ISS: 0975-766X CODE: IJPTFI Avalable Onlne through Research Artcle www.jptonlne.com A STATISTICAL APPROACH FOR SKI COLOUR SEGMETATIO USIG HIERARCHICAL CLUSTERIG B..Jagadesh*, A. V. S.. Murty Department of Computer Scence and Engneerng, K L Unversty, Vaddeswaram, Guntur (Dt.) Andhra Pradesh, IDIA. Department of Mathematcs, School of Advanced Scences, VIT Unversty, Vellore-63204, Taml adu, IDIA. Emal: nagajagadesh@gmal.com Receved on 06-08-206 Accepted on 27-08-206 Abstract: Sn color segmentaton plays a vtal role n dfferent applcatons such as Face Detecton, Face Recognton and Human Computer Interacton applcatons. To mprove the accuracy of sn colour segmentaton system, n ths paper a novel and new sn colour segmentaton algorthm s proposed based on statstcal approach under HSI colour space of the mage. The bvarate feature vector of the mage s to be model wth a Pearson type II a mxture (bvarate Beta mxture) model. The model parameters are estmated usng EM Algorthm. The ntalzaton of parameters s done through Herarchcal Clusterng and moment method of estmaton. The performance of the proposed sn colour segmentaton algorthm s studed by computng the mage segmentaton qualty metrcs (PRI, VOI and GCE) and comparng them wth that of bvarate Gaussan mxture model. The ROC curves plotted for the system also revealed that the proposed algorthm can segment the sn colour more effectvely than the exstng segmentaton algorthm for classfyng sn colour. Key Words: Bvarate Pearson type II a mxture model, sn colour segmentaton, HSI colour space, segmentaton qualty metrcs, Herarchcal Clusterng. I. Introducton Sn segmentaton s an mportant actvty n many real tme systems such as face detecton, face tracng etc. For effcent and effectve desgn of sn colour segmentaton algorthms t s needed to utlze statstcal modelng []. The feature for the detecton of sn regon s by sn colour, so that colour space plays an mportant role for feature extracton. Dfferent types of colour spaces are avalable n lterature such as RGB, ormalzed RGB, HSL, HIS, YCbCr, IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6627
YIQ, YUV, YES, CIE-Lab and CIE-Luv [2-7]. Among all these colour spaces HSI colour space has certan advantages snce t separate channels and outlne certan colour propertes whch are close to the vsual conjunctve system of human beng [8] [9]. In HSI colour space the hue and saturaton values are correlated through the ntensty. Hence recently n colour mage processng the HS bvarate feature vector s utlzed [0-2]. Recently much wor has been reported n lterature regardng sn colour segmentaton algorthms. Among all segmentaton algorthms the model based segmentaton methods are more effcent than other methods snce they capture the local and global nformaton of the mages more effectvely [3][4]. In model based sn colour segmentaton t s customary to assume that the feature vector assocated wth the colour mage s ether Gaussan or Gaussan mxture model. But the Gaussan or Gaussan mxture model have certan drawbacs le the feature vector n each regon are meso-urtc and havng nfnte range. In realty the feature vector n each regon of the mage (sn and non-sn regons) may not be meso-urtc and more so havng fnte range [5][6]. To overcome ths drawbac n sn colour segmentaton one has to nvestgate and analyze the sn colour segmentaton algorthm wth the assumpton of feature vector (conssts of hue and saturaton) follows a bvarate Pearson type II a model. Hence the whole mage can be characterzed by bvarate type II a Pearson mxture model. The rest of the paper s organzed as follows: secton 2 gven bref dscusson about bvarate Pearson type II a mxture model and ts propertes. Secton 3 deals wth the estmaton of the model parameters usng EM Algorthm. Secton 4 s to ntalze the model parameters usng moment method of estmaton and Herarchcal Clusterng algorthm. In Secton 5 the sn colour segmentaton algorthm s presented based on lelhood functon under Bayesan frame wor. In secton 6 the expermentaton and performance evaluaton of the proposed algorthm are dscussed. The expermentaton s carred wth sx face mages taen from Indan face database. The performance of the proposed algorthm s studed by computng the segmentaton qualty metrcs le PRI, GCE and VOI. The effcency of proposed algorthm s also studed through confuson matrx and ROC curves. Secton 7 deals wth concluson. 2. Bvarate Pearson type IIaα mxture model In sn colour analyss the entre mage s dvded nto two categores namely, sn and non-sn colour regons. The sn colour s dfferent from the colour of most other natural objects n the world. Here colour space s used to extract the feature vector for develop the statstcal model of the mage. Accordngly the hue and saturaton under HSI colour space are used for sn colour detecton. The statstcal observatons of hue and saturaton whch form a bvarate feature vector IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6628
match closely wth the bvarate Pearson type II a dstrbutons. The bvarate Pearson type II a gven by Kotz et al [7], s havng non-negatve and asymmetrc nature of the random varable. Here t s assumed that the feature vector of the pxel n sn or non-sn regons n the mage follows a bvarate Pearson type II a dstrbuton. The Jont Probablty densty functon of the feature vector s ( m n p) f ( x, y / ) x y ( x y) ( m) ( n) ( p) m n p m, n, p 0 x, y 0 and x y () s the parametrc set such that ( m, n, p), x denote the hue value and y denote the saturaton value of the pxel n the mage. Snce the entre mage s a collecton of sn and non-sn pxel regons whch are characterzed by a bvarate Pearson type II a dstrbuton, the feature vector assocated wth the whole mage s modeled as a two component bvarate Pearson type II a mxture model. Its Jont probablty densty functon s 2 h( x, y) f ( x, y / ) (2) where, 0 and 2 and f ( x, y ) s as gven equaton (). 3. Estmaton of the model parameters by expectaton maxmzaton algorthm. The lelhood functon of sample bvarate observatons ( x, y),( x2, y2),( x3, y3 ),...,( x, y) drawn from an mage wth probablty densty functon K h( x, y; ) f ( x, y ; ) where f s the probablty densty functon of a Pearson type s s II a mxture dstrbuton and s gven by K ( s s ) L( ) f ( x, y ; ) s (5) Ths mples that K ( s s ) log L( ) log f ( x, y ; ) s = K log( f ( x, y ; )) s s s (3) The model parameters are estmated by usng the Expectaton Maxmzaton Algorthm (E.M Algorthm). The updated equaton of the parameter s IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6629
B..Jagadesh* et al. /Internatonal Journal of Pharmacy & Technology [ ( ; )] for K =, 2. ( l) ( l) t xs, ys s = s ( ; ) l () l f ( xs, ys; ) 2 l () l f xs, ys (4) where, () l f ( xs, ys; ) s as gven equaton (). The updated equaton of m at ( l ) th teraton s ( l) ( l) t (, ; ) log( ) (, ; ) ( ( ) * ( ( )) ( ) * xs ys xs t xs ys m ( ) n p log log e m n p s s m n p ( m n p ) () ( m n )) * ( ) l m p log e t ( x, y ; ) ( m * log(log( e)) m * ( m ) * log( e) - s s ) 0 s m (5) where, ( m n p ) dgamma( m n p ) The updated equaton of n at ( l ) th teraton s ( l) ( l) t (, ; ) log( ) (, ; ) ( ( ) * ( ( )) xs ys ys t xs ys m ( ) n p log log e s s m n p ( m n p ) () ( m n p ) * ( m n p )) * log( e) l n t ( x, y ; ) ( n * log(log( e)) n * ( n ) * log( e) - s s ) 0 s n (6) where, ( m n p ) dgamma( m n p ) The updated equaton of p at ( l ) th teraton s ( l) ( l) t (, ; ) log( ) (, ; ) ( ( ) * ( ( )) xs ys xs ys t xs ys m n p log log e s s ( m n p ) ( m n p ) () ( m n p )* ( m n p )) * log( e) l p t ( x, y ; ) ( ( p ) * log(log( e)) ( p ) * ( p ) * log( e) s s s 0 ( p ) (7) where, ( m n p ) dgamma( m n p ) Solvng equatons (4) (5) (6) and (7) teratvely usng MATLAB code we get the revsed estmates of, m, n, p for K =, 2. 4. Intalzaton of model parameters by herarchcal clusterng algorthm. IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6630
In ths secton, we brefly dscuss the methods for ntalzaton of the model parameters to run the Expectaton Maxmzaton algorthm. The lelhood functon contans two components. The pxels of the whole mage are ntally dvded nto two parts namely, sn and non-sn regons by usng Herarchcal clusterng algorthm. The Expectaton- Maxmzaton algorthm requres the ntalzaton of the parameter and the model parameters based on the mxture model whch s usually consdered as nown apror. The value of can be tae n as 2.e.,, for =, 2 ntally. 2 The steps nvolved n Herarchcal Clusterng are gven n Johnson S.C. (967). We obtan the ntal estmates of the parameters m, n and p for each mage regon usng the method of moment estmators for bvarate Pearson type II a dstrbuton and for the parameters as for =, 2. 5. Sn colour segmentaton algorthm. After refnng the parameters the prme step s sn colour segmentaton, by allocatng the pxels to the sn or non-sn segments. Ths operaton s performed by segmentaton algorthm. The sn colour segmentaton algorthm conssts of the followng steps. Dvde the whole mage nto two regons usng Herarchcal clusterng algorthm 2. Obtan the ntal estmates of the model parameters usng the moment estmators as dscussed n secton 4 for each regon 3. Obtan the refned estmates of the model parameters by usng the EM-algorthm wth the updated equatons gven n secton 3. 4. Substtute the estmated parameter values n the mage jont probablty densty functon 2 K h( x, y) f ( x, y ; ) where f ( x, y / ) s as gven equaton (). 5. Segment the pxels as sn colour or non-sn colour pxel usng a threshold (t) and the lelhood functon such that L( x / ) t or L( x / ) t respectvely for 0 < t <. The optmal threshold value of t s determned computng true postve and false postve over the segmented regons and plottng the ROC Curve. IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 663
6. Expermental results and performance evaluaton. In ths secton, the performance of the developed sn colour segmentaton algorthm s evaluated. For ths purpose the sn mages are collected from Indan database http://www.face-rec.org/databases/. A random sample of 6 mages s taen from the Indan database and the feature vector conssts of hue and saturaton for each pxel of the each mage s computed utlzng HSI colour space. Wth the feature vector (H, S) each mage s modeled by usng the two component bvarate Pearson type II a mxture dstrbuton. The ntal values of the model parameters are obtaned by dvdng all the pxels n to two categores namely sn and non-sn regon usng Herarchcal Clusterng algorthm. Usng these ntal estmates and the updated equatons of the EM-Algorthm dscussed n secton.3 wth MATLAB code the refned estmates of model parameters are obtaned. Substtutng the refned estmates n the bvarate Pearson type II a jont probablty dstrbuton functon the sn colour and non-sn colour models of each mage are estmated. The segmentaton algorthm wth component maxmum lelhood under Bayesan frame and a threshold value t as dscussed n secton 5 s used to segment the mage. Fgure shows the orgnal and segmented mages. Fgure. Orgnal and Segmented Images. The developed algorthm performance s evaluated by comparng sn colour segmentaton algorthm wth the bvarate Gaussan mxture model wth K-means, bvarate Gaussan mxture model wth herarchcal and bvarate Pearson type II a mxture model wth K-means. Table. Present the mss classfcaton rate of the sn pxels of the sample mage usng proposed model and Gaussan mxture model wth K-means and Herarchcal clusterng algorthms. IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6632
Table. Mss Classfcaton rate of the classfer Model Msclassfcaton Rate BGMM wth K-means.2% BGMM wth Herarchcal 0.9% BPTII a MM wth K-means 7.8% BPTII a MM wth Herarchcal 7.2% From the Table. t s observed that the msclassfcaton rate of the classfer wth bvarate Pearson type II a mxture model (BPTII a MM) wth herarchcal s less compared to that of other models. The accuracy of the classfer s also studed for the sample mages by usng confuson matrx for sn and non-sn regons. Table.2 shows the values of TPR, FPR, Precson, Recall and F-measure for sn and non-sn segments of the sample mages. Table.2: Comparatve study of BGMM and BPTII a MM. Image Method TPR FPR Precson Recall F-measure Image (Female) Image2 (Male) Image3 (Female2) Image4 (Male2) Image 5 BGMM wth K-means 0.9285 0.875 0.9454 0.9285 0.9368 BGMM wth Herarchcal 0.9333 0.083 0.945 0.9333 0.939 BPTII a MM wth K-means 0.9642 0.0625 0.988 0.9642 0.9729 BPTII a MM wth Herarchcal 0.9708 0.046 0.9789 0.9708 0.9748 BGMM wth K-means 0.966 0.0833 0.9565 0.966 0.9363 BGMM wth Herarchcal 0.9250 0.0750 0.960 0.9250 0.9422 BPTII a MM wth K-means 0.9625 0.08 0.9788 0.9625 0.9705 BPTII a MM wth Herarchcal 0.9729 0.0458 0.9769 0.9729 0.9748 BGMM wth K-means 0.9307 0.20 0.958 0.9307 0.94 BGMM wth Herarchcal 0.946 0.0703 0.9599 0.946 0.9555 BPTII a MM wth K-means 0.9692 0.0629 0.9767 0.9692 0.9729 BPTII a MM wth Herarchcal 0.9750 0.046 0.9790 0.9750 0.9784 BGMM wth K-means 0.9259 0.0454 0.9803 0.9259 0.9523 BGMM wth Herarchcal 0.9354 0.0958 0.952 0.9354 0.9432 BPTII a MM wth K-means 0.9629 0.0363 0.9848 0.9629 0.9737 BPTII a MM wth Herarchcal 0.9770 0.046 0.979 0.9770 0.9780 BGMM wth K-means 0.8750 0.0625 0.9459 0.8750 0.9090 BGMM wth Herarchcal 0.8958 0.046 0.9772 0.8958 0.9343 IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6633
(Female3) BPTII a MM wth K-means 0.9800 0.087 0.9849 0.9800 0.9824 BPTII a MM wth Herarchcal 0.9833 0.025 0.990 0.9833 0.987 BGMM wth K-means 0.966 0.250 0.936 0.966 0.9240 Image 6 BGMM wth Herarchcal 0.9375 0.66 0.944 0.9375 0.9394 (Male3) BPTII a MM wth K-means 0.9770 0.046 0.979 0.9770 0.9777 BPTII a MM wth Herarchcal 0.9833 0.029 0.9853 0.9833 0.9842 From Table.2 t s obtaned that the F-measure value for the proposed classfer s more. Ths ndcates the proposed classfer perform better than that of Gaussan mxture model. Fgure.2 shows the ROC curves assocated wth the proposed sn colour classfer and the classfer wth other models. From Fgure.2 t s observed that the proposed classfer s havng less false detecton of the sn pxels compared to the classfer wth other models. The fgure also shows that can successfully dentfed the exposed sn regon ncludng face, hands and nec. The performance of the segmentaton algorthm s also studed by obtanng three segmentaton performance measures namely, Probablstc Rand Index (PRI) [8], Varaton of Informaton (VOI) [9], Global Consstency Error (GCE) [20], wth the sample mages. The computed values of the performance measures for the developed algorthm wth BPTIIa MM and GMM are presented n Table.3. Table.3: Segmentaton Performance Measures. Fg-2: ROC Curves. Image Method Performance Measures IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6634
Image (Female) Image 2 (Male) Image 3 (Female2) Image 4 (Male2) Image 5 (Female3) Image 6 (Male3) B..Jagadesh* et al. /Internatonal Journal of Pharmacy & Technology PRI GCE VOI BGMM wth K-means 0.528 0.2486 0.529 BGMM wth Herarchcal 0.628 0.2274 0.395 BPTII a MM wth K-means 0.694 0.928 0.0892 BPTII a MM wth Herarchcal 0.7452 0.429 0.086 BGMM wth K-means 0.5367 0.2249 0.098 BGMM wth Herarchcal 0.6267 0.297 0.093 BPTII a MM wth K-means 0.780 0.206 0.076 BPTII a MM wth Herarchcal 0.828 0.826 0.0649 BGMM wth K-means 0.4826 0.924 0.626 BGMM wth Herarchcal 0.4982 0.728 0.260 BPTII a MM wth K-means 0.672 0.28 0.0926 BPTII a MM wth Herarchcal 0.7625 0.0938 0.0728 BGMM wth K-means 0.624 0.362 0.472 BGMM wth Herarchcal 0.6928 0.90 0.046 BPTII a MM wth K-means 0.794 0.0972 0.083 BPTII a MM wth Herarchcal 0.847 0.0886 0.0792 BGMM wth K-means 0.5924 0.236 0.27 BGMM wth Herarchcal 0.608 0.200 0.038 BPTII a MM wth K-means 0.724 0.902 0.0672 BPTII a MM wth Herarchcal 0.7826 0.620 0.0576 BGMM wth K-means 0.628 0.947 0.428 BGMM wth Herarchcal 0.694 0.729 0.249 BPTII a MM wth K-means 0.825 0.0826 0.084 BPTII a MM wth Herarchcal 0.896 0.0642 0.0729 From the Table.3 t s observed the PRI value of the proposed algorthm for sample mages consdered for expermentaton are more than that of the value from the segmented algorthm based on other models and they are closed to. Smlarly the GCE and VOI values of the proposed algorthm are less than that of fnte Gaussan mxture model and close to 0. Ths reveals that the proposed segmentaton algorthm performs better than that of other algorthms. 7. Concluson In ths paper we proposed a sn colour segmentaton algorthm based on bvarate Pearson type mxture model usng HSI colour space. Here t s assumed that the bvarate feature vector (Hue and Saturaton) of the whole mage follows a bvarate Pearson type II a mxture dstrbuton whch s capable of characterzng the sn and non-sn colours n the mage. The model parameters are obtaned by dervng the updated equatons of the EM-Algorthm. The ntalzaton of the parameters s done usng Herarchcal clusterng algorthm and moment method of estmaton. The expermental results wth dfferent types of sx face mages taen from Indan database revealed that the proposed algorthm perform much IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6635
superor wth respect to mage segmentaton performance metrcs le PRI, GCE and VOI. A comparatve study of proposed model wth that of other models has shown the proposed algorthm outperform the exstng algorthms for some mages n sn colour segmentaton. Ths s also supported by ROC curves. References. Alexander Wong, Jacob Scharcans and Paul Feguth (20), Automatc Sn Leson Segmentaton va Iteratve Stochastc Regon Mergng, IEEE Trans. on Informaton Technology n Bomedcne, Vol.5, o.6,pp.929-936. 2. C. Chen, S.P. Chang (997), Detecton of human faces n colour mages, IEEE Proc. Vson Image Sgnal Process, Vol.44 (6) pp.384 388. 3. H. Wu, Q. Chen, M. Yachda (999), Face detecton from color mages usng a fuzzy pattern matchng method, IEEE Trans. Pattern Anal.Mach. Intell. Vol. 2 (6) pp.557 563.. 4. L.M. Bergasa, M. Mazo, A. Gardel, M.A. Sotelo, L. Boquete (2000), Unsupervsed and adaptve Gaussan sncolor model, Image Vson Comput. Vol.8 (2) pp.987 003. 5. D. Brown, I. Craw, J. Lewthwate (200), A SOM based approach to sn detecton wth applcaton n real tme systems, BMVC0. 6. S. McKenna, S. Gong, Y. Raja (998), Modelng facal colour and dentty wth Gaussan mxtures, Pattern Recognton Vol.3 (2) pp.883 892. 7. Y. Wang, B. Yuan (200), A novel approach for human face detecton from color mages under complex bacground, Pattern Recognton Vol.34 (0) pp.983 992. 8. G.V.S. Raj Kumar, K.Srnvasa Rao and P.Srnvasa Rao (20), Image Segmentaton and Retrvals based on fnte doubly truncated bvarate Gaussan mxture model and K-means, Internatonal Journal of Computer Applcatons, Vol. 25. o.5 pp.5-3. 9. Rafel C Gonzalez and Rchard E Woods (200), Dgtal Image Processng, Pearson educaton, Inda. 0. D. Brown, I. Craw, J. Lewthwate (200), A SOM based approach to sn detecton wth applcaton n real tme systems, BMVC0. IJPT Sep-206 Vol. 8 Issue o.3 6627-6637 Page 6636
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