Research Article Statistical Segmentation of Regions of Interest on a Mammographic Image

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1 Hndaw Publshng Corporaton EURASIP Journal on Advances n Sgnal Processng Volume 2007, Artcle ID 49482, 8 pages do: /2007/49482 Research Artcle Statstcal Segmentaton of Regons of Interest on a Mammographc Image Mouloud Adel, 1 Monque Rasgn, 1 Salah Bourennane, 1 and Valere Juhan 2 1 Insttut Fresnel, UMR-CNRS 6133, Equpe GSM, Domane Unverstare de Sant-Jérôme, Avenue Escadrlle Normande Nemen, Marselle Cedex 20, France 2 Servce de Radologe, Hôptal de la Tmone, 27, Boulevard Jean Mouln, Marselle Cedex 5, France Receved 16 November 2006; Revsed 11 Aprl 2007; Accepted 13 May 2007 Recommended by Jr Jan Ths paper deals wth segmentaton of breast anatomcal regons, pectoral muscle, fatty and fbroglandular regons, usng a Bayesan approach. Ths work s a part of a computer aded dagnoss project amng at evaluatng breast cancer rsk and ts assocaton wth characterstcs (densty, texture, etc.) of regons of nterest on dgtzed mammograms. Novelty n ths paper conssts n applyng and adaptng Markov random feld for detectng breast anatomcal regons on dgtzed mammograms whereas most of prevous works were focused on masses and mcrocalcfcatons. The developed method was tested on 50 dgtzed mammograms of the mn-mias database. Computer segmentaton s compared to manual one made by a radologst. A good agreement s obtaned on 68% of the mn-mias mammographc mage database used n ths study. Gven obtaned segmentaton results, the proposed method could be consdered as a satsfyng frst approach for segmentng regons of nterest n a breast. Copyrght 2007 Mouloud Adel et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. 1. INTRODUCTION Breast cancer s the leadng cause of death among all cancers for mddle-aged women. Currently t affects one woman out of eght and an ncrease of ths rate n the nearest future s expected. For the last 40 years, extensve means have been devoted to tacklng ths dsease but wthout the expected success. Efforts are now focused on early detecton and preventon. It s now known that screenng programs reduce the mortalty rate of about 30% for mddle-aged women. At present, mammography s the current standard for early breast cancer detecton. Mammographc mages are dffcult to analyse due to wde varaton of anatomcal patterns of each breast. One mportant task for radologsts when readng mammograms conssts n evaluatng the proporton of fatty and fbroglandular tssue wth respect to the whole breast. Mammographc densty s known to be an mportant ndcator of breast cancer rsk. There are four metrcs whch are used n practce to relate the mammographc parenchymal patterns and the rsk of breast cancer, namely: Wolfe s four parenchymal patterns [1], Boyd s sx class categores [2], BI-RADS [3], and Tabár s fve patterns [4]. The comparatve study of these four approaches on MIAS database [5] n partcular has been reported n [6]. In frst studes devoted to computer aded dagnoss and early detecton of breast cancer usng mage processng technques, analyss was performed on the whole mage wthout takng nto account dfferent densty, texture and anatomc regon levels, that radologsts use n ther nterpretaton [7]. Other methods have been proposed for anatomc regon segmentaton on dgtzed mammograms [8 12]. Aylward et al. [8] dvded a mammographc mage nto fve regons and then used geometrc and statstcal technques. Ferrar et al. [9] segmented the perpheral breast tssue wth an automatc thresholdng method based on Lloyd- Max quantfcaton. Matsubara et al. [10] segmented the fbroglandular tssue by means of horzontal and vertcal hstogram varance computaton followed by a local dscrmnant analyss. Zhou et al. [11] used a three-step segmentaton method to locate the fbroglandular edges whereas Ferrar et al. [12] segmented the fbroglandular dsc wth a statstcal method based on a Gaussan mxture modellng. Other segmentaton methods have been developed n the lterature but dd not focus on anatomcal regon segmentaton. Specfc problems such as perpheral breast tssue correcton [13, 14], npple automatc localzaton [15], breast densty quantfcaton [16], and ts assocaton wth the rsk of breast cancer [17 22] have been also nvestgated.

2 2 EURASIP Journal on Advances n Sgnal Processng However, most of classfcaton results n comparson wth expert assessment tend to be low. Masek et al. [23] used average hstograms of each orgnal mage densty class as a feature and reported an agreement of 62.42% whereas Zwggelaar et al. [24] and Muhmmah and Zwggelaar [25] obtan an agreement of 71.50% and 77.57% when usng statstcal grey-level hstogram modelng and classfcaton based on multresoluton hstogram nformaton, respectvely. Ths paper deals wth Bayesan segmentaton of breast anatomcal regons, namely: the pectoral muscle, the fbroglandular and fatty regons, on dgtzed mammograms. Novelty n ths paper s n applyng and adaptng a Markov random feld for detectng regon of dfferent tssues on mammographc dgtzed mages whereas most of prevous works were focused on abnormaltes (masses and mcrocalcfcatons). One of the objectves of ths study s to provde radologsts wth computer aded classfcaton tool for dscrmnatng anatomcal breast regons on a dgtzed mammograms and then for determnng more accurate proporton of fatty and fbroglandular tssue wth respect to whole breast. Moreover, ths study s a part of computer aded dagnoss project amng at studyng rsk of developng a breast cancer and ts assocaton wth the mammographc parenchymal patterns. After a bref ntroducton to Markov random felds (MRF) and Bayesan segmentaton n Secton 2, the method s developed and appled on dgtzed mammograms n Secton 3. Secton 4 shows obtaned results. Fnally, Secton 5 gves conclusons of the work. 2. MARKOV RANDOM FIELDS AND BAYESIAN SEGMENTATION 2.1. Image model and Markov random felds The man regons of nterest n a mammogram are shown n Fgure 1. They are the pectoral muscle, the fbroglandular and fatty tssues. Background outsde the breast s not consdered as a regon of nterest but t wll be taken nto account for the segmentaton process. In ths study, a statstcal segmentaton approach s adopted. It conssts n consderng the observed mammographc mage as a realzaton y of a random feld Y. Segmentng regons of nterest amounts to estmatng the label feld X (segmented verson where each pxel s assgned a label representng one of the regons descrbed above). Felds X and Y are defned on a rectangular lattce S of N pxels. To each spatal locaton (, j) oreachstes of S s assocated a random varable X (,j) or X s. Random varables X s take ther values n a set E ={0, 1, 2,..., M}, wherem s the number of classes. The set of all possble realzatons x of X s denoted by Ω X. By another way a neghborhood system V s of a pxel s S s defned as follows: V s ={t S} such that { } s/ V s, t V s = s V t, V = { V s, s S }. (1) Fatty tssue Fbroglandular tssue Background Pectoral muscle Fgure 1: Dgtzed mammogram wth ts regons of nterest. c 1 c 2 c 3 c 4 Fgure 2: Clques nduced by the eght-pont nearest-neghbour system. Gven a neghborhood system V s,aclquec S s ether a sngle ste (sngleton), or a subset of stes n whch each par of dstnct stes s the neghbor of each other. Clques wth only one pxel are denoted by c 1, those wth 2 pxels by c 2 and so on. For nstance Fgure 2 shows clques n an eght-nearest neghborhood system. Then X s a Markov random feld (MRF) relatvely to a neghbourhood system V f and only f (a) x Ω X, P(X = x) > 0 (b) s S, P ( X s = x s X t = x t, t S {s} ) = P ( ) X s = x s X s = x t, t V s, (2) where P(A/B) stands for the condtonal probablty of the event A gven the event B. Property (b) shows that probablty assocated wth random varable X s depends only on neghbours of ste s. Accordng to Hammersley-Clfford theorem [26], an MRF X relatvely to a neghborhood system V can equvalently be characterzed by a Gbbs dstrbuton, that s, the probablty P(X = x) can be expressed n the form P(X = x) = 1 ( Z exp ) U c (x), c C Z = ( exp ) U c (x), x Ω X c C where U c (x), known as clque potental functon, denotes statstcal dependence between pxels wthn a clque and thus depends only on the pxels that belong to ths clque c. C s the set of all possble clques c on S for the neghborhood (3)

3 Mouloud Adel et al. 3 system V under consderaton. c C U c (x)sanenergyfuncton. At last Z s a normalzng constant called the partton functon Bayesan segmentaton Image statstcal segmentaton schemes are generally based on optmzaton of some crteron. In our approach on mammoghraphc mages, the maxmum a posteror (MAP) estmate of the label feld X gven the observed mage y s used. Accordng to Bayes rule, we have P ( X = x Y = y ) = P(Y = y X = x)p(x = x), (4) P(Y = y) where P(X = x) s the pror probablty gven by (3) and P(Y = y) s a constant when y s a gven observed mage. The MAP estmate s found by maxmzng P(Y = y X = x)p(x = x). Probablty P(Y = y X = x) can be computed on the followng assumptons: (a) random varables Y s, s S, are condtonally ndependent gven the label feld X. In ths case: P ( Y = y X = x ) = P ( ) Y s = y s X s = x s (5) s S (b) condtonal probabltes P(Y s = y s X s = x s )satsfya gven model, for nstance a Gaussan one. Then t ensues from (3)and(5) that the a posteror probablty gven by (4) may be expressed as P ( X = x Y = y ) ( exp Ln ( P ( )) Y s = y s X s = x s s S ) (6) c C U c (x) Equaton (6) may be also wrtten n the form P ( X = x Y = y ) ( ( )) exp U X = x Y = y (7) wth U ( X = x Y = y ) = Ln ( P ( )) Y s = y s X s = x s s S + c C U c (x). Equaton (7) shows that the label feld X gven observed mage y s characterzed by a Gbbs dstrbuton and so that t s a Markov random feld too. The MAP estmate s equvalently obtaned by mnmzng a posteror energy U(X = x Y = y)(8). 3. SEGMENTATION OF MAMMOGRAPHIC IMAGES 3.1. Statstcal model used. (8) The above method s appled to dgtzed mammograms wth the followng assumptons: (a) regons to be segmented and classes are denoted by regon R and class,respectvely; (b) the condtonal probablty densty functon of random varable Y s, s SP(Y s = y s X s = x s ), s assumed to be Gaussan, that s, P ( ( ) 1 Y s = y s X s = x s = exp 2πσ ( ys μ ) 2 2σ 2 ), (9) where μ and σ 2 are the mean and the varance of class to whch x s s assocated wth. On the other hand, a relatvely smple type of dscrete-valued MRF called multlevel logstc (MLL) may be used for modelng regon formaton n mage segmentaton [27]. In our approach, the eght-nearest neghbour system (Fgure 2) s used, and because, clques contanng more than 2 pxels cause too much computatonal complexty, the only nonzero potentals of the MLL are assumed to be those correspondng to two-pxel clques. The potental functon U c (x) of a two-pxel clque c assocated wth a ste s s then defned by [28] { +βc f x t = x s s, t c, U c (x) = (10) β c otherwse, where the parameter β c s the same for every two-pxel clque, that s to say β c = β. The value of β nfluences the szes and shapes of the resultng regons: as β ncreases larger clusters are favored [29]. So thea posteror energy U (8) becomes U ( X = x Y = y ) = s S + (( ) 2 ) (ys μ xs +Ln ( ) ) 2πσ xs 2σ 2 x s c C 2 U c (x), (11) where μ xs and σ 2 x s are the mean and the varance of the class to whch x s s assocated wth and C 2 s the set of all two-pxel clques Intalzaton and parameters estmaton Mammographc mage segmentaton scheme s obtaned from three man steps: (a) ntalzaton of label feld X wth a choce of class number M (b) estmate of model parameters and label feld smulaton usng optmzaton methods for mnmzng the aposteror energy U (11); (c) stoppng condton. The two last stages (b) and (c) are teratve processes. In ths work, three ntalzatons are tested as follows. () Equal probablty quantzng [30] whch splts the grey level range of mage y nto several classes usng the probablty cumulatve functon of the mage accordng to an teratve process. Ths ntalzaton s denoted INIT A. () Unform quantzng of the grey-level range of mage y. Ths ntalzaton s denoted by INIT B.

4 4 EURASIP Journal on Advances n Sgnal Processng () An dentcal number of pxels per class. Ths ntalzaton s denoted by INIT C. For each ntalzaton, the number of classes was lmted to fve. Computaton of the a posteror U energy (11) needs mean and varance estmates for each class. These parameters are supposed unknown but are fxed. They were estmated from the emprcal Bayesan method accordng to the followng formulas: μ (k) = 1 N (k) ( σ 2 ) (k) = 1 N (k) s R (k) s R (k) y s, ( ys μ (k) ) 2, (12) ICM and SA algorthms Intalzaton of label feld X k = 0 Estmaton of μ (k) et σ (k) Smulaton of x (k) where R stands for regon whose pxels belong to class, N s the number of pxels n R and k s used to specfy the current teraton. Among several algorthms [31]used foru mnmzaton, two algorthms are proposed to fnd a reasonably good labelng: smulated annealng (SA) [32] because t s probabely one of the best known, and the Iterated condtonal modes (ICM) [33] whch s a fast determnstc verson of SA and provdes good segmentaton f a good ntal segmentaton s avalable. Smulated annealng s an algorthm dedcated to searchng the optmal confguraton of a Gbbs feld. For each ste s, a label λ s chosen at random n the label set E and the followng energy varaton s evaluated: ( ) ( ΔU s = U s Xs = λ V s (k) U s Xs = x s (k) ) V s (k), (13) where U s s computed from (11) by consderng only the ste s and ts neghborhood V s, x s (k) and V s (k) are the label and neghborhood of ste s at teraton k, respectvely.the β value, β = 50 used for clque potental U c (x) evaluaton was chosen as the one yeldng the best vsual segmentaton on several prelmnary tests. Label of ste s s then updated wth label λ f ΔU s 0. Otherwse (ΔU s < 0), label of ste s takes the λ value or keeps ts prevous value accordng to probabltes p and 1 p respectvely (p = exp( ΔU s )). ICM s also an teratve algorthm whch ams at mnmzng U ((11)). For each ste s ths method computes the local condtonal probabltes P ( X s = λ X r = x r (k) ), r V s (14) for every label λ of label set E. Labelofstes s then updated wth the value whch maxmzes these probabltes, that s, at teraton k +1: x (k+1) s = Arg max P ( X s = λ X r = x (k) ) r, r V s. (15) λ Ths algorthm s faster than the SA but needs a good ntalzaton for convergng. End False Rate > 0.5% Ture k = k +1 Fgure 3: Mammographc mage segmentaton scheme. Last stage n the segmentaton process concerns the stoppng condton. Ths condton s based on the rate of pxels changng ther label between two teratons, that s rate = wth δ ( x (k+1) s s S ( ( 1 δ x (k+1) s N, x s (k) )),, x s (k) ) 1 fx s (k+1) = 0 else, = x (k) s, (16) where k stands for the current teraton, N s the number of pxels n mage y. When ths rate s less than a gven threshold, the segmentaton process stops. For ths study we felt a thresholdng of 0.5% was small enough. The segmentaton scheme s summarzed n Fgure RESULTS AND DISCUSSION Ffty dgtzed mammograms of the mn-mammographc Image Analyss Socety (MIAS) database wth dfferent anatomcal patterns were chosen wth the help of radologsts, for evaluatng the proposed method. Images of mn-mias are those of MIAS database [5] (mammograms dgtzed at 50 μm/pxel) reduced to 200 μm/pxel and clpped/padded so that every mage s pxels. Ths database s gven wth a classfcaton nto three classes: fatty (F), glandular (G), and dense (D) breasts. Only normal cases were chosen for ths study and the proportons wthn each class were 16, 18, and 16 for fatty, glandular, and dense, respectvely. Radologsts were asked to defne manually the fbroglandular and the fatty regons as well as the pectoral

5 Mouloud Adel et al (%) (a) (b) Score Fgure 4: Ratng of segmentaton results. 3 muscle on each mage. Ths work was done by means of a computer montor wth IDL/ENVI software. Evaluaton of segmentaton results concerns only fbroglandular tssue. Indeed the rato of fbroglandular regon n comparson wth the whole breast regon s of mportance for radologsts when nterpretng mammograms. In partcular, t has been notced clncally that majorty of breast cancers were assocated wth glandular rather than fatty tssues [34]. For each mammographc mage, a qualty parameter ρ and a protocol [12] were ntroduced for quantfyng segmentaton results. Parameter ρ was defned as follows: ρ = A seg A manu A seg A manu, (17) where A seg s the set of pxels of the fbroglandular regon obtaned by computer segmentaton and A manu s the set of pxels of the same regon by manual segmentaton. A s the number of elements of set A. A score was then assocated wth each result accordng to the descrpton gven n Table 1. Actually, fnal results of teratve segmentaton algorthms used n ths work depend manly on the ntalzaton step. In theory, smulated annealng (SA) makes t possble to reach a global mnmum whatever the ntalzaton condtons are, but ths goal s not always obtaned and the SA converges often to a local mnmum. In the case of ICM, ntalzaton must be close to fnal soluton to assure a good segmentaton. Except for some few cases, Int A (equal probablty quantzng) s the ntalzaton method whch gave the best segmentaton results for ICM and SA. Segmentatons obtaned by both optmzaton methods (SA and ICM) were smlar wth nevertheless hgher number of teratons for smulated annealng (SA). Results ratngs related to protocol (c) (d) Fgure 5: Segmentaton results: (a) orgnal mammogram mdb041; (b) radologst s manual segmentaton; (c) obtaned segmentaton wth ntalzaton INIT A and ICM algorthm (10 teratons); (d) obtaned segmentaton compared to radologst s manual segmentaton (ρ = 0.77). Table 1: Rankng optons for evaluaton of segmentaton results. Score = 3 f 60% ρ 100% Score = 2 f 20% ρ 60% Score = 1fρ 20% Good segmentaton Average segmentaton Faled segmentaton gven n Table 1 are shown n Fgure 4. Ths table summarzes the best results obtaned when combnng Intalzaton methods (INIT A, INIT B,s and INIT C) and optmzaton algorthms (SA and ICM). Approxmately 68% of the cases (34 mammograms) were rated as good segmentaton (score 3) (agreement between manual and computer segmentatons hgher than 60%). These mammograms are those assocated wth D (dense) and G (glandular) classes where the fbroglandular tssue consttuted a compact regon and, n most of the cases separated from the pectoral muscle (Fgure 5). For medum scores (score 2) (agreement between manual and computer segmentatons s between 20% and 60%), the segmentaton method underestmated the fbroglandular regons. On these mammograms fbroglandular regons were surrounded by fbrous structure and ther edges were not very sharp. Results obtaned on such mammograms are shown n Fgure 6. Among the remanng cases (5 mammograms) lowest scores (score 1) (agreement between manual and computer segmentaton lower than 20%) were obtaned for breasts wth a very small fbroglandular regon, whch

6 6 EURASIP Journal on Advances n Sgnal Processng could be nterpreted as fatty breasts by radologsts. Moreover, fatty tssue was observed nsde the fbroglandular regon of these mammograms. For these cases the segmentaton method underestmated the fbroglandular regons (Fgure 7). 5. CONCLUSION (a) (b) In ths paper, a Bayesan segmentaton approach wth a Markov random feld model s presented and appled to regons of nterest on dgtzed mammographc mages. Bayesan method was used for estmatng model parameters as well as the MAP as optmzaton crteron. The obtaned results are promsng and lead us to consder ths method as a satsfyng approach for segmentng breast regons of nterest. An evaluaton of ths method on a large mage base s needed now. Lkewse characterzaton of the segmented regons by means of some parameters n order to correlate them wth false negatves breast cancer wll consttute a future step of ths work. (c) (d) Fgure 6: Segmentaton results: (a) orgnal mammogram mdb003; (b) radologst s manual segmentaton; (c) obtaned segmentaton wth ntalzaton INIT A and SA algorthm (80 teratons); (d) obtaned segmentaton compared to radologst s manual segmentaton (ρ = 0.58). (a) (c) (d) Fgure 7: Segmentaton results: (a) orgnal mammogram mdb009; (b) radologst s manual segmentaton; (c) obtaned segmentaton wth ntalzaton INIT A and SA algorthm (78 teratons); (d) obtaned segmentaton compared to radologst s manual segmentaton (ρ = 0.185). (b) REFERENCES [1] J. N. Wolfe, Rsk for breast cancer development determned by mammographc parenchymal pattern, Cancer, vol. 37, no. 5, pp , [2] N. F. Boyd, J. W. Byng, R. A. Jong, et al., Quanttatve classfcaton of mammographc denstes and breast cancer rsk: results from the Canadan Natonal Breast Screenng study, Journal of the Natonal Cancer Insttute, vol. 87, no. 9, pp , [3] ACR, Breast Imagng Reportng and Data System (BI-RADS), Amercan College of Radology, Reston, Va, USA, 2nd edton, [4] L. Tabár,T.Tot,andP.B.Dean,Breast Cancer: The Art and Scence of Early Detecton wth Mammography, Georg Theme, Stuttgart, Germany, [5] J. Sucklng, J. Parker, D. R. Dance, et al., The mammographc mage analyss socety dgtal mammogram database, n Proceedngs of the 2nd Internatonal Workshop on Dgtal Mammography, vol of Exerpta Medca, Internatonal Congress Seres, pp , York, England, July [6] I. Muhmmah, A. Olver, E. R. E. Denton, J. Pont, E. Pérez, and R. Zwggelaar, Comparson between Wolfe, Boyd, BI-RADS and Tabár based mammographc rsk assessment, n Proceedngs of the 8th Internatonal Workshop on Dgtal Mammography (IWDM 06), vol of Lecture Notes n Computer Scence, pp , Manchester, UK, June [7] R.M.Rangayyan,Bomedcal Image Analyss, CRC Press, Boca Raton, Fla, USA, [8] S. R. Aylward, B. M. Hemmnger, and E. D. Psano, Mxture modelng for dgtal mammogram dsplay and analyss, n Proceedngs of the 4th Internatonal Workshop on Dgtal Mammography (IWDM 98), pp , Njmegen, The Netherlands, June [9] R.J.Ferrar,R.M.Ragayyan,J.E.L.Desautels,andA.F.Frere, Segmentaton of mammograms: dentfcaton of the skn-ar

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Boggs, Stes of occurrence of malgnances n mammograms, n Proceedngs of the 4th Internatonal Workshop on Dgtal Mammography (IWDM 98), pp , Njmegen, The Netherlands, June Mouloud Adel receved hs Engneerng degree n electrcal engneerng n 1990 from the Ecole Natonale Supéreure d Electrcté et de Mécanque (ENSEM) of Nancy, France, and hs Ph.D. degree from the Insttut Natonal Polytechnque de Lorrane (INPL) of Nancy, n He s Professor Assstant at the Insttut Unverstare de Technologe de Marselle and hs research nterests nclude mage and sgnal processng for ndustral nspecton and computer aded detecton and dagnoss for medcal applcatons. Monque Rasgn receved the Doctorate degree n physcs from the Unversty of Marselle, France, n Snce 2006, she s an Emertus Professor at the Unversty of Ax-Marselle III. After numerous works manly devoted to surface roughness, order, dsorder, and percolaton through graph theory, her research nterest s orented, for some years now, towards medcal mage processng (mammograms and retnal angograms).

8 8 EURASIP Journal on Advances n Sgnal Processng Salah Bourennane receved hs Ph.D. degree from Insttut Natonal Polytechnque de Grenoble, France, n 1990 n sgnal processng. Currently, he s a full Professor at the Ecole Centrale de Marselle, France. Hs research nterests are n statstcal sgnal processng, array processng, mage processng, tensor sgnal processng, and performances analyss. Valere Juhan s a Radologst snce She leads the Department of Women s Imagng at the Unversty Hosptal la Tmone n Marselle, France. The man actvty of ths department s screenng, dagnoss, and follow up of breast cancer, usng mammography, breast US, and percutaneous magng-guded core bopsy. Valere Juhan s research nterests nclude new technologes of breast exploraton.