A Survey of Current Methods in Medical Image

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A Survey of Current Methods in Medical ImageSegmentation

DzungL. Phamé�ê , ChenyangXué , Jerry L. PrinceéëDepartmentof ElectricalandComputerEngineering,TheJohnsHopkinsUniversity

3400N. CharlesSt. Baltimore,MD 21218ìLaboratoryof PersonalityandCognition,NationalInstituteon Aging

5600NathanShockDr., Baltimore,MD 21224

KEYWORDS: medicalimaging,imageprocessing,classification,deformablemodels,magneticresonanceimaging

ABSTRACT: Imagesegmentationplaysacrucialrolein many medicalimagingapplicationsby automat-ing or facilitatingthedelineationof anatomicalstructuresandotherregionsof interest.We presenthereina critical appraisalof thecurrentstatusof semi-automatedandautomatedmethodsfor thesegmentationofanatomicalmedicalimages.Currentsegmentationapproachesarereviewed with an emphasisplacedonrevealingthe advantagesanddisadvantagesof thesemethodsfor medicalimagingapplications.The useof imagesegmentationin differentimagingmodalitiesis alsodescribedalongwith thedifficultiesencoun-teredin eachmodality. We concludewith a discussionon the future of imagesegmentationmethodsinbiomedicalresearch.

1 Introduction

Diagnosticimagingis aninvaluabletool in medicinetoday. Magneticresonanceimaging(MRI), computedtomography(CT), digital mammography, andotherimagingmodal-ities provide an effective meansfor noninvasively mappingthe anatomyof a subject.Thesetechnologieshave greatlyincreasedknowledgeof normalanddiseasedanatomyfor medicalresearchandareacritical componentin diagnosisandtreatmentplanning.

With the increasingsizeandnumberof medicalimages,theuseof computersin fa-cilitating their processingandanalysishasbecomenecessary. In particular, computeralgorithmsfor thedelineationof anatomicalstructuresandotherregionsof interestarea key componentin assistingandautomatingspecificradiologicaltasks. Thesealgo-rithms,calledimage segmentationalgorithms,play a vital role in numerousbiomedicalimagingapplicationssuchasthequantificationof tissuevolumes[98], diagnosis[176],localizationof pathology[208], study of anatomicalstructure[198], treatmentplan-ning [90], partial volumecorrectionof functional imagingdata[128], andcomputer-integratedsurgery[6, 61].

Methodsfor performingsegmentationsvarywidelydependingonthespecificapplica-tion, imagingmodality, andotherfactors.For example,thesegmentationof braintissuehasdifferentrequirementsfrom thesegmentationof theliver. Generalimagingartifactssuchasnoise,partialvolumeeffects,andmotioncanalsohavesignificantconsequenceson the performanceof segmentationalgorithms. Furthermore,eachimagingmodalityhasits own idiosyncrasieswith which to contend.Thereis currentlyno singlesegmen-tationmethodthatyieldsacceptableresultsfor every medicalimage.Methodsdo exist

1

ImageSegmentation 2

that aremoregeneralandcanbe appliedto a variety of data. However, methodsthatarespecializedto particularapplicationscanoftenachieve betterperformanceby takinginto accountprior knowledge. Selectionof anappropriateapproachto a segmentationproblemcanthereforebeadifficult dilemma.

This chapterprovidesanoverview of currentmethodsusedfor computerassistedorcomputerautomatedsegmentationof anatomicalmedicalimages.Methodsandapplica-tionsthathave appearedin therecentliteraturearebriefly described.A full descriptionof competingmethodsis beyond the scopeof this chapterandthe readersarereferredto referencesfor additionaldetails. We focusinsteadon providing thereaderan intro-ductionto thedifferentapplicationsof segmentationin medicalimagingandthevariousissuesthat mustbe confronted.Also, we refer only to the mostcommonlyusedradi-ological modalitiesfor imaginganatomy:magneticresonanceimaging(MRI), X-raycomputedtomography(CT), ultrasound,andX-ray projectionradiography. Most of theconceptsdescribed,however, areapplicableto otherimagingmodalitiesaswell.

This chapteris organizedasfollows. In Section2, commonterminologyandissuesassociatedwith thesegmentationof medicalimagesaredefinedanddiscussed.In Sec-tion 3, webriefly describemethodologiesusedin commonsegmentationapproaches.InSection4, we review thewaysin which segmentationmethodshave recentlybeenap-plied in differentimagingmodalities.Finally in Section5, importantissuesrelatingtothefutureof medicalimagesegmentationarediscussed.

2 Background

In thissectionwedefineterminologythatwill beusedthroughoutanddescribeimportantissuesin thesegmentationof medicalimages.

2.1 Definitions

An imageisacollectionof measurementsin two-dimensional(2-D)or three-dimensional(3-D) space.In medicalimages,thesemeasurementsor image intensitiescanberadia-tionabsorptionin X-ray imaging,acousticpressurein ultrasound,or RFsignalamplitudein MRI. If a singlemeasurementis madeat eachlocationin the image,thenthe imageis calleda scalar image. If morethanonemeasurementis made(eg. dual-echoMRI),the imageis calleda vectoror multi-channel image. Imagesmay be acquiredin thecontinuousdomainsuchasonX-ray film, or in discretespaceasin MRI. In 2-D discreteimages,thelocationof eachmeasurementis calledapixelandin 3-D images,it is calleda voxel. For simplicity, we will oftenusethe term“pixel” to refer to both the2-D and3-D cases.

Classically, imagesegmentationis definedasthe partitioningof an imageinto non-overlapping,constituentregionswhich arehomogeneouswith respectto somecharac-teristicsuchasintensityor texture[66, 59, 132]. If thedomainof theimageis givenbyí, thenthe segmentationproblemis to determinethe sets î}ï�ð í

whoseunion is theentireimage

í. Thus,thesetsthatmake upasegmentationmustsatisfy

í�ñ òóï%ôIõ î}ï (1)

whereî�ï]ö÷îsø ñúùfor û"üñþý

, andeachî�ï is connected.Ideally, asegmentationmethodfindsthosesetsthatcorrespondto distinctanatomicalstructuresor regionsof interestintheimage.

ImageSegmentation 3

Whentheconstraintthat regionsbeconnectedis removed,thendeterminingthesetsî}ï is calledpixel classificationandthesetsthemselvesarecalledclasses. Pixel classi-fication ratherthanclassicalsegmentationis often a desirablegoal in medicalimages,particularlywhendisconnectedregionsbelongingto the sametissueclassneedto beidentified.Determinationof thetotal numberof classesÿ in pixel classificationcanbea difficult problem[97]. Often,thevalueof ÿ is assumedto beknown basedon priorknowledgeof theanatomybeingconsidered.

Labelingis theprocessof assigninga meaningfuldesignationto eachregion or classandcanbeperformedseparatelyfrom segmentation.It mapsthenumericalindex û ofset î}ï , to ananatomicaldesignation.In medicalimaging,the labelsareoftenvisuallyobviousandcanbedetermineduponinspectionby a physicianor technician.Computerautomatedlabelingis desirablewhenlabelsarenotobviousandin automatedprocessingsystems.A typical situationinvolving labelingoccursin digital mammographywheretheimageis segmentedinto distinctregionsandtheregionsaresubsequentlylabeledasbeinghealthytissueor tumorous.

Methodswhichdelineateastructureor structuresin animage,includingbothclassicalsegmentationandpixel classificationmethods,areconsideredin this review. Althoughwe do not discussspecificlabeling methods,we will discussseveral techniquesthatperformbothsegmentationandlabelingsimultaneously.

Two fields closely relatedto segmentationthat we do not discusshereare featuredetectionandmotion estimation.The distinctionwe make betweensegmentationandfeaturedetectionis thatfeaturedetectionis concernedwith determiningthepresenceofsomeimagepropertywhile segmentationgenerallyassumesthatthepropertyis alreadypresentandattemptsto preciselylocalizeareasthatpossesstheproperty. For example,edgedetectionmethodscandeterminethe locationof edgesin an imagebut withoutfurtherprocessing,do not necessarilyextractany region of interest.Motion estimationmethodsoftenconsistof applyingsegmentationalgorithmsto timesequencesof images.Weconsiderthis applicationof segmentationto bea separatebranchof researchanddonot includeit in this review.

2.2 Dimensionality

Dimensionalityreferstowhetherasegmentationmethodoperatesin a2-D imagedomainor a 3-D imagedomain.Methodsthat rely solelyon imageintensitiesareindependentof the imagedomain. However, certainmethodssuchasdeformablemodels,Markovrandomfields,andregiongrowing (describedin Section3), incorporatespatialinforma-tion andmaythereforeoperatedifferentlydependingonthedimensionalityof theimage.Generally, 2-D methodsareappliedto 2-D imagesand3-D methodsareappliedto 3-Dimages.In somecases,however, 2-D methodsareappliedsequentiallyto theslicesof a3-D image[7, 52,103, 141]. Thismayarisebecauseof practicalreasonssuchaseaseofimplementation,lower computationalcomplexity, andreducedmemoryrequirements.In addition,certainstructuresaremoreeasilydefinedalong2-D slices.

A uniquesituationthat occursin medicalimagesegmentationis the delineationofregionsonanon-Euclideandomain,suchasin braincortex parcellation[148, 156]. Thisis essentiallysegmentationon a surfaceof measurements.Becausea surfaceis a 2-Dobjectfolded in 3-D space,segmentationon a surfacecannot be treatedasa standard2-D or 3-D problem. The modelingof spatialcharacteristicsalonga surfaceis muchmoredifficult thanin a standardimagingplanebecauseof the irregularsamplingusedby meshrepresentationsandbecauseof theneedto computegeodesics[89]. This is anemergingareaof researchandpreliminaryresultshave shown greatpromise.

ImageSegmentation 4

(a) (b)

Figure1: Illustrationof partialvolumeeffect: (a) Idealimage,(b) acquiredimage.

2.3 Softsegmentationandpartial volumeeffects

Segmentationsthat allow regions or classesto overlap are called soft segmentations.Soft segmentationsareimportantin medicalimagingbecauseof partial volumeeffects,wheremultiple tissuescontribute to a singlepixel or voxel resultingin a blurring ofintensityacrossboundaries.Figure1 illustrateshow thesamplingprocesscanresultinpartialvolumeeffects,leadingto ambiguitiesin structuraldefinitions.In Figure1b, it isdifficult to preciselydeterminetheboundariesof thetwo objects.A hard segmentationforcesa decisionof whethera pixel is insideor outsidetheobject. Soft segmentationson the other hand, retain more information from the original imageby allowing foruncertaintyin the locationof objectboundaries.Notethat thepoint spreadfunctionofanimagingdevice canbelarger thanthespatialextentof a singlepixel or voxel. Thus,partialvolumeeffectscancauseboundariesto beblurredacrosssignificantportionsofanimage.

In pixel classificationmethods,thenotionof asoftsegmentationstemsfromthegener-alizationof asetcharacteristicfunction. A characteristicfunctionis simplyanindicatorfunctionof whereapixel is insideor outsideits correspondingset.For a location

ý��í,

thecharacteristicfunction ��ï�� ý�� of theset î}ï is definedto be�Iï�� ý��Pñ�� ifý�� î�ï�

otherwise(2)

Characteristicfunctionscanbegeneralizedto membership functions[205] which neednotbebinaryvalued.Membershipfunctions ï�� ý�� satisfythefollowing constraints:�� ï�� ý�� û � ý (3)

ò�ï%ôIõ ï�� ý��ñ �� ý (4)

The valueof a membershipfunction ï�� ý�� canbe interpretedas the contribution ofclassû to location

ý. Thus,wherever membershipvaluesaregreaterthanzerofor two

or moreclasses,thoseclassesareoverlapping.Conversely, if themembershipfunctionis unity for somevalueof

ýand û , thenclassû is theonly contributing classat locationý

. Membershipfunctionscanbederivedusingfuzzyclusteringandclassifieralgorithms[140, 71], statisticalalgorithmsin which casethemembershipfunctionsareprobabilityfunctions[106, 197], or they canbecomputedasestimatesof partial volumefractions

ImageSegmentation 5

[24]. Softsegmentationsbasedonmembershipfunctionscanbeeasilyconvertedto hardsegmentationsby assigningapixel to its classwith thehighestmembershipvalue.

2.4 Continuousor discretesegmentations

Nearlyall medicalimagesusedfor imagesegmentationarerepresentedasdiscretesam-plesonauniformgrid. Segmentationmethodstypicallyoperateonthesamediscretegridastheimage.However, certainmethodssuchasdeformablemodels(seeSection3.7)arecapableof operatingin the continuousspatialdomain,therebyproviding the potentialfor subpixel accuracy in delineatingstructures.Subpixel accuracy is desirableparticu-larly whentheresolutionof theimageis onthesameorderof magnitudeasthestructureof interest.

Segmentationonthecontinuousdomainis notequivalentto partialvolumeestimationor othersoft segmentationmethods.Partial volumeestimationmethodsmerelyprovidethefractionof astructurewhichis presentin avoxel. Thismaybesufficient for quantifi-cationpurposesbut not in situationswherepreciselocalizationis required,suchasfortumorsin surgical or radiotherapy planning.Continuoussegmentationmethodsactuallyreconstructhow a structurepassesthrougha voxel. Althoughcontinuoussegmentationmethodshave subpixel or subvoxel resolution,their precisionandaccuracy arestill de-pendenton theresolutionof theoriginal data. Furthermore,this level of precisioncanbedifficult to validateonrealdata.

2.5 Interaction

Thetradeoff betweenmanualinteractionandperformanceis animportantconsiderationin any segmentationapplication.Manualinteractioncanimprove accuracy by incorpo-ratingprior knowledgeof anoperator. However, for largepopulationstudies,thiscanbelaboriousandtimeconsuming.

Thetypeof interactionrequiredby segmentationmethodscanrangefrom completelymanualdelineationof ananatomicalstructure,to theselectionof a seedpoint for a re-gion growing algorithm(seeSection3.2). Thedifferencesin thesetypesof interactionarethe amountof time andeffort required,aswell asthe amountof training requiredby anoperator. Methodsthatrely onmanualinteractioncanalsobevulnerableto relia-bility issues.However, even“automated”segmentationmethodstypically requiresomeinteractionfor specifyinginitial parametersthatcansignificantlyaffect performance.

2.6 Validation

In orderto quantifytheperformanceof a segmentationmethod,validationexperimentsarenecessary. Validationis typically performedusingoneof two differenttypesof truthmodels.Themoststraightforwardapproachto validationis by comparingtheautomatedsegmentationswith manuallyobtainedsegmentations(cf. [199, 186]). This approach,besidessuffering from thedrawbacksoutlinedin theprevioussection,doesnot guaran-teea perfecttruth modelsinceanoperator’s performancecanalsobeflawed. Theothercommonapproachto validatingsegmentationmethodsis throughthe useof physicalphantoms[102] or computationalphantoms[36]. Physicalphantomsprovide anaccu-ratedepictionof the imageacquisitionprocessbut typically do not presenta realisticrepresentationof anatomy. Computationalphantomscanbemorerealisticin this latterregard,but simulatetheimageacquisitionprocessusingonly simplifiedmodels.

ImageSegmentation 6

Oncea truth model is available, a figure of merit must be definedfor quantifyingaccuracy or precision(cf. [20]). The choiceof the figure of merit is dependentonthe applicationandcanbe basedon region informationsuchasthe numberof pixelsmisclassified,or boundaryinformationsuchasdistanceto thetrueboundary. A surveyon this topic is providedin [206].

3 Methods

In this section,we briefly describeseveral commonapproachesthat have appearedintherecentliteratureonmedicalimagesegmentation.Wedefineeachmethod,provideanoverview of how themethodis implemented,anddiscussits advantagesanddisadvan-tages. Although eachtechniqueis describedseparately, multiple techniquesareoftenusedin conjunctionwith oneanotherfor solvingdifferentsegmentationproblems.

We divide segmentationmethodsinto eightcategories: (1) thresholdingapproaches,(2) region growing approaches,(3) classifiers,(4) clusteringapproaches,(5) Markovrandomfield models,(6) artificial neuralnetworks,(7) deformablemodels,and(8) atlas-guidedapproaches.Othernotablemethodsthatdonotbelongto any of thesecategoriesaredescribedat theendof thissection.Of themethodsdiscussedin thissection,thresh-olding, classifier, clustering,andMarkov randomfield approachescanbe consideredpixel classificationmethods.

Most of theimagesegmentationmethodsthatwe will describecanbeposedasopti-mizationproblemswherethedesiredsegmentationminimizessomeenergy or costfunc-tion definedby theparticularapplication.In probabilisticmethods,this is equivalenttomaximizinga likelihoodor a posterioriprobability. Given the image � , we desirethesegmentation ! suchthat ! ñ ��#"%$�&�'(*) � ! � � � (5)

where ) , theenergy function,dependson theobserved image � anda segmentation! .Defininganappropriate) is amajordifficulty in designingsegmentationalgorithmsbe-causeof thewide varietyof imagepropertiesthatcanbeused,suchasintensity, edges,andtexture. In additionto informationderived from the image,prior knowledgecanalsobe incorporatedto further improve performance.The advantageof posinga seg-mentationasanoptimizationproblemis thatit preciselydefineswhatis desirablein thesegmentation. It is clear that for differentapplications,differentenergy functionsarenecessary.

Severalgeneralsurveys on imagesegmentationexist in theliterature[66, 132]. Addi-tionalsurveysonimagesegmentationspecificallyfor medicalimageshavealsoappeared[21, 11, 172, 208, 29, 6].

3.1 Thresholding

Thresholdingapproachessegmentscalarimagesby creatinga binarypartitioningof theimageintensities.Figure2ashows thehistogramof a scalarimagethatpossessesthreeapparentclassescorrespondingto the threemodes.A thresholdingprocedureattemptsto determineanintensityvalue,calledthethreshold, whichseparatesthedesiredclasses.Thesegmentationis thenachievedby groupingall pixelswith intensitygreaterthanthethresholdinto oneclass,andall otherpixelsinto anotherclass.Two potentialthresholdsareshown in Figure2aat thevalleys of thehistogram.Determinationof morethanonethresholdvalueis aprocesscalledmultithresholding[155].

ImageSegmentation 7

intensity

occu

renc

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y1

y2

(a) (b) (c)

Figure2: Featurespacemethodsandregion growing: (a) a histogramshowing threeapparentclasses,(b) a2-D featurespace,(c) exampleof regiongrowing.

Thresholdingis a simpleyet often effective meansfor obtaininga segmentationinimageswheredifferentstructureshave contrastingintensitiesor otherquantifiablefea-tures. Thepartition is usuallygeneratedinteractively, althoughautomatedmethodsdoexist [155]. For scalarimages,interactive methodscanbe basedon an operator’s vi-sualassessmentof theresultingsegmentationsincethethresholdingoperationis imple-mentablein real-time.

Thresholdingis oftenusedasaninitial stepin asequenceof imageprocessingopera-tions.Its mainlimitationsarethatin its simplestform only two classesaregeneratedandit cannot beappliedto multi-channelimages.In addition,thresholdingtypically doesnottake into accountthespatialcharacteristicsof animage.Thiscausesit to besensitiveto noiseandintensityinhomogeneities,which canoccurin magneticresonanceimages(seeSection4.2). Both theseartifactsessentiallycorrupt the histogramof the image,makingseparationmoredifficult. For thesereasons,variationsonclassicalthresholdinghave beenproposedfor medicalimagesegmentationthatincorporateinformationbasedon local intensities[104] andconnectivity [99]. A survey on thresholdingtechniquesisprovidedin [155].

3.2 Regiongrowing

Region growing is a techniquefor extractinga region of the imagethat is connectedbasedon somepredefinedcriteria. This criteriacanbebasedon intensityinformationand/oredgesin theimage[66]. In its simplestform, regiongrowing requiresaseedpointthat is manuallyselectedby anoperator, andextractsall pixelsconnectedto the initialseedwith thesameintensityvalue.This is depictedin Figure2b,whereregiongrowinghasbeenusedto isolateoneof thestructuresfrom Figure1a.

Like thresholding,region growing is not often usedalonebut within a setof imageprocessingoperations,particularlyfor the delineationof small, simplestructuressuchastumorsandlesions[57, 143]. Its primarydisadvantageis that it requiresmanualin-teractionto obtainthe seedpoint. Thus, for eachregion that needsto be extracted,aseedmustbeplanted.Split andmergealgorithmsarerelatedto region growing but donot requirea seedpoint [115]. Region growing canalsobesensitive to noise,causingextractedregionsto have holesor even becomedisconnected.Conversely, partial vol-umeeffectscancauseseparateregions to becomeconnected.To help alleviate theseproblems,a homotopicregion growing algorithmhasbeenproposedthatpreservesthetopologybetweenan initial region andan extractedregion [114]. Fuzzyanalogiestoregiongrowing have alsobeendeveloped[183].

ImageSegmentation 8

3.3 Classifiers

Classifiermethodsare patternrecognitiontechniquesthat seekto partition a featurespacederivedfrom theimageusingdatawith known labels[159, 11]. A featurespaceistherangespaceof any functionof theimage,with themostcommonfeaturespacebeingthe imageintensitiesthemselves. A histogram,asshown in Figure2a, is an exampleof a 1-D featurespace.Figure2c shows anexampleof a partitioned2-D featurespacewith two apparentclasses.All pixelswith theirassociatedfeaturesontheleft sideof thepartitionwould begroupedinto oneclass.Althoughthefeaturesusedcanberelatedtotextureor otherproperties,weassumefor simplicity thatthefeaturesaresimplyintensityvalues.

Classifiersareknown assupervisedmethodssincethey requiretrainingdatathataremanuallysegmentedandthenusedasreferencesfor automaticallysegmentingnew data.Thereareanumberof waysin whichtrainingdatacanbeappliedin classifiermethods.Asimpleclassifieris thenearest-neighborclassifier, whereeachpixel or voxel is classifiedin thesameclassasthetrainingdatumwith theclosestintensity. The û -nearest-neighbor(kNN) classifieris ageneralizationof thisapproach,wherethepixel is classifiedaccord-ing to themajority voteof the û closesttrainingdata.ThekNN classifieris considereda nonparametricclassifiersinceit makesno underlyingassumptionaboutthestatisticalstructureof thedata.Anothernonparametricclassifieris theParzenwindow, wheretheclassificationis madeaccordingto themajority votewithin a predefinedwindow of thefeaturespacecenteredat theunlabeledpixel intensity.

A commonly-usedparametricclassifieris the maximumlikelihood (ML) or Bayesclassifier. It assumesthatthepixel intensitiesareindependentsamplesfrom amixtureofprobabilitydistributions,usuallyGaussian.This mixture,calleda finite mixturemodel,is givenby theprobabilitydensityfunction, ��- ø�.#/ �#0 ��ñ ò�

ï%ôIõ 0 ï , ï��- ø1.#/ ï � (6)

where -Nø is the intensityof pixelý,, ï is a componentprobabilitydensityfunctionpa-

rameterizedby / ï , and / ñ32 /8õ �5454546� / ò87 . Thevariables0 ï aremixing coefficientsthatweight the contribution of eachdensityfunctionand 0 ñ92 0 õ �5454546�#0 ò87 . Trainingdatais collectedby obtainingrepresentative samplesfrom eachcomponentof the mixturemodel and then estimatingeach / ï accordingly. For Gaussianmixtures, this meansestimatingÿ means,covariances,andmixing coefficients. Classificationof new datais obtainedby assigningeachpixel to the classwith the highestposteriorprobability.Whenthedatatruly follows afinite Gaussianmixturedistribution, theML classifiercanperformwell and is capableof providing a soft segmentationcomposedof the poste-rior probabilities.Additional parametricandnonparametricclassifiersaredescribedin[208].

Standardclassifiersrequirethatthestructuresto besegmentedpossessdistinctquan-tifiablefeatures.Becausetrainingdatacanbelabeled,classifierscantransfertheselabelsto new dataaslongasthefeaturespacesufficiently distinguisheseachlabelaswell. Be-ing non-iterative, they arerelatively computationallyefficient andunlike thresholdingmethods,they canbe appliedto multi-channelimages. A disadvantageof classifiersis that they generallydo not performany spatialmodeling. This weaknesshasbeenaddressedin recentwork extendingclassifiermethodsto segmentingimagesthat arecorruptedby intensity inhomogeneities[197]. Neighborhoodandgeometricinforma-tion werealsoincorporatedinto a classifierapproachin [85]. Anotherdisadvantageistherequirementof manualinteractionfor obtainingtrainingdata. Trainingsetscanbe

ImageSegmentation 9

acquiredfor eachimagethat requiressegmenting,but this canbe time consumingandlaborious.On theotherhand,useof thesametrainingsetfor a large numberof scanscanleadto biasedresultswhich do not take into accountanatomicalandphysiologicalvariability betweendifferentsubjects.

3.4 Clustering

Clusteringalgorithmsessentiallyperformthesamefunctionasclassifiermethodswith-out theuseof trainingdata. Thus,they aretermedunsupervisedmethods.In ordertocompensatefor the lack of training data,clusteringmethodsiteratebetweensegment-ing the imageandcharacterizingthepropertiesof theeachclass.In a sense,clusteringmethodstrain themselvesusingtheavailabledata.

Threecommonlyusedclusteringalgorithmsarethe ÿ -meansor ISODATA algorithm[34], the fuzzy : -meansalgorithm [46, 11], and the expectation-maximization(EM)algorithm [102, 107]. The ÿ -meansclusteringalgorithm clustersdataby iterativelycomputingameanintensityfor eachclassandsegmentingtheimageby classifyingeachpixel in theclasswith theclosestmean[75]. Figure3b shows theresultof applyingtheÿ -meansalgorithmto asliceof a MR brainimagein Figure3a.Thenumberof classeswas assumedto be three,representing(from dark gray to white) cerebrospinalfluid,graymatter, andwhite matter. The fuzzy : -meansalgorithmgeneralizesthe ÿ -meansalgorithm[11], allowing for softsegmentationsbasedonfuzzysettheory[205]. TheEMalgorithmappliesthesameclusteringprincipleswith theunderlyingassumptionthatthedatafollows a Gaussianmixture model (seeEq. (6)). It iteratesbetweencomputingtheposteriorprobabilitiesandcomputingmaximumlikelihoodestimatesof themeans,covariances,andmixing coefficientsof themixturemodel.

Althoughclusteringalgorithmsdonot requiretrainingdata,they do requireaninitialsegmentation(or equivalently, initial parameters).TheEM algorithmhasdemonstratedgreatersensitivity to initialization thanthe ÿ -meansor fuzzy : -meansalgorithms[42].Likeclassifiermethods,clusteringalgorithmsdonotdirectly incorporatespatialmodel-ing andcanthereforebesensitive to noiseandintensityinhomogeneities.This lack ofspatialmodeling,however, canprovidesignificantadvantagesfor fastcomputation[69].Work on improving therobustnessof clusteringalgorithmsto intensityinhomogeneitiesin MR imageshasdemonstratedexcellentsuccess[58, 140]. Robustnessto noisecanbeincorporatedusingMarkov randomfield modelingasdescribedin thenext section.

3.5 Markov randomfieldmodels

Markov randomfield (MRF) modelingitself is not a segmentationmethodbut a sta-tistical modelwhich canbe usedwithin segmentationmethods.MRFs modelspatialinteractionsbetweenneighboringor nearbypixels. Theselocal correlationsprovide amechanismfor modelinga varietyof imageproperties[105]. In medicalimaging,theyaretypically usedto take into accountthefactthatmostpixelsbelongto thesameclassastheirneighboringpixels. In physicalterms,this impliesthatany anatomicalstructurethat consistsof only onepixel hasa very low probability of occurringundera MRFassumption.

MRFsareoftenincorporatedinto clusteringsegmentationalgorithmssuchasthe ÿ -meansalgorithmundera Bayesianprior model[133, 149, 70,58]. Thesegmentationisthenobtainedby maximizingthea posterioriprobabilityof thesegmentationgiventheimagedatausingiterative methodssuchasiteratedconditionalmodes[10] or simulatedannealing[54]. Figure3c, shows the robustnessto noisein a segmentationresulting

ImageSegmentation 10

(a) (b) (c)

Figure3: Segmentationof aMR brainimage:(a)original image,(b) segmentationusingthe ÿ -meansalgorithm,(c) segmentationusingthe ÿ -meansalgorithmwith a Markovrandomfield prior.

from an MRF prior. The segmentationis muchsmootherthanthe non-MRFresultofFigure3b.

A difficulty associatedwith MRF modelsis properselectionof theparameterscon-trolling the strengthof spatialinteractions[105]. Too high a settingcanresult in anexcessively smoothsegmentationanda lossof importantstructuraldetails.In addition,MRF methodsusuallyrequirecomputationallyintensive algorithms.Despitethesedis-advantages,MRFsarewidely usednot only to modelsegmentationclasses,but alsotomodelintensityinhomogeneitiesthatcanoccurin MR images[70] andtextureproperties[153].

3.6 Artificial neural networks

Artificial neuralnetworks (ANNs) aremassively parallelnetworks of processingele-mentsor nodesthat simulatebiological learning. Eachnodein an ANN is capableofperformingelementarycomputations.Learningis achieved throughthe adaptationofweightsassignedto the connectionsbetweennodes. A thoroughtreatmenton neuralnetworkscanbefoundin [27, 68].

ANNs representa paradigmfor machinelearningand can be usedin a variety ofwaysfor imagesegmentation.Themostwidely appliedusein medicalimagingis asaclassifier[64, 53], wheretheweightsaredeterminedusingtrainingdata,andtheANNis thenusedto segmentnew data.ANNs canalsobeusedin anunsupervisedfashionasaclusteringmethod[11, 152], aswell asfor deformablemodels[191].

Becauseof the many interconnectionsusedin a neuralnetwork, spatialinformationcaneasilybeincorporatedinto its classificationprocedures.AlthoughANNs areinher-ently parallel,their processingis usuallysimulatedon a standardserialcomputer, thusreducingthispotentialcomputationaladvantage.

3.7 Deformablemodels

Deformablemodelsarephysicallymotivated,model-basedtechniquesfor delineatingregion boundariesusingclosedparametriccurvesor surfacesthatdeformunderthe in-


(a) (b)

Figure4: (a) A 2-D exampleof usinga deformablecontourto extract theinnerwall ofthe left ventricleof a humanheartfrom anMR image. The initial deformablecontour(plottedin gray) andthe final convergedresult(plottedin white). (b) A 3-D exampleof usinga deformablesurfaceto reconstructthebraincorticalsurfacefrom a 3-D MRimage.

fluenceof internalandexternalforces.To delineateanobjectboundaryin an image,aclosedcurve or surfacemustfirst beplacednearthedesiredboundaryandthenallowedto undergo an iterative relaxationprocess. Internal forcesare computedfrom withinthecurve or surfaceto keepit smooththroughoutthedeformation.Externalforcesareusuallyderivedfrom theimageto drive thecurve or surfacetowardsthedesiredfeatureof interest.Figure4ashows anexampleof applyinga 2-D deformablemodelor activecontourto aMR heartimage.Theactive contourwasinitializedasacircle,andthenal-lowedto deformto theinnerboundaryof theleft ventricle.Figure4bshowsanexampleof a3-D deformablesurfacethatwasusedto extractthecerebralcortex from aMR headscan.

Mathematically, a deformablemodelmovesaccordingto its dynamicequationsandseekstheminimumof agivenenergy functional[87, 180]. Thedeformationof a typical2-D deformablemodelcanbecharacterizedby thefollowing dynamicequation:; �=< ��>@? ! �=< �BA �> A ? CED �=< ��> ! �=< �BA �> A ñGFIHKJML C FINPOML (7)

where ! �=< �BA � ñ ��Q��=< �BA � � -R�=< �BA �B� is a parametricrepresentationof the positionof themodelat a given time A , and ; �=< � and D �=< � areparametersrepresentingthemassden-sity anddampingdensityof themodel,respectively. Eq. (7) causesthemodelto moveaccordingto thedirectionandmagnitudeof theforceson theright handside.ThemostcommonlyusedinternalforcesareFIHKJMLÇñ >> <TS1U �=< � > ! �=< �BA �> < VXW >@?> < ?ZY�[ �=< � >@? !> < ?R\ (8)

whichrepresentinternalstretchingandbendingforces.Themostcommonlyusedexter-nal forcesarecomputedasthegradientof anedgemap(asshown in Figure4b).

Themainadvantagesof deformablemodelsaretheirability to directlygenerateclosedparametriccurvesor surfacesfrom imagesandtheir incorporationof asmoothnesscon-straintthatprovidesrobustnessto noiseandspuriousedges.A disadvantageis thatthey


(a) (b) (c)

Figure 5: Demonstrationof atlas warping: (a) templateimage, (b) target image,(c) warpedtemplate(Imagesprovidedcourtesyof G.E.ChristensenandM.I. Miller).

requiremanualinteractionto placeaninitial modelandchooseappropriateparameters.Reducingsensitivity to initializationhasbeena topic of researchthathasdemonstratedexcellentsuccess[33, 18,112, 201]. Standarddeformablemodelscanalsoexhibit poorconvergenceto concave boundaries.This difficulty canbealleviatedsomewhatthroughtheuseof pressureforces[33] andothermodifiedexternalforcemodels[201]. Anotherimportantextensionof deformablemodelsis theadaptivity of modeltopologyusinganimplicit representationratherthananexplicit parameterization[18, 112, 118]. A generalreview ondeformablemodelsin medicalimageanalysiscanbefoundin [119].

3.8 Atlas-guidedapproaches

Atlas-guidedapproachesarea powerful tool for medicalimagesegmentationwhenastandardatlasor templateis available.Theatlasis generatedby compilinginformationontheanatomythatrequiressegmenting.Thisatlasis thenusedasareferenceframeforsegmentingnew images.Conceptually, atlas-guidedapproachesaresimilar to classifiersexceptthey areimplementedin thespatialdomainof the imageratherthanin a featurespace.

Thestandardatlas-guidedapproachtreatssegmentationasaregistrationproblem(see[111] for adetailedsurvey onregistrationtechniques).It first findsaone-to-onetransfor-mationthatmapsapre-segmentedatlasimageto thetargetimagethatrequiressegment-ing. This processis oftenreferredto asatlaswarping. Thewarpingcanbeperformedusinglinear [175, 96, 151] transformationsbut becauseof anatomicalvariability, a se-quentialapplicationof linearandnon-linear[35, 39, 26, 156] transformationsis oftenused.An exampleof atlaswarpingfor a MR headscanis shown in Figure5 [26]. Be-causetheatlasis alreadysegmented,all structuralinformationis transferredto thetargetimage.This is shown in Figure6, wheretheTalairachbrainatlas[175] hasbeenmappedto anMR image[39].

Atlas-guidedapproacheshave beenappliedmainly in MR brainimaging.An advan-tageof atlas-guidedapproachesis thatlabelsaretransferredaswell asthesegmentation.They alsoprovideastandardsystemfor studyingmorphometricproperties[41, 181, 79].Evenwith non-linearregistrationmethodshowever, accuratesegmentationsof complexstructuresis difficult dueto anatomicalvariability. This is shown in Figure6 wherethecerebralcortex is not segmentedasaccuratelyasshown in Figure3. Thus,atlas-guided


Figure6: Threeslicesfrom a MR brain volumeoverlaid with a warpedatlas(Imagesprovidedcourtesyof C.A. Davatzikos).

approachesaregenerallybetter-suitedfor segmentationof structuresthatarestableoverthepopulationof study. Onemethodthathelpsmodelanatomicalvariability is theuseofprobabilisticatlases[181] but theserequireadditionaltimeandinteractionto accumulatedata.

3.9 Otherapproaches

Model-fitting is asegmentationmethodthattypically fits asimplegeometricshapesuchasanellipseor parabolato thelocationsof extractedimagefeaturesin animage[137].It is a techniquewhich is specializedto thestructurebeingsegmentedbut is easilyim-plementedandcanprovidegoodresultswhenthemodelis appropriate.A moregeneralapproachis to fit splinecurvesor surfaces[7] to the features.Themaindifficulty withmodel-fitting is that imagefeaturesmustfirst be extractedbeforethe fitting can takeplace.

Thewatershedalgorithmusesconceptsfrom mathematicalmorphology[59] to parti-tion imagesinto homogeneousregions[192]. Thismethodcansuffer from oversegmen-tation,which occurswhenthe imageis segmentedinto anunnecessarilylarge numberof regions. Thus,watershedalgorithmsin medicalimagingareusuallyfollowed by apostprocessingstepto mergeseparateregionsthatbelongto thesamestructure[161].

4 Modalities

In this section,we review the applicationof segmentationto variousmedicalimagingmodalities.Wedescribethespecificissuesrelevantto eachmodalityandtheanatomicalregionsfor which segmentationmethodshave beenapplied.For informationaboutthephysicsbehindtheimageacquisitionprocessin thesemodalities,see[110, 170].

4.1 Magneticresonanceimaging

Themajority of researchin medicalimagesegmentationpertainsto its usefor MR im-ages,especiallyin brain imaging. This is becauseof MR’s ability to provide a com-binationof high resolution(on the order of 1mm cubic voxels), excellent soft tissuecontrast,anda high signal-to-noiseratio. Furthermore,multi-channelMR imageswithvarying contrastcharacteristicscan be acquired,providing additionalinformation for


distinguishingbetweendifferentstructures.For generalreviews on thesegmentationofMR images,see[11, 139, 106, 208, 29]. Direct comparisonsof differentmethodsforsegmentingMR imagesarealsoavailable[187, 30, 64].

Becauseof its ability to derive contrastfrom a numberof tissueparameters,manydifferentpulsesequencesexist for acquiringMR images.Determiningtheoptimalpulsesequencefor obtainingaccuratesegmentations[147] is thereforeanimportantproblemthat requiresknowledgeof the underlyingtissuepropertiesof the anatomyto be seg-mented[141, 50]. Furthermore,becauseof theanatomicalandphysiologicalvariabilitybetweendifferentsubjects,differentpopulationsmayrequiredifferentpulsesequences[141].

Much of theliteratureon segmentationin MRI focusesspecificallyon thesegmenta-tion of headscansin normalsubjects.Therearethreegeneralgoalsin this application:1) extractthebrainvolume,2) segmentbrain tissueinto graymatter, white matter, andcerebrospinalfluid, and3) delineatespecificbrainstructuressuchasthecerebralcortexor thehippocampus.An exceptionto thiscategorizationis theuseof atlas-guidedmeth-ods[35], which arecapableof fully segmentingandlabelingall structuresof thebrainsimultaneously, but alsohave certaindisadvantages(seeSection3.8). Overviews on thesegmentationof neuroanatomyareprovidedin [32, 198].

Brain volumeextractionis a difficult problemin MR headscans,particularlyin T1-weightedimages. However, it is often a necessarystepbeforesegmentationof otherstructurescan take place. Problemsin brain volumeextractionarisebecausethereisa greatdealof overlapin intensityvaluesbetweenthe non-brainandbrain tissuesandbecausethetwo canoftenappearconnected.Onemethodto dealwith thesedifficultiesis to allow for somelossof brain tissuein a preliminarysegmentationstepand thento recover the tissueusingmorphologicalfilters [16, 156]. Several methodshave alsoapplieddeformablemodelsasa final stepin a sequenceof imageprocessingoperations[84, 1, 5]. Atlas-guidedapproacheshave alsobeenapplied[1].

Methodsthatattemptto segmentbrain tissueasgraymatter, white matter, andcere-brospinalfluid useeitherT1-weightedscalardata[77, 126, 72, 122, 149, 194] or mul-tispectraldata[189, 108, 24, 91, 55, 64, 30, 107, 67, 88, 182, 152]. The trendin theliteraturehasbeenfavoring theuseof T1-weighteddatawhich is capableof providinghigherresolutiondatawithout increasingacquisitiontimeandstill maintaininggoodtis-suecontrastandlow noise. Classifierapproaches[17, 197, 85], clusteringapproaches[64, 107, 140], neuralnetworkapproaches[64, 152], andMarkov randomfields[70, 149]have all beenusedfor brainsegmentation.Becausemostof thesemethodsarebasedonintensity information,a major concernis the presenceof intensityinhomogeneities,atopic discussedin the next section. Becausethe gray matterin the brain is thin andhighly convoluted,partialvolumeeffectsareanotherimportantconsideration.Efforts inmodelingpartialvolumeeffectshaveusedstatisticalmethods[24, 157, 158, 17,76, 95],soft segmentationderived throughfuzzy settheory[28, 13, 154, 140], andlinearfilters[166].

The automatedsegmentationof specificstructuresin brainsis an importantareaofresearchfor morphometricanalysis.Segmentationof the cerebralcortex hasreceivedmuch attentionwith most methodsemploying deformablemodels[52, 40, 120, 178,200]. Deformablemodelshave alsobeenusedfor segmentinga varietyof otherstruc-turessuchastheventricles[116, 195], thecorpuscallosum[41, 195], thehippocampus[4, 56], andothers[173, 190, 177]. Although not often employed for segmentingthecortex, atlas-guidedmethodsalsoappearwell-suitedfor segmentingsubcorticalbrainstructuressuchasthe ventricles[2, 142] andthe hippocampus[79]. Segmentationoftumorsandlesionsin the brain hasbeenappliedto magneticresonanceimagesusing


neuralnetworks [207], atlas-guidedapproaches[83], linear filters [166], fuzzy regiongrowing [185], anddeformablemodels[19]. Becauseof its complexity, this problemtypically requiresa sequenceof operators[196, 57].

Besidesheadscans,segmentationhasalsobeenusedfor extractinga varietyof otherstructures.Segmentationin cardiacimaginghasbeenusedfor delineatingthecavitiesof theleft ventricleusingregiongrowing andthresholdingapproaches[163, 44], aswellasdeformablemodels[12, 145, 9]. Deformablemodelsin cardiacimaging,however,are more often proposedfor tracking motion in the heart [8]. Markov randomfieldmodelshave beenusedfor segmentingkneeimages[25] aswell asmagneticresonanceangiograms(MRAs) [188]. Othermethodsfor segmentingMRAs includedeformablemodels[109] andthresholding[31]. Although MRA doesnot requirecatheterization,segmentationin standardangiographyis morecommonbecauseof its generallysuperiorcontrastandspatialandtemporalresolution[168, 48, 65, 47].

4.2 Intensityinhomogeneitiesin MRI

A major difficulty in the segmentationof MR imagesis the intensity inhomogeneityartifact[162, 37, 164], whichcausesashadingeffect to appearover theimage.Thisarti-factcansignificantlydegradetheperformanceof methodsthatassumethattheintensityvalueof a tissueclassis constantover the image.Figure7ashows anaxially acquiredMR imageof a femaleheartwith myocardialinfarction. Intensityinhomogeneitiesarenoticeableparticularnearthe breastareas.Numerousapproacheshave beenproposedin theliteraturefor performingtissueclassificationin thepresenceof intensityinhomo-geneityartifacts.Somemethodssuggestaprefilteringoperationthatattemptsto removethe inhomogeneityprior to actualsegmentation[108, 43, 123, 76, 100, 92, 14, 165].Methodsthat simultaneouslysegmentthe imagewhile estimatingthe inhomogeneityhowever, offer theadvantageof beingableto useintermediateinformationgainedfromthesegmentation.

Therearetwo prevailing approachesfor modelinginhomogeneitiesin methodsthatperform simultaneoussegmentation. The first approachassumesthat the meantis-sueintensityfor eachtissueclassis spatiallyvarying andindependentof oneanother[133, 202, 149, 130]. Thesecondapproachmodelstheinhomogeneitiesasamultiplica-tivegainfield [150, 140] or additivebiasfieldof theimagelogarithm[197, 62, 70, 85]. Itisunclearwhichof thesetwoprovidesmoreaccuratemodelingof inhomogeneityeffects,althoughthe secondapproachhasthe advantageof beingcomputationallylessexpen-sive. The secondapproachcanalsobe usedfor removing inhomogeneitiesby simplemultiplicationof theacquiredimageby thereciprocalof theestimatedgainfield. Fig-ure7 shows theresultsof applyingtheadaptive fuzzy : -meansalgorithmthatperformsa soft segmentationwhile compensatingfor intensityinhomogeneities[140]. Theheartimagewassegmentedinto threeclassesandFigure7d-f correspondto themembershipfunctionsfor thosethreeclasses.Figure7bshowsthegainfield estimatedfrom theorig-inal image.Thehardsegmentationin Figure7cwasobtainedasoutlinedin Section2.3.Notethatthering artifactpresentin Figure7eresultsfrom partialvolumeeffectscausingtheboundarybetweenfat,skin,andair to haveanintensitysimilarto thatof muscle.Thiseffect is commonandadisadvantageof intensity-basedpixel classificationmethods.

4.3 Chestradiography

Chestradiographshavenotreceivedmuchrecentattentionin thesegmentationliteraturepartlybecausetheprojectionnatureof theimagesmakesquantificationandlocalization


(a) (b) (c)

(d) (e) (f)

Figure7: Exampleof simultaneousinhomogeneitycorrectionandsoft segmentation:(a)MR heartimageacquiredusingafastspinechosequencein atrueaxialprescription,(b) estimatedgain field, (c) hardsegmentationinto threeclasses,(d)-(f) membershipfunctionsof thethreeclasses(Dataprovidedcourtesyof C. Constantinides).

a difficult taskand alsobecausetheir analysisoften doesnot requirea segmentation. Despitetheseissues,efforts have beenmadefor segmentingchestradiographsintoanatomicalregions using classifiers[121, 193] and Markov randomfields [193]. Inaddition, an algorithm hasbeenproposedfor delineatingposteriorrib bordersusingactive contourmodels[204].

4.4 Computedtomography

X-ray computedtomography(CT) alleviatessomeof the difficulties associatedwithprojectionradiographyandallows for 3-D imagingat resolutionsequalto or betterthanMRI. Soft tissuecontrastin CT is not asgoodasin MRI, but CT remainsthemodalityof choicefor imagingboneandbonetumors. Segmentationof bonecanbe achievedusing thresholdingand region growing operations[60] aswell as moresophisticatedmethodssuchasMarkov randomfields[135], deformablemodels[134, 177, 145, 129],andfuzzy region growing [183]. Oncesegmented,imagerenderingsareoftenusedtoprovidedetailedvisualizationof skeletalstructure[184].

Segmentationin CT hasalsobeenappliedto thoracicscansusingstatisticalclustering[102], a combinationof region growing and watershedalgorithms[199], a combina-tion of region growing and fuzzy logic [15], and deformablemodels[174, 78, 145].Somemethodshave beenappliedspecificallyfor the reconstructionof bronchialtrees[167, 136]. CT imageshave alsobeenusedin brainsegmentation[103], althoughMRimagingis presentlymorecommonin neuroimagingsegmentationapplications.In ad-


(a) (b) (c)

Figure8: Segmentationin digital mammography:(a)digitizedmammogramandradiol-ogist’s boundaryfor biopsy-proven malignanttumor, (b) resultof watershedalgorithm,(c) suspiciousregionsdeterminedby automatedmethod(Imagesprovided courtesyofC.E.Priebe).

dition, liver segmentationhasbeenperformedusingmodel-fitting[7], anddeformablemodels[116, 49, 127, 56]. Deformablemodelshave alsobeenappliedin otherCT seg-mentationapplications,including the delineationof abdominalaortic aneurysms[80],segmentationof thestomach[113], andsegmentationof theheart[117, 78,160].

4.5 Digital mammography

Segmentationin digital mammographyis typically performedfor localizationof tumors[143, 103], microcalcificationclusters[23, 74, 171], or other indicatorsof pathology[82]. In delineatingsuspiciousmassesfor mammography, segmentationmethodsaretypically employed in oneof two ways. In the first approach,the mammogramis ini-tially segmentedinto candidateregionswhich arethen labeledasbeingsuspiciousornormal[144, 104, 74, 86]. In thesecondapproach,theimageis first processedto detectfor thepresenceof pathologyanda segmentationis performedasa final stepto deter-mine its preciselocation[23, 94, 63, 22]. Thresholdingandits variationsarethemostoften usedsegmentationtechniquein mammography[144, 171, 23, 63, 74], althoughextensionsof region growing methodshave alsobeenproposed[94, 143]. A compar-ison of thresholdingandregion growing waspresentedin [82]. Becausepathologicalareasoftenpossessdifferenttextural propertiesin mammograms,Markov randomfieldmethodshave alsobeensuccessfullyemployed[104, 22].

Figure8 shows anexamplewherethemammogramis initially oversegmentedusinga watershedalgorithm.A statisticalclassifier[146] is thenusedto determinewhich re-gionscontainmicrocalcifications.This classificationstepis typically performedusingtextural properties.As illustratedin thefigure,falsepositivescanbea significantprob-lem in thedetectionof suspiciousmassesin mammograms(althoughin this case,theyfall outsidethebreastarea).For thesereasons,computerautomateddetectionin mam-mographyhasbeenusedonly asanaidto increasethereliability of aphysician’sdiagno-sis. Improvedinitial segmentationsmayleadto a reductionin false-positives.Notealsothataperfectdelineationof massesis difficult but notoftennecessaryin mammographysincedetectionis theprimarygoal.


4.6 Ultrasound

Segmentationalgorithmshavehadfairly limitedapplicationin ultrasoundimaging.Highlevelsof specklingpresentin ultrasoundimagesmake accuratesegmentationsdifficult.Furthermore,the real-timeacquisitionin ultrasoundmakes it bettersuitedfor motionestimationtasks(cf. [45, 124]) whereactive contours,becauseof their dynamicnature,areoftenused.Ultrasoundis alsooftenemployed in detectingpathologyusingtexturalclassifiers(cf. [125, 81]) but regionsof interestaretypically obtainedthroughmanualinteraction.

Nevertheless,someautomatedsegmentationwork hasbeenperformedin ultrasoundfor extractinga variety of structures.In [179], a thresholdingof intensityandtexturestatisticswasusedto segmentovariancysts.Deformablemodelshave hadgoodsuccessin ultrasoundapplicationssuchasin thesegmentationof echocardiograms[38, 160, 78,93]. In [101], anactive contourwasusedto determinetheboundaryof thecalcaneusinbroadbandultrasonicattenuationparameterimages,which arelessnoisy thanstandardultrasoundimages.In [19, 138], deformablemodelswereusedto determinethebound-aryof thefetusandthefetusheadrespectively. Deformablemodelshavealsobeenusedto segmentcystsin ultrasoundbreastimages[203]. Othermethodshave beenappliedfor thesegmentationof coronaryarteriesin intravascularultrasoundimages[169] andfor segmentingthepubicarchin transrectalultrasound[137].

4.7 Multimodal

Multimodal imagesegmentationattemptsto take advantageof the different kinds ofanatomicalinformationprovidedby differentimagingmodalities.For example,multi-modalimagingcantake advantageof theboneimagingcapabilitiesin CT andthesofttissueimagingcapabilitiesin MRI. In brain imaging, functional imagingdatacanbeusedto helpdelineatetumors[29]. Therearetwo majordifficulties in multimodalim-agesegmentation,however. First, multimodal datais not always available. Second,whenthe datais available,they aretypically not in the samealignment,andthereforerequireregistration[111]. Recentmethodshave beenproposedfor simultaneouslyreg-isteringandsegmentingmultimodalimages[3]. Oncetheimageshave beenregistered,standardmulti-channelsegmentationtechniquescanbeapplied.Segmentationof mul-timodal imageswastargetedspecificallyin [131] usingneuralnetworks, and in [73],whichpresentedaBayesianframework for simultaneousrestorationandsegmentation.

5 Conclusion

Futureresearchin thesegmentationof medicalimageswill strive towardsimproving theaccuracy, precision,andcomputationalspeedof segmentationmethods,aswell asreduc-ing theamountof manualinteraction.Accuracy andprecisioncanbeimprovedby incor-poratingprior informationfrom atlasesandby combiningdiscreteandcontinuous-basedsegmentationmethods.For increasingcomputationalefficiency, multiscaleprocessing(cf. [51]) andparallelizablemethodssuchasneuralnetworks appearto be promisingapproaches.Computationalefficiency will be particularly importantin real-timepro-cessingapplications.

Possiblythe most importantquestionsurroundingthe useof imagesegmentationisits applicationin clinical settings. Computerizedsegmentationmethodshave alreadydemonstratedtheir utility in researchapplicationsandarenow garneringincreasedusefor computeraideddiagnosisandradiotherapy planning. It is unlikely that automated


segmentationmethodswill ever replacephysiciansbut they will likely becomecrucialelementsof medicalimageanalysis.Segmentationmethodswill beparticularlyvaluablein areassuchascomputerintegratedsurgery, wherevisualizationof the anatomyis acritical component.

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