PERFORMANCE ANALYSIS OF CLUSTERING BASED IMAGE SEGMENTATION AND OPTIMIZATION METHODS

David C. Wyld, et al. (Eds): CCSEA, SEA, CLOUD, DKMP, CS & IT 05, pp. 245–254, 2012.
© CS & IT-CSCP 2012 DOI : 10.5121/csit.2012.2226
PERFORMANCE ANALYSIS OF CLUSTERING BASED IMAGE
SEGMENTATION AND OPTIMIZATION METHODS
Jaskirat kaur, Sunil Agrawal and Dr. Renu Vig
UIET, Panjab University, Chandigarh
jaskiratkaur17@gmail.com
ABSTRACT
Partitioning of an image into several constituent components is called image segmentation.
Myriad algorithms using different methods have been proposed for image segmentation. Many
clustering algorithms and optimization techniques are also being used for segmentation of
images. A major challenge in segmentation evaluation comes from the fundamental conflict
between generality and objectivity. As there is a glut of image segmentation techniques
available today, customer who is the real user of these techniques may get obfuscated. In this
paper to address the above described problem some image segmentation techniques are
evaluated based on their consistency in different applications. Based on the parameters used
quantification of different clustering algorithms is done.
.
KEYWORDS
PSO; DPSO; SC; RMSE; NK; PSNR
1. INTRODUCTION
Partitioning of an image into several constituent components is called image segmentation.
Segmentation is an important part of practically and automated image recognition systems,
because it at this moment extracts the intensity objects, for further processing such as description
or recognition [1]. It is widely used in exploratory pattern-analysis, grouping, decision making,
machine learning situations, including data mining, document retrieval and pattern classification
[2]. In many such above mentioned cases, there is little a priori information available about the
data and we need to make as many assumptions as possible. Under all these restrictions clustering
methodology is particularly appropriate for the exploration of interrelationship among the data
points to make an assessment of their structure [2].
Today many data clustering algorithms are being used for segmenting images. They are termed as
unsupervised methods for segmentation of images. In such techniques, image is separated into a
set of disjoint regions with each region associated with one of the finite number of classes that are
characterized by distinct parameters [3]. Therefore till date many types of segmentation
techniques have been developed and many data clustering techniques are being used for
segmentation of images [4].
A potential problem for a measure of consistency between different segmentations available is
that there is no unique segmentation of an image. For example two people may segment an image
differently because they either perceive the scene differently, or they segment at different

246 Computer Science & Information Technology (CS & IT)
granularities. If two different segmentations arise from different perceptual organizations of the
scene, then it is fair to declare the segmentations inconsistent [5].
A major challenge in segmentation evaluation comes from the fundamental conflict between
generality and objectivity. For general-purpose segmentation, segmentation accuracy may not be
well defined, while embedding the evaluation in a specific application, the evaluation results may
not be extensible to other applications. Reliable segmentation performance evaluation for
quantitatively positioning image segmentation is extremely important. In many prior works,
segmentation performance is evaluated by subjectively or objectively judging several sample
images. Such evaluations lack statistical meanings and may not be generalized to other images
and applications [4].
As there is a glut of image segmentation techniques available today, customer who is the real user
of these techniques may get obfuscated. In this paper to address the above described problem
performance analysis is carried out to classify and quantify different clustering algorithms based
on their consistency in different applications. This paper also describes the various performance
parameters on which consistency will be measured [3].
The rest of the paper is organized as follows: Section II discusses various clustering based image
segmentation techniques. Section III describes parameters used to measure consistency.
Experimental implementation and results are shown in Section IV. Section V concludes the paper.
2. CLUSTERING BASED IMAGE SEGMENTATION METHODS
Extracting information from an image is referred to as image analysis. It is one of the preliminary
steps in pattern recognition systems. Each region of the image is made up of set of pixels.
Partitioning an image into several disjoint segments is termed as image segmentation. It
simplifies and changes the representation of an image, transferring an image into something more
meaningful and easier to analyze. Typically it is used to locate objects of interest and boundaries
like lines, and curves in an image [1]. Segmentation algorithms are based on two basic properties
of an image intensity value: discontinuity and similarity. To study discontinuities in an image we
divide image based on the abrupt changes in intensity such as edges.
Mathematically the regions we obtain after partitioning an image is considered to be
homogeneous with respect to some image property of interest. Image property can be intensity,
color, or texture.
If
‫ܫ‬ = {‫ݔ‬௜௝, ݅ = 1 … ܰ௥, ݆ = 1 … ܰ௖} (1)
is the input image with ܰ௥ rows and ܰ௖ columns and measurement value ‫ݔ‬௜௝ at pixel (݅, ݆), then
the segmentation can be expressed as ݈ = {ܵଵ, … . , ܵ௞ } with the ݈௧௛ segment
ܵ௟ = {൫݅௟భ
, ݆௟భ
൯, … , ቀ݅௟ಿభ
, ݆௟ಿభ
ቁ} (2)
consisting of a connected subset of the pixel coordinates. No two segments share any pixel
locations and the union of all the segments covers the entire image.
An image may contain more than one object and segmenting the image in line with object
features in order to extract meaningful object has become a challenge for researchers in the field.
Segmentation can be achieved in a more efficient manner through clustering.

Computer Science & Information Technology (CS & IT) 247
Clustering is an interesting approach for finding similarities in data and putting similar data into
groups. Cluster partitions data set into several groups such that the similarity within a group is
larger than that among the groups. Clustering algorithms are used extensively not only to organize
and categorize data, but are also useful for data compression [6].
The segmentation of images presented to an image analysis system is critically dependent on the
scene to be sensed, the imaging geometry, configuration, and sensor used to convert the scene
into a digital image, and ultimately the desired output of the system [6].
The applicability of clustering methodology to the image segmentation problem was recognized
over three decades ago, and the paradigms underlying the initial pioneering efforts are still in use
today. It defines feature vectors at every image location called as pixel component of both
functions of image intensity and functions of pixel location itself.
Figure1. Feature representation for clustering
The basic idea of assigning pixel values is depicted in figure 1. In the above figure image
measurements and positions are transformed to features. Also clusters in feature space correspond
to image segments [6].
Good objectivity means that all the test images should have an unambiguous segmentation so that
segmentation evaluation can be conducted objectively. Good generality means that test images
should have a large variety so that the evaluation results can be extended to other images and
applications. There always exists a well known dilemma between objectivity and generality in
segmentation evaluation [4]. There is no such unique clustering technique which can segment all
types of images uniquely and unambiguously.
2.1. Fuzzy c-means Clustering Algorithm
In fuzzy clustering, the image pixel values can belong to more than one cluster, and associated
with each of the points are membership grades that indicate the degree to which the data points
belong to different clusters [7]. The input to FCM algorithm is, ݊ × ݉ matrix where ݊ is the
number of data and ݉ is the number of parameters, ܿ the number of clusters, the assumption
partition matrix ܷ, and the convergence value ‫.ܧ‬ The assumption partition matrix have ܿ number
of rows, ݊ number of columns, and contain values 0 to 1. The sum of every column has to be 1.
The first step in FCM algorithm is to calculate the cluster centers. This is a matrix ‫ݒ‬ of dimension
ܿ rows with ݉ columns. The second step is to calculate the distance matrix ‫.ܦ‬ The distance
matrix constitutes the Euclidean distance between every pixel and every cluster center. This is
matrix with ܿ rows and ݊ columns. From the distance matrix the partition matrix ܷ is calculated.
If the difference between the initial partition matrix and the calculated partition matrix is greater
than the convergence value then the entire process from calculating the cluster centers to the final

partition matrix. The final partition matrix is taken and is used for reconstructing the image.
Fuzzy c-Means function is taken as
‫ܬ‬௠(ܷ, ܻ) = ∑ ∑ (‫ݑ‬௝௞)௠
‫ܧ‬௝(‫ݔ‬௞)௖
௝ୀଵ
௡
௞ୀଵ (3)
Where Ω = { ‫ݔ‬௞ | k € [1, n]} is a training set containing ݊
unlabeled symbols ; Y = {‫ݕ‬௝ | j € [1,c]}} is the set of centers of clusters; ‫ܧ‬௝(‫ݔ‬௞) is a dissimilarity
measure between the sample ‫ݔ‬௞ and the cluster ‫ݕ‬௝ of a specific cluster j; ܷ = [‫ݑ‬௝௞] is the ܿ × ݊
fuzzy c partition matrix, containing the membership values of all samples in all clusters;
݉ € (1, ∞) is a control parameter of fuzziness. The clustering problem can be defined as the
minimization of ‫ܬ‬௠ with respect to Y, under the probabilistic constraint:
∑ ൫‫ݑ‬௝௞൯ = 1௖
௝ୀଵ (4)
The FCM algorithm consists in the iteration of the following formulas: for all j
‫ݕ‬௝ =
∑ (௨ೕೖ)೘ ௫ೖ
೙
ೖసభ
∑ (௨ೕೖ)೘೙
ೖసభ
(5)
And
‫ݑ‬௝௞ =ቂ ((∑ (
ாೕ (௫ೖ )
ா೗ (௫ೖ )
)
మ
೘షభ)௖
௟ୀଵ ቃ
ିଵ
݂݅ ‫ܧ‬௝(‫ݔ‬௞) > 0 ∀݆, ݇ (6)
Where in the case of Euclidean space:
‫ܧ‬௝ = |ห‫ݔ‬௞ − ‫ݕ‬௝ห|ଶ
(7)
If ݉ is chosen to be equal to be 1 the FCM function ‫ܬ‬௠ , equation 3 reduces to the expectation of
the global error denoted as <‫.>ܧ‬
< ‫ܧ‬ ≥ ∑ ∑ ‫ݑ‬௝௞‫ܧ‬௝
௖
௝ୀଵ
௡
௞ୀଵ (‫ݔ‬௞) (8)
2.2. Particle Swarm Optimisation
PSO has been originally introduced in terms of social behavior of particles. The individuals, called
particles are made to flow through the multidimensional search space. Each particle then tests a
possible solution to the multidimensional problem as it keeps on moving through the problem
space. The movement of the particles is influenced by two factors, the particle's best solution
(pbest) and the global best solution found by all the particles (gbest), which influence the particle's
velocity through the search space by creating an attractive force [9]. As a result, the particle
interacts with all neighbors and stores optimal location information in its memory. After each
iteration the pbest and gbest are updated respectively if a more optimal solution is found by the
particle or population. This process is continued iteratively until either the desired result is
achieved.
The PSO formulae defines each particle in the D-
dimensional space as xi =(xi1
,xi2
, ,xiD), where the subscript i
represents the particle number and the second subscript is the dimension. The memory of the
previous best position (pbest) is represented as Pi = ( pi1, pi2, , piD) and a velocity along each
dimension as vi = (vi1, vi2, , viD) . After each iteration, the velocity term is updated. The

particle's motion is influenced by its own best position Pi, as well as the global best position Pg
(gbest),[8]. The velocity is updated
by
vij (t +1) = wvij (t)+c1r1(pij(t)−xij(t))+c2r2(pgj(t)−xij(t)) (9)
And the position is updated by
xij (t +1) = xij(t) +vij(t +1) (10)
Constants c1, c2 determine the relative influence of the pbest and gbest and they are set to same
value. The memory of the PSO is controlled by w [13]. r1, r2 are randomly generated value
between 0 and 1. The PSO is usually executed with repeated application of (9) and (10) until a
specified number of iterations have been exceeded. Alternatively, the algorithm also can he
terminated when the velocity updates are close to zero over a number of iterations.
2.3. Darwinian Particle Swarm Optimisation
Darwinian PSO, in which many swarms of test solutions may exist at any time. Each swarm
individually performs just like an ordinary PSO algorithm with some rules governing the
collection of swarms that are designed to simulate natural selection [10]. The selection process
implemented is a selection of swarms within a constantly changing collection of swarms.
The basic assumptions made to implement Darwinian PSO are:
• The longer a swarm lives, the more chance it has of possessing offspring. This is
achieved by giving each swarm a constant, small chance of spawning a new swarm.
• A swarm will have its life-time extended (be rewarded) by finding a more fit state.
• A swarm will have its life-time reduced (be punished) for failing to find a more fit state.
Steps of Darwinian PSO
1) Particle and swarm initialization
Each PSO particle is an array of N numbers; the array could contain a binary string [11]. The
choice of the domain of the particle array elements, xi as well as the encoding of the test solution
as an array of numbers is motivated by the particular optimization problem. The discussion of
these details is therefore deferred until thetest problems are discussed. Each dimension of each
particle is randomly initialized on an appropriate range xmin ≤ xi≤ xmax. The velocities are also
randomly initialized on a range, vmin ≤ vi≤ vmax , that allows particles to traverse a significant fraction of the
range of xi in a single iteration when moving at vi = vmax .
The algorithm says to evolve an individual swarm, the fitness of all of the particles in the swarm
are evaluated. The neighborhood and individual best positions of each of the particles are updated.
The swarm spawns a new particle if a new global best fitness is found. A particle is deleted if the
swarm has failed to find a more fit state in an allotted number of steps.
2) Condition for deleting a swarm
A swarm's particle population, m is bounded such that, mmin ≤ m≤ mmax . When a swarm's
population falls below mmin , the swarm is deleted.
3) Condition for deleting a particle

The worst performing particle in the swarm is deleted using the following algorithm. The
number of times a swarm is evolved without finding an improved fitness is tracked with a search
counter, SC. If the swarm's search counter exceeds a maximum critical threshold, SCmax, a
particle is deleted from the swarm. When a swarm is created, its search counter is set to zero.
When a particle is deleted, the swarm's search counter is reset not to zero but to a value
approaching SCmax as the time during which the swarm makes no improvement in fitness
increases. The purpose of this reduction in tolerance for stagnation is to try to maintain a
collection of swarms that are actively improving. If Nkill is the number of particles deleted from
the swarm over a period in which there is no improvement in fitness, then the reset value of the
search counter is chosen to be
ܵ‫ܥ‬௖(ܰ௞௜௟௟) = ܵ‫ܥ‬௖
௠௔௫
ቂ1 −
ଵ
ேೖ೔೗೗ାଵ
ቃ (11)
4) Condition for spawning particles and swarms
At each step of the algorithm, each swarm may spawn a new swarm. To be able to spawn a new
swarm, an existing swarm must have Nkill = 0. If this condition is met and the maximum number
of swarms will not be exceeded, the swarm spawns a new swarm with probability p = f / Ns ,
where f is a uniform random number [0,1] and Ns is the number of swarms. The purpose of the
factor of 1/ Ns is to suppress swarm creation when there are large numbers of swarms in
existence. When a swarm spawns a new swarm, the spawning swarm (parent) is unaffected. To
form the spawned (child) swarm, half of the particles in the child are randomly selected from the
parent swarm and the other half are randomly selected from a random member of the swarm
collection (mate). The spawned or child swarm may inherit other attributes from either parent or
mate as necessary to design experimentation for the Darwinian PSO algorithm. A particle is
spawned whenever a swarm achieves a new global best fitness.
3. PARAMETERS TO MEASURE CONSISTENCY
1) Structural Content (SC)
SC =
∑ ∑ ௑(௝,௞)మಿ
ೖసభ
ಾ
ೕసభ
∑ ∑ ௑෠(௝,௞)మಿ
ೖసభ
ಾ
ೕసభ
(12)
The large value of structural content means that image is of poor quality [3].
2) Peak signal to noise ratio (PSNR)
PSNR = 10. ݈‫݃݋‬ଵ଴
‫ۏ‬
‫ێ‬
‫ێ‬
‫ۍ‬
୫ୟ୶ (௥(௫,௬))మ
భ
೙ೣ.೙೤
൥
∑ ∑ [ೝ(ೣ,೤)]మ೙೤షభ
బ
೙ೣషభ
బ
∑ ∑ [ೝ(ೣ,೤)ష೟(ೣ,೤)]మ೙೤షభ
బ
೙ೣషభ
బ
൩
‫ے‬
‫ۑ‬
‫ۑ‬
‫ې‬
(13)
The above equation calculates PSNR in decibels. The small value of PSNR means the
image is of poor quality [3].

3) Normalized Correlation Coefficient (NK)
NK =
∑ ∑ [௑(௝,௞)௑෠(௝,௞)]ಿ
ೖసభ
ಾ
ೕసభ
∑ ∑ [௑(௝,௞)మಿ
ೖసభ
ಾ
ೕసభ ]
(14)
4) Root mean square error (RMSE)
RMSE = ඨ
ଵ
௡ೣ.௡೤
ቈ
∑ ∑ [௥(௫,௬)]మ
೙೤షభ
బ
೙ೣషభ
బ
∑ ∑ [௥(௫,௬)ି௧(௫,௬)]మ
೙೤షభ
బ
೙ೣషభ
బ
቉ (15)
This is the simplest image quality measurement. The large value of RMSE means the
image is of poor quality.
RMSE and PSNR compares the input image r(x,y) with the output image t(x,y).
4. EXPERIMENTAL ANALYSIS AND RESULTS
In this section different clustering based image segmentation methods are applied to images from
different fields and the algorithms were tested for consistency for each application. One image
from each section is presented over here and the values of parameters are calculated. Numerical
values define the objectivity of different clustering algorithms.
TABLE I. IMAGES FROM DIFFERENT FIELDS AND THE PROCESSED OUTPUTS
Original Brain
tumour image
Original Remote sensing
image
Original
Architectural image
FCM processed
Image
FCM processed Image FCM processed
Image
PSO processed
Image at level 2
PSO processed Image at
level 2
PSO processed Image
at level 2
PSO processed
Image at level 4
PSO processed Image at
level 4
PSO processed Image
at level 4
Segmentation using FCM

DPSO processed
Image at level 2
DPSO processed Image at
level 2
DPSO processed
Image at level 2
DPSO processed
Image at level 4
DPSO processed Image at
level 4
DPSO processed
Image at level 4
TABLE II. RESULTS OF DEFFERENT PARAMETERS
BRAIN REMOTE SENSING ARCHITECTURAL
FCM
RMSE=112.3438
NK= 0.4767
PSNR= 52.7679
SC = 1.1280
PSO 2
RMSE=173.2386
NK = 0.9011
PSNR= 25.7444
SC = 1.1098
PSO 4
RMSE=160.7290
NK = 0.9504
PSNR= 26.0699
FCM
RMSE=113.0931
NK= 0.7117
PSNR= 58.4403
SC = 1.12883
PSO 2
RMSE=253.24
NK = 0.4914
PSNR= 24.0955
SC = 2.0379
PSO 4
RMSE=96.004
NK = 0.9956
PSNR= 71.70
FCM
RMSE=99.0902
NK = 0.9002
PSNR= 58.5770
SC = 0.9241
PSO 2
RMSE=250.63
NK = 0.7380
PSNR=24.141
SC = 1.4155
PSO 4
RMSE=240.28
NK = 0.9108
PSNR= 24.324

SC = 1.0524
DPSO 2
RMSE=173.2367
NK = 0.9000
PSNR= 25.7444
SC = 1.1111
DPSO 4
RMSE=160.8886
NK = 0.9495
PSNR=26.0656
SC=1.0533
SC = 2.8044
DPSO 2
RMSE=253.18
NK = 0.4900
PSNR= 24.096
SC = 2.0431
DPSO 4
RMSE=215.67
NK = 0.5155
PSNR= 24.793
SC = 1.19506
SC = 1.1864
DPSO 2
RMSE=250.62
NK = 0.7347
PSNR= 24.141
SC = 1.4231
DPSO 4
RMSE=236.61
NK = 1.0858
PSNR= 24.391
SC = 1.1899
From the above implementations observation was made not all algorithms work good for single
application. Parameters for performance measure were taken to test fuzzy c-Means clustering
algorithm, particle swarm optimization and its variation. 10 images each of remote sensing,
medical and architectural were taken and almost similar results were obtained. Table I shows the
original as well as the processed images of each algorithm. TableII contains all the numerical
values of the parameters taken. In medical images observation was made that FCM performs best
because 3 parameters in this case give best results and 1 in PSO 4. Similar observations were
made on other type of medical images. Similarly in remote sensing images PSO when segmented
at level 4 gives best results. In the case of architectural images either DPSO at level 4 or FCM
both work better. Choice between the two is made based on the application they are used for.
2.6. CONCLUSION
This paper compares the performance of a few clustering based image segmentation methods.
Fuzzy c-Means clustering algorithm, particle swarm optimization and Darwinian PSO are
discussed. Then to evaluate the consistency of different algorithms number of error measures are
discussed and calculated. For the parameters measured, it was demonstrated that single algorithm
will never work better for all fields. Based on these numerical values, objectivity of various
algorithms is defined and the performance it gives for particular application. In the future work
the performance analysis will be based on some newer optimization techniques as well as the
algorithms and comparison will be extended to wide range of applications.

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