关于马尔可夫随机场的一篇较好的综述

12520075JournalofImageandGraphicsVol.12,No.5May,2007:2005211214;:2006202217:(1974),2006,E2mail:[e-mail](,310027),:,,:TP391:A:100628961(2007)0520789210ASurveyoftheMarkovRandomFieldMethodforImageSegmentationLIXu2chao,ZHUShan2an(ElectricalEngineeringCollege,ZhejiangUniversity,Hangzhou310027)AbstractMarkovrandomfieldmethodisaveryactiveresearchfieldinimagesegmentation.ThispaperintroducestherelationshipbetweenageneraltheorybasedonMarkovrandomfieldmethodandtheimages,andprovidesageneralframeworkinimagesegmentation,includingtheconstructionofspatialandwaveletdomainimagemodels,theselectionoftheoptimizationcriterion,calculationofthenumberoflabeling,parameterestimationofimagemodelsandtherealizationofimagesegmentation.Theapplicationsofimagesegmentationarereviewed.Andafewpossibletrendsarediscussed.Keywordsmarkovrandomfield,imagesegmentation,bayesianprinciple,parameterestimation1,,,,,,,,,,[13],,,,,,,,,,,,,[46],,©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(markovrandomfield),MRFBayes,MRF,,,,:MRF,,MRF;MRF,,;MRF,();2060MRFBesagGibbsMRF[7],,MRF;MRF[8],,Bayes,,(),,,,MonteCarlo;MRF2[9,10]S={(i,j)1iN,1jM}MN,X={xssS}PsS,xsX,={1,2,,L}(X,xs),xs,S,X,L={(s)sS}S,:(s)S;s|(s);Ps,rS,s(r)Zr(s)r(s)s,(s)sS,cAS,c(clique),C,,s,,,;S,{(s)=S\s},,,s,:(n)(s)={rd(s,r)n,rs},n,d(),Pn0,(n)(s)(n+1)(s),1(1(a))(1(b))(a)(b)1Fig.1Oneandtwoorderneighborsystemandclique={=(s1,s2,,sMN)si,1iMN}(configuration),XMRF,:p(X=)0,P;p(Xs=xsXr=xr,rs,Pr(s))=p(Xs=xsXr=xr,Pr(s)),p()p(),p(),p()5MRF:sxs,ssMRF,©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[7],GibbsMRF5Gibbsp,:p()=[exp(-U()/T)]/Z(1),Z,T,U()=cCVc(),,C,Vc()c(potential),(s),scHammersley2CliffordGibbsMRF:MRF,Gibbs(s)MRFXGibbsp(xsxr,r(s))=exp-(cCVc(xsxr)TZs(2)(2)MRF,MRFVc(x),Gibbs,(s)MRF3MRF,,,,,,3.13.1.1,,,Isingmodel,PottsmodelAutologisticmodel,,Ising[11],,,,Smits[12],,,[12],,ChanMPETGibbs,[13],,MRI[14],,,,Chan,,ZhouWen2tu[15],,(,),MNS0={v=(d1,d2)},1d1M,1d2N={v,vS}s,vv,K={1,2,,k},K,MRFMLL(multilevellogistic),MLL,,MLL©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.()=iScountt=1(i,j)(t)i(,t)+0K(3),(,t),(t)i,v,:(t)i=A/(N(yi,yj)+B)(4)AB0,KN(yi,yj)=0,(t)i,[11],;0=0,[14]N(yi,yj)000,[15],,,,50,,1994,Bouman[16],,,,,,,,,Bouman,,Kam[17],3,Laferte[18],,;,3.1.2,3,,,Choi,[19],,36,,,,2(b),,,SunBouman[20],[20],FanGuo2liang[21],,,,JMCMS,,2(c)(b)HMT(a)(c)JMCMS2Fig.2Textureimageandsegmentationresults3.23.2.1,©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[22]Lena,,,,,[25],,()(),,[2326],,yS0MRFkk,2k(k=1,2,,K),:f(x)=Kk=1ckexp[-k(y-k)][k/2(1/)]=Kk=1ckp(yk,2k)(5),ck,k,2kk,,()Gamma,K0,m1,;=2,[27];=1,,,[28],Weibull,Rayleigh,[15],,(clutter)(shading)4,4,,,,L,U,V,3,3,3,3Bezier3,3.2.22001,ChoiHMT[19],,,,,3,3,,,HMT[29],HyeohkoChoi,2001,[30]3,,,3[19]2003,[31],3,,,,,2004,Sun,,Rayleigh[20]©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.()p(y),Bayes,,p(y):p(y)p(y)p()(6)(1)MAP(maximumaposterior)(),MAP,^=argmaxp(y)argmaxp(y)p()(7)MAP,,,MAP,,MRF,,MRF[32],MAP,,,(2)MPM[26,33]^s=argmaxp(sy)(8)MAP,MPMMAP,MAP,;MPMMPM,,MPM(3)^=E[p(y)](9)(9),,^(4)SMAP[16,34]^=argminE[Csmap((0),)Y=y](10)SMAP,,,,MAP;,,,MPM5()MRF,,,,,,,,(),,,,;,(1)AIC[35]AIC(k0)=argmin[-2lgL(ML^)+2ka](11),L(ML^),(),ML^,kaAIC,AICAIC[36],,,AIC(2)MDL[37]©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(k)=-lgL(ML^)+0.5kalnMN(12),MNAIC,MDL(),,,AIC,MDL2MCBV[38,39]MCBV(k)=-lgL(ML^)+0.5kak=12var(ML^)(13),var(ML^)MCBV,,MCBV,,Cramer2Rao(4)MGZ[40]k^=argmin[k1kkmax,MGZ(k)]MGZ(k)=[MDL(k)-MDL(kmax)]/N(14)MDL,,,0,e-N6MRF,:;;;Cramer2Rao[41],,,,6.1,,:,ChanGibbs,,,[13],,,,,[14],,,MLL(multilevellogistic),[42]HwanMonte2Carlo[43],ZhangJun[44],6.2(),,,;,,EM(expectationmaximization)[45]EM,,,,,,EM:E,;M,,,;,,,;Cramer2RaoEM,,,DAEM[14],,,,E,EMDAEMDAEMEMSA(simulateannealing)[46],,,,DAEMEM[15]GEM,MCEM,,©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[47],SARsea3:,,,;,,;,,,GibbsMRF,,,,,,;,(),,ICM(iteratedconditionalmodel)[48]GNC(graduatednonconvexity)[49]MFA(meanfieldannealing)MMD(modifiedmetropolisdynamics)[50],,,,SA,MarkovChainMonteCarlo(MCMC)Bayes,Gibbs(Gibbssampler)MetropolisHastings8(1),,,,,MLL,,,,,(2),,:;MSRF,SMAP,,(3),,Cramer2Rao,,,,9MRF,,,,,,,,,(References)1LeiT,SewchandW.StatisticalapproachtoX2rayCTimaginganditsapplicationsinimageanalysis2Part2:Anewstochasticmodel2basedimagesegmentationtechniqueforX2rayCTimages[J].IEEETransactionsonMedicalImage,1992,11(1):6269.2ZhangJ,ModestinoJW.Amodel2fittingapproachtoclustervaliditywithapplicationtostochasticmodel2basedimagesegmentation[J].©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(10):10091017.3ZhengRL,MacFallJR,HarringtonDP.Paramet