Unstructured Oncological Image Cluster Identification Using Improved Unsupervised Clustering Techniques

S.Sreedhar Kumar, Syed Thouheed Ahmed, Qin Xin, S.Sandeep, M.Madheswaranand Syed Muzamil Basha

1Dr.T.Thimmaiah Institute of Technology, VTU, KGF, Karnataka, India

2School of Computing & Information Technology, REVA University, Bengaluru, India

3Faculty of Science and Technology, University of the Faroe Islands, Faroe Islands, Denmark

4K S School of Engineering, Bengaluru, India

5Muthayammal Engineering College, Rasipuram, Tamil Nadu, India

Abstract: This paper presents, a new approach of Medical Image Pixels Clustering (MIPC), aims to trace the dissimilar patterns over the Magnetic Resonance (MR) image through the process of automatically identify the appropriate number of distinct clusters based on different improved unsupervised clustering schemes for enrichment, pattern predication and deeper investigation.The proposed MIPC consists of two stages: clustering and validation.In the clustering stage, the MIPC automatically identifies the distinct number of dissimilar clusters over the gray scale MR image based on three different improved unsupervised clustering schemes likely improved Limited Agglomerative Clustering (iLIAC), Dynamic Automatic Agglomerative Clustering (DAAC) and Optimum N-Means (ONM).In the second stage, the performance of MIPC approach is estimated by measuring Intra intimacy and Intra contrast of each individual cluster in the result of MR image based on proposed validation method namely Shreekum Intra Cluster Measure(SICM).Experimental results show that the MIPC approach is better suited for automatic identification of highly relative dissimilar clusters over the MR cancer images with higher Intra closeness and lower Intra contrast based on improved unsupervised clustering schemes.

Keywords: Magnetic resonance image; unsupervised clustering scheme; intra intimacy; intra contrast; iLIAC; shreekum intra cluster measure; medical image clustering

1 Introduction

Cluster based image segmentation is a significant and mathematical process in the MR image analysis system for deeper investigation, enhancement, tumor predication and pattern identification.Generally, it is defined as a process of dividing MR image pixels into different numbers of dissimilar sub regions based on pixel intensity similarity [1].The goal of cluster based image separation is to simplify or change the representation of an image into a version that is more meaningful and easier to investigate and identify.Recently, many of the researchers have been reported in [2], the cluster based segmentation process is applied in many medicine related application likely medical image segmentation, tumor or cancer predication, medical image enhancement, medical image compression,pattern identification, medical image classification and medical image retrieval.The result of the cluster based medical image separation is a finite number of dissimilar groups that jointly concealments the complete medical image and the quality of the clustering result depend on the superiority of the medical image quality.The major problem in the existing clustering schemes such as semi-supervised and unsupervised methods [3] is that to predetermine the appropriate number of clusters in the unstructured MR image pixel set and respectively the clustering quality is based on predetermined number of clusters.To overcome these issues, in this paper a new clustering technique called Medical Image Pixels Clustering, it intentions to automatically separate finite number of dissimilar patterns in the MR image based on different improved unsupervised clustering schemes without predetermined knowledge for deeper investigation, enhancement, pattern predication and analysis.

2 Literature Reviews

Several methods are available for cluster based MR image segmentation process including kmeans, fuzzy C-means, neural network, fuzzy clustering and hierarchical clustering methods reported in[4-7].The k-means technique is a semi-supervised partitioned clustering technique and is an iterative procedure that directly decomposes the MR image pixel set into many dissimilar clusters or regions by minimizing the criterion function (e.g., sum-of-square-error) [8].Many of the authors suggested problem in the K-Means technique is that the entire segmentation result quality of MR image is based on predetermined k number of centroid pixel values.In [9], the authors Jianwei et al.have reported an improved K-Means technique MR brain image segmentation.The improved K-Means scheme is used to identify K distinct clusters over the disordered MR brain image with higher accuracy compared to existing scheme.

Another popular method called fuzzy c-means clustering (FCM) technique was reported in[10,11].This method is suited to partition the noise-free image into a finest number of groups.Many researchers suggested that the drawback with this method is that it failed to segment images corrupted by noise or inaccurate edges.In [12] the authors Yogita et al.have reported a detail survey of fuzzy C-means (FCM) with intensity inhomogeneity correction and noise robustness.They are discussed how the FCM schemes is better suitable to identify distinct tissues such as cerebrospinal fluid,gray matter and white matter over the MR brain image.The authors Senthilkumar et al.[13] have presented a modified fuzzy C-means clustering scheme to identify the normal and abnormal tissues likely white matter, gray matter, cerebrospinal and tumor part respectively over the MRI brain image.The clustering scheme consists of pre-processing and segmentation stages.In the pre-processing stage,the authors are applied wrapping based curvelet transform over the MR brain image and removed the noise.Similarly,they are applied improved fuzzy C-Means technique [14,15] and segmented the normal and abnormal tumor cells over the MR brain image based on spatial information.In [16], the authors Jinn et al.have reported a hierarchical genetic algorithm with fuzzy learning vector quantization network to partition a multi-spectral MR brain image.The evaluation of this approach was based on a real case of a MR brain image of an individual suffering from meningioma.

The author’s Chong et al.[17] have presented hybrid clustering scheme combined with morphological operations to improve the performance of MR image segmentation and reduced the non-brain tissue in the brain image.Firstly, the authors applied wiener filter and morphological operations over the MR image due to remove the non-brain tissue.Next, they are used combination of K-Means++and kernel-based fuzzy C-Means algorithm to identify distinct tumor regions in the MR image without noise.In [18,19], the authors Kalyanapu et al.have presented a clustering scheme namely unified iterative partitioned fuzzy clustering (U-IPFC).The U-IPFC scheme uses to identify distinct tissues over the MR brain image with good accuracy.The authors in [18,19] have claimed that the U-IPFC has produced higher accuracy result compared to FCM and K-means schemes.The authors Arul et al.in [20] presented a hierarchical clustering based segmentation (HCS) scheme to identify the distinct groups in hierarchy manner over the dynamic contrast enhanced magnetic resonance (DCSMR)image pixel set.The authors claimed that the HCS scheme is acted a semi-quantitative analytical tool to discover the DCEMR images.Next, the same authors Arul et al.in [21] have extended the detailed research of MR image segmentation based on hierarchical clustering scheme.The authors have experimented HCS scheme over the Multi-parametric Magnetic Resonance Imaging (MPMRI)and identified finite number of dissimilar tissue patterns by sequence of merging process.Another author Filipovych et al.in [22] reported hierarchical clustering scheme based image segmentation and it uses to identify predetermined number of dissimilar clusters in the tree manner over the gray scale image.

3 Proposed Image Pixel Clustering Approach

This section describes detailed study of the MIPC approach of image pixels classification.The MIPC scheme consists of two stages clustering and validation.The first stage automatically identifies the distinct number of highly relative clusters over the gray scale image dataset based on three different improved unsupervised clustering schemes iLIAC, DAAC and ONM in distinct manner.The second stage, it estimates the intra cluster intimacy and intra cluster contrast over the result of clustering stage based on the proposed SICM scheme.The stages involved in the MIPC approach are illustrated in the Fig.1 and the different stages are described in below subsections.

Figure 1: Original MR images: (a) Brain_1, (b) Brain_2, (c) Brain_3 (d) Breast_1 (e) Breast_2

3.1 Clustering Stage

This stage automatically identifies the distinct number of dissimilar clusters on the gray scale image based on three different improved clustering schemes iLIAC [23,24], DAAC [25] and ONM [26]in separate manner.Initially, the digital gray-scale image divides into (2 * 2) sizes of non-overlapping blocks and the image containsnobjects plus is defined asX=xi,xi=xijfori= 1,2,...,nandj= 0,1,2,...,d, whereXrepresents the dataset of MR image withnobjects or blocks,xirepresents theithobject or block in datasetX,ndenotes the size of MRI image datasetX,xijis thejthpixel value inithobject in datasetXandddenotes the number of pixels belongs into the each individual block in datasetX.The MIPC approach identifies distinct clusters over the image datasetXusing three different improved clustering schemes iLIAC, DAAC and ONM.The clustering schemes are described below subsections.

3.2 MIPC Using iLIAC Scheme

The MIPC approach identifies distinct number of dissimilar clusters over the MRI image datasetX=xifori= 1,2,...,nbased on improved agglomerative clustering iLIAC scheme [23] and it consists of three stages feature extraction, control merge cost, clustering.In the feature extraction stage, the iLIAC scheme is extracted single feature value over each individual vector or block in the MR image vector setX=xifori= 1,2,...,nwithdpixelsxi=xijforj= 0,1,2,...,dbased on statistical mean operation and is defined in the Eq.(1) as

wherexijrepresents thejthpixel value inithobject that belongs in to the vector setXandddenotes the number of pixel values inithobject inXforj= 1,2,...,d.Next, it computes the control merge costs(φ) over the MRI image feature dataset=, fori= 0, 1, ..,nbased on standard statistical function and is defined in the Eq.(2) as

where,sd() denotes the standard deviation of MR image feature dataset=and is defined in the Eq.(3) as:

where,(d(i,j))is the Euclidean distance betweenithandjthclusters that belong to the input cluster setis defined as in Eq.(6), whereiandjindicateithandjthclusters in the cluster set.Subsequently,it identifies the closest cluster pair (i,j) with a minimum merge cost Δdover the matrixUdijwhich is defined a

Next, the identified closest clusters pair (i,j) with minimum merge cost Δdis compared with optimum merge cost.If the minimum merge costΔdof cluster pair(i,j)is lesser than control merges cost (φ) then it is merge the cluster pair (i,j) into a single clusterij.Later it updates the merged clusterijintoiby standard statistical average method and is defined in Eq.(8) as

Then, updates the merged clusterstatus bycijintoci, wherecidenotes the status of theithcluster and subsequently it modifies the size of merged clusterby

where,NiandNjrepresent the number of related objects inithandjthclusters respectively.After, deletes thejthcluster in the input cluster setXincluding its statuscjand sizeNjrespectively.Then, it reduces the input cluster set size to {n=n- 1}.The above process is repeated until the minimum merge cost of the cluster pair Δdexceeds the control merge cost (φ).Finally, the iLIAC produces appropriate number of distinct clusters in the cluster setCover the MR image vector setXand is defined asC=cl, forl= 0,1,2,...,K, wherecldenotes thelthcluster withNsimilar objects or blocks that belongs to the resulting clusterCandKrepresents the number of distinct clusters in the cluster setCforl= 1,2,...,K.

Algorithm 1: iLIAC Input: MR Image dataset X with n Objects or Blocks Output: Classificationd

4 MIPC Using DAAC Scheme

Similarly, the MIPC approach is tested the same MRI image datasetX=xifori= 1,2,...,nusing DAAC scheme [24].It consists of two stages Distinct Representative Object Count (DROC) and Clustering.The DROC traces the count of distinct representative objects over the MRI image datasetX=xibased on occurrence of each individual object in dataset.It consists of three steps, in the first step,it represents the each object in the datasetX=xifori= 1,2,...,nwithdfeaturesf= 0,1,...,dinto single value=based on a statistical mean operation, whereis the representative value ofithobject in MRI image datasetXand is defined in Eq.(10) as

wherexifrepresents thefthfeature inithobject that belongs to the MR image datasetX.Next, the DROC scheme measures the tally of each object occurrenceCOO()in dataset=,fori= 0,...,nand is defined in Eq.(11) as:

Here,COVidenotes the sum of occurrence ofithvector inXandMOrepresents the maximum occurrence threshold and it uses to limit the count ofKdistinct representative objects with maximum existence in the MRI image datasetX.In the clustering stage, first, it calculates the upper triangular distance matrixUdijfor input cluster setX=xifori= 1,2,...,nthrough Euclidean distance metric and it estimated by

where,ndenotes the number of clusters in the input cluster setXandd(xi,xj) is the Euclidean distance betweenithandjthclusters in the cluster setXand is computed as

In this,xildenotes thefthfeature in theithcluster that belongs to the cluster setXanddrepresents the number of features in clusterxi=xilforf= 1,2,...,d.Next, the DAAC scheme traces the adjoining clusters pair (xi,xj) with lowest merging cost ? on the distance matrixUdijand is expressed in the Eq.(15) as:

where,d(xi,xj) denotes the Euclidean distance betweenithandjthMR image vectors in the MR image dataset or vector set (X).The Eq.(15) finds the adjoining clusters pair (xi,xj) with lowest merge cost ? and then compare the number of clusters does not exceed the sum of representative valueK.If the number of clustersiis not exceed theK, then the adjoining cluster pair (xi,xj) is combined into a same clusterxijwhich subsequently computes the centroid over the new clusterxiusing Eq.(16) and is defined as:

Next, updates the combined clusterxistatus into respectivecithroughci∪cj→ci,wherecidenotes the status of theithcluster and subsequently it modifies the size of combined clusterxibymi∪mj→mi,where,miandmjrepresent number of related objects inithandjthclusters respectively.After, it removes thejthcluster in the input cluster setXincluding its statusCjand sizeNjrespectively and reduces the input cluster set size by one.The above process is repeated until the number of dissimilar clusters in the cluster set is equal toKand afterward the results withKdistrict clusters are defined as {c1,c2,...,cK}.

5 MIPC Using ONM Scheme

Similarly, in this subsection, the MIPC approach is partitioned the MRI image dataset into distinct number of different clusters based on improved partitioned clustering ONM scheme[25,26].It consists of two stages likely dissimilar spatial centroid vector (DSCV) and partitioning respectively.In the DSCV stage, the ONM approach identifies the distinct number of centroid vectors over input MRI image vector setX=xibased on occurrence of objects in the datasetX.First, it computes rate of repetition of each spatial vectorOV(Xi) over the datasetX=xi, fori= 0,...,nand is defined in Eq.(17) as:

Algorithm 2: DAAC Input: MR Image Vector set X Containing n Vectors x0,x1,...,xnwith d pixels and Threshold (MO)Output: Generate K Distinct Clusters C = {c1, c2, ...,cK}Begin 1.Represent each object in MRI image dataset X into single dimensionalimages/BZ_283_736_2805_776_2866.png using Eq.(10)2.Measure the count of occurrence of each individual vector COV(images/BZ_283_736_2805_776_2866.pngi) inimages/BZ_283_736_2805_776_2866.png =images/BZ_283_736_2805_776_2866.pngifor i = 0,1,2,...,n as described in Eq.(11)3.Identifyrepresentativeobjectsin X basedoncountofobjectoccurrences COV(images/BZ_283_736_2805_776_2866.pngi)andthreshold MO as described in Eq.(12)4.Count (sum) the number of representative vectors in X using Eq.(12) and obtain the count in N 5.Consider each vector as an individual cluster in the input dataset X = xifor i = 0,1,...,n 6.Compute the upper triangular matrix Udijas given in Eq.(13).7.Find the closest clusters pairs (xi,xj) with minimum merge cost ? over Udijas given in Eq.(15).8.Merge the closest cluster pairs (xi,xj) into single cluster xijas described in Eq.(16)9.Update the newly merged cluster xijinto xias described in Eq.(16)10.Update the status of newly merged cluster xiin ciby ci∪cj→ci 11.Update the size of newly merged cluster by mi= mi+ mj 12.Delete jthcluster (xi), cluster status (cj) and its size (mj) respectively.13.Reduce X size by one.14.Repeat steps 6 to 13 until the size of the cluster set n is equal to K 15.Obtain the final clustering result in C End

where,xiandxjrepresentithandjthvectors that belongs in to the MR image vector setX,ndenotes the size ofXandTis the threshold that limit the similarity distance betweenithandjthvectors.If the differenceofithandjthobjectsislesserthanT,itmeansthatthejthobjectissimilartoithobjectorvector that belongs to the MR image datasetX.In the second step, it finds the distinct number of different Centroid Vector (CV) in datasetXbased on object occurrenceOV(xi) and is computed by

In this,OVidenotes the rate of occurrence ofithvector inXandCCrepresents the Control Centroid that intends to dynamically identify the appropriate number of spatial centroid vector in MRI image datasetXand is determined in form ofCV=CVl, forl= 1,...,N,f= 1,2,...,dandl= 1,...,N, where,CVlis in the partitioning stage, the ONM approach divides the MR image vector set into optimum number ofNdiscrete clusters based on distinct centroid vectors.The clustering stage consists of three steps.In the first step, it measures the distance of each individual vector in vector setXover theNcentroid vectors inCV=CVlforl= 1,2,...,Nandf= 0,1,...,dbased on Euclidean distance and is defined in Eq.(19) as

where,d(xi,CVl) represents the Euclidean distance betweenithvector inXandlthcentroid inCVand is computed by

Here,xifdenotes thefthfeature ofithvector inXandCVlfrepresents thefthfeature oflthcentroid vector.Second step, it finds the closest centroid vector of each individual object in datasetX=xiwith minimum Euclidean distance which computed at step 1 and respectively it assign theithobject inXinto its closestlthcluster in cluster setC=clforl= 0,1,...,Nand is defined in Eq.(21) as

In the last step, it modifies the centroid of each individual cluster in cluster setC=cl, forl=0,...,Nandcl=cljforj= 0,1,...,Rand is defined in Eq.(22) as:

In this,cijdenotes thejthobject inlthcluster in cluster setCandRlis the size oflthcluster in cluster setC.

Algorithm 3: ONM Input: MR Image vector set X Containing n vectors x0,x1,...,xnwith d features and Threshold (CC)Output: Cluster set C Containing N Clusters {c1,c2,...,cN}Begin 1.Measures the occurrence of each vector OV(xi) in X as described in Eq.(18)2.Find distinct number of centroid vector CV = CVlfor l = 0,...,N on input dataset X based on object occurrence OV(xi) and Control Centroid (CC) as expressed in Eqs.(17) and (18)3.Measure the distance of X over the N distinct centroids CV = CVlfor l = 0,...,N based on Euclidean distance as described in Eqs.(19) and (20)4.Divide the input dataset X into distinct number of clusters C = clfor l = 0,...,K based on distinct number of centroid objects by using Eq.(21).5.Update the centroids in CV = CVlby using Eq.(22).6.Repeat the steps from 4 to 5 until current iteration result is similar to previous iteration result.7.Obtain the clustering result in C.End

6 Cluster Validation Stage

This stage presents, the MIPC scheme estimates the closeness and separation among the data objects in each individual cluster in the cluster set of MR image vector set based on proposed cluster validation scheme (SICM).The proposed (SICM) is an improved version of existing validation techniques as reported in [27-29] and it aims to validate the quality of each individual cluster in the cluster set of MR image that identified by MIPC scheme based on probability concept.The SICM consists of two measures Intra Intimacy (II) and Intra Contrast (IC).The II measure uses to estimate the closeness of each individual vector with other vectors in the same clusterOC(cli), where,clirepresents theithobject in thelthcluster in cluster setCwithKclusters and the vector closenessVC(cli) measure is defined in the Eq.(23) as

where,clifis thefthpixel value injthvector in thelthcluster that belongs into the cluster setCforl= 0, 1, 2,...,K, |cl| is the size of thelthcluster forj= 0, 1, 2,...,N,θ denotes the predetermined threshold or constant that uses to limit the difference between two objects.Next, the IC calculates the overall intra cluster intimacyICIamong the cluster setCbased on individual cluster closenessVC(cli)within the same cluster set and is defined in the Eq.(24) as

Similarly, the intra contrast measure aims to estimate the intra disparity among the vectors within the same cluster in the cluster set.First, it measures the intra disparityVD(cl)of each individual vectorcl=cljforj= 0,1,2,...,Nwith other vectors within the same cluster in the cluster setC=clforl= 0, 1, 2,...,Kand it defined in the below given Eq.(25) as:

Subsequently, the IC measure estimates the overall intra cluster contrastICC(C) over the cluster setCwithKdistinct clusters based on intra vector disparityVD(cl) of each individual cluster in the cluster setC=clforl= 0, 1, 2,...,Kand is computed by,

Algorithm 4: SICM Input: Resulting Cluster C Containing K Distinct Cluster C = {c1,c2,...,cK}Output: Overall Intra Cluster Intimacy ICI(C) and Intra Cluster Contrast ICC(C)Begin 1.Compute the closeness of each individual vector VC(cli) with other vectors cl = clj, j =0,1,2,...,N in the same cluster clas expressed in Eq.(24)2.Evaluate the overall intra cluster closeness of resulting cluster C based on VC(cl) for l = 1,2,...,K using Eq.(25) and the result is obtained in ICI(C).(Continued)

3.Computetheintradisparity OD(cli)ofeachindividualvectorciiwithotherobjectsin thesame cluster clin the cluster set C = clfor l = 1,...,K based on Eq.(26)4.Calculate the overall inter cluster contrast ICC(C) of resulting cluster C = clwith K distinct cluster based on intra disparity of each individual cluster OD(cli) in the cluster set C using Eq.(26).End

7 Complexity Analysis

This section discovers the computational complexity of MIPC approach has tested over MR image dataset by three different improved unsupervised clustering schemes namely iLIAC,DAAC and ONM.The MIPC system consumes timeO(nd)to split the digital MR imageXintonnon overlapping blocks or vectors withdpixels, wherenis the number of vectors or blocks or vectors in the input digital MR image vector setXand is describes asX=xifori= 0,1,2,...,n,xi=xifforf= 0,1,2,...,d.Ahmed et al.[30]have presented automatic segmentation and detection of brain tumor is a notoriously complicated issue in magnetic methods are limited for detection of tumor in multimodal brain MRI.This work analyses the segmentation performance of existing state of art method improved Fuzzy C-Means clustering (FCMC) method and marker-controlled watershed method to carry out accurate brain tumor detection and enhance the segmentation results.Next, the complexity analysis of MIPC system is performing in the clustering stage including different clustering schemes iLIAC, DAAC and ONM respectively as described in the below.

7.1 MIPC (iLIAC)

First, it requires timeO(nd) to extract the single feature over each individual vector or block in the MR image vector setX=xiwithnvectors based on Eq.(1) and the extracted features are obtained in dataset=fori= 0,1,2,...,n.Next, it consumesO(n) time to compute the control merge cost(φ) over the MR image feature dataset () withndata elements.Afterward, in the every iteration the iLIAC clustering scheme needs timeO((n(n- 1)/2) + 1 + 1) to construct upper triangular distance matrixUd() over the cluster set () withnclusters, identifies closest cluster pair (xi,xj) and update the cluster set () respectively.The MIPC system needs timeO((n(n- 1)/2) + 1 + 1) for (n-K) iterations to identify the appropriate number of dissimilar clusters based on iLIAC scheme without user input.Overall the MIPC (iLIAC) system consumes timeO((((n(n- 1))/2) + 1 + 1)(n-K) + (nd))to process and identifies applicable number (K) of dissimilar clusters over the MR image vector set ().

7.2 MIPC (DAAC)

In the first stage, the (DAAC) clustering scheme needs timeO(nK) to identify number of distinct representative objects over the MR image feature set=withnobjects based on DROC method,where,Kis the number of representative objects in image feature set ().Next stage, it consumptions timeO((n(n- 1)/2) + 1 + 1) to build upper triangular matrix over the MR image vector setX,identifies closest vector pair (xi,xj) with higher similarity and update the vector setX.Overall the MIPC (DAAC) scheme is required timeO(((n(n- 1)/2) + 1 + 1)(n-K) + (nd) + (nK)) to identify finest number (K) of dissimilar clusters that belongs into the MR image vector setXwithout predetermined knowledge, where, (n-K) is the number of iterations.

7.3 MIPC (ONM)

Initially,the(ONM)clustering scheme consumptionsO(ndK)time to identify appropriate number of dissimilar centroid vectors over the MR image vector setX=xi,xi=xij, fori= 0,1,2,...,nandj= 0,1,...,dbased on DCV method, where,Kis the number of centroid vectors that belongs in to the vector setX.In the partitioning stage, the ONM scheme takes timeO(ndKr) to iteratively split the MR image vector setXinto finest number ofKdistinct highly relative clusters, where,ris the number of iterations.As a whole,the MIPC(DAAC)system has required timeO(ndKr+ndK)to identify finest number (K) of dissimilar clusters that belongs into the MR image vector setX.

8 Results & Discussions

This section presents the MIPC approach, experimented on MR gray scale medical images based on three different improved unsupervised clustering schemes iLIAC, DAAC and ONM respectively.For the experimental purpose, we have taken 100 natural 100 2-D gray scale MR medical images with different sizes such as (120 * 120), (124 * 124) and (130 * 130) respectively and the grey values in the range 0-255.

A subset of this dataset containing ten sample standard MR brain and breast images via, Brain_1,Brain_2, Brain_3, Breast_1 and Breast_2 are reported as representative in this subsection.The sample MRI images are used in many research experiments as reported in (Lai & Huang 2011; Qi et al.2015; Yong & Shuying 2007).Fig.1 shows the five standard MRI gray scale images Brain_1, Brain_2,Brain_3,Breast_1and Breast_2as illustrated in Figs.2a-2e respectively.In this experiment,each block of size (2 * 2) is considered as a vector and hence each sample image contains 3844, 4225, 3600, 3844 and 4225 vectors respectively.

Figure 2: Result of the MIPC scheme tested on the ten gray scale images using iLIAC approach indicated in Fig.1: (a) Result of brain_1 (b) Result of brain_2 (c) Result of brain_3 (d) Result of breast_1 (e) Result of breast_2

Firstly, the MIPC approach identifies distinct number of dissimilar clusters over the seven gray scale medical image datasets based on iLIAC scheme.Initially, it computes the control merge cost over seven gray scale MR images and the results are obtained in Tab.1 as 7.87, 7.51, 7.71, 7.85, 7.44 respectively.Then it followed by computation of upper triangular distance matrix and in the case of sample gray scale MRI image datasets are presented in Fig.2.The clustering scheme could identify 24, 25, 24, 25 and 25 distinct clusters over the MRI images in the Fig.2.The results are incorporated in the Tab.1.Fig.3 demonstrates the clustering result of the iLIAC scheme has tested the MRI images likely Brain_1, Brain_2, Brain_3, Breast_1 and Breast_2 as obtained in Figs.2a-2e respectively.

Table 1: Result of MIPC scheme tested on seven gray scale MRl images using iLIAC clustering algorithm

Similarly, the MIPC approach detects distinct number of unrelated clusters on same five MR image datasets based on DAAC scheme.Primarily, it automatically traces the distinct representative objects over the five MR images as illustrated in Fig.2 based on frequency of maximum occurrence(MO=15) and the count of distinct representative objects are obtained in Tab.2 as 33, 27, 33, 39,27 respectively.The Maximum Occurrence is a predetermined threshold which used to dynamically find the appropriate number of distinct representative objects in dataset.Then it followed by sequence of merging process and divides the each individual image dataset into distinct number of dissimilar clusters based on count of representative objects as presented in Tab.3.In the case of sample gray scale image datasets presented in Fig.3, the clustering scheme could identify 33, 27, 33, 39 and 27 distinct clusters.The resulting clusters of the clustering scheme are incorporated in the Tab.2.Fig.3 demonstrates the clustering result of the MIPC (DAAC) on five gray scale MR images Brain_1,Brain_2, Brain_3, Breast_1 and Breast_2 as obtained in Figs.3a-3e, 3 respectively.

Figure 3: Result of the MIPC scheme tested on the ten gray scale MR images using DAAC approach indicated in Fig.2: (a) Result of brain_1 (b) Result of brain_2 (c) Result of brain_3 (d) Result of breast_1 (e) Result of breast_2

Table 2: Result of MIPC (DAAC) scheme tested on five gray scale MR images

Table 3: Result of MIPC (ONM) scheme tested on five MR images

In the same way, the MIPC approach divides the MR image dataset into distinct number of discrete clusters based on ONM scheme.In the beginning, it robotically traces the distinct number spatial centroid objects on each individual gray scale MR image dataset based on control centroid (CC=15)and the results are incorporated in Tab.3.The Control Centroid (CC) is a user defined threshold that is used to generate the spatial centroid objects in dataset dynamically.Then it followed by iterative process and divides the each individual image dataset into distinct number of dissimilar clusters based on spatial centroid objects as presented in Tab.3.The resulting clusters of the five gray scale MR images are incorporated in the Tab.3.Fig.4 demonstrates the clustering result of the MIPC (ONM)on five gray scale medical images Brain_1, Brain_2, Brain_3, Breast_1 and Breast_2 as obtained in Figs.4a-4e respectively.

Figure 4: Result of the MIPC scheme tested on the ten MR images using DAAC approach indicated in Fig.2: (a) Result of brain_1 (b) Result of brain_2 (c) Result of brain_3 (d) Result of breast_1 (e)Result of breast_2

The performance of the MIPC approach with three improved clustering schemes has been validated based on improved SICM schemes.It calculates the intra intimacy and intra cluster contrast over the each individual cluster in cluster set of MR images which tested by MIPC approach and the clustering results as shown in Tabs.1-3 respectively.Initially, it measures the size of each individual cluster over the results of the five gray scale medical images Brain_1, Brain_2, Brain_3, Breast_1 and Breast_2 respectively.Next, it estimates the intra closeness (OC) and intra disparity (OD) in % among the individual cluster of these sample medical image datasets results based on the centroid of the each individual cluster.

Then, it followed to calculate the overall intra intimacyICI(C) in % over the results of the MIPC approach with three different clustering schemes iLIAC, DAAC and ONM respectively.Subsequently,it produced 60.06, 56.43, 53.37, 73.39, 77.92; 77.28, 88.27, 77.27, 82.51, 85.39; 72.14, 73.58, 70.215,79.17,83.39for the sample gray scale image datasets Brain_1,Brain_2,Brain_3,Breast_1and Breast_2 respectively.The estimated results of sample medical image datasets as obtained in Tab.4.Similarly,the overall intra cluster contrasICC(C) is calculated over the clustering results of MR images which obtained by MIPC scheme based on intra disparity measures.

The validation results of MR images which tested by iLIAC,DAAC and ONM clustering schemes are obtained in Tab.5 as 39.93, 43.56, 46.62, 26.60, 22.075; 22.71, 11.72, 22.72, 17.48, 14.60 and 27.85, 26.41, 29.78, 20.82, 16.60 respectively.It is clearly shown in the performance measurement results as illustrated in Figs.4, 5, and 6 that the proposed SICM has flawlessly estimated intra cluster intimacy and intra cluster contrast over the result of MR cancer image.Accordingly to the performance measurement results, that the DAAC clustering schemes has identified appropriate number of dissimilar groups (Normal & Abnormal regions) over the MR cancer images with good accuracy compared to ONM and iLIAC schemes without predetermined input.Similarly, the ONM scheme has produced better clustering results with higher intra closeness and lower intra contrast compared to iLIAC scheme.

Table 4: Comparison of intra closeness measures among results of MR images with tested by iLIAC,DAAC and ONM clustering schemes

Table 5: Comparison of intra separation measures among results of MR images with tested by with iLIAC, DAAC and ONM clustering schemes

Figure 5: Comparisons of (ICI) performance measure over clustering results of MR images tested by improved unsupervised clustering schemes iLIAC, DAAC and ONM

Figure 6: Evaluations of (ICC) performance measure over clustering results of MR images tested by improved unsupervised clustering schemes iLIAC, DAAC and ONM

9 Conclusion

This article presents Inherent Image Pixels Classification using three different improved unsupervised clustering schemes iLIAC, DAAC and ONM.The MIPC approach is aimed to trace the dissimilar pattern over the gray scale medical image through automatic identification of the distinct number of highly relative clusters in the medical image dataset based on improved unsupervised cluster schemes for deeper investigation and analysis.First, the MIPC approach automatically identifies the distinct number of dissimilar clusters over the medical image dataset based on three different clustering schemes iLIAC, DAAC and ONM in the separate manner.Next, the results of the MR images are validated based on proposed SICM scheme.We tested the MIPC approach with three improved unsupervised clustering schemes on five gray scale cancer MR images likely Brain_1,Brain_2,Brain_3,Breast_1 and Breast_2.According to the experimental results, the MIPC approach is more efficient and effective for automatic identification of the maximum number of highly relative clusters including normal and abnormal regions over the gray-scale MR cancer image with higher intra intimacy and lower intra contrast.After conducting various experiments, we concluded that the MIPC approach is better suitable to identify appropriate number of dissimilar regions (normal & abnormal), improving clusters quality and validate the clustering result for plateful to investigate (normal & abnormal regions) the dissimilar patterns in the MR cancer images.

Acknowledgement:This work is supported by Faculty of Science and Technology, University of the Faroe Islands, Faroe Islands, Denmark and REVA University, Bengaluru.The authors like to extend thanks to reviewers and experimental continuation of experts in this research.

Funding Statement:The authors received no specific funding for this study.

Conflicts of Interest:The authors declare that they have no conflicts of interest to report regarding the present study.