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\title{Image Segmentation for Animal Images using Finite Mixture of Pearson type VI Distribution}
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\begin{document}

             \author[1]{  chandoo}

             \author[2]{K. Srinivasa  Rao}

             \author[3]{P. Srinivasa  Rao}

             \affil[1]{  GITAM University}

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\date{\small \em Received: 10 December 2013 Accepted: 2 January 2014 Published: 15 January 2014}

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\begin{abstract}
        


Image Segmentation is one of the significant tool for analyzing images, the feature vector of the images are different for different types of images. In remote sensing, Environmental ecological systems, forest studies, conservation of rare animals, the animal images are more important. In this paper we developed and analyze an image segmentation algorithm using mixture of Pearson Type VI Distribution. The Pearsonian Type VI Distribution will characterize the image regions of animal images. The appropriateness Pearsonian Type VI distribution for the pixel intensities of image region in animal images is carried by fitting Pearsonian Type VI Distribution to set of animal images taken from Berkeley image data set. The image segmentation algorithm is developed using EM algorithm for estimating the parameters of the model and maximum likelihood for image component under Bayesian framework. For fast convergence of EM algorithm the initial estimates of the model parameters are obtained by dividing the whole image into K image regions using K-means and Hierarchical clustering algorithm and utilizing the moment method of estimates. The performance of proposed algorithm is studied by conducting an experiment with set of animal images and computing image quality metrics such as PRI, GCE and VOI. A comparative study of developed image segmentation by Gaussian Mixture model and found the proposed algorithm performed better for animal images due to asymmetrically distributed nature of pixel intensities in the image regions.

\end{abstract}


\keywords{EM algorithm, image segmentation, performance measures, type VI pearsonian.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
n image processing and retrievals image analysis plays a dominant role. The major task in image analysis is extracting useful information using features of the image. Generally image analysis techniques broadly grouping into groups namely \hyperref[b0]{(1)} Structural methods (2) Statistical methods Raj Kumar et al  {\ref (2011)}, among these two groups statistical methods are much popular. In Statistical methods one of the prime considerations is dividing whole image into different image regions using probability distributions. This type of method is usually referred as image Pal N. R. (1993), \hyperref[b0]{Cheng et al (2001)}, Srinivasa et al  {\ref (2007)},  {\ref Srinivas Y et al (2010)}, Prasad Reddy et al  {\ref (2007)} have reviewed the image segmentation methods. There is no unique image segmentation method available for analyzing all images. The image segmentation is basically dependent on type of images. The image broadly categorized into four types of categories . They are \hyperref[b0]{(1)} Images on Earth (2) images of Humans and animals (3) images on sky (4) images on Water and (5) images of Nature. Among these categories the images of Human beings and Animals are in different in nature and features are associated with these images are different from others in some statistical sense. These images are Skewed in nature. Hence the image segmentation methods based on Gaussian mixture model given by Cheng et al (2001), Yamazaki T. et al (1998), Zhang Z.H et al (2003), Lie T. et al  {\ref (1993)} may not suit well. Even the methods given by Sesha sayee et al (2011), Srinivasa et al (2011) are also may not suit since these methods also focus on symmetry of the pixel intensities in the image region. Hence to have suitable and more appropriate image segmentation methods for animals, an image segmentation method using a mixture of Pearsonian Type VI Distribution is developed and analyzed. Here it is assumed that whole image is characterized by a mixture of Pearsonian Type VI probability model. The Pearsonian Type VI Distribution is skewed in nature having long upper tails. This distribution also includes several distributions as particular case. From the Berkeley image data set collected over animal images. It is evident that the pixel intensities of these images are well categorized by mixture of Pearsonian Type VI Distribution. The model parameters are estimated by updated equations of EM algorithm. The initial values of the model parameters of EM Algorithm are carried using Histograms of the whole image and K-means and Hierarchical clustering Algorithm and moment method of estimates. The image segmentation algorithm is developed through Maximum Likelihood component under Bayesian frame. The performance of image segmentation algorithm is skewed using image quality metrics and ground truth values. The comparative study of proposed algorithm with that of Gaussian Mixture Model is also carried. Usually the entire image is considered as a union of several image regions in low level image analysis and the image data is quantified by pixel intensities in each image region. Because of the fact that the brightness measured at a point in the image is influenced by various random factors like environmental conditions, vision, moisture, lighting etc, the pixel intensity ( , ) z f x y = for a given point ( pixel ) (x, y) is a random variable. It is generally assumed that the pixel intensities of the region follow a Pearson Type VI distribution in order to model the pixel intensities of the animal and human image regions. The probability density function of the pixel intensity is ( ) ( )2 1 2 1 1 1 2 ( 1)\textbf{1 2 2}\par
( / , , )\par
)i i i i q q s i s i i i i q q i i i i i i z a z f z a q q a B q q q a z ? ? ? + ? = ? ? + ? <\par
The entire animal and human image is a collection of regions which are characterized by Pearson Type VI distribution. Here, it is assumed that the pixel intensities of the whole image follows a Kcomponent mixture of Pearson Type VI distribution and its probability density function is of the form1 1 2 ( ) ( / , , )\textbf{(2) 1}K i i i i i p z f z a q q i ? = ? =\par
where, K is number of regions , 0 ? i ? ? 1 are weights such that ? i ? = 1 and1 1 2 ( / , , ) i i i i\par
f z a q q is as given in equation ( \hyperref[formula_0]{1}). In the whole image ? i is the weight associated with i th region. Usually the intensities of the pixel in the image regions are statistically correlated and can be reduced by spatial averaging ( Kelly P.A. et al ( 1998 ) ) or spatial sampling ( Lei T. and Sewehand W. ( 1992 )) .The pixels are considered to be uncorrelated and independent after reduction of correlation. The mean pixel intensity of the whole image is( ) 1 i i K E Z i ? µ = ? = 
\section[{III. Estimation of the Model Parameters by EM Algorithm}]{III. Estimation of the Model Parameters by EM Algorithm}\par
In this section we derive the updated equations of the model parameters using Expectation Maximization (EM) algorithm. The likelihood function of the observations 1 2   , ,..., N z z z drawn from an image isN ( ) 1 ( ) ( , ) l s L p z s ? ? = = ? ( ) N That is ( ) ( , ) 1 1 ? ? = = = K L f z s i i i s ? ? ? ( ) Thisimplies log ( ) log ( , ) 1 1 ? ? = = = N K L f z s i i s i ? ? ?\par
Where1 1 2\par
( , , , ; 1, 2,..., )i i i i a q q i K ? ? = =\par
is the set of parameters. 
\section[{(}]{(}\par
) ( )2 1 2 1 ( 1) 1 2 2 log ( ) log ,\textbf{(3)}( ) ( 1, 1) 1 1 i i i i q q i s i s q q i i i i N K z a z L a B q q q s i ? ? ? ? + ? ? ? = ? ? ? ? ? ? + = = ? ? ? ?\par
The first step of the EM algorithm requires the estimation of the likelihood function of the sample observations. 
\section[{a) E-Step}]{a) E-Step}\par
In the expectation (E) step, the expectation value of log ( ) L ? with respect to the initial parametervector ? (0) is ( ) [ ] (0) ; log ( ) / (0) = Q z , belongs to any region K is ( ) ( ) ( ) ( ) ( , ) ( , ) ( ) ( , ) ( ) ( ) ( ) ( , )\textbf{( , ) 1 =}= ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? l l l l f z f z l s s k k k k t z s k K l l l p z f z\par
Following the heuristic arguments of Jeff A. Bilmes (1997) we have( ) ( ) ( ) ( ) ( ) ( ) ( )\textbf{1 1}\par
;\par
( , ) log ( , ) log (5)= = = + ?? K N l l l l i s i s i i s Q t z f z ? ? ? ? ?\par
But we have ( ) ( )2 1 2 1 1 1 2 ( 1) 1 2 2 ( / , , )\textbf{( ) ( 1, 1)}i i i i q q s i s i i i i q q i i i i z a z f z a q q a B q q q ? ? + ? = ? ? + ( D D D D ) Year 2014 F II.\par
Mixture of Pearson Type vi Distribution\par
( , ) log ( , ) log 1 1K N l l l l Q t z f z s s i i i i s ? ? ? ? ? ? ? = + = = b) M-Step\par
For obtaining the estimation of the model parameters one has to maximize ( )( ) ; l Q ? ?\par
such that ?? i = 1. This can be solved by applying the standard solution method for constrained maximum by constructing the first order Lagrange type function, ( )( ) ( ) (log ( )) 1 (6) 1 K l l S E L i i ? ? ? ? = + ? = ? ? ? ? ? ?\par
where, ? is Lagrangian multiplier combining the constraint with the log likelihood function to be maximized.\par
Hence,0 ? = ? S i ?\par
. This implies( ) ( ) 2 1 2 1 ( ) i ( 1) 1 1 1 2 2 1 ( , ) log log ( ) ( 1, 1) 1 0 i i i i q q K N s i s l i s q q i s i i i i i K i i z a z t z a B q q q ? ? ? ? ? ? ? + = = = ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? = ? ? ? ? ?? ? This implies 1 1 ( ) ( , ) 0 i s i N l t z i ? ? ? + = ? =\par
Summing both sides over all observations, we get ? = -N Therefore ( , )? = = ? N l i i s s t z N ? ?\par
The updated equation of i ? for ( l +1) th iteration is( ) 1 ( ) 1 1 ( , ) N l l i i s s t z N ? ? + = = ? ( ) 1 ( ) ( ) ( , )\textbf{1}( ) ( ) 1 ( , ) 1 l i l l N f z i i s K l l s N f z i i s i ? ? ? ? ? + ? = ? = ? ? ? ? = ? ? ? ?\textbf{(7) Therefore ( ) ( )}\par
; 0l i Q a ? ? ? = ? implies ( ) 1 log ( ; ) 0 l i L E a ? ? ? ? ? = ? ? ? ? ? ( ) ( ) ( ) ( ) ( )\textbf{1 1}\par
( , ) log ( , ) log 0K N l l l i s i s i i s i t z f z a ? ? ? = = ? ? ? ? ? + = ? ? ? ? ? 
\section[{??}]{??}\par
The updated equation of i a at ( l +1)th iteration is ( )2 1 2 ( ) ( ) ( ) ( ) ( 1) ( ) ( ) 1 ( 1) ( , )\textbf{( , )}i i i i i l l l l N s i s l l l s i s q q z a t z a t z q ? ? + = ? ? ? ? + ? ? ? = ? ? ? ? ? For updating the parameter 1 i q , i = 1, 2, ?, K\par
we consider the derivative of ( )( ) ; l Q ? ?\par
with respect to1 i\par
q and equate it to zero. We have ( )( )\textbf{( )}\par
; log ( ; )l l Q E L ? ? ? ? ? ? = ? ? Therefore ( ) ( ) 1 ; 0 l i Q q ? ? ? = ? implies ( ) 1 log ( ; ) 0 l i L E q ? ? ? ? ? = ? ? ? ? ? ( ) ( ) ( ) ( ) ( ) 1 1 1 ( , ) log ( , ) log 0 K N l l l i s i s i i s i t z f z q ? ? ? = = ? ? ? + = ? ? ? ? ? ?? ( ) 1 1 ( ) 0 1 2 0 1 ( , ) 1 (8) log (\textbf{2 1)}\par
( 1) ( , )l N i s i s l i i i i i s s t z q a q q q t z z ? ? ? ? = ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? + + ? ? ? ? ? ? ? ? ? ? ? ? ? ?\par
The updated equation of1 i q at ( l +1)th iteration is 1 1 2 1 ( ) ( 1) 1 ( ) ( ) ( ) ( ) 0 0 ( , ) 1 (9) log (\textbf{2 1)}\par
( 1) ( , )i i i i l N l i s s l l l l i i s s t z q a q q q t z z ? ? ? ? + = ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? + + ? ? ? ? ? ? ? ? ? ? ? ? ? ?\par
For updating the parameter2 i q , i = 1, 2, ?, K we consider the derivative of ( )\textbf{( )}\par
; l Q ? ? with respect to 2 i q and equate it to zero. We have ( )( ) ( ) ; log ( ; ) l l Q E L ? ? ? ? ? ? = ? ? Therefore ( ) ( ) 2 ; 0 l i Q q ? ? ? = ? implies ( ) 2 log ( ; ) 0 l i L E q ? ? ? ? ? = ? ? ? ? ? ( ) ( ) ( ) ( ) ( )\textbf{1 1 2}\par
( , ) log ( , ) log 0K N l l l i s i s i i s i t z f z q ? ? ? = = ? ? ? + = ? ? ? ? ? ?? ( ) 1 2 ( ) 0 1 2 0 2 1 ( , )\textbf{(10) ( ) log}\par
( 2 1) ( ) ( , ) The mixing parameters ? i and the model parameters q i1 , q i2 are usually considered as known apriori. Drawing a random sample from the entire image \hyperref[b14]{( Mclanchan G. and Peel D. (2000)}) is the most commonly used method for initializing parameters. This method shows better performance, if the sample size is large and its computational time is heavily increased. When the sample size is small, there are some small regions which may not be sampled. To divide the whole image into various homogeneous regions we use the K -Means algorithm. In this algorithm the centroids of the clusters are recomputed as soon as the pixel joins a cluster.N l i s s i N l s i i i i i s s i t z q z a q q q t z a ? ? ? ? = = = ? ? ? + ? ? + ? ? ? ? ? ? ? The updated equation of 2 i q at ( l +1)th iteration is 2 1 2 2 ( ) ( 1)\textbf{1}( ) ( ) ( ) ( ) 0 0 1 ( , )\textbf{(11)}( ) log ( 2 1) ( ) ( , ) i i i i N l i s l s N l l l l s i i s s i t z q z a q q q t z a ? ? ? ? + = = = ? ? ? + ? ? + ? ? ? ? ? ? ? Where ( ) ( ) ( ) ( ) ( ) 1 ( , ) ( , ) ( , ) l l l i i s i s K l l i i s i f z t z f z ? ? ? ? ? = = ? IV. 
\section[{a) K-Means Clustering Algorithm}]{a) K-Means Clustering Algorithm}\par
It is one of the simplest clustering technique with a primary goal to find the partition of the data which minimizes the squared error or the sum of squared distances between all the points and their respective cluster centers (Rose H. Turi, (  {\ref 2001})). This K-means algorithm uses an iterative procedure and this procedure minimizes the sum of distances from each object to its cluster centroid, over all clusters. This procedure consists of the following steps. 1) Randomly choose K data points from the whole dataset as initial clusters. These data points represent initial cluster centroids. 2) Calculate Euclidean distance of each data point from each cluster centre and assign the data points to its nearest cluster centre. 3) Calculate new cluster centre so that squared error distance of each cluster should be minimum. 4) Repeat step 2 and 3 until clustering centers do not change. 5) Stop the process.\par
In the above algorithm, once only if all points have been allocated to their closed cluster centre then the cluster centers are updated. The advantage of this algorithm is that it is a very simple method, and based on intuition about the nature of a cluster, which is that the within cluster error should be as small as possible. The disadvantage of the K-Means algorithm is that the number of clusters must be supplied as a parameter, leading to the user having to decide what the best number of clusters for the image is (Rose H. Turi, (2001)). Success of K-means algorithm depends on the parameter K, number of clusters in image.\par
After determining the final values of K (number of regions) , we obtain the initial estimates of1 2\par
, , andi i i i\par
a q q ? for the i th region using the segmented region pixel intensities with Pearson Type VI distribution .The initial estimate ? i is taken as ? i =1/K, where i = 1,2,...,K. The parameters 1 i q and 2 i q are estimated by the method of moments as first moment µ 1 and its three central moments (µ 2, µ 3 and µ 4 ). 
\section[{b) Hierarchical Clustering Algorithm}]{b) Hierarchical Clustering Algorithm}\par
In order to utilize the EM algorithm we have to initialize the parameter ? i and the model parameters q i1 , q i2 which are generally considered as known apriori. The initial values of ? i can be taken as ? i =1/K where, K is the number of image regions obtained from the Hierarchical clustering algorithm \hyperref[b7]{(Marr D. et al (1980)}). The steps involved in hierarchical clustering algorithm are as follows.\par
Step 1: Start by assigning each item to a segment. Each of the N items, are associated with N segments, each containing just one item. Let the distances (similarities) between the segments be the same as the distances (similarities) between the items they contain.\par
Step 2: Find the closest (most similar) pair of segments and merge them into a single segment. The number of segments is now reduced by one. Compute distances (similarities) between the new segments and each of the old segments.\par
Step 3: Repeat steps 2 and 3 until all items are segmented.\par
Step 3 can be done in different ways, namely i) Single-Linkage ii) Complete-Linkage and iii) Average-Linkage segmenting. We consider the Average -Linkage methodology. Average-Linkage segmenting (also called the unweighted pair-group method using arithmetic averages), is one of the most widely used hierarchical clustering algorithms. The average linkage algorithm is obtained by defining the distance between two segments to be the average distance between a point in one segment and a point in the other segment. The algorithm is an agglomerative scheme that erases rows and columns in the proximity matrix as old segments are merged into new ones.\par
The proximity matrix is D = [d(i,j)]. The segments are assigned sequence numbers 0,1.., (n-1) and L(k) is the level of the K th segment. A segment with a sequence number m is denoted by (m) and the proximity between segments (r) and (s) is denoted d [(r), (s)]. The algorithm is composed of the following steps: Begin with the disjoint segment having level L(0) = 0 and sequence number m = 0.\par
Find the average dissimilar pair of segments in the current segment, say pair [(r), (s)],for all pairs of segments in the current segment. and (s) and adding a row and column corresponding to the newly formed segment. The proximity between the new segment, denoted (r, s) and old segment( K )is defined in this way.i j (r,s) K (r,s) K d(i,j) N N d = ? ?\par
where d(i, j) is the distance between object i in the cluster ( r, s ) and object j in the cluster K, and N (r,s) and N (k) are the number of items in the clusters ( r, s ) and K respectively. The above procedure is repeated till the distance between two clusters is less than the specified threshold value.\par
We obtain the initial estimates of q i1 , q i2 and ? i for the i th region using the segmented region pixel intensities with the moment method given by Pearsonian Type VI distribution, only after determining the final values of K (number of regions). After getting these initial estimates, the final refined estimates of the parameters through EM algorithm given in section (III) is obtained.\par
V. 
\section[{Segmentation Algorithm}]{Segmentation Algorithm}\par
In this section, the characteristics of the image segmentation algorithm are projected. After refining the parameters, the first step in image segmentation is allocating the pixels to the segments of the image. This operation is performed by Segmentation Algorithm which consists of four steps.\par
Step 1: Plot the histogram of the whole image.\par
Step 2: Obtain the initial estimates of the model parameters using K-Means algorithm and moment estimates for each image region as discussed in section IV.\par
Step 3: Obtain the refined estimates of the model parameters q i1 ,q i2 and ? i for i=1, 2, ..., K using the EM algorithm with the updated equations given by ( \hyperref[formula_26]{7}), (  {\ref 9}) and ( \hyperref[formula_42]{11}) respectively in section III.\par
Step 4: Assign each pixel into the corresponding j th region (segment) according to the maximum likelihood of the j th component L j. That is , ( ) ( )2 1 2 1 j ( 1) 1 2 2 L ( ) ( 1, 1) max j j j j q q s i s q q j k j j j j z a z a q q q ? ? ? + ? ? ? ? = ? ? ? ? + ? ? ? ? 1 2\par
, .i i j j a z q q ? ? < ? ? < < ? VI. 
\section[{Experimental Results}]{Experimental Results}\par
The performance of the developed a segmentation method for the natural images, which are considered on the earth. For implementing this algorithm, we need to initialize the model parameters, which are usually done by using moment method of estimations. Initially the feature vector is divided into The initial estimates of the number of the regions K in each image are obtained and given in Table  {\ref 1}.Table 1 : Initial Estimates Of K IMAGE TIGER EAGLE NEST BIRD FACE Estimate of K 2 3 4 4\par
From Table  {\ref 1}, we observe that the image TIGER has two segments, images EAGLE has three segments and images NEST BIRD AND FACE have four segments each. The initial values of the model parameters mi1,mi2, qi1,qi2 and ?i for i = 1, 2, ?, K , for each image region are computed by the method given in section III.\par
By making use of these initial estimates and the updated equations of the EM Algorithm given in Section III, the final estimates of the model parameters for each image are obtained and presented in Tables 2.a,2.b, 2.c, and 2.d for different images.  \par
1) 06892 0.988622 0.00316 7.37 0.0032 i i l s s s z z f z z z ? ? + + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? = + + ? ? + ? ? 0.0626 1.06892\textbf{( 1)}\par
1.06892 0.06256 000)  ( 1 0.06 6 ,\textbf{2 1) ? ?}s i i z z E ? ? ? + + + ? ? + ? ? ? ? + ? ? ? ? ? ? ? ? ? ? + + 1, .642036 0.405 1 3 ) + +\par
The estimated probability density function of the pixel intensities of the image NEST BIRD is ? + + + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + +\par
The estimated probability density function of the pixel intensities of the image FACE is  ( i i l s z z f z ? ? + ? ? ? ? + ? ? ? ? ? ? ? ? ? = + + + + ( ) ( )\textbf{(}i i z z ? + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + +\par
Using the estimated probability density function and image segmentation algorithm given in section III, the image segmentation is done for the five images under consideration. The original and segmented images are shown in Figure \hyperref[fig_8]{2}    
\section[{Initialization of Parameters by Hierarchical Clustering Algorithm}]{Initialization of Parameters by Hierarchical Clustering Algorithm}\par
In this section, we evaluate the efficiency of the proposed image segmentation algorithm. For this purpose of evaluation the images are collected from the Berkeley image data set. For this we need to randomly pick four images from the database and feature vector consisting of gray value for each pixel of the image. The feature vector in each image is modeled by using Pearsonian Type VI \& Pearsonian Type I Distribution. By dividing all the pixel into different regions using Hierarchical Clustering Algorithm, the initial values of model parameters mi1, mi2, qi1,qi2 and ?i are obtained. Using these values and the updated equations of EM-Algorithm discussed in section III with MATLAB code, the final values of the model parameters are calculated and presented in the tables 3.a, 3.b, \hyperref[b2]{3} ( D D D D\par
)Year 2014 F Table-3.a Table-3.b Table-3.c\par
Substituting the final estimates of the model parameters, the probability density function of pixel intensities of each image is estimated.\par
The estimated probability density function of the pixel intensities of the image TIGER is ( )  (0.6101) (1.7071) (0.6101)\textbf{(1.7071) ( ) (0}i i l s z z f z ? ? + + ? ? ? ? + ? ? ? ? ? ? ? ? ? = + + + + (40.i i z z ? + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + + 
\section[{The estimated probability density function of the pixel intensities the image EAGLE is}]{The estimated probability density function of the pixel intensities the image EAGLE is}\par
The estimated probability density function of the pixel intensities of the image NEST BIRD is ( )         (0.31705) (0.7971) (0.31705) (0.7971) ( ) (0.31705 0.7971 1) ( (0.8124)(-0.39174) (-0.8320) 1 1 -0.39174 -0.8320 , (-0.39174 -0.8320) (0.31705 1, 0.7971 1) (0.6205)(-0.2174) i i l s z z f z ? ? + + ? ? ? ? + ? ? ? ? ? ? ? ? ? = + + + + (2.i i i z z z ? + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + + ? ? + ? ? ? ? + (0.i i i z z z ? + + ? ? ? ? ? ? ? + + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + +\textbf{65}i i i i z z z z ? + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + + ? ? + ? ? ? ? ? + (0.i i z z ? + + + ? ? ? ? ? ? + + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + .\textbf{4979}i i i i z z z z ? + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + + ? ? + ? ? ? ? ? + (0.? ? + + + + ? ? ? ? ? ? + + + ? ? ? ? + ? ? ? ? ? ? ? ? ? + + +\textbf{1} 
\section[{Performance Evalution}]{Performance Evalution}\par
In this paper we have conducted the experiment and also examined its performance by making use of the image segmentation algorithm. The performance evaluation of this segmentation technique is carried by obtaining the three performance measures From Table \hyperref[tab_15]{4 it}  (iii) variation of information (VOI). By computing the segmentation performance measures namely VOI, PRI and GCE for the five images under study using Pearsonian Type VI Distribution (PTVID-K), the performance of the developed algorithm is studied. The computed values of the performance measures for the developed algorithm and the earlier existing finite Gaussian mixture model(GMM) with K-means algorithm and Hierarchical algorithm are presented in Table \hyperref[tab_15]{4} for a comparative study.  For the above retrieved images FACE, NEST BIRD AND EAGLE The calculated image quality measures using proposed PTVID and GMM with Kmeans and Hierarchical algorithm are displayed in the Table  {\ref 5}. 
\section[{Table 5 : Comparative Study of Image Quality Metrics}]{Table 5 : Comparative Study of Image Quality Metrics}\par
Image Segmentation for Animal Images using Finite Mixture of Pearson type VI Distribution mentioned quality metrics we can retrieve images accurately by using the proposed algorithm. A comparative study is done on the algorithm based on finite Gaussian mixture model with the proposed algorithm and it reveals that the MSE of the proposed model is less than that of the finite Gaussian mixture model. The performance of the proposed model in retrieving the images is better than the finite Gaussian mixture model by making use of these quality metrics. 
\section[{IX.}]{IX.} 
\section[{Conclusion}]{Conclusion}\par
In this paper, by using finite mixture of Pearsonian Type VI distribution a new model image segmentation is introduced and analyzed. The pixel intensities of animal images better characterizes the mixture of Pearsonian Type VI distribution which is validated through experiment with Berkeley image data set. The model parameters are estimated by using the EM Algorithm. By using the Maximum Likelihood estimates, the Segmentation Algorithm is developed under Bayesian framework. The Experiment on the Berkeley image data set reveals that this image segmentation method outperforms in segmenting the animal images then that of the existing algorithm basing on Gaussian mixture model with respect to image segmentation quality metrics such as PRI, GCE and VOI. The proposed algorithm is much useful for image analysis and image retrievals. The image that is developed can be extended with a K-dimensional feature vector for color images which will be takes as elsewhere. It is perceived that all the image quality measures for the five images are meeting the standard criteria as given in the Table  {\ref 5}. Basing on the above  
\section[{IMA GE}]{IMA GE}
\begin{quote}
Quality\end{quote}
\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_2}F}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-3.png}
\caption{\label{fig_3}1 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-4.png}
\caption{\label{fig_4}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-5.png}
\caption{\label{fig_8}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_9}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-7.png}
\caption{\label{fig_11}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_12}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-9.png}
\caption{\label{fig_13}Figure 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.03448534936138242\textwidth}P{0.0006386175807663411\textwidth}P{0.0012772351615326822\textwidth}P{0.0012772351615326822\textwidth}P{0.0006386175807663411\textwidth}P{0.20499624342599548\textwidth}P{0.05300525920360631\textwidth}P{0.0006386175807663411\textwidth}P{0.0006386175807663411\textwidth}P{0.08429752066115702\textwidth}P{0.09579263711495117\textwidth}P{0.17242674680691208\textwidth}P{0.06641622839969948\textwidth}P{0.0683320811419985\textwidth}P{0.043425995492111194\textwidth}P{0.021712997746055597\textwidth}}
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep .c\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep and 3.d\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{6}{l}{Estimated Values Of The Parameters For TIGER Image}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Number of Image Regions (K =2)}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Estimation of Initial\tabcellsep Estimation of Final\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{5}{l}{Parameters}\tabcellsep Parameters by\tabcellsep Parameters by EM\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Hierarchical clustering}\tabcellsep Algorithm\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Image Region\tabcellsep Image Region\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 1\tabcellsep 2\tabcellsep 1\tabcellsep 2\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{?}\tabcellsep \multicolumn{2}{l}{i}\tabcellsep 0.500\tabcellsep 0.500\tabcellsep 2.01257\tabcellsep -1.01257\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{4}{l}{1 i a}\tabcellsep -75.717\tabcellsep -11.7563\tabcellsep -1.6508\tabcellsep -0.0459\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep i a\tabcellsep \multicolumn{3}{l}{2}\tabcellsep 82.970\tabcellsep 740.670\tabcellsep 88.3755\tabcellsep -28057.91\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{4}{l}{1 i m}\tabcellsep 0.4771\tabcellsep 0.0156\tabcellsep 0.6101\tabcellsep 40.2429\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{3}{l}{i m}\tabcellsep 2\tabcellsep -0.5228\tabcellsep -0.9843\tabcellsep 1.7071\tabcellsep 0.01562\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{6}{l}{Estimated Values Of The Parameters For EAGLE Image}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Number of Image Regions (K =3)}\\
\multicolumn{5}{l}{Parameters}\tabcellsep \multicolumn{6}{l}{Estimation of Initial Parameters by}\tabcellsep Estimation of Final Parameters by EM\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{6}{l}{Hierarchical clustering}\tabcellsep Algorithm\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{5}{l}{Image Region}\tabcellsep Image Region\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 1\tabcellsep \tabcellsep \tabcellsep \tabcellsep 2\tabcellsep 3\tabcellsep 1\tabcellsep 2\tabcellsep 3\\
\multicolumn{3}{l}{?}\tabcellsep \multicolumn{2}{l}{i}\tabcellsep 0.333\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{0.333}\tabcellsep 0.333\tabcellsep 0.4574\tabcellsep 0.1921\tabcellsep 0.3503\\
\multicolumn{5}{l}{1 i a}\tabcellsep -29.580\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{-99.0809}\tabcellsep -41.2789\tabcellsep -0.1968\tabcellsep 0.6095\tabcellsep -0.05994\\
\multicolumn{2}{l}{i a}\tabcellsep \multicolumn{3}{l}{2}\tabcellsep 22.567\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{14.1523}\tabcellsep 35.7243\tabcellsep -0.7845\tabcellsep -0.70016\tabcellsep -1.0802\\
\multicolumn{5}{l}{1 i m}\tabcellsep 0.5672\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{0.87501}\tabcellsep 0.53606\tabcellsep 0.26831\tabcellsep 2.08306\tabcellsep 2.50880\\
\multicolumn{4}{l}{i m}\tabcellsep 2\tabcellsep -0.4327\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{-0.1249}\tabcellsep -0.4639\tabcellsep 0.67742\tabcellsep 0.61615\tabcellsep 0.44170\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{6}{l}{Estimated Values Of The Parameters For NEST BIRD Image}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Number of Image Regions (K =4)\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{6}{l}{Estimation of Initial Parameters by}\tabcellsep Estimation of Final Parameters by EM\\
\multicolumn{5}{l}{Parameters}\tabcellsep \tabcellsep \multicolumn{5}{l}{Hierarchical clustering}\tabcellsep Algorithm\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Image Region}\tabcellsep Image Region\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep 1\tabcellsep \tabcellsep \tabcellsep \tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\\
\multicolumn{2}{l}{?}\tabcellsep \multicolumn{2}{l}{i}\tabcellsep \tabcellsep 0.250\tabcellsep \multicolumn{4}{l}{0.250}\tabcellsep 0.250\tabcellsep 0.25\tabcellsep 0.8124\tabcellsep 0.6205\tabcellsep -0.1252\tabcellsep -0.3077\\
\multicolumn{4}{l}{1 i a}\tabcellsep \tabcellsep -29.742\tabcellsep \multicolumn{4}{l}{-42.662}\tabcellsep -22.721\tabcellsep -13.326\tabcellsep -0.39174\tabcellsep -0.2174\tabcellsep -0.5579\tabcellsep -0.0467\\
i a\tabcellsep \multicolumn{3}{l}{2}\tabcellsep \tabcellsep 22.299\tabcellsep \multicolumn{4}{l}{18.108}\tabcellsep 27.072\tabcellsep 75.188\tabcellsep -0.8320\tabcellsep -0.7572\tabcellsep 17.451\tabcellsep 1018.7\\
\multicolumn{5}{l}{1 i m}\tabcellsep 0.5715\tabcellsep \multicolumn{4}{l}{0.7020}\tabcellsep 0.4563\tabcellsep 0.1506\tabcellsep 0.31705\tabcellsep 2.2480\tabcellsep 2.7025\tabcellsep 5.3865\\
\multicolumn{3}{l}{i m}\tabcellsep \multicolumn{2}{l}{2}\tabcellsep -0.4284\tabcellsep \multicolumn{4}{l}{-0.2979}\tabcellsep -0.5436\tabcellsep -0.8494\tabcellsep 0.7971\tabcellsep 0.5349\tabcellsep 0.3905\tabcellsep 0.14647\end{longtable} \par
 
\caption{\label{tab_6}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.09824120603015075\textwidth}P{0.1452261306532663\textwidth}P{0.5467336683417086\textwidth}P{0.04698492462311558\textwidth}P{0.012814070351758793\textwidth}}
\tabcellsep \tabcellsep \multicolumn{2}{l}{PERFORMACE}\\
\multicolumn{2}{l}{IMAGES METHOD}\tabcellsep \tabcellsep MEASURES\\
\tabcellsep \tabcellsep PRI\tabcellsep GCE\tabcellsep VOI\\
\tabcellsep GMM\tabcellsep \multicolumn{2}{l}{0.8234 0.4956 2.568}\\
TIGER\tabcellsep PTVID-K\tabcellsep \multicolumn{2}{l}{0.9896 0.4742 1.921}\\
\tabcellsep PTVID-H\tabcellsep \multicolumn{2}{l}{0.9897 0.4762 1.920}\\
\tabcellsep GMM\tabcellsep \multicolumn{2}{l}{0.8423 0.7006 8.354}\\
EAGLE\tabcellsep PTVID-K\tabcellsep \multicolumn{2}{l}{0.8505 0.7109 7.577}\\
\tabcellsep PTVID-H\tabcellsep \multicolumn{2}{l}{0.8627 0.7054 7.2002}\end{longtable} \par
 
\caption{\label{tab_15}Table 4 :}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US) Global Journal of Computer Science and Technology} 			\footnote{© 2014 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[
			Jahne
		 ()]{b3}\label{b3} 	 		\textit{A Practical Hand Book on Image segmentation for Scientific Applications},  		 			Jahne 		.  		1995. CRC Press.  	 
\bibitem[Pal and Pal ()]{b17}\label{b17} 	 		‘A Review On Image Segmentation Techniques’.  		 			S K Pal 		,  		 			N R Pal 		.  	 	 		\textit{Pattern Recognition}  		1993. 26  (9)  p. .  	 
\bibitem[Paulinas and Usinskas ()]{b6}\label{b6} 	 		‘A survey of genentic algorithms applications for image enhancement and segmentation’.  		 			Mantas Paulinas 		,  		 			Andrius Usinskas 		.  	 	 		\textit{Information Technology and control}  		2007. 36  (3)  p. .  	 
\bibitem[Rose and Turi ()]{b13}\label{b13} 	 		\textit{Cluster Based Image Segmentation},  		 			H Rose 		,  		 			Turi 		.  		2001. Monash University, Australia.  	 	 (Ph.d Thesis) 
\bibitem[Cheng ()]{b0}\label{b0} 	 		\textit{Color Image Segmentation: Advances and Prospects" Pattern Recognition},  		 			Cheng 		.  		2001. 34 p. .  	 
\bibitem[Meila ()]{b15}\label{b15} 	 		‘Comparing Clustering -An axiomatic view’.  		 			Meila 		.  	 	 		\textit{proceedings of the 22nd International Conference on Machine Learning},  				 (the 22nd International Conference on Machine Learning)  		2005. p. .  	 
\bibitem[Eskicioglu and Fisher ()]{b1}\label{b1} 	 		‘Image Quality Measures and their Performance’.  		 			M A Eskicioglu 		,  		 			P S Fisher 		.  	 	 		\textit{IEEE Transactions On Communications}  		1995. 43  (12)  p. .  	 
\bibitem[Gvs Rajkumar et al. ()]{b2}\label{b2} 	 		‘Image Segmentation and Retrievals based on Finite Doubly Truncated Bivariate Gaussian Mixture Model and K-Means’.  		 			K Gvs Rajkumar 		,  		 			Srinivasa 		,  		 			And P Rao 		,  		 			- Srinivasa Rao 		.  	 	 		\textit{International Journal of Computer Applications (IJCA)}  		2011. 25  (4)  p. .  	 	 (Accepted for Publication) 
\bibitem[Seshashayee et al. ()]{b8}\label{b8} 	 		‘Image Segmentation Based on a Finite Generalized New Symmetric Mixture Model with K -Means’.  		 			M Seshashayee 		,  		 			K Rao 		,  		 			Ch Satyanarayana And 		,  		 			P Srinivasa Rao 		.  	 	 		\textit{International journal of Computer Science Issues}  		2011. 8  (3)  p. .  	 
\bibitem[Image Segmentation for Animal Images using Finite Mixture of Pearson type VI Distribution conference on Adv. Computer control]{b10}\label{b10} 	 		‘Image Segmentation for Animal Images using Finite Mixture of Pearson type VI Distribution conference on’.  	 	 		\textit{Adv. Computer control}  		p. .  	 
\bibitem[Raut ()]{b21}\label{b21} 	 		\textit{Image segmentation-A State-Of-Art survey for Prediction},  		 			Shital Raut 		.  		2009.  	 	 (International) 
\bibitem[Mclanchan and Peel ()]{b14}\label{b14} 	 		 			G Mclanchan 		,  		 			D Peel 		.  		\textit{The EM Algorithm For Parameter Estimations},  				 (New York)  		2000. John Wiley and Sons.  	 
\bibitem[Lei ()]{b5}\label{b5} 	 		‘Performance Evaluation of Finite Normal Mixture Model -Based Image Segmentation Techniques’.  		 			T Lei 		.  	 	 		\textit{IEEE Transactions On Image Processing}  		2003. 12  (10)  p. .  	 
\bibitem[Seshashayee et al. ()]{b9}\label{b9} 	 		 			M Seshashayee 		,  		 			K Rao 		,  		 			Ch Satyanarayana And 		,  		 			P Srinivasa Rao 		.  	 	 		\textit{Studies on Image Segmentation method Based on a New Symmetric Mixture Model with K -Means},  				2011. 11 p. .  	 
\bibitem[Prasad Reddy]{b18}\label{b18} 	 		‘Srinivasa Rao And Srinivas supervised image segmentation using finite Generalized Gaussian mixture model with EM \& K-Means algorithm’.  		 			P V G D Prasad Reddy 		,  		 			K 		.  	 	 		\textit{International Journal of Computer Science and Network Security}  		7  (4)  p. .  	 
\bibitem[Prasad Reddy]{b19}\label{b19} 	 		‘Srinivasa Rao And Srinivas Yerramalle-(2007), supervised image segmentation using finite Generalized Gaussian mixture model with EM \& K-Means algorithm’.  		 			P V G D Prasad Reddy 		,  		 			K 		.  	 	 		\textit{International Journal of Computer Science and Network Security}  		7  (4)  p. .  	 
\bibitem[Kelly ()]{b4}\label{b4} 	 		‘Statistical approach to Xray CT imaging and its applications in image analysis’.  		 			P A Kelly 		.  	 	 		\textit{IEEE Trans. Med. Imag}  		1998. 11  (1)  p. .  	 
\bibitem[Marr ()]{b7}\label{b7} 	 		‘Theory of Edge Detection’.  		 			D Marr 		.  	 	 		\textit{Proceedings of Royal Society London}  		1980. 207 p. .  	 
\bibitem[Srinivas Yerramalle And and Rao ()]{b12}\label{b12} 	 		‘Unsupervised image classification using finite truncated Gaussian mixture model’.  		 			K Srinivasa Srinivas Yerramalle And 		,  		 			Rao 		.  	 	 		\textit{Journal of Ultra Science for Physical Sciences}  		2007. 19  (1)  p. .  	 
\bibitem[Srinivas ()]{b20}\label{b20} 	 		‘Unsupervised Image Segmentation based on Finite Doubly Truncated Gaussian Mixture model with K-Means algorithm’.  		 			Y Srinivas 		.  	 	 		\textit{International Journal of Physical Sciences}  		2007. 19 p. .  	 
\bibitem[Srinivas Yerramalle et al. ()]{b11}\label{b11} 	 		‘Unsupervised image segmentation using generalized Gaussian distribution with hierarchical clustering’.  		 			K Srinivas Yerramalle 		,  		 			P V G D Rao 		,  		 			- Prasad Reddy 		.  	 	 		\textit{Journal of advanced research in computer engineering}  		2010. 4  (1)  p. .  	 
\bibitem[Nasios and Bors ()]{b16}\label{b16} 	 		‘Variational learning for Gaussian Mixtures’.  		 			N Nasios 		,  		 			A G Bors 		.  	 	 		\textit{IEEE Transactions on Systems, Man and Cybernetics}  		2006. 36  (4)  p. .  	 	 (Part B : Cybernetics) 
\end{bibitemlist}
 			 		 	 
\end{document}
