I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 Published Online March 2016 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijigsp.2016.03.06 Studies on Texture Segmentation Using D- Dimensional Generalized Gaussian Distribution integrated with Hierarchical Clustering

K. Naveen Kumar Department of IT, GIT, GITAM University, Visakhapatnam Email: [email protected], [email protected]

K. Srinivasa Rao Department of Statistics, Andhra University, Visakhapatnam Email: [email protected]

Y.Srinivas Department of IT, GIT, GITAM University, Visakhapatnam Email: [email protected]

Ch. Satyanarayana Department of CSE, JNTUK-Kakinada, Kakinada Email: [email protected]

Abstract—Texture deals with the visual properties of an spatial inter relationships between the pixels in an image. image. Texture analysis plays a dominant role for image Texture usually refers the pattern in an image which segmentation. In texture segmentation, model based includes coarseness, complexity, fineness, shape, methods are superior to model free methods with respect directionality and strength [1,2]. Several segmentation to segmentation methods. This paper addresses the methods for texture segmentation have been developed application of multivariate generalized Gaussian mixture for analysing the images considering the texture surfaces probability model for segmenting the texture of an image [3-8]. Among these methods, model based methods using integrating with hierarchical clustering. Here the feature probability distribution gained lot of importance. These vector associated with the texture is derived through methods are often known as parametric texture DCT coefficients of the image blocks. The model classification methods. parameters are estimated using EM algorithm. The Several model based texture classification methods initialization of model parameters is done through have been developed using Gaussian distribution or hierarchical clustering algorithm and moment method of Gaussian mixture distribution [9-11]. The major estimation. The texture segmentation algorithm is drawback of the texture segmentation method based on developed using component maximum likelihood under Gaussian model or Gaussian mixture models is the Bayesian frame. The performance of the proposed segmentation quality metrics still remain inferior to the algorithm is carried through experimentation on five standard values such as PRI close to one, GCE close to image textures selected randomly from the Brodatz zero and VOI being low. This is due to the fact that the texture database. The texture segmentation performance feature vector associated with texture of the image measures such as GCE, PRI and VOI have revealed that regions may not be meso-kurtic. To improve the this method outperform over the existing methods of efficiency of the texture segmentation algorithm, one has texture segmentation using Gaussian mixture model. to consider the generalization of the Gaussian This is also supported by computing confusion matrix, distribution for characterising the feature vector accuracy, specificity, sensitivity and F-measure. associated with the texture of the image region. With this motivation, a texture segmentation algorithm is Index Terms—Multivariate generalised Gaussian developed and analysed using multivariate generalized mixture model, texture segmentation, EM-algorithm, Gaussian mixture model. The generalized Gaussian DCT coefficients, segmentation quality metrics. distribution includes several of the platy-kurtic, lepto- kurtic and meso-kurtic distributions. This also includes Gaussian distribution as a particular case [12]. The I. INTRODUCTION feature vector of the texture associated with the image is extracted through DCT coefficients using the heuristic The arrangement of constituent particles of a material arguments of Yu-Len Huang(2005) [13]. Assuming that is referred as Texture. The texture is influenced by the feature vector of the whole image is characterised by

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 46 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian Distribution integrated with Hierarchical Clustering

the multivariate generalized Gaussian mixture model ij x  (A() ij ij with the feature vector, the segmentation algorithm by D ij K() ij integrating heuristic method of segmentation, g(x / )ij ij e(2) r  2 hierarchical clustering [14] is developed. j1 ij The rest of the paper is organised as follows. Section 2 deals with the generalized Gaussian mixture model and where, ,,   are location, scale and shape its properties. Section 3 deals with extraction of the ij ij ij feature vector using DCT coefficients. Section 4 deals parameters. with extraction of model parameters using EM algorithm. 1/ 2 Section 5 is concerned with initialisation of parameters (3/ ) with hierarchical clustering and moment method of (1/ ) K() estimation. Section 6 deals with texture segmentation (1/ ) under Bayesian using component mixture model. Section /2 7 deals with performance evaluation of proposed (3/ ) A() algorithm through experimentation on five images taken (1/ ) from Brodatz texture dataset [15]. Section 8 deals with comparative study of proposed algorithm with that of other model based Gaussian segmentation algorithms. with ()denoting gamma function. Section 9 is to present the conclusions along with future Each parameter 0 controls the shape of GGD. scope for further research in this area. Expanding and rearranging the terms in (2), we get

1/ 2  /2 ij (3/ ) (3/ ) xij ij ULTIVARIATE ENERALIZED AUSSIAN IXTURE  II. M G G M D  (1/ ) (1/  ) ij MODEL  g(xr / ) e (1/  )2 j In texture analysis, the entire image texture is j1 (3) considered as a union of several repetitive patterns. In this section, we briefly discuss the probability This implies, distribution (model) used for characterizing the feature D  (4) vector of the texture. After extracting the feature vector 1 xij ij of each individual texture it can be modeled by a suitable  exp  21A(,) probability distribution such that the characteristics of j1 A( ,  )  (1  )   the feature vector should match the statistical theoretical characteristics of the distribution. The feature vector When  =1, the corresponding generalized Gaussian characterizing the image is to follow M-component corresponds to a Laplacian or double exponential mixture distribution. Therefore we develop and analyze distribution. When =2, the corresponding generalized the textures in an image by considering that the feature vectors representing textures follow M-component Gaussian corresponds to Gaussian distribution. In limiting cases, equation (4) converges to a multivariate generalized Gaussian mixture distribution   , (MGGMM) model. The joint probability density function uniform distribution in (  3  ,   3  ) and when of the feature vector associated with each individual , the distribution becomes degenerate are in texture is  0  x  M (1) p(xr / )  w i g i x rr,  i1 where, xr (x rij ), j=1,2,…..D, is D dimensional random vector represents the feature vector. i = 1, 2, .M representing the groups, r = 1, 2….T representing the samples.  is a parametric set such that (,,)    , wi is the component weight such that M and is the probability of ith class gxi rr, Fig.1. Generalized Gaussian pdf’s for different values of shape  w1i  i1 parameter . representing by the feature vectors of the image and the D-dimensional generalized Gaussian distribution is of The mean value of the generalized Gaussian the form[16]. distribution is

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian 47 Distribution integrated with Hierarchical Clustering

 xij ij these, the 2D discrete cosine transformation is robust and    1 A(,) ij E(x ) xe dx simple for extracting the features. No serious attempt is ij 1  2 (1  )A(  ,  )  made to utilise DCT coefficients for extracting the  (5) feature of the texture of the image even though the DCT coefficients are capable of maintaining regularity, The GGD is symmetric with respect to  , hence the complexity of the texture. This is possible since the DCT odd center moments are zero i.e., t , t = uses orthogonal transformation of the cosine function. E xij ij  0 The advantage is DCT can convert the texture of the 1,3,5,…. The even center moments can be obtained from image from time domain to frequency domain [19]. This absolute center moments and given by motivated us to consider DCT coefficients for extracting the feature vector associated with texture of the image. r / 2 To compute the feature vector associated with image 2 1   t 1  ij      texture, we divide whole image into M x M blocks. t     Exij  ij  Following the heuristic arguments given by Gonzalez 31     [20], 2D DCT coefficients in each block are computed.         (6) These coefficients are selected in a zigzag pattern up to number of 16 coefficients in each block. The 16 The variance is coefficients are considered since in many of the face recognition algorithms, it is established that 16 var(x) = E(x x)2  E(x  ) 2   2 coefficients provide sufficient information in the block. (7) These 16 coefficients in each block are considered as a sample feature vector and the total N=M x M blocks The model can have one covariance matrix for a provide Nx16 data matrix for the feature vector of the generalized Gaussian density of the class. The covariance whole image. matrix  can be full or diagonal. In this paper, the diagonal covariance matrix ix considered. This choice based on the initial experimental results. Therefore, IV. ESTIMATION OF MODEL PARAMETERS USING EM ALGORITHM 2 ... i1 In this section, we consider estimation of model ...2  i2 parameters using EM algorithm that maximizes the i  .... likelihood function of the model [21]. The sample  ... 2 iD (8) observations (DCT Coefficients) (x1 ,x 2 ,...... x r ) are drawn from image texture which is characterized by the As a result of diagonal covariance matrix for the joint probability density function feature vector, the features are independent and the probability density function of the feature vector is M p(xr / )  w i g i x r ,   i1 x  ij exp ij ij (9)  D A(,)ij ij where, is given in the above equation (9).  gxi r, gi (x rr / )  1 j1 2 1  A(  ,  ) The likelihood function is ij ij ij T M L( )  wi g i x r ,  D r1 i1  fij (x rij ) j1 (10) ij x  exp ij ij  TDM A(,)ij ij    wi  1 III. FEATURE VECTOR EXTRACTION r 1i1  j 1 2 1  A(  ,  ) ij ij ij  One of the important step in segmentation of texture of  (11) an image is extracting the features associated with the texture regions of the image. Texture is the inherent This implies, pattern perceived by the image in forming the pixel intensities. Much work had been reported in literature T M regarding feature vector extraction of texture images [17, log L( )  log wii g (xr ,  ) 18].Some of the important methods associated with r1 i1 feature vector extraction are PCA, KLT, Fourier transformations and DCT cosine transformations. Among

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 48 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian Distribution integrated with Hierarchical Clustering

TM ij (l) x  log(w)t(x,r  )  exp ij ij ii  r 1 i 1 TM D A(,)ij ij    TMD x  ij   log wi  ij ij 1 (l)  log  log21   A(,)t(x,  r  ) r 1 i 1 j1 1   ij ij i 2 1  A(  ,  ) A(,)ij  ij  ij ij ij r 1 i  1 j  1  ij  (12) (15) M-Step: To find the refined estimates of parameters To maximize (l) , we can maximize the term wi , ij and ij for i=1,2,3,…M ; j=1,2,……,D. Q( , ) (l) we maximize the expected value likelihood or log containing wi and containing  independently, since they are not related. likelihood function. The shape parameter ij is estimated To update the component weights wi of the model, we using the procedure given by Shaoquan YU (2012) [22]. maximize the likelihood function such that M To estimate , we use the EM algorithm  w1i  i1 which consists of two steps namely, Expectation (E) Step We construct the first order Lagrange type function as and Maximization (M) Step. The first step of EM algorithm is to estimate initial parameters TMM(l) L= log(w)t(x,(l) )   w  1 i ir   i from a given texture image data. r 1 i  1 i  1 (16) E-Step: where,  is Lagrange multiplier and maximizing this Given the estimates, (l) (,) (l)  (l) for i=1,2,…M; ij ij Lagrange function with respect to wi, we have to j=1,2,3,…..D differentiate L with respect to wi and equate to zero i.e., One can estimate probability density function as  L  0 implies wi M

p(xt / )  w i g i x r ,  TMM(l) i1 (l) log(w)t(x,r  )   w  1  0 wwi i  i iir 1 i  1 i  1 (17) The conditional probability of any observation xr th belongs to M class is This implies,

(l) (l) t(x/i r  )  p((i/x),  ) T 1 (l) (l) ti (xr , )    0 w g (xr , ) w  ii r1 i (l) pi (xr , ) w g (x ,(l) ) Therefore,  ii r M T  wi g i x r , t (x ,(l) )   w i1 (13) iir r1

The expected value of L ( ) is  Summing i=1, 2, 3,…M, we have

(0) Q( , ) = E log L( / xr ) (l)   (14) MT t (x ,(l) )   i r Following heuristic arguments of Jeff A Bilmes (1997) i 1 r 1 [23], we get Therefore, TM Q(, (l) )  log(w.g(x,  (l) )t(x,  (l) ) i irr i T r 1 i 1 t (x ,(l) ) T w iir r1 (18) TM log(w ) t (x , (l) )  ii r r 1 i 1 Hence, updated equations for wi is ij x  exp ij ij  MD A(,)ij ij T (l) (l) (l) 1 w .g (xr , ) log ti (xr , ) w(l 1)  i i i 1 j 1 1 i  2 1  A(  ,  ) M (l) (l) ij ij T w .g (x , ) ij r1  i i r  i1 (19) 

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian 49 Distribution integrated with Hierarchical Clustering

where (l) (l) (l) are the estimates at ith iteration. This is a non trivial equation, explicit expression for   ij,  ij  ij is complicated.

Updating ij: To updateij, solve equation (21) by using Newton’s Raphson method and obtain (l 1) . (l) ij For updating ij, we consider derivative of Q( , ) This provides the refined estimates for . For with respect to for i=1,2,…..M, j=1,2,….D and explicit estimate of , consider the special cases. equate to zero. Case 1: The Gaussian case, ij =2 leads  Q( , (l) )  0 implies TT ij (l)(l) (l) (l 1) t(x,irr ).(x rij  ij )  t(x, i  ).(x rij   ij )  TMTM r 1 r 1 log(w)t(x,(l) )  g(x,  (l) )t(x,  (l) )  0 i ir  i r i r This implies, ij r 1 i  1 r  1 i  1 (22) T (l) (l) (20) (x )w g (xr , )  riji i (l 1) r1 ij T This implies, (l) (l) w g (xr , )  i i r1 ij x  exp rij ij  TMTMD A(,)ij ij Case 2: consider for  (l) (l) ij 1 log(w)t(x,i irr )   log t(x, i  )  0 ij 1 r 1 i  1 r  1 i  1 j  1 2 1  A(  ,  ) ij ij ij   11    TTxx ij    ij (l)rij ij(l)ij 11 (l) rij ij (l 1)  ij  ti (xrr , ) sign  x rij   t i (x ,  ) sign   x rij   ij  ij  r 1A(,)A(,)ij  ij  r 1   ij  ij  Since involves only one element of feature vector, This implies, mean , the equation reduces to 1 T 1 (l) (l) ij  (x )w g (xr , ) TM ij  tiji i  1 (l)xrij ij (l) (l 1) r1 log21    logA(,   )t(x,rr  )  t(x,  )0     ij ij i i ij 1 ij  ijA(,)  ij  ij r 1 i 1  T ij 1 w(l) g (x ,(l) )  i i r This implies r1 (23)

 For general case: we can also develop a general T ij T  xrij ij (l) t (xr ,  )  0 approximation without using numerical method for r1 A(,)   i r1 ij ij ij updating (l 1) by adopting an axiom that of the form  ij ij On simplification, we get which must be a weighted average of data vectors with weights provided by some power of the assignment 1 probabilities of those data vectors, notified in part by T x  ij rij ij (l) ij 1 sign t (xr ,  )( x  )  0 symmetry of system, and in part by pragmatism leads to  ijA(,) i rij ij r1 ij ij T (l) A(N,)ij This implies  ti (xr , ) (x tij ) (l 1) r1 ij T 1 A(N,) T x  ij (l) ij (l) rij ij ij 1 t (xr , ) t (xr , ) sign .(x  )  0 for   1  i  iA(,) rij ij ij r1 ij ij r1 (24)

where, A(N, ) is some function =1 for 2 and must Therefore, ij ij be equal to 1 for , in the case of N=2, we have ij 1  11   1 TTxx  ij     ij ij (l)rij ij (l)ij 11 (l) rij ij (l1)  ij  t(x,)signirr  x rij    t(x,)sign i    x rij   A(,)A(,)  ij    ij  also observed that A(N, ) must be increasing function r 1ij ij  r 1  ij ij  ij (21) of ij .

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 50 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian Distribution integrated with Hierarchical Clustering

V. INITIALIZATION OF MODEL PARAMETERS Updating ij : The efficiency of the EM algorithm in estimating the For updating , we consider maximization of (l) ij Q( , ) parameters is heavily dependent on the number of groups with respect to for i=1,2,…..M, j=1,2,….D. That is and the initial estimates of the model parameters w and for i=1,2,3,…M; j=1,2,..,D.Usually in EM i, ij ij  algorithm, the mixing parameter and the distribution Q( , (l) )  0 implies wi ij parameters ijand ij are given with some initial values. A commonly used method in initialization is by TMTM  (l) (l) (l) (25) drawing a random sample from the entire data. To utilize log(w)t(x,r )  g(x, r  )t(x, r  )  0  i i  i i the EM-algorithm, we have to initialize the parameters ij r 1 i  1 r  1 i  1 which are usually considered as known apriori. The initial value of wi can be taken as wi =1/M, where M is Therefore, the number of texture image regions obtained from the Hierarchical clustering algorithm. Then obtain the initial ij x  estimates of the parameters through sample moments as exp rij ij  TMTMD A(,)ij ij  (l) (l) log(w)t(x,i irr )   log t(x, i  )0  ij 1 wi= 1/M r 1 i  1 r  1 i  1 j  1 2 1  A(  ,  )  ij ij th ij  = S.D of M Class  ij T  = 1 ij  xrij Since involves only one element feature vector, we T r1 have Substituting these values as the initial estimates, the refined estimates of the parameters can be obtained using 3  1 T  EM Algorithm by simultaneously solving the equations (l) ij ji 1  t(x,)ir  log  ij  . (x rij  ij )  0 19, 24 and 26 using MATLAB. ij1  ij r1   ij VI. TEXTURE SEGMENTATION ALGORITHM This implies Once the texture is considered, the main purpose is to 3 identify the regions of interest. The following algorithm  1 T x   can be adopted for texture segmentation using (l) ij rij ij ij 1 ti (xr , ) .   0  1  multivariate generalized Gaussian mixture model. r1 1 ij   ij  ij ij Step 1: Obtain the feature vectors from the texture image using technique presented in feature vector This implies extraction section. Step 2: Divide the samples into M groups by

3 Hierarchical clustering Algorithm. 2. T  11 (l) ij 2 Step 3: Find the mean vector, variance vector,  ti (xr , ) . x rij  ijij   ij ij  0 1 ij and for each class of the multivariate data. r1  ij ij  ij Step 4: Take wi = 1/M, for i=1,2,3,…..M.

Step 5: Obtain the refined estimates of wi, ijand ij Therefore, for each class using the updated equations of the EM algorithm. 1 Step 6: Assign each feature vector into the 3 ij th  corresponding j region (segment) according to the T  1 th (l) ij maximum likelihood of the j component Lj.  ti (xr , ) . x rij  ij ij r1 1  ij  ij (l 1)  th ij T That is, Feature vector xt is assigned to the j region (l)  ti (xr , ) for which is maximum, where, r1 L j     (26)

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian 51 Distribution integrated with Hierarchical Clustering

 x   ij segmentation map can be viewed as a refinement of exp ij ij D A(,) segmentation. ij ij Lj  max  For a perfect match, every region in one of the j1 1 2 1A ( , ) ij ij segmentations must be identical to, or a refinement (i.e., ij a subset) of, a region in the other segmentation [26]. (27) The image Performance measures namely, PRI, GCE, VOI are computed for all the five images with respect to the developed model, Generalized Gaussian Mixture VII. PERFORMANCE EVALUATION Model Hierarchical algorithm to that of other models To demonstrate the ability of the developed model, based on Gaussian mixture are presented in Table 1. texture segmentation is to be performed by using the The results show that the segmentation performance dataset of textures available in the Brodatz Texture measures of the proposed segmentation algorithm based databases. For each texture image, hierarchical algorithm on multivariate generalized Gaussian mixture model are is employed over the multivariate data of feature vectors close to the optimal values of PRI, GCE and VOI. to divide in to M groups. For each group, the initial Table 1. Segmentation Performance Measures of the Textured Images estimate of the parameters wi, ijand ij are obtained using heuristics clustering and moment estimators. Using Segmentation Performance Measures Description Model PRI GCE VOI these initial estimates, the refined estimates are GMM-K 0.389 0.351 1.192 calculated based on the updated equations obtained GMM-H 0.428 0.311 1.181 Image 1 through EM Algorithm. With these values, texture MGGMM-K 0.511 0.292 1.176 segmentation is performed based of the assignment of the MGGMM-H 0.732 0.222 1.060 data to a particular group for the likelihood is maximum. GMM-K 0.542 0.580 2.558 GMM-H 0.558 0.565 2.480 Image 2 Then the segmentation image is drawn based on the MGGMM-K 0.648 0.489 2.420 application of the developed algorithm. The performance MGGMM-H 0.721 0.380 1.923 evaluation parameters are calculated and compared with GMM-K 0.654 0.325 1.458 GMM-H 0.685 0.321 1.355 the earlier models. Image 3 MGGMM-K 0.780 0.229 1.345 MGGMM-H 0.848 0.152 1.242 GMM-K 0.547 0.351 1.321 GMM-H 0.558 0.345 1.315 Image 4 MGGMM-K 0.633 0.301 1.290 MGGMM-H 0.721 0.249 1.230 GMM-K 0.532 0.590 1.478 GMM-H 0.569 0.575 1.425 Image 5 MGGMM-K 0.558 0.572 1.468 MGGMM-H 0.625 0.552 1.301

VIII. COMPARATIVE STUDY Fig.2. Original and segmented texture images using proposed model with K-means and Hierarchical clustering algorithm. The developed algorithm performance is evaluated by comparing the algorithm with the Gaussian mixture The performance of the developed texture image model with K-means and Hierarchical clustering. Table 2 segmentation method is studied by obtaining the image presents the miss classification rate of the pixels of the segmentation performance measures namely; sample using the proposed model and Gaussian mixture Probabilistic Rand Index (PRI), the Variation of model. Information (VOI) and Global Consistency Error (GCE). The Rand index given by Unnikrishnan et al., (2007) Table 2. Miss classification Rate of the Classifier counts the fraction of pairs of pixels whose labeling are consistent between the computed segmentation and the Model Miss-classification Rate ground truth. This quantitative measure is easily GMM-K 20% extended to the Probabilistic Rand index (PRI) given by GMM-H 18% Unnikrishnan et al., (2007) [24]. MGGMM-K 15% The variation of information (VOI) metric given by MGGMM-H 12% Meila (2007) is based on relationship between a point and its cluster. It uses mutual information metric and From the Table 2, it is observed that the entropy to approximate the distance between two misclassification rate of the classifier with the clustering’s across the lattice of possible clustering’s. It multivariate generalized Gaussian mixture model is less measures the amount of information that is lost or gained when compared to that of GMM. in changing from one clustering to another [25].The The accuracy of the classifier is also studied for the Global Consistency Error (GCE) given by Martin D. et sample images by using confusion matrix for segmented al., (2001) measures the extent to which one regions and computing the metrics [27]. Table 3 shows

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 52 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian Distribution integrated with Hierarchical Clustering the values of Accuracy, Sensitivity, Specificity, Precision, image texture. Recall, F-Measure for the segmented regions in the

Table 3. Comparative study of MGGMM with Hierarchical clustering Algorithm and earlier Gaussian mixture models.

Sensitivity 1-Specificity Description Model Accuracy Precision Recall F-Measure (TPR) (FPR)

GMM-K 0.71 0.72 0.32 0.68 0.72 0.70 GMM-H 0.73 0.74 0.28 0.7 0.74 0.72 MGGM Image 1 0.75 0.75 0.21 0.72 0.75 0.73 M-K MGGM 0.81 0.81 0.16 0.85 0.81 0.83 M-H GMM-K 0.62 0.69 0.28 0.68 0.69 0.68 GMM-H 0.64 0.71 0.22 0.72 0.71 0.71 MGGM Image 2 0.69 0.73 0.19 0.76 0.73 0.74 M-K MGGM 0.74 0.81 0.15 0.82 0.81 0.81 M-H GMM-K 0.79 0.72 0.34 0.69 0.72 0.70 GMM-H 0.82 0.74 0.31 0.72 0.74 0.73 MGGM Image 3 0.86 0.79 0.26 0.75 0.79 0.77 M-K MGGM 0.89 0.84 0.21 0.89 0.84 0.86 M-H GMM-K 0.81 0.71 0.33 0.65 0.71 0.68 GMM-H 0.82 0.72 0.29 0.68 0.72 0.70 MGGM Image 4 0.84 0.76 0.27 0.72 0.76 0.74 M-K MGGM 0.86 0.82 0.24 0.81 0.82 0.81 M-H GMM-K 0.58 0.68 0.38 0.59 0.68 0.68 GMM-H 0.65 0.72 0.32 0.62 0.72 0.72 MGGM Image 5 0.62 0.70 0.34 0.61 0.70 0.71 M-K MGGM 0.69 0.78 0.20 0.72 0.78 0.74 M-H

From Table 3, it is observed that the F-measure value convergence of EM algorithm. The initial values of the for the proposed classifier is more than the earlier model parameters are obtained by integrating Gaussian mixture models. This indicates that the hierarchical clustering with the moment method of proposed classifier perform well than that of Gaussian estimation. Experimentation with five randomly taken mixture model. images from Brodatz texture database supported the superior performance of the proposed algorithm over the texture segmentation algorithm based on Gaussian IX. CONCLUSIONS mixture model with respect to the segmentation performance measures such as PRI, GCE and VOI. The This paper addresses a new and novel method for confusion matrix computed along with F-measure also segmenting the texture of an image using multivariate supported the outperformance of the proposed algorithm. generalized Gaussian mixture model distribution. Here, The texture segmentation algorithm is useful for the feature vector representing the texture of the image is analyzing several image textures for efficient analysis of derived through DCT coefficients. The texture of the the systems. It is possible to further extend this proposed whole image is characterized by a multivariate algorithm by considering other methods of initialization generalized Gaussian mixture distribution. The of parameters such as fuzzy c means, MDL and MML. It generalized Gaussian distribution includes Gaussian and is also possible to induce neighborhood information in Laplace distributions as particular cases and several other extracting the feature vector which will be considered probability models which are platy-kurtic, lepto-kurtic elsewhere. and meso-kurtic. Hence, this method is capable of characterizing the textures of several images for which REFERENCES the feature vector may be one among having platy-kurtic, lepto-kurtic and meso-kurtic distributions in the image [1] Amadasun M., King R., (1989), "Textural features regions. The model parameters such as shape and scale corresponding to textural properties," IEEE Transactions are estimated through EM algorithm. The shape on Systems, Man and Cybernetics, Vol. 19(5), pp.1264- parameter is estimated using sample kurtosis for 1274. reducing the computational complexity with respect to

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Clustering, Classification, and Discriminant Analysis", Mr. K. Naveen Kumar is presently Assistant Journal of Iranian Statistical Society, Journal of Iranian Professor in the department of Information Statistical Society. Technology, GIT, GITAM University, [12] G. V. S. Raj Kumar, K. Srinivasa Rao and P. Srinivasa Visakhapatnam. He presented several research Rao (2011), ―Image segmentation and Retrievals based on papers in national and international finite doubly truncated bivariate Gaussain mixture model conferences/seminars and journals of good and K-means‖, International Journal of Computer repute. He guided several students for getting their M.Tech Applications, Volume 25(5), pp.5-13. Degrees in field of Computer Science Engineering. His current [13] Yu-Len Huang (2005), ―A fast method for textural research interests include image processing and network analysis of DCT-based image‖, Journal of Information security. Science and Engineering, Volume 21, pp.181-194.

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image segmentation using finite doubly truncated Dr. K. Srinivasa Rao is presently working as Gaussian mixture model and Hierarchical clustering‖, Professor, Department of Statistics, Andhra Journal of Current Science , Vol.93(4), pp.507-514. University, Visakhapatnam. He is elected chief [15] P. Brodatz,(1966)―Texture: a photographic album for editor of Journal of ISPS and elected Vice- artists and designers,‖, Dover, New President of Operation Research of India. He York,USA(http.://sipi.usc.edu/database/database.php?volu guided 52 students for Ph.D in Statistics, me=textures). Mathematics, Computer Science, Electronics and [16] M.S.Allili and Nizar Bougila (2008), ―Finite generalized Communications Engineering, Industrial Engineering and Gaussian mixture modeling and applications to image and Operations Research. He published more than 130 research video foreground segmentation‖, Journal of Electronic papers in National and International journals with high Imaging, Volume 17(13), pp.05-13 reputation. His research interests are Image Processing, [17] C. Lu, P. Chung and C. Chen(1997), ―Unsupervised Communication Systems, Data Mining and Stochastic models. Texture Segmentation via Wavelet Transform‖, IEEE

Trans. on Pattern Recognition, Volume 30(5), pp. 729-742.

[18] T. P. Weldon, W.E. Higgins (1996), ―Design of multiple Dr. Y. Srinivas is currently Professor and Gabor filters for texture segmentation‖, Proc. of Intl. Conf. Head in the department of Information on Acoustics, Speech and Signal Processing, pp.2243- Technology, GIT, GITAM University, 2246. Visakhapatnam. He guided more than 09 Ph.D [19] Rao K.R. and Yip P. (1990), ―Discrete Cosine Transform students and published more than 102 research – Algorithms, Advantages, Applications‖, Academic press, papers in peer reviewed Journals. His research New York, USA.

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54 54 Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian Distribution integrated with Hierarchical Clustering

interests include image processing, Data mining and Speech security. He published more than 45 research papers in recognition. international journals and guided M.Tech and Ph.D students.

Dr. Ch. Satyanarayana is currently Professor in Computer Science and Engineering Department at Jawaharlal Nehru Technological University -Kakinada. He has 17 years of experience. His area of interest is on Image processing, Database Management, Network

How to cite this paper: K. Naveen Kumar, K. Srinivasa Rao, Y.Srinivas, Ch. Satyanarayana,"Studies on Texture Segmentation Using D-Dimensional Generalized Gaussian Distribution integrated with Hierarchical Clustering", International Journal of Image, Graphics and Signal Processing(IJIGSP), Vol.8, No.3, pp.45-54, 2016.DOI: 10.5815/ijigsp.2016.03.06

Copyright © 2016 MECS I.J. Image, Graphics and Signal Processing, 2016, 3, 45-54