Integration of spatial fuzzy clustering with level set for efficient image segmentation

The controlling parameters of level set evolution are also estimated from the results of clustering. The fuzzy level set algorithm is enhanced with locally regularized evolution. Such improvements facilitate level set manipulation and lead to more robust segmentation. Performance evaluation of the proposed algorithm was carried on medical images from different modalities.

Integration of Spatial Fuzzy Clustering with Level Set for

Efficient Image Segmentation

N UmaDevi 1 ,R.Poongodi 2

1

Research Supervisor, Head, Department of Computer Science and Information Technology, Sri Jayendra Saraswathy MahaVidyalayaCollege of Arts and Science,

Coimbatore-5, India

umadevigayathri@rediffmail.com

2

ResearchScholar, Sri Jayendra Saraswathy Maha VidyalayaCollege of Arts and Science,

Coimbatore-5, India

poongodi.ct@gmail.com

Abstract:Image segmentation plays a crucial role in numerous biomedical imaging applications, assisting technicians or health care professionals during the diagnosis of various diseases.A new fuzzy level set algorithm is proposed in this paper

to facilitate medical image segmentation which is able to directly evolve from the initial segmentation of spatial fuzzy clustering The Spatial induced fuzzy c-means using pixel classification and level set methods are utilizing dynamic variational boundaries for image segmentation The controlling parameters of level set evolution are also estimated from the results of clustering The fuzzy level set algorithm is enhanced with locally regularized evolution Such improvements facilitate level set manipulation and lead to more robust segmentation Performance evaluation of the proposed algorithm was carried on medical images from different modalities

Keywords: Fuzzy clustering, Level set, Gradient

Medical imaging modalities provide an effective means of

noninvasively mapping the anatomy of a subject

Examples include magnetic resonance imaging (MRI),

computed tomography (CT), computed radiography (CR),

and ultrasonography (US) These technologies

haveincreased our knowledge of normal and diseased

anatomy and are critical components in diagnosis

Image segmentation algorithms are important in many

medical imaging applications such as the quantification of

tissue volumes [7], diagnosis [9], localization of pathology

[11], study of anatomical structure [10], treatment

planning [6] and computer-integrated surgery [1], [4]

Among many image segmentation algorithms, fuzzy set

theory has become increasingly attractive due to itsrobust

–ness for ambiguity and can retain much more

information than any other segmentation methods Fuzzy

sets were introduced in 1965 by LotfiZadeh to reconcile

mathematical modeling and human knowledge in the

engineering sciences [12], and fuzzy algorithms are

widely used today in advanced information technology

[2] Fuzzy C-Means (FCM) is one of the most well-known

algorithms in image segmentation, and partitions medical

images into non-overlapping, constituent regions that are

homogeneous with respect to some characteristics such as

texture intensity [5][3][8] However, for large data set,

FCM requires substantial amount of time which limits its

applicability It is not successful in segmenting the noise

image because the algorithm disregards of spatial constraint information.If we speedup the computations involved in FCM, technicians and other health care professionals could access patient information with nearly

no restrictions of time

2 RELATED WORK

2.1 Image Segmentation: Fuzzy C-Means

Image Segmentation is the process of partitioning an image into non-intersecting regions such that each region

is homogeneous and the union of no two adjacent regions

is homogeneous

Fuzzy c-means (FCM) clustering has been widely used in image segmentation However, in spite of its computational efficiency and wide-spread prevalence, the FCM algorithm does not take the spatial information of pixels into consideration, and hence may result in low robustness to noise and less accurate segmentation Application-specific integrated circuits (ASICs) can meet requirements for high performance and low power consumption in image segmentation algorithms General-purpose microprocessors (GPPs) or digital signal processors (DSPs) offer the necessary programmability and flexibility for various applications In addition, GPP manufacturers are also aware of the increased importance

of multimedia applications and have included multimedia

extensions to their architectures to improve the

performance of multimedia workloads

2.1 Cluster Validity Functions

One of the fundamental challenges of clustering is how to

evaluate results, without auxiliary information A common

approach for evaluation of clustering results is to use

validity indexes Clustering validation is a technique to

find a set of clusters that best fits natural partitions

(number of clusters) without any class information

Generally speaking, there are two types of clustering

techniques, which are based on external criteria and

internal criteria

• External validation: Based on previous knowledge about

data

• Internal validation: Based on the information intrinsicto

the data alone

Considering these two types of cluster validation

todetermine the correct number of groups from a dataset,

one option is to use external validation indexes for which

a priori knowledge of dataset information is required, but

it is hard to say if they can be used in real problems

Another option is to use internal validity indexes which do

not require a priori information from dataset

3 OUR CONTRIBUTION

The fuzzy clustering based on image intensity is done by

initial segmentation which employs level set methods for

object refinement by tracking boundary variation The

widely used conventional fuzzy c-means for medical

image segmentations has limitations because of its

squared-norm distance measure to measure the similarity

between centers and data objects of medical images which

are corrupted by heavy noise, outliers, and other imaging

artifacts To overcome the limitations the proposed

technique Kernel Induced Possibilistic Fuzzy C – Means

(KFCM) with Level Set Segmentation has been

introduced Compared to previous method FCM, the

proposed KFCM algorithm has significantly improved in

the following aspects First, the KFCM incorporates

spatial information during an adaptive optimization, which

eliminates the intermediate morphological operations

Second, the controlling parameters of level set

segmentation are now derived from the results of fuzzy

clustering directly Finally the proposed algorithm is more

robust to noise and outliers, and still retains computational

simplicity

3.1 Fuzzy Objective

The fuzzy c-means assigns pixels to c partitions by using

fuzzy memberships Let X = {x1, x2, x3… xn} denote an image with n pixels to be partioned into c clusters, where

x i (i = 1, 2, 3 n) is the pixel intensity The objective function is to discover nonlinear relationships among data, kernel methods use embedding mappings that map features of the data to new feature spaces The proposed technique Kernel Induced Possibilistic Fuzzy C-Means (KFCM) is an iterative clustering technique that minimizes the objective function

Given an image dataset, X = {x1…xn}⊂R p, the original

KFCM algorithm partitions X into c fuzzy subsets by

minimizing the following objective function as,

2

m

ik

where c is the number of clusters and selected as a specified value;nis the number of data points, u ik themembership of x k in class i, satisfying the

1 1

c ik i

u





the quantity controlling clustering fuzziness, and V the set

of cluster centers or prototypes (v i∈R p)

3.2 Kernel Induced PossibilisticFuzzy C-Means

In fuzzy clustering, the centroid and the scope of each subclass are estimated adaptively in order to minimize a pre-defined cost function It is one of the most popular algorithms in fuzzy, and has been applied in medical problems The fuzzy utilizes a membership function to

indicate the degree of membership of the n th object to the

m th cluster which is justifiable for medical image segmentation, as physiological tissues are usually not homogeneous

The fuzzy utilizes a membership function to indicate the degree of membership in finding the allocate space and allocate resources which is justifiable for medical image segmentation

Kernel Induced Possibilistic Fuzzy C Means (KFCM) clustering algorithm is incorporates the spatial neighborhood information with traditional FCM and updating the objective function of each cluster The KFCM uses the probabilistic constraint that the memberships of a data point across classes are sum to one The kernel induced possibilistic c-means algorithm is used

to minimize the objective function using Gaussian kernel function

The Gaussian function ηiare estimated using,

1

1

n m

ik k i

n m

k

K

u







(2)

The fuzzy membership function u ik is that the edges

connecting the inner data points in a cluster may have a

larger ―degree of belonging‖ to a cluster than the

―peripheral‖ edges (which, in a sense, reflects a greater

―strength of connectivity‖ between a pair of data points)

For instance, the edges (indexed i) connecting the inner

point in a cluster (indexed k) are assigned u ik = 1 whereas

the edges linking the boundary points in a cluster have

u ik< 1

Each cluster is represented by a data point called a cluster

center, and the method searches for clusters so as to

maximize a fitness function called net similarity The

method is iterative and stops after maximum iterations

(default of 500) It automatically determines the number

of clusters, based on the input p, which is an Nx1 matrix

of real numbers called preferences A good choice is to set

all preference values to the median of the similarity

values The number of identified clusters can be increased

or decreased by changing this value accordingly

The objective function in the clustering problem becomes

more general so that the weights of data points are being

taken into account, as follows:

S(C) = ui j km , kλk + γ jk

n

j=1

Ck i=1

(C k ) (𝟑)

𝐾

𝑘 =1

where C denotes the decomposition of the given clusters,

C 1 , …, C K are not-necessarily disjointclustersin the

decomposition C, γ denotes the modulatingargument,S(C)

denotes the total strength of connectivity cluster,

designates, as in the edge connectivity of cluster, the

weight u i(j) k,k is the membership degree of i(j) containing

data point j in cluster k, and finally, it is the fitness of

cluster j to cluster k

3.3 Level Set Segmentation

The fuzzy using pixel classification with level set methods

utilizes dynamic variational boundaries for image

segmentation Segmenting images by means of active

contours is well known approach instead of parametric

characterization of active contours.Level set methods

embed them into a time dependent PDE function It is

possible to approximate the evolution of active contours implicitly by tracking the zero level set

The level set evolution of active contour implicitly tracking the zero level setΓ(t),

𝜙 𝑡, 𝑥, 𝑦 < 0 𝑥, 𝑦 𝑖𝑠 𝑖𝑛𝑠𝑖𝑑𝑒 Γ 𝑡

𝜙 𝑡, 𝑥, 𝑦 = 0 𝑥, 𝑦 𝑖𝑠 𝑎𝑡 Γ 𝑡

𝜙 𝑡, 𝑥, 𝑦 > 0 𝑥, 𝑦 𝑖𝑠 𝑜𝑢𝑡𝑠𝑖𝑑𝑒 Γ(𝑡)

(4)

3.4 Fuzzy With Level Set Algorithm

Both fuzzy algorithms and level set methods are general-purposed computational model that can be applied to problems of any dimensions A new fuzzy level set algorithm is proposed for automated medical image segmentation The algorithm automates the initialization and parameter configuration of the level set segmentation, using Kernel Fuzzy clustering

A new fuzzy level set algorithm automates the initialization and parameter configuration of the level set segmentation, using spatial kernel fuzzy clustering It employs a KFCM with spatial constraints to determine the approximate contours of interest in a medical image Benefitting from the flexible initializations, the enhanced level set function can accommodate KFCM results directly for evolution The enhancement achieves several practical benefits The objective function now is derived from spatial fuzzy clustering directly The level set function will automatically slow down the evolution and will become totally dependent on the smoothing term

4 IMPLEMENTATION

Step 1: Infuzzy clustering process, the input MRI image and number of clusters areto be initialized In this process, fuzzy objective function, membership function and weights are calculated To separate the partition matrix with help of cluster centroid value, the distance matrix is used to find the similarity index value of black and white pixels of the image In the last iteration, the final partitioned objective function is derived

Step 2:Contour plot is defined to separate thebackground and foreground region in the image The regionsof object

in binary images are found using initial contour and perimeter functions

Step 3: 2-D convolution process, Gaussian filter function creates an image smoothness value which returns the central part of the image convolution

Step 4: The image pixel directionsare estimated with the help of gradient function which can either be scalars to specify the spacing between points in each direction or

vectors to specify the coordinates of the values along

corresponding dimensions The variation in space of any

quantity can be represented (e.g graphically) by a slope

The gradient represents the steepness and direction of that

slope

Step 5: The Neumann boundary or second-type boundary

condition is a type of boundary condition, named after

Carl Neumann When imposed on an ordinary or a partial

differential equation, it specifies the values that the

derivative of a solution is to take on the boundary of the

domain

Step 6: In Level set evolution there arethree types of

processes that are integratedin the final segmentation (i)

The Neumann boundary condition specifies the normal

derivative of the function on a surface (ii) The Direct

Adaptive Controller method is used by a controller which

must adapt to a controlled system with parameters which

vary, or are initially uncertain (iii) The curvature central

method is used to separate the gradient coordinate’s

directions and sum of these points is used to find out the

position which evaluates the final segmentation

5 RESULTS

The result of experiments and performance evolution were

carried on medical images from different modalities,

including an ultrasound image, liver tumors and MRI slice

of cerebral tissues Both the algorithms of spatial Kernel

Fuzzy induced Clustering and fuzzy level set method were

implemented in matlab R2010 The experiments were

designed to evaluate the usefulness of initial fuzzy

clustering for level set segmentation It adopted the fast

level set algorithm as in the curve optimization, where the

initialization was by manual demarcation, intensity

thersholding and Spatial KFCM Due to weak boundaries

and strong background noise, manual initialization did not

lead to an optimal level set segmentation The intensity

thersholding and fuzzy clustering attracted the dynamic

curve quickly to the boundaries of interest

For the preprocessing process the following measures are

used, the structural similarity (SSIM) index is a method

for measuring the similarity between two images The

SSIM index is a full reference metric, in other words, the

measuring of image quality based on an initial

uncompressed or distortion-free image as reference

Table - 1 shows the comparison of SSIM between the two

methods FCM and SKFC – Level Set

Table 1: Structural Similarity Ratio Comparison

Level Set Liver tumor 0.8002 0.9706 Ultrasound carotid

artery

The test image is matched with existing database to identify high frequency regions The Peak signal-to-noise ratio (PSNR) fraction is most commonly used to measure the quality of reconstruction of lossy compression coder – decoder The signal in this case is the original data, and the noise is the error introduced by compression

2

20 log ( ) 10 log ( ) 1

[ ( , ) ( , )]

I

m n

i j

PSNR MAX MSE

MSE I i j K i j

mn

 

 

(5)

Table 2: Peak Signal to Noise Ratio Comparison Image type FCM SKFC – Level

Set Liver tumor +47.139dB +47.560dB Ultrasound

carotid artery

0 0.5 1

FCM SKFC –

Level Set

Figure 5 : Comparison of FCM and SKFC -Level Set Methods using SSIM

Structural Similarity Ratio

Liver tumor

Ultrasound carotid artery

The liver tumor segmentation from the MRI scan is done

by the fast level set evolution Segmentation is difficult

because of the weak and irregular boundaries The liver

tissue itself is in-homogeneous, due to blood vessels

Again, it is challenging to determine an optimal

initialization and the corresponding level set parameters

The results show that a fuzzy clustering has the best

performance in terms of level set evolution The proposed

algorithm seems trivial in medical images with

comparatively clear boundaries However, in images

without distinct boundaries, it would be very important to

control the motion of the level set contours In contrast,

the new fuzzy level set algorithm is able to find out the

controlling parameters from fuzzy clustering

automatically

Fig 1: Kernel Induced Possibilistic C-means Cluster

Indexing of Liver tumor Result

Fig 2:SKFC level set segmentation of CT Liver tissue

The ultrasound carotid artery tumor is done the SKFC level set algorithm The improvements are used to incorporate fuzzy clustering into level set segmentation for an automatic parameter configuration Fig 3&4 illustrates its performance on the ultrasound image of carotid artery

Fig 3: Kernel Induced Possibilistic C-means Cluster indexing ultrasound carotid artery Result

Fig 4: SKFC level set segmentation of ultrasound carotid artery

6 CONCLUSION

In this paper we have worked with a spatial kernel induced Fuzzy level set algorithm that has been proposed for automated MRI image segmentation The enhanced FCM algorithms with spatial information can approximate the boundaries of interest well The level set evolution will start from a region close to the genuine boundaries The algorithm estimates the controlling parameters from spatial clustering automatically This has reduced the manual intervention Finally the fuzzy level set evolution

is modified locally by means of spatial fuzzy clustering All these improvements lead to a robust algorithm for medical image segmentation

38

39

40

41

42

43

44

45

46

47

48

49

FCM SKFC - Level Set

Figure 6: Comparison of FCM and SKFC

-Levelset using PSNR

Peak Signal to Noise Ratio

Liver Tumor

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