Automatic tissue and structural segmentation of neonatal brain MRI using Expectation-Maximization

Transcription

1 Automatc tssue and structural segmentaton of neonatal bran MRI usng Exectaton-Maxmaton Antonos Marooulos 1, Chrstan Ledg 2, Paul Alabar 3, Ahmed Serag 2, Joseh V. Hanal 3, A. Davd Edwards 3, Serena J. Counsell 3, and Danel Ruecert 2 1 Centre for the Develong Bran, Imeral College, London, Unted Kngdom, 2 Comutng, Imeral College, London, Unted Kngdom and 3 Dvson of Imagng Scences and Bomedcal Engneerng, Kng s College, London, Unted Kngdom Abstract. Accurate automated mage segmentaton n neonates s challengng due to the lower contrast-to-nose rato comared to adult scans, the artal volume effect and large anatomcal varaton. In ths aer, we resent a technque for bran segmentaton nto dfferent tssues and structures of nterest. Atlas rors and subect-secfc tssue rors are used to ntale an Exectaton- Maxmaton (EM scheme. The roosed mlementaton ncororates a Marov Random Feld ( regularaton to account for the satal deendenc of labels, ror relaxaton to adat the rors accordng to the ndvdual bran aearance and artal volume (PV correcton. The algorthm s evaluated aganst manuall segmented data from the eobrans12 MICCAI challenge. 1 Introducton Magnetc Resonance (MR magng s ncreasngl beng used to assess bran develoment n neonates. Manual segmentaton s extremel tme consumng and so an accurate automatc segmentaton technque s requred. Segmentaton of neonatal MR mages s consderabl more challengng than the segmentaton of adult bran MR mages due to the lower contrast-to-nose rato (CR, the artal volume (PV effect as a result of the nverted whte matter sgnal ntenst and the large changes n aearance of the bran from the earl reterm erod to term-equvalent age. A number of studes have been roosed for the segmentaton of tssues n the neonatal mages [1 5]. Most of the methods use rors n form of temlates that are non-rgdl regstered to the subect mage n order to roagate ror anatomcal nowledge to the subect sace. The rors are often combned wth a model of the mage ntenstes to refne the labels and can be adated accordng to the subect mage [5, 6]. In ths aer, we roose an Exectaton-Maxmaton (EM framewor for the segmentaton of neonatal brans nto 7 regons: cerebrosnal flud (CSF, gre matter (GM, unmelnated whte matter (WM, branstem, cerebellum, basal gangla and thalam and ventrcles. Prors of these structures are roagated wth the use of a

2 robablstc atlas and are combned wth rors obtaned wth the use of a clusterng technque to rovde a good ntalaton of the EM algorthm. Our mlementaton ncludes a Marov Random Feld ( scheme to enale the roxmt of anatomcall dstant regons, adataton of the rors and PV correcton smlar to revous studes [2, 5]. 2 Methods 2.1 Subects The methodolog descrbed n ths aer has been aled to the T2 mages of the subects rovded from the eobrans12 MICCAI challenge [7]. Three dfferent sets of mages were rovded: axal scans acqured at 40 wees corrected age (set 1 wth 2 tranng and 3 test data, coronal scans acqured at 30 wees corrected age (set 2 wth 2 tranng and 3 test data, and coronal scans acqured 40 wees corrected age (set 3 wth 3 test data. All of the mages were sull stred usng the Bran Extracton Tool (BET [8] and corrected for feld nhomogenet usng the 4 algorthm [9]. 2.2 Atlas Prors In ths stud we used the satotemoral non-rgd atlas develoed b [10] to roagate the robablstc satal ror of each structure accordng to age. For each subect the corresondng atlas temlate accordng to age was rgdl, affnel and nonrgdl regstered to the subect sace. The non-rgd regstraton aled wthn ths stud uses normaled mutual nformaton (MI as the smlart measure wth freeform deformatons and control ont grd sacngs of 20mm, 10mm, 5mm and 2.5mm [11]. The satal ror of each structure s then transformed nto the subect s natve sace. Snce some structures of the temlate had dfferent defntons than the delneatons rovded from the challenge, the satal rors were manuall modfed to coml to the rotocol of the challenge. The CSF ror was dvded nto left and rght ventrcle and the extra-cerebral CSF. Parts of the dee gra matter ma were extracted and merged wth the cortcal gra matter ma and the branstem mas was altered to result n a better agreement to the challenge structure defntons. 2.3 Subect secfc tssue rors Subect-secfc rors that reflect the tssue roortons of the ndvdual mages were obtaned wth the use of -means clusterng [12]. The mage ntenstes of each subect were segmented nto four classes that reresent the three tssue membershs (CSF, GM, WM and the bacground. The ntenstes that belong to the hgher ntenst class were subsequentl dvded nto two arts wth another -means scheme. The lower art s manl attrbuted to the low CSF ntenstes and the hgh WM ntenstes often found around the term equvalent age n the frontal and occtal lobe. The

3 hgher ntenst class corresonds to the ure CSF ntenstes. A Gaussan dstrbuton s ntaled wth each of the fve resultng -means classes centrods and varances. The normaled lelhoods of the Gaussans reresent the tssue ror for the 5 classes (extra-cranal sace, GM, WM, hgh ntenst WM/low ntenst CSF, CSF. To avod local mnma wth the use of -means, the tssue rors were blurred wth a Gaussan ernel. The atlas rors of each subect roagated from the atlas are combned wth the - means tssue rors to result n refned rors for the structures n the natve sace of the subect. The combned rors are used to ntale the mxng coeffcents of the EM algorthm, rovdng a better ntalaton than the atlas rors alone. The resultng classes ntroduced nto the EM model are: CSF, low ntenst CSF, GM, hgh ntenst WM, WM, basal gangla and thalam, branstem, cerebellum, left ventrcle, rght ventrcle and outsde sace. 2.4 Exectaton-Maxmaton formulaton In ths stud we adot a methodolog smlar to [2, 5, 13] for the segmentaton of the neonatal mages. The mage s aroxmated wth a Gaussan mxture of the K 11 structures descrbed n the revous secton. The label 1,.., K of each voxel 1,2,.., s reresented wth the varable e, where e s a unt vector wth the -th comonent equal to 1. The ror dstrbuton of the P e, s rovded b the subect-secfc s,.e. ( structure rors for each of the structures, as descrbed n the revous secton. Assumng that the observed ntenst of the voxel s ndeendent from the rest of the voxels n the mage, the segmentaton roblem can be formalsed as the Maxmum a Posteror (MAP estmaton of the means µ and standard devatons σ of the Gaussans of the K structures, Φ { µ µ. 1, 2,.,µ Κ,σ1, σ2,..., σ K} [13]. The arameters Φˆ are estmated wth the EM algorthm, at each teraton m as: Exectaton ste: ( e,φ ( m+ 1 ( m P K 1 ( m ( e,φ P( e ( m P( e,φ P( e P (1 where ( m P ( e,φ G( µ, σ the lelhood of the Gaussan dstrbuton G wth arameters µ, σ.

4 Maxmaton ste: ( m+ 1 ( σ µ 2 ( m ( m+ 1 ( m+ 1 ( µ ( m+ 1 ( m+ 1 1 ( m+ 1 2 (2 However, snce each voxel's ntenst s deendent on the surroundng voxels, we nclude a satal regularaton term that enforces a smooth labellng among neghbourng voxels [13]. The regularaton term s mlemented wth a that s a non-bnar extenson of a multclass Potts model as defned n [5], P ( e P( e,φ, where K 1 e e U U ( e,,φ ( e,,φ are the frst-order neghbours of voxel. U s the energ functon : (3 U ( e,,φ 1 G x l s x l + s l l + l s l (4 Here s { s,s, s } x mage. The connectvt strength matrx, accounts for the ansotroc sacng n each drecton of the G s defned a ror accordng to the anatomcal roxmt of the structures. Due to anatomcal varablt, we assume that the roortons are not nown a ror. Instead, we consder as a samle drawn from a dstrbuton derved from the statstcal atlas,.e., we consder them as a osteror of a Drchlet dstrbuton. Here, s udated b

5 ( α +α( G 1 (5 where G s a Gaussan ernel. The amount of relaxaton s deendent on the arameter α, 0 α 1, controllng the amount of adataton of the rors. In our exerments the relaxaton factor s set to α0.5. The enalt ntroduced b the allows a smooth labelng b removng solated voxels. However, n regons that msclassfed voxels are neghborng each other, the energ wll not be suffcent to remove them snce the wll favor each other through the term. To account for ths roblem we adoted a nowledge-based drven aroach based on morhologcal oeratons smlar to [2]. The rors of the detected msclassfed structure m, and the arorate structures c are adated as c c + w c ( λ m 1 (6 m λ m (7 c where w c the arorate structures adataton weght accordng to c n n the ror robablt. λ s set to 0.5 n all the exerments. Addtonall, a searate PV class as descrbed n [5] s defned between GM and WM for the earl neonatal scans (30 wees. The PV class s merged after the EM convergence to the wm class n order to mrove the boundar of the resultng WM. The low ntenst CSF class s aended to the ure CSF class and the hgh ntenst WM class to the ure WM class. Voxels that belong to small, connected comonents of the segmented branstem and cerebellum are reclassfed accordng to the maxmum osteror robablt of the rest of the classes and holes nsde the ventrcles are flled n. 3 Results The erformance of the roosed algorthm was assessed on the test data rovded b the challenge. Snce the melnated wm class was not segmented wth the roosed technque, the results are resented for the rest of the structures. The average Dce coeffcents and 95 th -ercentle Hausdorff dstances wth resect to the manual segmentaton for the dfferent structures are resented n Table 1 and 2 resectvel. Set 1 Set 2 Set 3 Over all sets gm dgm wm branstem

6 cerebellum ventrcles csf average Table 1. Average Dce coeffcents of the segmented structures Set 1 Set 2 Set 3 Over all sets gm dgm wm branstem cerebellum ventrcles csf average Table 2. Average 95 th -ercentle Hausdorff dstance of the segmented structures The average runtme of the roosed automatc segmentaton technque s 95 mnutes er subect. The segmentatons of all the subects were run n arallel on a server wth 24 cores and 64 GB RAM. 4 Concluson We have resented an algorthm for the segmentaton of neonatal T2 mages nto 7 structures: CSF, GM, unmelnated WM, branstem, cerebellum, basal gangla and thalam and ventrcles. Prors of each structure are roagated from a satotemoral robablstc atlas and are combned wth subect-secfc tssue rors obtaned wth -means. The resultng structures rors are used to ntale an EM otmaton. Our mlementaton ncludes a term, PV correcton and relaxaton of the labels to refne the structures. The qualt of the algorthm s assessed accordng to the manuall segmented neonatal brans rovded b the MICCAI challenge. References 1. Prastawa, M., Glmore, J.H., Ln, W., Gerg, G.: Automatc segmentaton of MR mages of the develong newborn bran. Med Image Anal. 9, ( Xue, H., Srnvasan, L., Jang, S., Rutherford, M., Edwards, A.D., Ruecert, D., Hanal, J.V.: Automatc segmentaton and reconstructon of the cortex from neonatal MRI. euromage. 38, (2007.

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