Research Article Segmentation of Bone with Region Based Active Contour Model in PD Weighted MR Images of Shoulder

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1 Computatonal and Mathematcal Methods n Medcne Volume 2015, Artcle ID , 13 pages Research Artcle Segmentaton of Bone wth Regon Based Actve Contour Model n PD Weghted MR Images of Shoulder Aysun Sezer, 1 Hasan Basr Sezer, 2 and Songul Albayrak 1 1 Computer Engneerng Department, Yldz Techncal Unversty, Istanbul, Turkey 2 Orthopaedc and Traumatology Clnc, Ssl Hamdye Etfal Tranng and Research Hosptal, Istanbul, Turkey Correspondence should be addressed to Aysun Sezer; sezeraysun@gmal.com Receved 14 February 2015; Revsed 6 Aprl 2015; Accepted 13 Aprl 2015 Academc Edtor: Chuangyn Dang Copyrght 2015 Aysun Sezer 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. Proton densty (PD) weghted MR mages present nhomogenety problem, low sgnal to nose rato (SNR) and cannot defne bone borders clearly. Segmentaton of PD weghted mages s hampered wth these propertes of PD weghted mages whch even lmt the vsual nspecton. The purpose of ths study s to determne the effectveness of segmentaton of humeral head from axal PD MR mages wth actve contour wthout edge (ACWE) model. We ncluded 219 mages from our orgnal data set. We extended the use of speckle reducng ansotropc dffuson (SRAD) n PD MR mages by estmaton of standard devaton of nose (SDN) from ROI. To overcome the problem of ntalzaton of the ntal contour of these regon based methods, the locaton of the ntal contour was automatcally determned wth use of crcular Hough transform. For comparson, sgned pressure force (SPF), fuzzy C-means, and Gaussan mxture models were appled and segmentaton results of all four methods were also compared wth the manual segmentaton results of an expert. Expermental results on our own database show promsng results. Ths s the frst study n the lterature to segment normal and pathologcal humeral heads from PD weghted MR mages. 1. Introducton Shoulder nstablty consttutes an mportant mass of the shoulder surgery n orthopedcs. Shoulder jont has a very wde range of moton and t s susceptble to nstablty because of less congruent bony relatons. Shoulder nstablty s a condton n whch relaton between glenod and humeral head s lost n a poston or under physologcal jont reacton forces. Instablty may cause jont dysfuncton and may result n dslocaton of the jont whch may cause further soft tssue andbonedamagemakngdsruptonofanatomcalstructures worse. Instablty of shoulder jont s a result of dsrupton n bony structures or soft tssues. MRI s wdely used to detect shoulder pathologes because t s able to demonstrate both bony and soft tssue pathologeswhchsessentaltomakeaccuratedagnoss.the humeral head beng part of the bony structure of the shoulder jont plays an mportant role n shoulder nstablty. Segmentaton of bone has prmary mportance n order to defne the anatomcal borders and locaton of the lesons. Dfferent magng modaltes are able to detect bony structures. Computerzed Tomography (CT) and T1 weghted mageswerestudedtobesuccessfulnbonesegmentaton n the lterature. Pérez et al. used a hybrd, statstcal, and geometrcal model based on Chan-Vese to segment bone and soft tssues n T1 coronal shoulder MR mages. They reported that ther model provded correct classfcaton of bone but poor classfcaton of soft tssues [1]. Nguyen et al. studed sagttal T1 weghted shoulder mages. They used an ntegrated regon based and gradent based supervsed method to segment humeral head. Ther average success rate measured over entre database was 96.32% [2]. Chaou et al. segmented bony structures by usng a recognton based segmentaton method from CT mages wth 96% success rate [3]. There s no sngle modalty whch can demonstrate bony edges and bone edema wth hgh performance at the same tme. CT and T1 weghted MR mages are more successful n demonstratng bone edges. Transton between soft tssues and bone s sharper n CT and T1 weghted MRI. However

2 2 Computatonal and Mathematcal Methods n Medcne these modaltes cannot supply suffcent nformaton about bone edema. Axal PD weghted MRI of shoulder s the mostly used sequence beng able to present both bony and soft tssue components of nstablty synchronously. PD weghted MRI s also able to demonstrate bony edema whch s a sgn of the magntude and locaton of bone trauma and a common source of pan. However there s a very smooth transton zone between bone and soft tssues, makng segmentaton of bone edges more dffcult. Another parameter that aggravates the segmentaton process s nose. PD weghted MR mages have poorer SNR than T1 weghted MR and CT mages. Many researchers and numerous applcatons n medcal mages have been devoted to use nonlnear dffuson flters such as ansotropc dffuson (AD) and speckle reducng ansotropc dffuson (SRAD) to reduce nose whle preservng mage edges [4 6]. AD method has been appled to reduce nose n CT [7] MR[8] and ultrasound mages wth good results. AD method encourages dffuson n the homogeneous regon whle nhbtng dffuson at edges. However t s not drectonal and leaves some nose n the neghborhood of the edges. SRAD method s drectonal that t nhbts smoothng n drectons perpendcular to edges and encourages smoothng parallel to the edges not leavng nose n the vcnty of edges. SRAD was ntroduced as a useful technque to reduce speckle nose n ultrasound and satellte mages successfully [4, 6]. Not only speckle nose but also other types of nose can be reducedbysradncasethestandarddevatonofnose (SDN) s estmated [9]. There s a wde varety of methods proposed to segment background and the object pxels among whch the actve contour model (ACM) was one of the most successful methods. The basc dea of the ACM s to evolve a curve under some constrants to extract the desred object based on energy mnmzng method. Exstng AC methods for mage segmentaton can be categorzed nto two classes: edge based models [10, 11] and regonbased models[12 15]. Edge based models utlze mage gradent as an addtonal constrant to construct force to drect the moton of the contour. These models usually have edge based stoppng constrant to ntercept the contour evoluton on the object boundares [10]. Hgh nose and weak or defcent borders of humeralheadnpdmagesmakeedgebasedmethodsless sutable. Regon based actve contour methods have many advantages over the edge based methods. Frst the regon based methods do not depend on the mage gradent and utlze mage statstcal nformaton nsde and outsde the contour to control evoluton. They can satsfactorly segment mages wth weak edges and wthout edges. Second, the segmentaton result s less dependent on the locaton of the ntal contour and they can effectvely detect the exteror and nteror boundares smultaneously. Chan-Vese model s one of the most popular regon based models whch s based on a smplfed Mumford-Shah segmentaton technques [12]. Chan-Vese model has been successfully appled to bnary phase segmentaton wth assumpton that each mage regon s statstcally homogeneous. Ths assumpton s a lmtaton of ts applcaton n nhomogeneous regons. In order to solve ths lmtaton of Chan-Vese model, Vese and Chan [14] and Tsa et al. [15] proposed pecewse smooth (PS) models whch can deal wth part of the problem [12]. However, PS models have hgh computatonal costs. Moreover segmentaton result s stll dependent on the ntal contour placement. L at al. proposed a local bnary fttng (LBF) model to solve the problem caused by ntensty nhomogenety [16]. LBF model uses local statstcal nformaton, especally the localntenstymean,naregonbasedactvecontourmodel. However the ntensty nhomogenety problem cannot be solved wth usng partcular unform dstrbuton because ntensty nonunformty n a desred object can show varatons n dfferent postons. Use of more than one knd of specfc dstrbuton s needed to descrbe the varaton of ntensty nonunformty n each regon. To solve ths problem N et al. proposed control of evoluton of contour by usng the hstogram of the ntensty; however they experenced lmtatons n segmentaton of natural mages [17, 18]. Ge et al. defned a new regularzaton term wth the ansotropc dffuson process based on the structure tensor and the dualty theory. They computed the statstcal nformaton of magntude of gradent to approxmate the varaton of the ntensty by the ansotropc dffuson process [13]. Hybrd regon based actve contour (HRBAC) models were proposed recently to segment mages wth ntensty nhomogenety [19, 20]. HRBAC models, lke SPF model [21] and geodesc ntensty fttng model [22], combne merts of the tradtonal geodesc actve contour (GAC) model, whch s an edge based actve contour model, and regon based Chan-Vese model. Despte all of these models whch were ntended to solve the ntensty nhomogenety problem t s yet to be solved. The common problem of all these methods s senstvty to ntalzaton. The problem of ntal contour was studed by Wang et al. They proposed to combne the local and global ntensty nformaton [23]. The lmtaton of the study was the devaton of the real object boundary when the ntal contour was close to the object boundares. Lu and Peng proposed to use degraded Chan-Vese model, the segmentaton result of whch s taken as ntal contour of proposed local regon based Chan-Vese model. Ther model can segment mages wth ntensty nhomogenety; although ths method s computatonally effcent, the success rates are stll senstve to the ntal contour [24]. In ths paper we studed humeral head (bone) segmentaton n axal PD MRI of shoulder. In the frst step we appled SRAD method and homomorphc flter. SRAD s very senstve to the estmaton of SDN and normally calculated n a homogenous area [4, 9]. We estmated ths parameter from area of nterest where there s more tssue ntensty than background to reduce Rcan nose. By ths way we extended use of SRAD n PD MR mages. Nose reducton wth SRAD makes a good contrbuton to the correcton of nhomogenety because the mage nose s a factor that affects quantty of nhomogenety. But nose reducton wth SRAD alone s not enough for satsfactory correcton of nhomogenety n the mage. Thus we supported SRAD method wth homomorphc flter. Ths flter separates low and hgh frequency components n an mage and enhances changes n hgh frequency component and suppresses changes n low

3 Computatonal and Mathematcal Methods n Medcne 3 (a) (b) (c) Fgure 1: PD weghted axal MR mages of left shoulder wth (a) normal humeral head, (b) edematous humeral head, and (c) humeral head wth Hll-Sachs leson. frequency component to obtan more homogenous mages. Moreover, the homomorphc flter s n ts essences a lnear flter and s quntessentally used for nose reducton or sgnal feature extracton f the sgnal (PD MR mage) s dstorted by addtve nose. Regon based actve contour models have ablty to segment very weak edges of humeral head but they are senstve to the locaton of ntal crcle. In the second step ths problem was handled wth the automatc detecton of the ntal contour n each shoulder mage. We used crcular Hough transform to automatcally detect the locaton of the humeral head from PD weghted MR mages. Result parameters obtaned by crcular Hough transform were used todentfytheroiandtheplaceofntalcontour. In the last step we appled ACWE method [12]tosegment humeralheadntheroi.wecomparedresultsofacwe wth SPF and clusterng methods of fuzzy C-means (FCM) and Gaussan mxture model (GMM). ACWE has a global segmentaton property and provdes to segment all objects n the ROI. SPF has a local property whch provdes to only extract a desred object by settng the ntal contour surroundng or ntersectng the humeral head boundares [21]. All segmentaton results were compared wth the manual segmentaton results of an orthopedc specalst. Note that some part of results of the segmentaton of normal humeral heads n ths paper was reported n our recent conference paper [25]. Ths paper s organzed as follows. In Secton 2 descrpton of materals and methods, steps of preprocessng, segmentaton, and postprocessng methods are descrbed. Expermental results and evaluaton are gven n Secton 3, followedbysomedscussonnsecton 4. Ths paper s summarzed n Secton Materal and Methods MRI s a standard of protocol n evaluaton of the shoulder nstablty. We used 2D PD weghted MR mages of shoulder whch can successfully demonstrate the pathologes that cause shoulder nstablty. MRI has the capacty to present 3D mages; however pathologcal changes n shoulder nstablty may be hdden n 3D mages. 3D MRI has no advantage over 2D MRI n demonstratng the whole pathology. The humeral head s the part of the bony structure of the shoulder jont. The pathologes of humeral head n shoulder nstablty can be categorzed as bone edema and dsrupton of bone borders (e.g., Hll-Sachs leson). In ths study we segmented normal humeral heads, humeral heads wth bone edema, and Hll-Sachs leson from 2D axal PD MR mages. A normal humeral head mage of left shoulder s shown n Fgure 1(a). Humeral head wth edema s demonstrated n Fgure 1(b). The amount and the locaton of bone edema change accordng to patent. Hll-Sachs leson occurs when the humeral head has a compresson fracture where the dstrbuton of ntensty values ncreases and shape of humeral head changes (Fgure1(c)). We ncluded shoulder MR mages of 219 patents who have been admtted to Ssl Hamdye Etfal Tranng and Research Hosptal. We used 1.5 Tesla PD weghted MR mages. The sze of the DICOM mage was pxels. The slce thckness was 4 mllmeters. We grouped patents accordng to appearance of humeral head as normal, edematous,andhll-sachsdeformty.thenumbersofthepatents were 81 n normal group, 100 n edematous group, and 38 n Hll-Sachs group. Segmentaton of humeral head from PD weghted MR mages was not studed n lterature and there was no avalable database. The orgnal data set was collected by authors. Segmentaton process n ths study may be categorzed nto three steps as preprocessng, segmentaton, and postprocessng (Fgure2) Steps of Image Preprocessng Nose Reducton Usng Speckle Reducng Ansotropc Dffuson (SRAD). MR mages can be categorzed nto two classes: hgh resoluton wth hgh SNR and hgh resoluton wth low SNR. Hgh resoluton wth hgh SNR s a consequence of ncreased acquston tme of MRI whch s not feasble due to the patent comfort. Nose reducton n PD weghted MR mages has an mportant effect on segmentaton success as much as correcton of ntensty nhomogenety.

4 4 Computatonal and Mathematcal Methods n Medcne SRAD ACWE method Morphologcal operatons Database Homomorphc flter Determnaton of ROI SPF method FCM method GMM method Anatomcal knowledge Connected component labellng Result Preprocessng step Segmentaton step Postprocessng step Fgure 2: The flow chart of the segmentaton steps by ACWE and the comparson methods of SPF, FCM, and GMM. (a) (b) (c) (d) Fgure 3: (a) Orgnal PD weghted MRI, (b) mage obtaned after SRAD method, (c) result of the homomorphc flter, and (d) result obtaned after usng SRAD method and homomorphc flter. Owng to the fact that the dstrbuton of the nose n PD mages s not Gaussan, nose problem cannot be solved suffcently by tradtonal nose reducton methods such as Gaussan flter and medan flter [8]. PD weghted MR mages have a very smooth transton zone between soft tssues and bone (Fgure 3(a)). There s need of a method whch decreases nose wthout deteroratng the mportant anatomcal and pathologcal detals of humeral head. AD method was proved to produce successful results n medcal magng area; however AD method leaves some remanng nose n the vcnty of edges after flterng [4, 7, 8]. We used SRAD whch s a drectonal method that overcomes ths problem by nhbtng smoothng parallel to edge and enhancng smoothng n perpendcular drecton (Fgure 3(b)). SRAD method demonstrates good speckle nose suppresson n ultrasound, satellte mages, and MRI. The weak sde of SRAD method s ts senstvty to the SDN. Through the accurate estmaton of SDN SRAD method can be appled for all knds of nose not only for speckle nose [9]. SRAD method s a combnaton of AD and speckle reducng Lee flter. The partal dfferental equaton (PDE) of AD s gven as follows n contnuous doman, where I 0 s the ntal mage, c( ) s the dffuson coeffcent, s gradent operator, and dv s dvergence operator: I = dv [c ( I ) I], (1) t I (t =0) =I 0. (2) We used SRAD to decrease nose n the PD weghted MR mages. Gven an ntensty mage I 0 (x, y) havng fnte power andnozerovaluesoverthemagesupportdomanω, the output mage I(x, y; t) s evolved accordng to the followng format of the PDE of SRAD [4], where I(x, y; t) s the ntensty mage estmated at poston x, y at the dffuson tme t; Ω denotes the border of Ω; n s the outher normal to the Ω: ( I (x, y; t) = dv [c (q) I (x, y; t)], (3) t I(x,y;0)=I 0 (x, y), I (x, y; t) ) =0. n Ω SRAD uses the format of the PDE of AD. Selecton of dffuson coeffcent s the man dfference between AD and SRAD methods ((1) and (3)): c(q) (4) 1 (5) =[ 1+[q 2 (x, y; t) q0 2 (t)]/[q2 0 (t) (1 + q2 0 (t))]]. SRAD nherts nstantaneous coeffcent of varaton (ICOV) andspecklescalefunctonprototypeofleeflter.icov serves as the edge detector. ICOV s a functon of the mage

5 Computatonal and Mathematcal Methods n Medcne 5 normalzed gradent magntude I/I and normalzed Laplacan 2 I/I defned n relaton wth the adaptve coeffcent of theleeflter [4] expressed as follows: q(x,y;t)= (1/2)( I /I)2 (1/16) ( 2 I/I) 2 [1 + (1/4) ( 2 I/I) 2 ]. (6) Speckle scale functon q 0 (t) controls amount of smoothng appledtothemagebysradandcomputedfromahomogeneous regon of fully developed speckle by var [z (t)] q 0 (t) =. (7) z (t) Butwehavecalculatedspecklescalefunctonontheforeground where the humeral head s domnant than other tssues. Ths way, we assure that the background has no effect over the estmaton of Rcan nose present n MRI. The var[z(t)] and z(t) are ntensty varance and mean over humeral head regon at tme t Homomorphc Flter. Despteprogressnthescanner technology, MR mages stll have mperfectons lke low SNR, ntensty nhomogenety due to the bas feld, and other artfacts. Intensty nhomogenety adversely affects vsual nspecton and segmentaton. Numerous methods have been ntroduced to elmnate ntensty nhomogenety n MR mages [26]. Homomorphc flterng assumes that ntensty nhomogenety s a low frequency artfact that can be separated from hgh frequency sgnal by low pass flterng. Pérez et al. used homomorphc flter n the mage preprocessng step to segment bone and soft tssues on T1 weghted MR mages wth good results [1]. Accordng to homomorphc flterng model, each pxel value f(x, y) can be expressed as the product of a low frequency llumnaton component (x, y) and a hgh frequency reflectance component r(x, y) as follows: f (x, y) = (x, y) r (x, y). (8) The homomorphc system for mage enhancement s based on the separaton of ndependent low and hgh frequency components. To facltate ther separate processng by takng logarthmc transform of (8),thus g(x, y) = ln (f (x, y)) = ln [ (x, y) r (x, y)] (9) = ln ( (x, y)) + ln (r (x, y)). Fourer transform s appled to (9),whereG(u, V), I(u, V),and R(u, V) represent the Fourer transform of g(x, y),ln((x, y)), and ln(r(x, y)), respectvely. Consder G (u, V) =I(u, V) +R(u, V). (10) Applyng a hgh pass flter H(u, V) n the frequency doman to enhance changes n reflectance and suppressng changes n llumnaton are as follows: G (u, V) =I(u, V) H (u, V) +R(u, V) H (u, V). (11) We used a Gaussan hgh pass flter nstead of Butterworth hgh pass flter normally used n homomorphc flterng to remove the llumnaton component. Inverse Fourer transform s appled to (11) to obtan g(u, V) whch represent the nverse Fourer transform of G(u, V): g (u, V) = (u, V) + r (u, V). (12) Exponental form exp( g(u, V)) s used to reverse logarthmc effecttoobtanthemageafterenhancement. Our strategy for correcton of nhomogenety s to use the homomorphc flter to elmnate ntensty nhomogenety n the preprocessng step just after nose reducton wth SRAD method (Fgures 3(c) and 3(d)).We combnedadvantages of SRAD and homomorphc flter before applcaton of regon based actve contour models Determnaton of Regon of Interest (ROI). The Hough transform s wdely used n pattern recognton and computer vson for the detecton of regular curves. Humeral head has a round cross-sectonal shape n axal PD MR mages. Crcular Hough transform has an ablty to detect crcular shapes based on parametrc equaton of crcle [27]. Ths method provdes detecton of humeral head for each PD weghted MR mage wthout affectng mage nose (Fgure4). Ths method s also very tolerant to gaps n feature boundary descrptons; thus t can also fnd defectve shape of humeral head resultng from the edema and deformty. Fgure 4(b) shows detecton of humeral head from a PD weghted left shoulder MR mage. The shape of the humeral head s not exactly a crcle; thus some parts of the area of nterest may reman out of the crcle defned by crcular Hough transform. To nvolve whole humeral head n ROI we enlarged radus of crcle found by crcular Hough transform. Common problem of regon based actve contour models s dependence of segmentaton success on the ntal contour placement [23, 24]. We acheved ths problem by automatcally determnng locaton of ntal contour n the ROI Segmentaton Methods Actve Contours wthout Edges (ACWE) Model. ACWE, known also as Chan-Vese model, s a regon based actve contour model and has successful applcatons n many papers and felds [1, 7, 12]. ACWE model utlzes statstcal nformaton nsde and outsde the contour nstead of mage gradent. An evolvng curve C = ω,wthω Ω an open subset, nsde (C) denotes the regon ω whch represents the foreground pxels and outsde (C) denotes the regon Ω\ω whch represents the background pxels. Chan-Vese model s formulated by mnmzng the followng energy functon wth the level set formulaton [12], (14): F(c 1,c 2,C) =λ 1 u 0 (x, y) c 1 2 H(φ(x,y))dxdy Ω +λ 2 u 0 (x, y) c 2 2 (1 H (φ (x, y))) dx dy. Ω (13)

6 6 Computatonal and Mathematcal Methods n Medcne (a) (b) Fgure 4: (a) Orgnal MR mage of left shoulder and (b) detecton of humeral head by usng the crcular Hough transform. Wth the level set method we assume C = ω = {(x, y) Ω : φ (x, y) = 0}, ω = {(x, y) Ω : φ (x, y) > 0}, Ω\ω = {(x, y) Ω : φ (x, y) < 0}. (14) The mage u 0 sassumedtobecomposedoftworegons of constant ntenstes: c 1 (the average ntenstes nsde the contour) and c 2 (the average ntenstes outsde the contour). The constants c 1 and c 2 canbefoundbymnmzng(13): c 1 (φ) = Ω u 0H(φ(x,y))dxdy Ω H(φ(x,y))dxdy, (15) c 2 (φ) = Ω u 0 (1 H (φ (x, y))) dx dy Ω (1 H (φ (x, y))) dx dy. (16) Usng the Heavsde functon H(φ) and the Drac functon δ(φ) defned by Chan and Vese, the energy functon can be expressed as follows: φ t =δ(φ) [μ ( φ φ ) V λ 1 (1 c 1 ) 2 +λ 2 (1 c 2 ) 2 ], (17) where V 0, λ 1 0, λ 2 0,andμ 0are fxed parameters; V parameter s used to ncrease propagaton speed; λ 1 and λ 2 parameters control the force nsde and outsde the contour; μ manpulates the smoothness of zero level set [12]. If μ value s large t detects only large objects whle when μ value s small, small szed objects can also be detected. ACWE model can satsfactorly segment a desred object havng weak and defcent edges. Ths property of ACWE model matches up wth our needs because PD mages have a very poor transton between soft tssues and bones and some part of the border of bone s destroyed especally n mages whch has bone edema and cortcal deformty. On the other hand PD mages have a low SNR than other MR modaltes whch s also sutable for ACWE model whch has ablty to segment nosy mages. The weak ponts of ths model are the assumpton of each mage regon as homogeneous and senstvty to ntalzaton. Some related methods were proposed to solve ntensty nhomogenety problem [13, 16]. Some of them deal wth part of the problem and to some extent they could perform segmentaton of nhomogeneous objects. Our data set was composed of humeral heads presentng a wde morphologcal varance due to traumatc changes n borders and edema n thebone.thereforethevaranceofthelocatonandmagntude of bone and edema would render prevously proposed methods less effcent n the humeral head segmentaton from PD weghted MR mages. Instead of correcton of nhomogenety durng applcaton of regon based models we appled segmentaton methods after ntensty nhomogenety was decreased wth preprocessng. Besdes, these methods cannot provde a reasonable soluton to the ntalzaton of the ntal contour [24]. When ACWE method was appled to the orgnal PD weghted axal MR mages segmentaton of humeral head was notably unsatsfactory as shown n Fgure 5(b). SRAD method was appled to decrease nose and homomorphc flter was used to obtan more homogeneous mages. In the next step ntal contour was automatcally ntalzed n the humeral head. A better segmentaton result was reached as shown n Fgure 5(c). The humeral head was segmented from determned ROI wth the same preprocessng step. As shown n Fgure 5(d), segmentaton success of humeral head was ncreased. Fgure 5(d) also demonstrates some whte pxels n the humeral head representng the edematous area of the humeral head Sgned Pressure Force (SPF) Model. SPF model s a combnaton of GAC [11] and regon based Chan-Vese

7 Computatonal and Mathematcal Methods n Medcne 7 (a) (b) (c) (d) Fgure 5: (a) Orgnal PD weghted MR mage of shoulder, (b) bnary segmentaton result of ACWE method wthout preprocessng operaton, (c) segmentaton result wth ACWE after applcaton of the SRAD and homomorphc flter, and (d) segmentaton result of ACWE n ROI wth the same preprocessng steps n (c). model [12] and possesses a local segmentaton property. SPF model s able to segment selectvely the desred object by settng ntal contour ntersectng or surroundng the desred boundares. Ths model has advantages over GAC and Chan-Vese model. GAC model utlzes mage gradent to construct an edge stoppng functon whereas SPF model uses statstcal nformaton to ntercept contour evoluton on the object boundares. Zhang et al. stated that SPF method was capable of handlng objects wth weak or damaged boundares. Furthermore they suggested that SPF model was able to segment objects wth nhomogeneous nteror ntensty compared to Chan-Vese model [21]. In our data set some of the humeral heads had edema nsde and weak or damaged surroundng edges. We appled SPF model to our data set and compared advantages of global segmentaton property of ACWE method wth local segmentaton property of SPF. SPF functon was defned as follows: I (x) (c spf (I (x)) = 1 +c 2 )/2 max ( I (x) (c (18) 1 +c 2 )/2 ), where c 1 and c 2 are defned n (15) and (16),respectvely.The level set formulaton of SPF model s as follows: φ t = spf (I (x)) ( φ φ, φ +α) φ + spf (I (x)) (19) where α s the balloon force term to shrnk and expand the contour. Letusobservemagenavectorxj, j = 1,2,...,n and {1,2,...,k},andk sthenumberofregons.themxture of Gaussan dstrbuton s assumed as n the followng form: f (x) = p >0are weghts such that k =1 p =1: k =1 p N(x μ,σ 2 ) (20) 2 N (μ,σ 2 ) = 1 σ 2π exp ( (x μ ) ). (21) Steps of EM-MAP Algorthm. (1)Anyclassfcatonmethod couldbeusedtontalzeparameterofθ (0).Inourcasewe used K-means clusterng method to defne ntal parameter of means (μ (0) k θ (0) = (p (0) 1,...,p(0) 2σ 2 ),varancesσ(0) k,andweghtsp(0) k : k,μ(0) 1,...,μ(0) k,σ(0) 1,...,σ(0) k ). (22) (2) E-step: p (r) s the dscrete pror probablty n stage r and p (r+1) j s the dscrete posteror probablty n the next stage whch s calculated by the Bayes rule as follows: p (r+1) j (3) M-step: =p (r+1) ( x j ) = p(r) p (r+1) = 1 n n p (r) j, j=1 N(x j μ (r),σ 2(r) f(x j ) ). (23) Gaussan Mxture Model (GMM). GMM s wdely appled for segmentaton n many felds. We used GMM clusterng model to segment humeral head and the parameters of the model were estmated by usng expectaton maxmzaton (EM) algorthm [28]. We appled ths model n ROI defned by crcular Hough transform (Fgure 6(a)). μ (r+1) σ 2(r+1) = n j=1 p(r+1) j n p (r+1) x j = n j=1 p(r+1) j (x j μ (r+1) n p (r+1), ) 2. (24)

8 8 Computatonal and Mathematcal Methods n Medcne (a) (b) (c) Fgure 6: (a) Demonstraton of orgnal MR mages of shoulder n determned ROI by crcular Hough transform. (b) Segmentaton result by usng FCM method. (c) Segmenaton result of GMM. (4) E-step and M-step terated untl convergence to the arbtrary error: e 2 <ε. (25) GMM provdes to segment normal humeral head mages wth two labels (Fgure 6(c)) Fuzzy C-Means (FCM) Method. FCM method provdes to assgn pxels to each cluster based on mnmzng the sum of dstances from each pxel to every cluster centrod weghted by ts correspondng membershp. The objectve cost functon was mnmzed by assgnng hgh membershp values to pxels whose ntenstes are close to the centrod of ts partcular class and low membershp values are assgned when the pxels are far from the centrod. Let X=(x 1,x 2,...,x N ) represent an mage wth N pxels to be parttoned nto c cluster [29]. The cost functon s defned as follows: N c u m j j=1 =1 J= x j V 2, (26) where u j defnes the membershp of pxel x j n the th cluster and V s the cluster center. Fuzzy coeffcent represented by m and m=2s used n ths study. The membershp functon s updated teratvely by 1 u j =. c k=1 ( x j V / x (27) j V k )2/(m 1) Each cluster center s updated as follows: V = N j=1 um j x j N. (28) j=1 um j FCM model provdes to segment normal humeral head mages wth two labels (Fgure 6(b)) Postprocessng. ThesegmentedobjectafteruseofACWE or SPF contans soft tssue components especally tendons whch have a smlar ntensty value wth humeral head (Fgures 7(a) and 7(b)). After enlargement of the crcle found wth the crcular Hough transform the scapular edge was also labeled as humeral head (Fgures 8(a) and 8(b)). Scapula and some parts of tendons are located at the borders of the ROI crcle. To elmnate scapula and tendon regons we appled specfc morphologcal operatons and connected component labelng method n the lght of anatomcal localzaton of tendons. We determned the sde of the humeral head by usng hstogramofanmage.thescapulaslocatedatthesame drecton wth the shoulder sde and n the perphery of the crcle. Accordng to the left and rght shoulder mages we may defne the locaton of scapula area by usng radus and center of crcle whch was obtaned from crcular Hough transform. In the scapula area we have done some eroson operatons wth crcular structurng element. Connected component labelng method was used to detect connected regons n the complement of the bnary mage. Next the boundary of the humerus was labeled n red color (Fgures 8(c), 8(d), and 8(e)).Inthelaststepthewhtepxelsresultngfromthebone edema were flled to get the fnal result. 3. Expermental Results and Evaluaton Experments were carred out wth MATLAB 7.11 n Wndows XPplatformona2.5GHzIntel(R)core(TM)personal computer wth 4 GB of RAM. The manual segmentaton tool was prepared n MATLAB envronment and performed by usng a mouse. To evaluate the success of segmentaton we compared the segmentaton results wth the manually segmented areas determned by the orthopedc specalst. Smlarty of segmented mages s compared by Sorensen- Dce metrc to fnd the success rates. We segmented normal and edematous humeral heads and humeral heads wth Hll-Sachs deformty wth ACWE and SPF methods (Fgures 9(a), 9(b), 9(c), and 9(d)).

9 Computatonal and Mathematcal Methods n Medcne 9 (a) (b) Fgure 7: (a) Axal PD weghted MRI of shoulder; (b) bceps and subscapulars tendons are demonstrated n red area. The boundary of scapula and humeral head s colored n green and blue, respectvely. (a) (b) (c) (d) (e) Fgure 8: Steps of postprocessng. (a) ROI as a result of crcular Hough transform. (b) The segmentaton result n the ROI area. (c) The result of specfc morphologcal operaton and connected component labellng. (d) The fllng of whte pxels resultng from bone edema. (e) Segmentaton result. The parameters used for ACWE are μ = 0.2, λ 1 = 0.7, λ 2 =1, V =1,andε = 1.5. λ 1 and λ 2 parameters affect the unformty and the resultng force nsde and outsde the contour, respectvely. In our study we set λ 1 < λ 2 because we had unform backgrounds and foreground contanng varyng grayscale objects. In order to detect smaller szed objects we assgned a small value to μ parameter. The parameters used for SPF method are p=1, σ=2, K=5,andε = 1.5.

10 10 Computatonal and Mathematcal Methods n Medcne (a) (b) (c) (d) Fgure 9: Segmentaton results of normal, edematous humeral heads and humeral head wth Hll-Sachs deformty were demonstrated n frst, second, and thrd rows, respectvely. Column (a) orgnal mages, (b) manual segmentaton results by an expert, (c) segmentaton results of ACWE method, and (d) segmentaton results of SPF method. Methods and data Table 1: Segmentaton results of three groups of humeral heads before and after postprocessng operaton. Normal humeral head Average success rate before postprocessng [%] Average success rate after postprocessng [%] Humeral head wth edema Humeral head wth Hll-Sachs leson Average success rate Normal humeral head Humeral head wth edema Humeral head wth Hll-Sachs leson Average success rate Number of data ACWE method SPF method We operated ACWE and SPF methods on determned ROI n 81 normal axal PD MR mages. The average success rates of the ACWE and SPF before postprocessng accordng to Sorensen-Dce metrc were 90.79% and 88.42%, respectvely. After postprocessng operaton segmentaton results were ncreased to 92.17% n ACWE and 90.30% n SPF method as shown n Table 1. We appled ACWE and SPF methods also n 100 edematous humeral heads and 38 humeral heads havng Hll- Sachs deformty. The success rate of ACWE and SPF were

11 Computatonal and Mathematcal Methods n Medcne 11 Table 2: Segmentaton results obtaned by usng ACWE, SPF, GMM, and FCM methods. Methods Success rate for 81 normal MR mages [%] ACWE method SPF method GMM method FCM method Average success rate Maxmum segmentaton success Mnmum segmentaton success % and % n edematous and defectve humeral heads, respectvely. Success rates of both of the methods ncreased approxmately by 1-2% n edematous and defectve humeral heads after postprocessng operaton as shown n Table 1. FCM and GMM were appled to whole data set; however they provded unsatsfactory results even wth normal mages (Table 2). As predcted, unsuccessful results were also obtaned n edematous and defectve humeral heads. FCM and GMM are vulnerable to pathologc changes n the humeral head lke edema and Hll-Sachs deformty because of the changes n ntensty of bone and blurred borders and defcent edges n these condtons. 4. Dscusson The deal MRI study to evaluate shoulder nstablty s 2D axal PD slces n clncal studes. PD weghted mages are gratfyng n demonstraton of bony edema that may help clncans n the explanaton of shoulder pan or the amount and place of trauma. Segmentaton of the humeral head from axal PD weghted shoulder MRI slces s complcated by four man reasons. The frst and global reason s the nnate feature PD weghted MRI whch has a low SNR. The other mportant lmtaton s the soft transton between bony humeral head and surroundng soft tssues. The thrd dffculty results from the addtonal trauma to the humeral head that may cause bone edema n the ROI n varable amount and dstrbuton. Changng amount and dstrbuton of edema aggravates ntensty nhomogenety problem. The fourth ssue that may hassle bony segmentaton s the change of the shape of the humeral head after dslocaton (Hll-Sachs leson). These dffcultes may also have adverse effects on vsual nspecton. We recognzed that wthout preprocessng step ACWE and SPF were unsuccessful n the entre PD MR mages. In the mage processng the mage nose s a factor that affects nhomogenety quantty. SRAD method s preferable because t decreases nose whle protectng weak edges of humeral head. Applcaton of SRAD to the Rcan nose n apdweghtedmrmagewascarredoutbyestmatng SDN from foreground. The use of homomorphc flter after SRAD further decreases nhomogenety. Even though the decrease n the ntensty nhomogenety and the reducton of nose cannot be detected easly wth pure nspecton (Fgures 3(b) and 3(c)), there s a remarkable and vsually nspectable progress n the results of segmentaton of preprocessed mages when compared to the unprocessed mages as shown n Fgures5(b) and 5(c).After nosereductonand decreased nhomogenety n PD mages ACWE and SPF would be estmatedtoworkonpdweghtedmages. The problem of the ntalzaton of the ntal contour s another ssue to be solved to reach the desred success rates. ACWE and SPF can be operated wth hgh success rates for segmentaton of round cross-sectonal objects wth predetermnaton of the locaton of the ntal contour automatcally wth crcular Hough transform. The most mportant obstacle affectng the success of the segmentaton was the soft tssues (bceps and subscapulars tendons) and the remanng of scapula n the neghborhood of humeral head. It s very hard to elmnate the tendon tssues from the humeral head because of the smlarty of ther ntenstes n PD weghted mages. In the postprocessng step we elmnated surroundng tssues wth a specfc morphologcal operaton and usng the knowledge of the anatomcal structures. In case of edema the ntensty of the bone area ncreases and the borders of bone area blur. Defcent edges have addtve effect on hamperng the segmentaton process. The overall results of segmentaton n edematous and defectve heads were lower than normal group by 1.97% 3.27% for ACWE method and by 0.98% 5.61% for SPF method, respectvely. Moreover edema of the humeral head was labeled n whte causng whte pxels n the segmented humeral head resemblng oversegmentaton. Even n the humeral heads selected as vsually normal there may be some mnor edema whchshardtodetectbyvsualnspectoncausngsmall areas of whte pxels (Fgure5(d)). Although n some cases lke n Fgures 9(c) and 9(d) there s not a vsually nspectable dfference between segmentaton success of ACWE and SPF, the average success rate of ACWE was approxmately 2 4% superor to SPF method n all cases. Although ths dfference seems small t s mportant n medcal decson makng (Table 2), because deformty of the humeral head n Hll-Sachs leson and locaton of edema n posttraumatc cases have a perpherc placement n the segmented humeral head whch renders slght mprovements crtcal n reachng the correct dagnoss. The number of teratons and computatonal tme of the ACWE and SPF methods when operated n ROI were sec and sec, respectvely. Although the computatonal cost of ACWE method was hgher, ts success rate was also hgher than SPF method. Determnaton of ROI ncreased the success of the segmentaton by decreasng the studed area and tme to the desred lmts. A number of teratons decrease by approxmately tenfolds by determnng ROI area. The clusterng methods of FCM and GMM were able to segment humeral head n normal group wth lower success

12 12 Computatonal and Mathematcal Methods n Medcne rates than ACWE and SPF. These methods could not provde reasonable results n edematous humeral heads or humeral heads wth Hll-Sachs deformty. 5. Conclusons In ths study humeral head segmentaton was performed on PD weghted axal slces of the shoulder MRI. There s no perfect method to vsualze shoulder nstablty; yet there s a perfect method to segment the humeral head. To overcome the problems of magng and to ncrease the success rates of the ACWE and SPF methods preprocessng and postprocessngstepshavecrucalmportance.ourorgnaldatasetwhch s composed of patents s therefore a lmtaton of ths study. Manual segmentaton wth a mouse s the other lmtaton. There remans some mpurtes after manual segmentaton whch may affect the control group data negatvely also affectng the fnal result. However the overall results of our study are stll promsng. 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