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International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com July 2018, Volume 6, Issue 7, ISSN 2349-4476
9 Ajala Funmilola A., Fenwa O.D, Oyeleye C.O
Performance Evaluation of Selected Clustering Algorithms for
Image Segmentation
1*Ajala Funmilola A., 2*Fenwa O.D, 3*Oyeleye C.O 123.Department of Computer Science and Engineering, Faculty of Engineering and Technology, Ladoke Akintola
University of Technology, Ogbomoso, Oyo State, Nigeria
ABSTRACT
Clustering algorithm is one of the image segmentation algorithms that is an unsupervised learning task; where one needs
to identify a finite set of categories known as clusters to classify pixels.. Many clustering algorithms have been used for
image segmentation. Hence, this research evaluated the performance of selected clustering algorithms (K Means, Fuzzy
C Means, and Fuzzy KC Means) for medical image segmentation using segmentation time, segmentation accuracy, and
memory utilization. The three algorithms were implemented on Matrix Laboratory 7.1 (R0011a) and 25 medical images
were used for testing. The average result for K Means, Fuzzy C Means and Fuzzy KC Means algorithms were
13.4766ms, 45.5964ms and 6.6188ms respectively for segmentation time, the average result for K Means, Fuzzy C Means
and Fuzzy KC Means algorithms were 5.0925, 10.1119 and 3.6380 respectively for segmentation accuracy, while the
average result for K Means, Fuzzy C Means and Fuzzy KC Means algorithms were 10.9299 bit, 86.5671 bit and
10.1193bit respectively for memory consumption.
Keywords: Clustering, Segmentation, K-Means, Fuzzy C Means, Fuzzy KC Means
1. INTRODUCTION
Image segmentation is one of the most widespread means to classify correctly the pixels of an image in a decision
oriented applications. Most computer vision and image analysis problems require a segmentation stage in order to detect
objects or divide the image into regions that can be considered homogeneous according to a given criterion, such as
colour, motion, texture, et cetera ( Thangaraj and Kesavadas 2011). It refers to the process of partitioning a digital image
into multiple segments (sets of pixels, also known as super-pixels). Segmentation can be classified into: Clustering
segmentation, Edge Based Segmentation, Model-Based Segmentation, Thresholding segmentation Method, Region
Based Segmentation Methods, Segmentation Methods Based on Partial Differential Equation (PDE) and Artificial Neural
Network.
Clustering uses no training stages, it trains using available data. There exist different types of clustering segmentation
algorithms which are: K means, Fuzzy C Means, Fuzzy KC Means, Fuzzy E Means, Fuzzy K Means, Agglomerative
Hierarchical, Density-Based Clustering Algorithm (DBSCAN), Iterative Self-Organizing Data Analysis Technique
Algorithm (ISODATA). Out of these clustering algorithms, this work compared only K Means, Fuzzy C Means and
Fuzzy KC Means clustering algorithms because they are the major algorithms been used for medical image segmentation
.
2. LITERATURE REVIEW
Image Segmentation
Segmentation of images is one of the interesting applications of image processing techniques that have attracted a notable
amount of attention in the past few years (Lei Ma et al, 2005). It is a technique for dividing the image into meaningful
sub regions or objects with same attributes, and usually it is image and application dependent. Several segmentation
methods have been proposed for a number of algorithms based on different methods. There are Pixel based segmentation,
edge based segmentation, model-based segmentation, thresholding method, region based segmentation methods,
segmentation methods based on partial differential equation (PDE), Segmentation based on artificial neural network
Segmentation Based On Clustering
Image clustering is an unsupervised learning task; where one needs to identify a finite set of categories known as clusters
to classify pixels. Clustering use no training stages rather train themselves using available data. Clustering is mainly used
when classes are known in advance. A similarity criteria is defined between pixels, and then similar pixels are grouped
together to form clusters. Approaches based on internal and external approach makes use of relative criteria and relies on
finding the best clustering scheme that meets certain assumptions and requires predefined input parameters values
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com July 2018, Volume 6, Issue 7, ISSN 2349-4476
10 Ajala Funmilola A., Fenwa O.D, Oyeleye C.O
(Harikumar, 2012). The main advantage of clustering is that interesting patterns and structures can be found directly from
very large data sets with little or no background knowledge. The cluster results are subjective and implementation
dependent. K-means clustering is a simple clustering method with low computational complexity. The clusters produced
by K-means clustering do not overlap. The Fuzzy C-means clustering algorithm is a soft segmentation method that has
been used extensively for segmentation of MRI brain images (Christ and Parvathi, 2011). The three major clustering
algorithm segmentation types which are K Means, Fuzzy C Means and Fuzzy-KC-Means are examined in this study.
Fuzzy Clustering Segmentation
In real time applications, one of the most difficult tasks in image analysis and computer vision is to classify the pixel in
an image correctly when there are no crisp boundaries between objects in an image. In order to address this difficulty,
fuzzy clustering techniques are used. Fuzzy clustering techniques classify pixel values with great extent of accuracy and
it is basically suitable for decision oriented applications like tissue classification and tumor detection etc. Fuzzy
clustering divides the input pixels into clusters or groups on the basis of some similarity criterion, such that similar pixels
belong to same cluster. Similarity criterion used can be: distance, connectivity, intensity. The resulting partition improves
the understanding of human beings and helps in a more informed decision making.
The advantage of fuzzy system is that they are easy to understand, as the membership function partition the data-space
properly. Fuzzy clustering algorithms include FCM algorithm, Gustafson-Kessel (GK), Gaussian mixture decomposition
(GMD), Fuzzy C varieties (FCV), AFC, FCS, FCSS, FCQS, FCRS algorithm.
Fuzzy C-Means Clustering Segmentation Algorithm
The Fuzzy C-Means clustering segmentation algorithm is an overlapping and soft segmentation method that has been
used extensively for segmentation of MRI brain images. It has been one of the widely used clustering methods for image
segmentation minimizing square of error, FCM produces good segmentation results for relatively easy images without
estimating the density distribution of the image (Christ and Parvathi, 2011).
FCM algorithm is one of the most popular fuzzy clustering techniques, originally proposed by Dunn in 1973 and
modified by Bezdek in 1981. It is an approach where the data points have their membership values with the cluster
centers, which will be updated iteratively. FCM is able to determine, and in turn, iteratively update the membership
values of a data point with the pre-defined number of clusters. Thus, a data point can be the member of all clusters with
the corresponding membership values. The philosophy of FCM has been extensively used in deferent fields of research
anda large number of variants of FCM algorithm had been proposed. (Naz, Majeed, Irshad, 2010).
Fuzzy K-C Means Clustering Segmentation Algorithm
FKCM proposed by (Ajala et. al., 2012) performed accurately well by hybridizing the concept of k-means and FCM in a
two-step dimensional folds. This implies that after segmentation with k-means has been done, the resulting image is then
passed to FCM for further processing. This could lead to loss of data, and other important information.
Related Works
Several works have been done in the area of medical image clustering algorithm. Some of the works are discussed in this
section.
Daguspta (2012) performed demarcation of brain tumor using modified Fuzzy C Means (MFCM) the area of the
segmented tumor generated from the MFCM segmentation was evaluated using renowned model. Also in 2010,Mamata
implemented neuro-fuzzy logic for the classification of MRI images to detect cancer. Logeswari and McKiernan
(2010) also implemented Self Organizing Map (SOM) for medical image segmentation. According to their research,
segmentation has two phases. In the first phase, the MRI brain images are acquired form patient database. In that film
artifact and noise are removed. In the second phase the image segmentation is done.
In new unsupervised method, the main disadvantage of conventional FCM algorithm is that it is very sensitive to noise.
As MRI images may contain noise, so FCM algorithm needs to be modified so that it can avoid misclassification in noisy
images. Christ and Parvathi, (2011) proposed segmentation of medical image using Clustering and Watershed
Algorithms. The experimental results had shown that the proposed methods of using K-Means clustering and FCM
clustering exclusively to obtain a primary segmentation of MRI brain images before applying the marker controlled
watershed segmentation to them is effective.
FCM clustering also called ISODATA, is data clustering method in which each data point belongs to a cluster to a degree
specified by a membership value. FCM is used in many applications like pattern recognition, classification, and image
segmentation. FCM divides a collection of n vectors c fuzzy groups and finds a cluster centre in each group such
that a cost function of dissimilarity measure is minimized. However, there is no guarantee that ensures that FCM
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com July 2018, Volume 6, Issue 7, ISSN 2349-4476
11 Ajala Funmilola A., Fenwa O.D, Oyeleye C.O
converges to an optimum solution. The performance is based on the initial cluster centres. FCM also suffers from the
presence of outliers and noise and it is difficult to identify the initial partitions (Christ and Parvathi, 2011).
Harikumar, Kumar, and karthick, (2012) performance analysis for quality measures using K means clustering and EM
Models in segmentation of medical images. EM algorithm is a statistical estimation algorithm used for finding maximum
likelihood estimates of parameters in probabilistic models.
Srinivas and Srikanth (2012) developed a scientific approach for segmentation and clustering technique of improved K-
Means and Neural Networks. The simulation results showed that the proposed updating methods have significantly
improved the performance of improved K-Means clustering algorithm.
Ajala et al., (2012) were able to develop a hybridized Fuzzy KC Means segmentation process on medical images. They
incorporated an image processed with K Means and finally segmented the output result with FCM. FKCM is a method
generated from both FCM and KM but it carries more of FCM properties than that of K Means. Fuzzy KC means
works on grey scale images like FCM and generates the same number of iterations as in FCM. Dasgupta (2012) did a
survey on image segmentation using FCM for the clustering. Their results showed that incorporation of spatial
information in to the objective function of standard FCM that yields successful results for robust and effective image
segmentation of noisy images and techniques like depth of field (DOF) be applied to segment coloured images.
Joseph, Senthil, and Manikandan (2014) worked on the tumor segmentation method, which shows that the goal of
segmentation is not only to segment but as much as possible tell us the required volume of segmentation which
necessarily helps in further image processing techniques such as feature extraction. This also tells us the amount of time
the segmentation process takes (as time is a major factor in image processing). Other scholarly works have treated
segmentation in-depth, but none has been able to tell which of these segmentation process works well in terms of
segmentation time, accuracy, and memory consumption.
3. METHODOLOGY
Research Approach
In this work, an image processing procedural steps was that involves the following steps were used.
Image Acquisition
Twenty-five medical images were obtained from Medscape online database repository for the analysis; the medical
images were images of brain, foetus, iris, jaw bone, eye, teeth, finger, lung, ear, and Red Blood Cell. Samples of the
images were depicted in Figure 3.1
Image Pre-processing
Pre-processing of images is necessary before any image analysis can be carried out. It involves filtering, selecting,
randomizing, resizing and removal of objects that could affect the proper processing of the images. Gaussian Filtering
algorithm was used to pre-process the acquired images to remove unwanted effects from the image and to prepare the
images for further processing.
Teeth Brain Foetus finger iris
jaw bone Lung ear eye Brain
Figure 3.1 Samples of the images acquired [source: www.Medscape]
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com July 2018, Volume 6, Issue 7, ISSN 2349-4476
12 Ajala Funmilola A., Fenwa O.D, Oyeleye C.O
Step 1:Input the image to be segmented
Step 2: Let N = number of data points image
Step 3: Let K = numbersof clusters which is given by the user.
Step 4 : Let X1,…,Xm are N,
Step 5: Choose C1,…, CK cluster centres.
Step 6: Distance between each pixel and each cluster centre is found.
Step 7: The distance function is given by
J= |𝑥𝑗 − 𝑐𝑗| for i=1,…,N and for j=1,…,k,
where𝑥𝑗 − 𝑐𝑗 is the absolute difference of the distance
between a data point and the cluster centers indicates the
distance of the N data points from their respective cluster
centres.
Step 8. Distribute the data points x among the k clusters using the
relation
𝑥𝜀𝐶𝑗 if |𝑥 − 𝑐𝑖| < |𝑥 − 𝑐𝑗| for i= 1,2…,k, i ≠ 𝑗
where C1denotes the data points whose cluster centres is Cj
Step 9: Update cluster Centre is given as
Cj= 1
𝑚𝑖∑ 𝑋 𝑓𝑜𝑟 𝑖 = 1, … 𝑘,𝑥𝑖𝑗
Where, 𝑚𝑖is the number of objects in the datasets𝐶𝑖, Where, 𝐶𝑖
is the 1st cluster centre and c1 is the centre of cluster Ci
Step 10: Repeat Step 8 to Step 9 till convergence is met.
Algorithms for the three selected segmentation methods to be compared were shown in this section. Figure3.2 to figure
3.4 depicted the algorithms for KM, FCM and FKCM respectively.
KM Clustering Segmentation Algorithm
Figure 3.2 Algorithm for K-means segmentation [source: Ajala et al., 2012]
FKCM Clustering Segmentation Algorithm
Figure 3.4 Algorithm for Fuzzy KC means segmentation [source: Ajala et al., 2012]
Step 1: Input the image to be segmented
Step 2: Get the number of colors in the image by looking for the a*b*
space
Step 3: Assign the number of colors to be cluster no; that is C=no of
colors
Step 4: Choose an appropriate level of cluster fuzziness f > 1.
Step 5: Initialize the N × C ×M sized membership matrix U, at random,
Step 6: Determine the cluster centers CCjm, for jth cluster and its mth
dimension by using the expression ∑ 𝑈𝑖𝑗𝑚
𝑓𝑥𝑖𝑚
𝑁𝑖=1
∑ 𝑈𝑖𝑗𝑚𝑓𝑁
𝑖=1
Step 7: Calculate the Euclidean distance between ith data point and jth
cluster center using repetitive structure
Step8: Update fuzzy membership grade point n according.
Step 9: Repeat from Step 6 to Step 8 until the changes of pre-specified
termination criterion is reached
Step 10: Stop and output the image.
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com July 2018, Volume 6, Issue 7, ISSN 2349-4476
13 Ajala Funmilola A., Fenwa O.D, Oyeleye C.O
Figure 3.3 Algorithm for Fuzzy C-means segmentation [source: Ajalaet al., 2012]
4. RESULTS AND DISCUSSION
For the purpose of proper evaluation, twenty-five different medical images were analysed using the three segmentation
algorithms. The average result of K Means algorithm for 25 images gave segmentation time, segmentation accuracy and
memory utilization of 13.4766ms, 5.0925, and 10.9299bit respectively, average result of Fuzzy C Means algorithm for 25
images gave segmentation time, segmentation accuracy and memory utilization of 45.5964ms, 10.1119, and 86.5671 bit,
respectively while average result of Fuzzy KC Means algorithm for 25 images gave segmentation time, accuracy, and
memory utilization of 6.6188ms, 3.6380, and 10.1193bit respectively.
Table 4.1: Average results for twenty-five images
K-Means Fuzzy-C-Means Fuzzy KC Means
Segmentation
Time(ms) 13.47660684 45.5963509 6.618811368
Accuracy 5.09248565 10.11186351 3.638078481
Memory
Utilization(bit) 10.92993161 86.56710315 10.11935232
Three images out of the 25 images three were randomly picked for evaluation called image 1,5 and 10. Figure 4.2 and
table 4.5,figure 4.3 and table 4.6, and figure 4.4 and table 4.7 depicted the graphics user interface and result for
segmentation time, segmentation accuracy and memory utilization for images 1, 5 and 10respectively.
Step 1: Input the image to be segmented
Step 2: If image = coloured image
Step 3: Let M-dimensional N data points represented by xi (i = 1, 2, . . .
,N), are to be clustered.
Step 4: Assume the number of clusters to be made here 2 ≤ C = C, w ≤ N.
Step 5: Choose an appropriate level of cluster fuzziness f > 1.
Step 6: Initialize the N × C ×M sized membership matrix U, at random,
such that Uijm∈ [0, 1] and PC j=1 Uijm = 1.0, for each i and a
fixed value of m.
Step 7: Determine the cluster centres CCjm, for jth cluster and its mth
dimension by using the expression given below:
CCjm= ∑ 𝑈𝑖𝑗𝑚
𝑓𝑥𝑖𝑚
𝑁𝑖=1
∑ 𝑈𝑖𝑗𝑚𝑓𝑁
𝑖=1
Step 8: Update fuzzy membership matrix U according to Dijm If Dijm>
0,
𝑈𝑖𝑗𝑚 =
1
∑ (𝐷𝑖𝑗𝑚𝐷𝑖𝑐𝑚
2𝑗−1
)𝑐𝑐−1
If Dijm= 0, then the data point coincides with the corresponding
data point of jth cluster center CCjm and it has the full
membership value, that is, Uijm = 1.0,
Step 9: Repeat Step 5 to Step 7 until the changes in U ≤ ǫ,
Step10: Stop
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com July 2018, Volume 6, Issue 7, ISSN 2349-4476
14 Ajala Funmilola A., Fenwa O.D, Oyeleye C.O
Table 4.8 and figure 4.5, table 4.9 and figure 4.6 and table 4.10 and figure 4.7 show the evaluation result of image
segmentation time, Segmentation accuracy and memory utilization for the three randomly selected images from the 25
sample images used.
The evaluation result showed that FCM has the highest memory utilization compared to KM and FKCM while FKCM
has the fastest segmentation time and highest segmentation accuracy compared to KM and FCM.
Metrics
K-
Means
Fuzzy-C-
Means
Fuzzy KC
Means
Segmentation
Time(ms) 6.1697 27.5528 4.17933
Accuracy 4.945 4.53 3.601
Memory
Utilization(bit) 1.1 1.104 1.104
Metrics
K-
Means
Fuzzy-C-
Means
Fuzzy KC
Means
Segmentation
Time(ms) 6.6724 58.2106
3.0098
Accuracy 53.67 49.16
39.08
Memory
Utilization(bit) 11.26 11.18
11.17
Metrics
K-
Means
Fuzzy-C-
Means
Fuzzy KC
Means
Segmentation
Time(ms) 6.7003 48.089 3.7732
Accuracy 53.62 49.12 39.09 Memory
Utilization(bit) 11.38 11.25 11.136
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com July 2018, Volume 6, Issue 7, ISSN 2349-4476
15 Ajala Funmilola A., Fenwa O.D, Oyeleye C.O
5. Conclusion
In this work, an evaluation of three different clustering segmentation algorithms was considered which are K Means,
Fuzzy C Means, and Fuzzy KC Means. The algorithms were implemented using Matrix Laboratory 7.1 (R0011a)
toolbox, the parameters evaluated include segmentation time, segmentation accuracy, and memory utilization.
The result showed that Fuzzy C Means has the highest memory utilization compared to K Means and Fuzzy KC Means
while Fuzzy KC Means has the fastest segmentation time and highest segmentation accuracy compared to K Means and
Fuzzy C Means.
6. REFERENCES
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