Color Image Segmentation by Multilevel Thresholding using a Two Stage Optimization Approach and Fusion Rafika HARRABI and Ezzedine BEN BRAIEK

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1 ISSN: ISO 900:008 Certfed Volume 3, Issue, May 04 Color Image Segmentaton by Multlevel Thresholdng usng a To Stage Optmaton Approach and Fuson Rafka HARRABI and Eedne BEN BRAIEK Abstract In ths paper, e propose a ne color mage segmentaton method based on a multlevel thresholdng algorthm and data fuson technques. We have revsed the Otsu method for selectng optmal threshold values for both unmodal and bmodal dstrbutons, and tested the performance of the ne automatc thresholdng method called the TSMO (To-Stage Mult-level Thresholdng) on the color mages segmentaton. Ths algorthm s teratve and outperforms Otsu s method by greatly reducng the teratons requred for computng the beteen-class varance n an mage. For segmentaton, e proceed n to steps. In the frst step, e begn by dentfyng the optmal threshold of the trstmul (R, G and B). In the second step, segmentaton results for the three color components are ntegrated through the fuson rule, n order to get a fnal relable and accurate segmentaton result. Expermental segmentaton results on medcal and textured color mages demonstrate the value of combng the thresholdng technque and fuson rule for color mage segmentaton. The obtaned results sho the robustness of the proposed method. Index Terms Multlevel thresholdng, Segmentaton, Medcal mage, fuson, thresholdng, Otsu method. I. INTRODUCTION Image segmentaton serves as the key of mage analyss and pattern recognton [] []. It s one of the most dffcult tasks n mage processng, hch determnes the qualty of the fnal result of analyss [3] [4]. The mage segmentaton s a process of dvdng an mage nto dfferent regons such that each regon s homogeneous, but the unon of any to regons s not [4] [5]. More recent research has focused on color mage segmentaton due to ts demandng need [6] [7]. In color mage segmentaton, color of a pxel s gven as three values correspondng to the three component mages R (Red), G (Green) and B (Blue). At present, color mage segmentaton methods are manly extended from monochrome segmentaton approaches by beng mplemented n dfferent color space. Gray level segmentaton methods can be appled drectly to each component of a color space, and then the results can be combned n some ay to obtan a fnal segmentaton result [4] [8]. Thresholdng [9] [0] [] s dely used n many mage processng applcatons such as () medcal mage applcatons []; () automatc vsual nspecton of defects [3] [4]; (3) optcal character recognton [5], and (4) detecton of vdeo change [6] [7]. Otsu s method [8] s one of the better ays of mage segmentaton, here the mage contans only to classes. Ths method selects the threshold value by maxmng the separablty of the classes n gray levels. It effcent for thresholdng an mage th a hstogram of bmodal dstrbuton, but they are mpractcal hen extended to multlevel thresholdng. To mprove the effcency of Otsu s method, Deng-Yuan Huang et al. [9] have proposed a ne fast algorthm called the TSMO method (To-Stage Multthreshold Otsu method). The TSMO method outperforms Otsu s method by greatly reducng the teratons requred for computng the beteen-class varance n an mage. In the past, many authors have addressed the problem of color mage segmentaton usng dfferent methods [0] [] [] [3] and, n partcular, several researchers have nvestgated the hybrd methods for color mage segmentaton [4] [5 [6]. In ths context, Lm et al. [7] have proposed a color mage segmentaton method based on the Thresholdng and the Fuy C-means technques (TFCM). The methodology uses a coarse-fne concept to reduce the computatonal burden requred for the FCM algorthm. Wth the same obectve, S. Ben Chaabane et al. [6] have proposed a color cells mages segmentaton method based on hstogram thresholdng and Dempster-Shafer evdence theory (TDS). The obectve s to rebuld each cell from the three prmtve colors (R, G and B) of the orgnal mage. From an ntal segmentaton obtaned by usng the hstogram thresholdng, one seeks a segmentaton hch represents as ell as possble the ponts really formng part of the cells, as also the number of the cells. Also, Zhu et al. [5], have proposed a segmentaton method based on Fuy c-means algorthm and Dempster-Shafer evdence theory (FCMDS). The membershp degree of each pxel comng from the dfferent mages to be combned s obtaned by applyng the FCM algorthm to the gray level of the three component mages (R, G and B). Then, the DS combnaton rule and decson are appled to obtan the fnal segmentaton. The color segmentaton method, proposed n ths paper, s conceptually dfferent and explores a ne strategy. In fact, nstead of consderng an elaborate and better desgned color segmentaton method, our technque rather explores the possble alternatve of combnng automatc thresholdng algorthm and data fuson technques. After the determnaton of the optmal threshold of each component mage, the fuson rule s used to obtan the fnal segmentaton results. The optmal thresholds of each component mage are computed usng the to-stage Otsu optmaton approach [9]. Then, segmentaton results for the three color components are 4

2 ISSN: ISO 900:008 Certfed Volume 3, Issue, May 04 ntegrated through a fuson rule n order to get a fnal relable and accurate segmentaton result. Ths method s appled to color mage segmentaton, here e am at provdng help to the doctor for the follo-up of the dseases of the breast cancer. The obectve s to rebuld each cell from a seres of three component mages (R, G and B). From an ntal segmentaton obtaned by usng the automatc thresholdng technque, one seeks a segmentaton hch represents as ell as possble the cells, n order to gve to the doctors a schema of the ponts really formng part of the cells, as also the number of the cells. Secton ntroduces the proposed method for color mage segmentaton. The expermental results are dscussed n Secton 3, and the concluson s gven n Secton 4. II. THE PROPOSED METHOD For color mages th RGB representaton, the color of a pxel s a mxture of the three prmtve colors red, green, and blue. By applyng a segmentaton technque to the red, green or blue color features, n ths case, a regon can be recogned n one of the three components but s not dentfed by the other components. Ths shos the hgh correlaton among the R, G, and B components [4] [6] [8]. By hgh correlaton, e mean that f the ntensty changes, all the three components ll change accordngly. In ths context, color mage segmentaton usng data fuson technques appears to be an nterestng method. The segmentaton method, proposed n ths paper, s conceptually dfferent and explores a ne strategy. In fact, nstead of consderng an elaborate segmentaton procedure, our technque rather explores the possblty of combnng several approaches. Ths method s an hybrd mage segmentaton technque hch ntegrates the results of the automatc thresholdng algorthm and data fuson technque, n hch the thresholdng technque s used to select the optmal threshold n each mage to be combned. In ths ork, e are nterested n color mage segmentaton of cells n the breast mages. The problem s to separate cells from the background. The ntal segmentaton maps hch ll then be fused together are smply gven, n our applcaton, by the automatc thresholdng technque [9], appled on the three prmtve colors (R, G and B). Then the combnaton rule s used to obtan the fnal segmentaton results. Ths technque allos obtanng an optmal segmented mage, superor to versus exstng technques [5] [6] [7]. A. Recursve Otsu Method Hstogram thresholdng s one of the dely used technques for monochrome mage segmentaton. Otsu s method s one of the better ays of mage segmentaton, hch selects a global threshold value by maxmng the separablty of the classes n gray levels. Ths method s effcent for thresholdng a hstogram th bmodal dstrbuton, but t s neffcent f there s a large class number M requred n an mage due to the fact that t nvolves a large number of repettous computatons of the ero- and frst-order cumulatve moments of the gray-level hstogram. A comprehensve survey of mage thresholdng methods s provded n [9] [0]. To sgnfcantly mprove the defcences n Otsu s method th regard to selectng the mult-level threshold, e use an algorthm called the To-stage Multthreshold Otsu s method (TSMO). A general concept of the TSMO method s gven n Ref. [9]. The dea of ths method s qute smple and straghtforard: to greatly reduce the teratons requred for calculatng the eroth and frst-order moments of a class. In the frst stage of the TSMO method, the hstogram of an mage th L gray levels s dvded nto M groups hch contan N gray levels. Let denote the groups of the total mage space; then 0,,..., M, here represents the group number. Hence, each group contans a certan range of gray levels as follos: 0 contans a range of gray levels 0,,..., N, th gray levels N, N,...,N,...,, q th gray Z levels qn qn,..., q Z, N,..., and the last group M th gray levels ( M ) N,( M ) N,..., M N. The number of cumulatve pxels (the eroth- order th cumulatve moment), n the q group denoted by g q can be calculated as: q N g () q f qn here f represents the number of pxels th gray level. Snce each group contans N gray levels, the correspondng gray level value for each group can be consdered as a mean value for those N gray levels. Therefore, the correspondng gray level value or mean th ntensty (the frst-order cumulatve moment), n the q group denoted by can be calculated as: q q q q N q N qn g f q N f qn f qn Hence, Otsu s method can be appled to fnd the optmal threshold by maxmng the beteen-class varance B th the sets of and g. The optmal threshold hch s also regarded as the number of the group nto hch the maxmum varance of the beteen-class,.e.,, falls th the correspondng group s defned as: 0 M B B max arg max (3) If an mage can be dvded nto to classes, C and C, by, here class C conssts the group from to, () 0 5

3 0 M ISSN: ISO 900:008 Certfed Volume 3, Issue, May 04 and class C contans the other groups B. Fuson of the Segmentaton Map th to, M then the numbers of the cumulatve The optmal threshold T s automatcally determned by the pxels and the means for the to classes, respectvely, are to-stage Otsu optmaton approach, as descrbed n secton gven by:.. Gven an optmal threshold, e.g. T R,, the R s functon classfes the pxels on the Red component nto to opposte g (4) classes: obects versus background, g (5) and S (6) S (7) here S and S are the frst-order cumulatve moments for classes C and C, respectvely S g (8) S 0 M g Thus, the maxmum varance of the beteen-class B max, can be easly found usng the modfed verson of Otsu s method proposed by Lao et al. [8]. In the case of b-level thresholdng M, the maxmum varance of the beteen-class s defned as: B max M k k k S S S ST S N here M s the class number n an mage, and That s S S T (9) (0) S T s the sum of S S, and N s the total number of pxels n an mage. S N () In the second stage of the TSMO method, snce contans the gray levels th ' B max ( )N to ( ) N n hch ( ) ( ) occurs has already been found n the frst stage, Otsu s method can be appled agan to group n a smlar fashon to found the optmal threshold T. Hence ' T arg max ( ) ( t) () ( ) N t( ) N B as: R s nt errest obect f R( TR (3) 0 background f R( TR In fact, the pxel ( x, s classfed as an nterest obect (the cells n the bomedcal mage) f ts gray level pxel R s hgher than the optmal threshold determned automatcally by the to stage Otsu s thresholdng technque, n hch case s set to. Otherse, t s classfed as a background pxel and s set to 0. Therefore, an analogous segmentaton procedure s further performed on the components G and B, as: nt errest obect f G( TG Gs (4) 0 background f G( TG nt errest obect f B( TB Bs (5) 0 background f B( TB here G and B ndcate the gray level of the Green and Blue pxel at ( x, and T G and T B ndcate the respectve optmal thresholds. These optmal thresholds are also determned automatcally by the to-stage Otsu optmaton approach descrbed n Secton.. Once the segmentaton results for the three components (R, G and B) are formed, ther ont edge s calculated accordng to the follong formula: nt errest obect f Rs S Gs Bs (6) 0 background otherse Pxel ( x, s classfed as an obect f t s so classfed by at least one of ts three color components, n hch case S s set to. Otherse, t s classfed as a background pxel and S s set to 0. The maor steps of the proposed segmentaton method are depcted n the flochart shon n Fg.. 6

4 ISSN: ISO 900:008 Certfed Volume 3, Issue, May 04 Fg. Flochart of the proposed method. III. EXPERIMENTAL RESULTS AND DISCUSSION To evaluate the effcency and accuracy of the proposed method, the results are compared versus exstng methods, as descrbed earler. The effcency evaluatons for these dfferent methods are carred out on the Matlab softare 7.. For the accuracy evaluatons, the segmentaton senstvty method s used to determne the number of correctly classfed pxels. The evaluated color cells mages th 00 test mages and synthetc mages th 70 test mages ere used; some sample mages are shon n Fgure. The mages orgnally are stored n RGB format. Each of the prmtve color (red, green and blue) takes 8 bts and has the ntensty range from 0 to 55. (a) (b) (c) (d) Fg 3. Segmentaton results on a complex medcal mage ( classes, varous cells). (a) Orgnal mage (56x56x56) color medcal mage th RGB descrpton, (b) Red resultng mage by TSMO method, (c) Green resultng mage by TSMO method, (d) Blue resultng mage by TSMO method. The select thresholds are 97; 08 and 5, respectvely. Fg. Data set used n the experment. Telve ere selected for a comparson study. The patterns are numbered from through, startng at the upper left-hand corner. Fgure 3 shos a medcal mage provded by a cancer hosptal. Fgures 3(b), (c) and (d) sho the fnal segmentaton results obtaned from the TSOM appled to Red, Green and Blue components, respectvely. The selected thresholds are 97; 08 and 5, respectvely. Comparng Fgures 3(b), 3(c), and 3(d), one can see that the dfferent cells of the mage are much better segmented n (b) than those n (c) and (d). Also, the frst resultng mage contans some mssng features n one of the cells, hch do not exst n the other resultng mages. Ths shos the lack of nformaton hen usng only one nformaton source and may be explaned by the hgh degree of correlaton among of the three components of the RGB 7

5 ISSN: ISO 900:008 Certfed Volume 3, Issue, May 04 color space. Hence, t demonstrates the necessty of the mergng process. For purpose of comparson, e apply the proposed approach and some exstng approaches to the same-color mage segmentaton. The latter methods nclude those of Lm et al. [7], Ben Chaabane et al. [6] and Zhu et al. [5]. (a) (b) (c) (d) (e) (f) Fg 4. Comparson of the proposed segmentaton method th other exstng methods on a medcal mage, (a) orgnal mage th RGB representaton, (b) segmentaton based on TFCM method, (c) segmentaton based on TDS method, (d) segmentaton based on FCMDS method, (e) segmentaton based on the proposed method, and (f) reference segmented mage. Table. Segmentaton senstvty From TFCM, TDS, FCMDS and the proposed method for the Data set Shon n Fg. TFCM TDS FCMDS TSMO AND FUSION (PROPOSED METHOD) SENSITIVITY SEGMENTATION (%) Image Image Image Image Image Image Image Image Image Image Image Image The segmentaton results obtaned by TFCM [7], TDS [6] and FCMDS [5] methods are shon n Fgs. 4(b), (c) and (d), respectvely. Fg. 4(e) shos the segmentaton based on TSOM and Fuson (proposed method) and Fg. 4(f) represent the reference segmented mage. In fact, the cells are exactly and homogeneously segmented n Fg. 4(e), hch s not the case n Fg. 4(b), (c) and (d). To evaluate the performance of the proposed segmentaton algorthm, ts accuracy as recorded. Regardng the accuracy, Tables lsts the segmentaton senstvty of the dfferent methods for the data set used n the experment. The segmentaton senstvty [9] [30], s determned as follos: N pcc Sens(%) 00 N M (7) th: Sen (%), N pcc, N M denote respectvely the segmentaton senstvty (%), the number of correctly classfed pxels and the dmenson of the mage. 8

6 ISSN: ISO 900:008 Certfed Also, to evaluate the performance of the proposed color-segmentaton method, e tested many color synthetc mages. Volume 3, Issue, May 04 Fg. 5(a) gves the orgnal synthetc mage, Fg. 5(b) represent the N M synthetc mage here a salt and pepper nose of D densty as added. Ths affects approxmately ( D N M) pxels. (a) (b) (c) (d) (e) (f) Fg 5. Comparson of the proposed segmentaton method th other exstng methods on a medcal mage, (a) orgnal mage th RGB representaton, (b) color synthetc mage dsturbed th a salt and pepper nose, (c) segmentaton based on TFCM method, (d) segmentaton based on TDS method, (e) segmentaton based on FCMDS method, and (f) segmentaton based on the proposed method. Fgs. 5(c), (d), and (e) sho the segmentaton results obtaned by TFCM, TDS and FCMDS methods, respectvely. Fg. 5(f) shos the segmentaton based on proposed method. Comparng Fgs. 5(c), (d), (e), and (f), e observe that the to regons are correctly segmented n Fg. 5(f), shong the complementary nformaton provded by three prmtve colors and the effcacty of the TSMO method for determnng the mult-level thresholds of an mage. The performance of the proposed method s qute acceptable. It can be seen from Table that 3.6% 0.64% and 0.55% of pxels ere ncorrectly segmented for the TFCM, TDS and FCMDS methods, respectvely, but only 03.3% are ncorrectly segmented pxels by our proposed method. Comparng Fgs. 5(c),(d), and (e) th (f), e can see that the mage resultng from the proposed method s much clearer than the one resultng from the TFCM, TDS and FCMDS based methods. IV. CONCLUSION In ths paper, e have proposed a ne method to color mage segmentaton based on mult-level thresholdng technque and data fuson. In the frst phase, unform regons are dentfed n each prmtve color va a thresholdng operaton. Then, the combnaton rule s appled to fuse the three prmtve colors. Instead of consderng an elaborate and better desgned segmentaton model of bomedcal and textured mages, our technque rather explores the possble alternatve of combnng to segmentaton technques n order to get a good consstency segmentaton results. The results obtaned demonstrated the sgnfcant mproved performance n segmentaton. The proposed method can be useful for color mage segmentaton. V. ACKNOWLEDGMENT The authors ould lke to thank Dr. Khaled Ben Romdhane, from the Cancer Servce of Salah Aae Hosptal, Bab Saadoun, Tuns, for hs help and hs thoughtful comments. REFERENCES [] MJ Kon, YJ Han, IH Shn and HW Park. Herarchcal fuy segmentaton of bran MR mages. Int. J. Imag. Syst. Technol., 3(): 5-5, 003. [] Navon E, Mller O, A. Averbuch. Color mage segmentaton based on adaptve local thresholds. Image Vson Comput. 3(): [3] S. Ben Chaabane, M. Sayad, F. Fnaech, and E. Brassart, Dempster-Shafer evdence theory for mage segmentaton: applcaton n cells mages, Internatonal Journal of Sgnal Processng, vol. 5, no.,

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