Performance Evaluation of Selected Clustering Algorithms ...Clustering uses no training stages, it...

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

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(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





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]


http://www.medscape/




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.





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





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





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

Ajala Funmilola A, Oke O.A, Adedeji T.O, Alade O.M, Adewusi E.A. (2012). “Fuzzy KC-means Clustering

Algorithm for Medical Image Segmentation”. Journal of Information Engineering and Applications. Vol 2, No.6, pp

21-32

Bezdek, J.C. (1981) “Pattern Recognition with Fuzzy Objective Function Algorithms”. Kluwer Academic

Publishers, Norwell, MA, USA, 1981

Christ, M. C. J. and Parvathi, R. M. S. (2011). “Segmentation of Medical Image using Clustering and Watershed

Algorithms” .American Journal of Applied Sciences 8 (12): 1349-1352, 2011 ISSN 1546-9239

Dasgupta, A. (2012). “Demarcation of Brain Tumor Using Modified Fuzzy C-Means”. International Journal of

Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 4, July-August 2012, pp.529-533

Joseph, P. R., Senthil, S., and Manikandan, M. (2014).“Brain Tumor MRI Image Segmentation And Detection In

Image Processing”. IJRET: International Journal of Research in Engineering and Technology. Page 1-5

HariKumar, R., Kumar, V., and Karthick, G. (2012).“Performance Analysis for Quality Measures Using K means

Clustering and EM Models in Segmentation of Medical Images”. International Journal of Soft Computing and

Engineering (IJSCE), Vol-1, No.6, 2012.

Logeswari, T. andKarnan, M. (2010). “An Improved Implementation of Brain Tumor Detection Using

Segmentation Based on Hierarchical Self Organizing Map”.International Journal of Computer Theory and

Engineering, Vol. 2, No. 4, August, 2010 1793-8201

Pal, N.R.—Bezdek, J.C.(1995).“On Cluster Validity for the Fuzzy C-Means Model”.IEEEFS, Vol. 3, 1995, No. 3, p.

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Priya, R. K., Thangaraj, C. and Kesavadas, C. (2011).“Fuzzy C-Means method for Colour Image Segmentation with

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