges from about 4.3 9 1014 Hertz to about 7 9 1014
Hertz. Individual colors are identified by their dominant
wavelength k (which represent hue), excitation purity
(which represent saturation) and luminance (which repre-
sents intensity). We often refer to color by their dominant
wave length. Using this notation, colors range from about
400 nm for violet to about 700 nm for red. Computer sci-
entists use color models to describe different colors.
Many different color models exist in computer graphics.
Each model uses its own 3D coordinate system to identify
uniquely individual colors. Some models (e.g., CIE XYZ,
CIE LUV) are capable of representing all colors from the
visible color domain. Other models (e.g., RGB, HSV) are
restricted to a subset of this domain. Certain models (e.g.,
CIE LUV, CIE Lab, Munsell) have been designed to try to
provide other useful properties like isoluminance and
control over perceived color difference.
RGB color space is one of the most widely used color
spaces for processing and storing of digital image data,
where it is a color space originated from CRT (or similar)
display applications, and it is convenient to describe color
as a combination of three colored rays (red, green and
blue). Still, because of its high correlation between chan-
nels, significant perceptual non-uniformity and mixing of
chrominance and luminance data, this color space is not
favorable choice for color analysis and segmentation
applications.
When there was a need for the user to specify color
properties numerically, hue-saturation-based color spaces
were appeared. Hue defines the dominant color (such as
red, green, purple and yellow) of an area; saturation
measures the colorfulness of an area in proportion to its
brightness [18]. The ‘‘intensity’’, ‘‘lightness’’ or ‘‘value’’ is
related to the color luminance.
The transformation of RGB to HSI color space is
invariant to high intensity at white light, ambient light and
surface orientations relative to the light source; conse-
quently, they can be a suitable choice for color segmen-
tation methods.
By following non-linear equations, RGB color space is
transformed to HIS color space, which has the advantage
that intensity component is separated from chrominance
components:
H ¼ arccos12ððR� GÞ þ ðR� BÞÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiððR� GÞ2 þ ðR� BÞðG� BÞÞ
q
S ¼ 1� 3MinðR;G;BÞRþ Gþ B
I ¼ 1
3ðRþ Gþ BÞ: ð2Þ
The intensity varies according to environment conditions,
but simply discarding luminance information affects the
model’s accuracy. Moallem et al. [19] proposed an opti-
mum color space by combining color components with
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123
different weights. In this research, ((1/2) H, S, (2/3) I) is
chosen by trial and error. Here, we introduce a novel
method to achieve the most affective color space. A (aH,
bS, cI) color space is considered, where a, b and c are the
key parameters they should be selected to make an opti-
mum color space. To materialize a precise system, genetic
algorithm (GA) is applied to set the a, b and c values. GA
is the most extended group of evolutionary technique
known, which rely on the use of a selection, crossover and
mutation operators [17]. Here, GA characteristics are as
follows:
Initial population = 150
Crossover coefficients = 0.67
Mutation coefficient = 0.005
Migration coefficient = 0.35.
The a, b and c are chromosomes of the GA, whose
fitness function compares the whole detected target pixels
in the sample images with the actual number of these pixels
and attempts to minimize the difference. In this way,
optimum values are obtained to accurate segmentation.
2.2 Decision-making system
To segment an arbitrary image, pixels with special color
through the image should be searched. This color can be any
color like red, green, blue, yellow, etc., or the color of particular
object such as vegetables, fruits or even human body skin.
Sugeno fuzzy system used is a 1-input, 1-output system
applying the Euclidean distance between the color of each
pixel to the average target color sub-space as an input, and
the likelihood of being target pixel as an output. A total of
150,000 color vectors, which contain the pixel of target
color and also any other color, should be provided as a
training data set. Our FIS is designed by neuro-adaptive
learning techniques. These techniques provide a method for
the fuzzy modeling produce to learn information about a
data set, in order to compute the membership function
parameters that best allow the associated fuzzy inference
system to track the given input/output data. This learning
method works similarly to that of neural networks.
Here, first subtractive clustering [20] is implemented on
data. After deciding about number of MFs with this
method, a hybrid learning algorithm to identify parameters
of Sugeno-type fuzzy inference system is used. It applies a
combination of the least-square method and the back
propagation gradient descent method for training FIS
membership function parameters to emulate a given
training data set. The outputs are linear, and weighted
average method is used for defuzzification [16].
When the sample image is used as an input for designed
FIS, an output image is a gray-level image. The intensity of
each pixel shows the probability of being a target color vector.
We need a binary image to make mask and segment region of
interest. So, the value as the threshold should be selected.
After investigating various results and with error and trial,
87 % is chosen as the best threshold value. It means that the
pixels with 87 % likelihood or more are regarded as target
pixels. The binary image is formed by setting target pixels to 1
and all other pixels to 0. After this, morphological processing,
which consists of opening followed by closing [21], is
accomplished to acquire separated and connected regions.
3 Examples of proposed system applications
To show the efficiency of this method, we design two
systems for skin color and special object like potato
detection, respectively. Moreover, proposed algorithms are
applicable in wide range of applications to segment any
region of interest (ROI) with special color.
3.1 Skin color segmentation
Human skin color detector can be so useful for the
understanding the image where human are subject of
observation. Skin color has proved to be robust cue for face
detection, localization and tracking and can help detect a
human limb or torso, within a picture. Image content fil-
tering, content-aware video compression and image color
balancing applications can also benefit from automatic
detection of skin in images [22].
To have a skin color detector in first step, we make a
training set that contains 1,500 skin and non-skin color
vectors. A fuzzy inference system is designed, for pictures in
(H, S, I) color space, using the described process in Sect. 2.2.
The input MF is shown in Fig. 2, and outputs are linear
functions. To better understanding the semantic meanings,
which are Not Skin, Low probability Skin, Rather Skin and
Skin, is assigned to four obtained clusters.
This system contains 20 nodes and 4 fuzzy rules. If we
define Z = {Not Skin, Low probability Skin, Rather Skin,
Skin}, then the rules are:
IF input is Z THEN output is Z:
After system designing, it is applied to form optimum color
space; 0.81, 0.97 and 0.24 are obtained, respectively, for a,
b and c coefficients. So, (0.81H, 0.97S, 0.24I) is introduced
as the best color space to skin color detection. As the
intensity is the main difference of various skin colors, the
intensity coefficient (c) is much less than a and b.
3.2 Potato color segmentation
Recognizing different kinds of vegetables and fruits is a
recurrent task in supermarkets, where the cashier must be
Neural Comput & Applic
123
able to point out not only the species of a particular fruit
(i.e., banana, apple, pear) but also its variety (i.e., Golden
Delicious, Jonagold, Fuji), which will determine its price.
The use of barcodes has mostly ended this problem for
packaged products [23]. Beside this, vegetable recognizer
system is applicable in industry to recognize defected
products and quality control. Generally, a computer vision
algorithm for a defect detection system includes two main
stages. In the first stage, a proper segmentation algorithm
should be applied on the input image to separate purpose
objects from background and the second stage consists of a
proper defect detection algorithm that is used on the pur-
pose objects. The quality of the segmentation algorithm
plays an important role in improving the output of defect
detection stage.
Utilizing proposed method, a system for segmentation of
potato color is proposed. Designing steps are similar to
what detailed in previous section. The differences just lie in
the number of obtained clusters, which are three and called:
{Potato, Rather-Potato, and Not-potato}, and obviously
optimum color space. Here, (0.91H, 0.68S, 0.5I) is obtained
as the optimum color space. Input membership function is
shown in Fig. 3.
4 Experimental results
To evaluate the performance of the proposed color image
segmentation, some experiments are carried out to detect
human body skin and potato color detection, in two
databases.
For skin detection, we use Bao image database [24].
This database includes 370 face images from various races,
mostly from Asia, with wide range of size, lighting and
background.
To segment potato color, the proposed algorithm is tried
on over more than totally 250 images. These images are
from different databases with different backgrounds,
including USDA, CFIA and an obtained potatoes image
database from Ardabil (Iran’s northern west area).
To better understanding of color space effect, each
algorithm is applied in three different color spaces includ-
ing: (H, S, I), ((1/2) H, S, (2/3) I) and obtained optimum
color space. As described in Sect. 3, (0.81H, 0.97S, 0.24I)
and (0.91H, 0.68S, 0.5I) are optimized color spaces for skin
and potato color segmentation, respectively. The designed
FIS is applied over all images in databases to segment ROI.
In the case of any image as system input, designed FIS
presents a gray-level image, as output which, intensity of
each pixel, shows the probability of being a target color
vector. As 87 % is chosen as the best threshold value, pixels
with 87 % likelihood or more are regarded as target pixels.
After morphological processing in obtained binary images,
separated and connected regions are acquired.
Results are summarized in Table 1. As it is observable,
our optimized color space improves the output perfor-
mance compare to other spaces. So, it can be concluded
that designed system, especially in optimized color space,
is applicable as a reliable technique to segment any color
through the input color image.
Some examples of segmented skin and potato regions
are depicted in Fig. 4. For more details refer to [25–27].
5 Conclusion and future works
In this paper, a fuzzy method was suggested to color image
segmentation in a novel optimized color model. Designed
system was an optimized neuro-fuzzy one, which applies
an image as input and could reveal the likelihood of
belonging to special color group, for each pixel, in a gray-
Fig. 2 Input membership function for skin segmentation system Fig. 3 Input membership function for potato segmentation system
Table 1 Obtained detection rates (%)
Color space (H, S, I) ((1/2) H, S, (2/3) I) Optimized
color space
Skin segmentation 90.54 94.05 97.29
Potato segmentation 91.6 95.2 98
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123
level image as an output. To improve system accuracy, a
new method was suggested to obtain optimum color space,
which applied GA to achieve the best values of a, b and cfor (aH, bS, cI) color space. Proposed system was designed
for two special applications, which contains skin and potato
color segmentation. Experimental results showed accept-
able detection rates, especially in optimum color space.
Described method in this paper is capable to be tuned
for any color segmentation or object detection applications.
Moreover, color space optimization method is a robust
algorithm that could be utilized in image processing pur-
poses, generally.
Designing a full automatic system to segment all the
different colors in an image and utilizing such a system to
object detection are possible ways to try.
References
1. Gonzalez R, Woods RE, Eddins SL (2004) Digital image pro-
cessing using MATLAB. Pearson Prentice Hall, Englewood
Cliffs, pp 237–241
2. Schalkoff RJ (1992) Pattern recognition, statistical, structural and
neural approaches. Wiley, New York
3. Wesolkowski S, Jernigan ME, Dony RD (1999) Global color
image segmentation strategies: euclidean distance vs. vector
angle, neural networks for signal processing IX. IEEE Press,
Piscataway, pp 419–428
4. Wesolkowski S, Tominaga S, Dony RD (2001) Shading and
highlight invariant color image segmentation using the MPC
algorithm, SPIE color imaging: device-independent color, color
hardcopy, and graphic arts VI. USA, San Jose
5. Cheng HD, Jiang XH, Sun Y, Wang J (2001) Color image seg-
mentation: advances and prospects. Pattern Recogn
34:2259–2281
Fig. 4 Obtained images from: a skin color segmentation and b potato color segmentation, algorithms
Neural Comput & Applic
123
6. Zhang H, Fritts JE, Goldman SA (2008) Image segmentation
evaluation: a survey of unsupervised methods. Computer vision
and image understanding, pp 260–280
7. Littmann E, Ritter H (1997) Adaptive color segmentation a
comparison of neural and statistical methods. IEEE Trans Neural
Network 8:175–185
8. Uchiyama T, Arbib MA (1994) Color image segmentation using
competitive learning. IEEE Trans Pattern Anal Mach Intell
16(12):1197–1206
9. Cheng HD, Sun Y (2001) A hierarchical approach to color image
segmentation using homogeneity. IEEE Trans Image Process
9:2071–2082
10. Macaire L, Ultre V, Postaire J-G (1996) Determination of com-
patibility coefficients for color edge detection by relaxation.
International conference on image processing, pp 1045–1048
11. Huang Q, Dom B, Megiddo N, Niblack W (1996) Segmenting
and representing background in color images. International con-
ference on pattern recognition, pp 13–17
12. Udupa JK, Samarasekera S (1996) Fuzzy connectedness and
object definition: theory, algorithms and applications in image
segmentation. Graph Models Image Process 58:246–261
13. Huang CL (1999) Pattern image segmentation using modified
Hopfield model. Pattern Recognit Lett 13:345–353
14. Tsuda K, Minoh M, Ikeda K (1996) Extracting straight lines by
sequential fuzzy clustering. Pattern Recognit Lett 17:643–649
15. Yen J, Langary R (1998) Fuzzy logic. Prentice hall
16. Sivanandum SN, Sumathi S, Deepa SN (2007) Introduction to
fuzzy logic using MATLAB. Springer, Berlin, Heidelberg
17. Cao YJ, Wu QH (1999) Teaching genetic algorithm using
MATLAB. Int J Elect Eng Educ 36:139–153
18. Kakumanu P, Makrogiannis S, Bourbaki N (2007) A survey of
skin-color modeling and detection methods. Pattern Recognit
40:1106–1122
19. Moallem P, Somayeh Mousavi B, Monadjemi SA (2011) A novel
fuzzy rule base system for pose independent faces detection. Appl
Soft Comput 11:1801–1810
20. Priyono A, Ridwan M (2005) Generation of fuzzy rules with
subtractive clustering. J Teknol 43:143–153
21. Davies R (2004) Machine vision. Morgan Kaufman, San Mateo
22. Gejgus P, Placek J, Sperka M (2004) Skin color segmentation
method based on mixture of Gaussians and its application in
learning system for finger alphabet. In: International conference
on computer systems and technologies. Comp Sys Tech
23. Rocha A, Hauagge DC, Wainer J, Goldenstein S (2010) Auto-
matic fruit and vegetable classification from images. Comput
Elect Agric 70:96–104
24. http://www.facedetection.com
25. Razmjooy N, Somayeh Mousavi B, Soleymani F (2012) A real-
time mathematical computer method for potato inspection using
machine vision. Comput Math Appl 63:268–279
26. Liu Z, Song YQ, Chen JM, Xie CH, Zhu F (2012) Color image
segmentation using nonparametric mixture models with multivari-
ate orthogonal polynomials. Neural Comput Appl 21(4):801–811
27. Jude Hemanth D, Kezi Selva Vijila C, Anitha J (2009) Appli-
cation of neuro-fuzzy model for MR brain tumor image classi-
fication. Biomed Soft Comput Human Sci 16(1):95–102
Neural Comput & Applic
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