医学图像分割专家讲座

医学图像分割许向阳华中科技大学医学图像信息研究中心1医学图像分割专家讲座第1页讨论内容图像分割概述阈值分割医学图像分割专家讲座第2页1、图像分割概述将不一样区域区分开来，这些区域是互不相交，每一个区域都满足特定区域一致性。其分割目标是为了将感兴趣区域提取出来，从而为定量、定性分析提供基础，同时它也是三维可视化基础。医学图像分割专家讲座第3页1、图像分割概述⑤P(gk(x,y)Ugj(x,y))=FALSE.

任意相邻部分合并都会破坏这种一致性。医学图像分割专家讲座第4页1、图像分割概述假如连通性约束被取消，那么对像素集合划分就称为分类(Classification),每一个像素集称为类(Class)。经典分割和像素分类通称为分割。医学图像分割专家讲座第5页基于区域分割方法基于边缘分割方法结合区域与边界信息方法基于含糊集理论方法基于神经网络方法基于数学形态学方法图谱引导（Atlas-guided）方法1、图像分割概述医学图像分割专家讲座第6页1、图像分割概述基于区域分割方法利用区域内相同性（一致性）

阈值分割区域生长和分裂合并分类器和聚类基于随机场方法其它基于统计学方法医学图像分割专家讲座第7页1、图像分割概述基于边缘分割方法利用区域之间差异性

并行微分算子曲面拟正当基于边界曲线拟合方法串行边界查找医学图像分割专家讲座第8页医学图像特点:含糊、不均匀、个体差异、复杂多样灰度不均匀:不均匀组织器官、磁场等伪影和噪声:成像设备不足、组织蠕动边缘含糊:局部体效应边缘不明确:病变组织1、图像分割概述医学图像分割专家讲座第9页局部体效应(partialvolumeeffects)1、图像分割概述IdealImageAcquiredImage医学图像分割专家讲座第10页医学图像分割方法公共特点：分割算法面向详细分割任务，没有通用方法愈加重视各种分割算法有效结合需要利用医学中大量领域知识交互式分割方法受到日益重视

医学图像分割是一项十分困难任务，至今依然没有取得圆满处理。1、图像分割概述医学图像分割专家讲座第11页2、阈值分割阈值分割是最常见一个分割方法。它基于对灰度图像一个假设：目标或背景内相邻象素间灰度值是相似，但不一样目标或背景象素在灰度上有差异，反应在图像直方图上，不一样目标和背景则对应不一样峰。选取阈值应位于两个峰之间谷，从而将各个峰分开医学图像分割专家讲座第12页CT图像中皮肤骨骼分割2、阈值分割医学图像分割专家讲座第13页阈值分割三种技术方案直接门限法间接门限法对图像进行预处理后再利用门限法。拉氏或梯度运算，邻域平均多门限法2、阈值分割医学图像分割专家讲座第14页多门限法2、阈值分割乳腺钼靶图像单门限分割多门限分割医学图像分割专家讲座第15页

门限确实定方法

依据直方图确定门限最小误判概率准则下最正确门限最大类间距准则下最正确门限最大类间类内距离比准则下最正确门限最大熵准则下最正确门限依据二维直方图确定图像分割门限边缘灰度作为分割门限分水岭方法2、阈值分割医学图像分割专家讲座第16页阈值分割优点简单，常作为预处理方法阈值分割缺点不适合用于多通道图像不适合用于特征值相差不大图像不适合用于各物体灰度值有较大重合图像对噪声和灰度不均匀敏感2、阈值分割医学图像分割专家讲座第17页ThresholdingThesimplestandmostefficientimagesegmentationmethodisthresholding.Thresholdingistosegmenttheimageintotworegionsaccordingtothegraylevelofimagepixels.IfthegraylevelishigherthanthegiventhresholdT,theoutputatthispixelissetto1,otherwiseitissetto0.医学图像分割专家讲座第18页ImageThresholdingOriginalimageSegmentedimage(T=128,145)医学图像分割专家讲座第19页DeterminationofThresholdInthresholdingmethod,themostdifficultistodetermineapropervalueofthethreshold.Therearedifferenttypesofthethreshold:Globalthreshold(constantthreshold)Adaptivethreshold医学图像分割专家讲座第20页DeterminationofGlobalthresholdIftheobjectandbackgroundhavedifferentdistributions,thevalueoftheglobalthresholdcanbedeterminedbycalculatingthehistogramoftheimage.Theglobalthresholdcanalsobedeterminedinteractively.Thethresholdcanalsobedeterminedbyoptimization.医学图像分割专家讲座第21页Determinationoftheglobal

thresholdfromhistogramT=150医学图像分割专家讲座第22页TheOtsuAlgorithmIftischosenasathreshold,andp(i)isthenormalizedhistogram0K-1NbitsmeansK=2Nt医学图像分割专家讲座第23页TheOtsuAlgorithmmeansvariancesMeansandvarianceforeachclass医学图像分割专家讲座第24页TheOtsuAlgorithmStatisticaldiscriminationmeasurebasedonvariancebetweenclasses:Runthroughallpossiblevaluesoft,andpicktheonethatmaximizesthediscriminationmeasure:ChosenThreshold医学图像分割专家讲座第25页TheOtsuAlgorithmForeachpotentialthresholdT,1.Separatethepixelsintotwoclustersaccordingtothethreshold.2.Findthemeanofeachcluster.3.Squarethedifferencebetweenthemeans.4.Calculatetheobjectfunctionof

.5.FindtheoptimalthresholdT*thatmaximizesthevalueof.医学图像分割专家讲座第26页DeterminationofOtsu’sthreshold医学图像分割专家讲座第27页AutomaticThresholdbasedonmeanandstandarddeviationAutomaticthresholdbasedonmeanandstandarddeviation:wherearetheautomaticthresholdatthepoint(i,j),themeanandstandarddeviationoftheneighborsof(i,j),i.e.,alocalwindow,kistheweightandcanbearealnumber.医学图像分割专家讲座第28页Determinationofthreshold

bymaximumentropyWhatisanentropy?EntropyisthemeasurementoftheinformationcontentinaprobabilitydistributionMaximumentropysegmentationistoselectsuchathresholdthattheentropiesinbothobjectandbackgroundareashavemaximumdistributions.医学图像分割专家讲座第29页依据二维直方图确定图像分割门限灰度－平均灰度直方图平均灰度－局部方差直方图最大熵灰度－梯度直方图采取聚类方法，分三类平均灰度－局部方差直方图最大熵医学图像分割专家讲座第30页Determinationofthreshold

by2-DHistogramDefinitionof2Dhistogram:Supposef(x,y)tobeanimageofNxNpixels.Itsgraylevelisfrom0toL-1.Segmenttheimagebyusingthefollowingequation:whereForthe2Dthresholdingmethod,itconsiderstheaveragegraylevelofthepoint(x,y)simultaneouslyasfollows.

医学图像分割专家讲座第31页Determinationofthreshold

by2-DHistogramTheaveragegraylevelatthepoint(x,y)ofitsnxnneighborsis:whereForthe2Dthresholdingmethod,itconsiderstheaveragegraylevelofthepoint(x,y)simultaneously,i.e.,use(f(x,y),g(x,y))torepresentanimageandtosegmenttheimagewith2Dvectorthreshold(S,T):

医学图像分割专家讲座第32页Determinationofthreshold

by2-DHistogram

whereForoneimage,letrijtobetheoccurrencenumberofgrayleveliandtheaveragegraylevelj,wecandefinethejointprobabilityas:Piscalledthe2Dhistogramoftheimagef(x,y)

医学图像分割专家讲座第33页Determinationofthreshold

by2-DHistogram

Ifthethresholdvectoris(S,T),the2Dhistogramwillbedividedinto4parts:InPart0andPart1,i.e.,theobjectorbackground,thegraylevelandtheaverageisclose,whileinPart2andpart3,thedifferencebetweenthegraylevelandtheaverageisbig,whichiscorrespondingtotheboundarypoints.2Dhistogramofimage医学图像分割专家讲座第34页Determinationofthreshold

by2-DHistogramThemaximumentropyforthe2Dhistogramistodetermineathresholdvector(S,T)suchthatwecandividetheimageintoobject(A)andbackground(B)withtheprobabilityof

where

医学图像分割专家讲座第35页Determinationofthreshold

by2-DHistogramThegoalofsegmentationistolettheentropiesintheobjectandbackgroundareasasbigaspossible,

Themaximumentropiesoftheobjectandbackgroundwillcorrespondtotheoptimalthresholdvector(S,T).

医学图像分割专家讲座第36页Determinationofthreshold

by2-DHistogram-Experiment医学图像分割专家讲座第37页Determinationofthreshold

byFuzzyEntropyTheBlockBandBlockWaredefinedinFig.1(a)and(b).Fourfuzzysets,BrightX,DarkX,BrightY,DarkY,aredefinedbasedontheS-functionandthecorrespondingZ-functionsasfollows:(Z()=1-s())医学图像分割专家讲座第38页DeterminationofThreshold

byFuzzyEntropy医学图像分割专家讲座第39页Determinationofthreshold

byFuzzyEntropyThefuzzyrelationBrightisasubsetofthefullCartesianproductspaceX×Y

Similarly,

医学图像分割专家讲座第40页DefinitionofFuzzyEntropyLetAbeafuzzysetwithmembershipfunction,wherearethepossibleoutputsfromsourceAwiththeprobability.ThefuzzyentropysetAisdefinedas:

Thetotalimageentropyisdefinedas:

医学图像分割专家讲座第41页Determinationofthreshold

byFuzzyEntropyAsshowninFig.1(a),thedarkblockBlockBcanbedividedintoanonfuzzyregionRBandafuzzyregionR1Similarly,thebrightblockBlockWiscomposedofanonfuzzyregionRWandafuzzyregionR2,asshowninFig.1(b)

医学图像分割专家讲座第42页Determinationofthreshold

byFuzzyEntropyThefollowingfourentropiescanbecalculated:

wherenxyistheelementinthe2-Dhistogramwhichrepresentsthenumberofoccurencesofthepair(x,y)医学图像分割专家讲座第43页Tofindthebestsetofa,b,andcisanoptimizationproblemwhichcanbesolvedbydifferentoptimizationmethods.Forexample,wecanusegeneticalgorithmtosearchfortheoptimalsolution.Theproposedmethodconsistsofthefollowingthreemajorsteps:1)findthe2-Dhistogramoftheimage;2)performfuzzypartitiononthe2-Dhistogram;3)computethefuzzyentropy.Step1)needstobeexecuteonlyoncewhileSteps2)and3)areperformediterativelyforeachsetof(a,b,c).Theoptimum(a,b,c)determinesthefuzzyregion(i.e.,interval[a,c]).Thethresholdisselectedasthecrossoverpointofthemembershipfunctionwhichhasmembership0.5implyingthelargestfuzziness.Determinationofthreshold

byFuzzyEntropy医学图像分割专家讲座第44页Determinationofthreshold

byFuzzyEntropy医学图像分割专家讲座第45页Determinationofthreshold

byFuzzyEntropy-Experiment1医学图像分割专家讲座第46页Comparisonofglobalandlocalthresholdsegmentation医学图像分割专家讲座第47页Determinationofthreshold

byFuzzyEntropy-Experiment2HPDCE/9000医学图像分割专家讲座第48页K-meansclusteringK-meansfollowasimpleandeasywaytoclassifyagivendatasetthroughacertainnumberofclusters(assumekclusters)fixedapriori.Themainideaistodefinekcentroids,oneforeachcluster.Thesecentroidsshoudbeplacedinacunningwaybecauseofdifferentlocationcausesdifferentresult.So,thebetterchoiceistoplacethemasmuchaspossiblefarawayfromeachother.Thenextstepistotakeeachpointbelongingtoagivendatasetandassociateittothenearestcentroid.Whennopointispending,thefirststepiscompletedandanearlygroupageisdone.Atthispointweneedtore-calculateknewcentroidsasbarycentersoftheclustersresultingfromthepreviousstep.Afterwehavetheseknewcentroids,anewbindinghastobedonebetweenthesamedatasetpointsandthenearestnewcentroid.Aloophasbeengenerated.Asaresultofthisloopwemaynoticethatthekcentroidschangetheirlocationstepbystepuntilnomorechangesaredone.Inotherwordscentroidsdonotmoveanymore.医学图像分割专家讲座第49页K-meansclusteringFinally,thisalgorithmaimsatminimizinganobjectivefunction,inthiscaseasquarederrorfunction.Theobjectivefunction

whereisachosendistancemeasurebetweenadatapointxjiandtheclustercentrecj,isanindicatorofthedistanceofthendatapointsfromtheirrespectiveclustercentroids.医学图像分割专家讲座第50页K-meansclusteringAlgorithmThealgorithmiscomposedofthefollowingsteps:1.PlaceKpointsintothespacerepresentedbytheobjectsthatarebeingclustered.Thesepointsrepresentinitialgroupcentroids.2.Assigneachobjecttothe