Automatic localization of the optic disc

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ComputerizedMedicalImagingandGraphics37 (2013) 409–417

ContentslistsavailableatScienceDirect

Computerized

Medical

Imaging

and

Graphics

j ou rn a l h om ep a ge :w w w . e l s e v i e r . c o m / l o c a t e / c o m p m e d i m a g

Automatic

localization

of

the

optic

disc

by

combining

vascular

and

intensity

information

Ana

Maria

Mendonc¸

a

a,b,∗

_,

_António

_Sousa

a,c

_,

_Luís

_Mendonc¸

_a

d

_,

_Aurélio

_Campilho

a,b a_INEB_–_Instituto_de_Engenharia_Biomédica,_Universidade_do_Porto,_Porto,_Portugal

b_FEUP_–_Faculdade_de_Engenharia,_Universidade_do_Porto,_Porto,_Portugal

c_ISEP_–_Instituto_Superior_de_Engenharia,_Instituto_Politécnico_do_Porto,_Porto,_Portugal d_Servic¸_o_de_Oftalmologia_–_Hospital_de_Braga,_Braga,_Portugal

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received7December2012

Receivedinrevisedform19April2013 Accepted25April2013

Keywords:

Retinalimageanalysis Opticdisclocalization Retinalvesselsegmentation Entropy

a

b

s

t

r

a

c

t

Thispaperdescribesanewmethodologyforautomaticlocationoftheopticdiscinretinalimages,basedon thecombinationofinformationtakenfromthebloodvesselnetworkwithintensitydata.Thedistribution ofvesselorientationsaroundanimagepointisquantifiedusingthenewconceptofentropyofvascular directions.TherobustnessofthemethodforODlocalizationisimprovedbyconstrainingthesearchfor maximalvaluesofentropytoimageareaswithhighintensities.Themethodwasabletoobtainavalid locationfortheopticdiscin1357outofthe1361imagesofthefourdatasets.

1. Introduction

Theopticdisc(OD)isoneofthemajorlandmarksthatstand outfromtheobservationofahumanretina.ODlocalizationis fre-quentlyrequiredfortheimplementationofimageanalysis-based solutionsfortheassessmentandfollow-upofseveraleye condi-tions.DetectionoftheODisrelevantinglaucomatouseyesasthis disorderaffectstheshapeandappearanceofthedisc,butitcanalso beusefulfordifferentiatingfromwhitelesionsrelatedtodiabetic retinopathy,orfromdrusenassociatedwithage-relatedmacular degeneration[1].KnowledgeaboutODpositionisalsorequiredfor automatingthedeterminationofdiagnosticindexesfor hyperten-siveretinopathy,suchastheArteriolar-to-Venulardiameterratio (AVR)[2].

TheODistheentrypointofthenervousand bloodsystems intotheretinaandisoftenthebrightestregioninafundusimage. These two distinctive features have been the major strategies forautomatingthelocalizationanddetectionoftheODreported intheliterature.Approachesthatrely onfeatures derivedfrom colorincludetheuseofmaximalintensity,maximalvariance,or theevaluationofimagevariationalongspecificdirections[3–6], template-matching[7,8],Houghtransform[4,10]anddeformable

∗_{Corresponding}_author_at:_INEB,_Campus_da_FEUP,_Rua_Dr._Roberto_Frias,_s/n,

4200-465Porto,Portugal.Tel.:+351225081859.

E-mailaddresses:amendon@fe.up.pt(A.M.Mendonc¸a),asousa@eu.ipp.pt (A.Sousa),luismendonc@gmail.com(L.Mendonc¸a),campilho@fe.up.pt (A.Campilho).

models[8,9].Severalauthorshaveproposedmethodsthatusethe bloodvesselnetworkasastartingpointforODdetection[11–15]. Solutionscombiningthesimultaneousdetectionofseveralretinal structuresaredescribedin[16,17].

Thispaperdescribesamethodforautomatingthelocalization oftheODincoloreyefundusimages,bycombininginformation extractedfromthevascularnetworkwithintensitydataobtained fromthered(R)andgreen(G)channelsoftheRGBrepresentation. Thedistributionandvariabilityofvesselsaroundeachimagepoint areestimatedusingtheconceptofentropyofvasculardirections, whichassociateshighvaluesofthismeasurewiththeoccurrenceof alargenumberofvesselswithmultipleorientations.This informa-tionisthencombinedwiththehighestimageintensities,withthe goaloflocalizingpixelswherebothentropyandintensityare maxi-mized.Thehereinproposedapproachisanimprovedandextended versionofthemethodpreviously presentedbytheauthorsofa conferencepaperin[18].Themajordifferencesbetweenthetwo solutionsare:theinitialcalculationoftheentropyofvascular direc-tionsusinga lowresolutionimage;theuseoftheentropymap forevaluatingthequalityofthevascularsegmentationand decid-ingonthecriteriaforestimatingthelocalizationofthedisc;and theinclusionofapost-processingstepforobtainingthefinalOD position.

The paper is organized as follows. Section 2 describes the methodologythatwasdevelopedforautomatingthelocalization of thedisc.Theresultsobtainedusingthe imagesof four pub-liclyavailabledatabases,DRIVE[19],STARE[20],MESSIDOR[21], andINSPIRE-AVR[22],arereportedinSection3.Finally,Section4

presentssomeconclusions.

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410 A.M.Mendonc¸aetal./ComputerizedMedicalImagingandGraphics37 (2013) 409–417

Fig.1. Originalimages(left),segmentedvascularnetworks(middle),andentropymaps(right).

2. Methodologyforopticdisclocalization

2.1. Overviewofthemethodology

ThefirstphaseofthemethodistheestimationofaninitialOD positionthroughtheapplicationofthealgorithmdescribedin[18]

toalowresolutionversionoftheoriginalimage.Inthismethod theentropyofvasculardirectionsisusedforquantifyingboththe occurrenceandthediversityofvesselorientationsaroundapixel. Afterthesegmentationofthevascularnetwork,amapwiththe entropyofvasculardirectionsiscalculatedforthefundusimage. AnintensitymaprepresentingtheEuclideandistanceofthered (R)andgreen(G)componentstotheoriginoftheRGBcolor coor-dinatesisgeneratedfromthecolorimageoftheretina;thismap isafterwardssegmentedtoretainjustthepixelswiththelargest distancevalues,whicharefurtheranalyzedtogeneratearestricted setofhighintensityODcandidates.TheinitialODlocationisthe candidatewherethemaximumvalueofentropyoccurs.

Thesecondphaseofthealgorithm,whichisnewintheherein proposedsolution,iseitheravalidationorarecalculationofthe discposition.Whenvalues ofentropyarelow,andinparticular theabsolutemaximumofentropyortheentropyintheestimated ODlocation,thequalityofthevascularsegmentationisnotreliable andanewestimatefordiscpositionissearchedforusingmainly intensitycriteria.Forhighvaluesofentropy,theinitialOD posi-tionisvalidatedifallotherlocalmaximaofentropyoccurringin differentimagelocationsshowlowervalueswhencomparedwith theonecorrespondingtothecurrentestimationforODposition.On theotherhand,ifseveralidenticallocalmaximaarefound,the pro-cessforestimatingtheODpositionisrepeatedonceagainusingthe fullresolutionimage.Afinalpost-processingphaseisappliedtoa restrictedregionaroundtheestimatedpositionofthedisc,inorder togetthefinalODlocationastheweightedcentroidoftheregion formedbythecombinationofvesselandintensitysegmentation locationresults.Themainprocessingphasesrequiredforlocating theODaredetailedinthefollowingsubsections.

2.2. Entropyofvasculardirections

TheODisaregionoftheeyefunduswherethevesselsaremore orlessdistributedinallpossibledirections.Forevaluatingthe con-vergenceandvariabilityofvesseldirectionsintheneighborhood

ofeachpointinaretinalimage,anewmeasurewasproposedin

[18]basedonthedefinitionofentropyproposedbyShannon.The entropyofvasculardirectionsiscalculatedusing(1),wherenisthe numberofdirectionsandpitheprobabilityofoccurrenceofvessels

indirectioni.

H=−

n

i=1

pi logpi (1)

Inordertocalculatetheentropymapofaretinalimage,adirection needstobeassociatedtoeveryvesselpixel.Thesegmentationof retinalbloodvesselsisaccomplishedusingthealgorithmproposed in[23],andtoobtainthevesseldirectioninformationa matched-filteringapproachsimilartotheonedescribedin[24]isapplied. Forthispurposeagrey-scaleversionoftheoriginalRGBimageis sequentiallyprocessedwithtwelvetwo-dimensionalmatched fil-ters,eachoneadaptedtoaspecificdirection;thehighestfiltering outputforavesselpointdefinesthedirectionofthevesselatthat point.

Theentropymapisdeterminedbasedonthenormalized his-togramofvesseldirectionsinawindowcenteredoneachimage point.Foreveryvesselpixelinsidethiswindow,twodirectionsare considered:anabsolutedirection,takenfromthevesseldirection map,andarelativedirectionwhichisthedirectionofthevector thatlinksthevesselpixeltothewindowcenter.Thehistogramof vesseldirectionsonlyretainsinformationforthosevesselpoints whoseabsoluteandrelativedirectionsarecoincident.

Fig.1showstwooriginalretinalimages,theirsegmented vas-cularnetworksandthecorrespondingentropymaps.Ascanbe observed,entropyvaluesclearlyincreasenearandinsidevessels andinparticularintheODregion.

Tocalculatetheentropyateachimagepoint,ahistogramof ves-seldirectionsneedstobedeterminedinawindowcenteredatthat point.Thesizeofthiswindowshouldbelargeenoughtocapturethe diversityofvesseldistributionaroundthepoint,andsmallenough tokeepprocessingtimelow.In[18]awindowsizeof351×151

pixelswassetfortheimagesoftheDRIVEandSTAREdatabases. Inthemethodhereindescribed,theimagesareinitiallyreducedto halfineachdimensionandthewindowforentropycalculationis decreasedaccordinglyto[175×75]pixels.Inbothcases,

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A.M.Mendonc¸aetal./ComputerizedMedicalImagingandGraphics37 (2013) 409–417 411

Fig.2.(a)Originalretinalimage;(b)segmentedvascularnetwork;(c)entropymapcalculatedusingfullresolutionimages;(d)entropymapcalculatedusinglowresolution images.

tendtospreadmainlyintheverticaldirectionbeforeformingthe twomainvesselarcadesaroundthemacula.Asaresult,theentropy valuesontheserectangularwindowsaremoreselectivethanthose obtainedusingsquareneighborhoods.Moreover,anincreased dis-criminationbetweentheODareaandotherretinalregionswhere relevantconcentrationsofvesselsoccurisachieved.

Entropymapsforboththeoriginalretinalimageandits size-reduced version are presented in Fig. 2. As can be observed, nooverallsignificantdifferencescanbefoundbetweenthetwo entropymaps,althoughamoredetailedanalysisoflocal distribu-tionofvaluescanrevealsharperlocalmaximaforthefullresolution image. Despite this, in good quality images thelow resolution entropyvalueshavenoinfluenceonthefinalcalculatedOD posi-tion.

2.3. InitialestimationofODlocation

Thedirectcalculationoftheabsolutemaximumofentropyis sufficientforestimatingtheODlocationinmostretinalimages. However,whenthevesselsaroundthediscarenotwellsegmented, mainlyduetopoorimagequalityorpathologicalconditions,the entropymapcontainsseverallocalmaximaandthesimple detec-tionofthelargestvaluemaynotbeabletoidentifythecorrect ODlocation.Inordertorestricttheareasinwhichthelocal maxi-mumofentropyissearchedfor,brightintensity,whichisanother characteristicfeatureofanormalOD,istakenintoaccount.

AstheODisusuallyayellowishbrightregioninanormalimage oftheretina,anddoesnotcontainimportantcontentsintheblue channel,wederiveanimagefromthered(R)andgreen(G) com-ponentsfromtheoriginalRGBimage,using(2).Inthisimage,I,a

pixelvalueisrepresentedastheEuclideandistance,intheRGplane, fromtheoriginofthecolorcoordinatesystem.

I(x,y)=

R(x,y)2+G(x,y)2 (2)

Aimingatreducingtheinfluenceofthevesselsinthesubsequent selectionofcandidateregions,theimageisprocessedwitha clos-ingmorphologicaloperatorusingastructuringelementadapted tovesselsize.Thisimageisafterwardssubmittedtoillumination equalization,asdescribedbyEq.(3),whereIW(x,y)isthe

aver-ageintensityofpixelsinsideawindowWcenteredonthespatial coordinates(x,y).

Ieq(x,y)=I(x,y)+0.5−I_W(x,y) (3)

Eq. (3) performs an intensity rescaling operation aiming at obtaininganimagewithaspecifiedaveragevalueequalto0.5, whichcorrespondstothecentralvalueinthe[0–1]rangeusedfor representingintensities.

Toselectaninitialsetofcandidateareasonly10%ofthehighest intensitypointsofimageIeqarekept.Asthenumberofregionsis

stilllarge,animage-dependentthresholdiscalculatedandapplied toobtainthefinalsetofcandidateareaswhereinthemaximum valueofentropywillbesearchedfor,andthenusedforobtaining theODposition.Thethresholdvalue,T,iscalculatedbasedonthe mean,mmax,andstandarddeviation,smax,ofintensitymaximain

theconnectedregionsoftheinitialset,asestablishedin(4).These intensitymaximaaretakenfromthegreencomponentofthe orig-inalRGBimageafterilluminationequalization(Geq).Thisimage

isusedinsteadofIeqforthresholdestimationbecauseofitshigher

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Fig.3. (a)OriginalimageshowingtheestimatedODlocation(blackcross)andabsolutemaximumofentropy(whitedot);(b)lowresolutionentropymap;(c)Ieq;(d)Geq; (e)intensitysegmentedimage;(f)finalsetofsegmentsafterdilationwiththevaluesofentropyoverlapped.

Thresholdedareasaredilatedusingastructuringelementadapted tovesselcaliber;thiswideningoperationisparticularlyimportant neartheODasthevesselshavehighvaluesofentropyandarenot includedinthesetofcandidateareasduetotheirlowintensity val-ues.Finally,thepointwiththemaximumvalueofentropyissetas theinitialestimationofODlocation.

T=

mmax ifsmax>0.1mmax mmax+2smax allothercases

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Finalandintermediateresultsoftheprocessingsequencefor attaininganinitialODpositionareillustratedinFig.3.Fig.3ashows theoriginalimagewiththeestimatedODposition(blackcross);in thisimage,theabsolutemaximumofentropy(whitedot)is coin-cidentwiththeestimatedODlocation.Fig.3b–dpresentthelow resolutionentropymap,Ieq,andGeq,respectively.Finally,theinitial

andfinalsetsofcandidatesobtainedfromtheintensity-segmented imageareshowninFig.3eandf;inthislastimage,thevaluesof entropyforeachselectedimagepixelarealsodepicted.

2.4. ValidationofestimatedODlocation

Theevaluationofthemaximumoftheentropyprovedableto locatetheODinthegreatmajority ofretinalimages.However, whenthevascularstructureneartheODisnotentirelyvisibleor isaffectedbysomepathology,thesearchfortheabsolute maxi-mumofthemeasuremaybeinsufficientforreachingasuitablefinal result.Nevertheless,inmostsituationsthesearchforthemaximal valueofentropy,combinedwiththeoccurrenceofhighintensities, isadequateforachievingacorrectODlocation.

Inafewsituations,especiallywhenthequalityoftheretinal imageislow(mainlyduetoproblemsinimageacquisition),the segmentedvasculaturearoundthedisciseitherinaccurateor sim-plymissing,andtheestimatedpositionoftheODasdescribedin theprevioussubsectiondoesnothittheopticdisc.Inothercases, theexistenceofveryintensepathologicallesionsnearthevessels mayintroduceerroneoussegmentsinthevasculartreeand mis-leadtheODestimationalgorithm.Anotherproblemisthattheuse oflowresolutionimagesforentropycalculationcangiverisetothe

existenceofseverallocalmaximawithsimilarvaluesindistinct imagepositions,which,injustafewcases,canpreventthe abso-lutemaximumofentropyfrombeingassociatedwiththeactualOD location.

Inordertocopewiththeselimitations,avalidation phaseis included.Forthispurpose,thefollowingpropertiesareevaluated onthelowresolutionentropymap:(i)theabsolutemaximumof entropy;(ii)therelationoftheentropyvaluefortheestimatedOD positiontotheabsolutemaximumofentropy;(iii)thepresenceof otherlocalmaximawhosevaluesaresimilartotheentropyvalue oftheestimatedODposition.

Theabsolutemaximumofentropyprovedaneffectivemeasure forassessingthequalityofthevascularsegmentation,withlow values ofthis indicatorgenerally associatedwithunreliableOD estimation.Ontheotherhand,whentheabsolutemaximumvalue ishigh, theentropyvaluefortheestimatedODpositionshould notbebelowanimage-dependentthresholdvalue(setas60%of theimageabsolutemaximum),topreventsituationswherethe intensitycriterionmostlydeterminestheselectedODlocation.

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Fig.4. Resultsofvalidationphase.(a)Originalimagesshowingtheabsolutemaximumofentropy(blackdot),theinitialODpositionestimation(whitecross)andtheresult ofnewODlocationestimationresultingfromthevalidationphase(graycross);(b)segmentedvascularnetworks;(c)entropymaps;(d)selectedsetofintensitycandidates.

theabsolutemaximumofentropyobtainedinthefirstphasewas belowthespecifiedthresholdandwasconsideredunreliable;the exampledepictedinthebottomrowpresentsanimageshowing severalhighentropymaxima,wheretherecalculationofOD posi-tionusingthefullresolutionimagesallowedacorrectsolutionin thevalidationphase.

2.5. RefinementofODlocation

Thefinalphaseoftheproposedmethodologyaimsatrefining thediscpositionpreviouslyestimated.Thisfinalpost-processing phaseisappliedonarestrictedcircularregioncenteredonthe esti-matedODpositionwithdiameterequalto1.5timestheexpected discdiameter.Theunderlyingideaisthattheregionofthedisccan bereconstructedifthevessel-andintensity-segmentedimagesare addedtogether.Anewvalue,combiningentropyandintensityby theirgeometricmean,isassignedtoeachpixelofthisnewimage. Theweightedcentroidofthecircularregioncenteredonthe previ-ouslyestimatedODlocationisconsideredthefinalpositionofthe opticdisccenter.

TheprocessforobtainingthefinalODpositionisillustratedin

Fig.5.Thesegmentedvasculature(Fig.5a)andthesetofintensity candidates(Fig.5b)arecombinedtogettheimagepresentedin

Fig.5c.ThecircularrestrictedareacenteredontheestimatedOD location,witheachpixelweightedbythecombinationofentropy andintensityvalues,isshowninFig.5d.Finally,Fig.5eshowsthe originalimagewiththeODpositionsbefore(whitecross)andafter (blackcross)therefinementstep.

3. Results

ThemethodologyforODlocalizationwasevaluatedusingthe imagesoffourpubliclyavailabledatabases,DRIVE[19],STARE[20], MESSIDOR[21],andINSPIRE-AVR[22].TheDRIVEdatabaseconsists of40colorimagesoftheretina(565×_584,₂₄_bits),_where₃₃_do

notshowsignsofpathology.NoinformationregardingODposition ispubliclyavailableforthisdataset.

TheSTAREdatabasecontains81eyefundusimages(700×605,

24bits)thatwereinitiallyselectedbyHooveretal.[11]for eval-uatingtheirmethodforODlocalization.Thisdatasetconsistsof 31imagesofnormalretinas,and50imagesshowingsomekind of pathology. The MESSIDOR database consistsof 1200 images

groupedintothreesubsetsfromdifferentophthalmologic depart-ments.Thisdatasetcontainsimageswithdistinctsizes(980×_1440,

1488×2240,1536×2304,24bits).Allimageswereacquiredusing

anon-mydriaticretinographwitha45◦_field_of_view,₈₀₀_with_and

400withoutpupildilation.Thelastsetofimagesisformedfrom the40imagesofthetestsetoftheINSPIRE-AVRdatabase.These highresolutionimages(2048×2392,24bits)arecenteredonthe

discandwereacquiredwitha30◦_field_of_view.

Theentropymapsusedinthefirstphaseofthemethodwere obtainedbasedonvesseldirectionhistogramscalculatedona rect-angularwindowof175×75pixelscenteredineachimagepixel.

TheimagesoftheMESSIDORandINSPIRE-AVRdatasetswere ini-tiallydownsizedtodimensionssimilartotheDRIVEandSTARE images(usingscalefactorsof1/1.5and1/2.5forMESSIDOR,and 1/4forINSPIRE).Beforecomputationofentropy,allimageswere onceagainreducedbyhalfineachdimension.Although computa-tiontimeisstillslightlydependentontheoriginalsizeoftheimage, assomeoftheoperationsareperformedusingthefullimagesize(or thesizethatresultsfromthefirstscalingstepfortheMessidorand Inspire-AVRdatabases),areductionof1/12intheprocessingtime wasingeneralachievedforalldatabases.Forinstance,inDRIVE imagesthetimerequiredtoprocessfullresolutionimages(about 90s)wasreducedtoanaveragevalueof8s.

Theparametervaluesthatrequiredadaptationtoeachspecific datasetinthepreviousmethod[18]arenowfixedandidenticalfor alldatabases.Theproposedapproachonlydependsontwo param-eters:oneisthescalingfactorjustmentioned,andtheotheristhe lowerlimitfortheabsolutemaximumofentropy,whichisusedto decidewhethertheentropymapisorisnotreliableforODlocation, asexplainedinSection2.4.Whilethevalueofthescaling parame-terisautomaticallyderivedfromtheoriginalimagesize,thelimit forentropyisobtainedfromtheaverageandstandarddeviation oftheentropymaximaforeachdataset.Identicallimitswereused foralldatabasesexceptMESSIDOR,asentropyvaluesforthisset areslightlysmaller,because,onaverage,thenumberofsegmented vesselpixelsinthedownscaledimagesislower.

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Fig.5.(a)Vesselsegmentedimage;(b)intensitycandidates;(c)combinationof(a)and(b);(d)circularregionaroundestimatedOD;(e)originalretinalimagewithfinal (blackcross)andestimated(whitecross)ODpositions.

180pixelsasestablishedin[25].Duetothevariabilityofthe MESSI-DORimages,thedefinitionofonesinglecriterionfordiscdiameter isnotpossible,soadetectedpositionwasconsideredvalidifitwas insidetheOD;theseresultswereassessedbytheauthorsunderthe guidanceofanexpert.

Theresultsobtainedforthefourdatabasesaresummarizedin

Table1.ThenumbersofsuccessfulODdetectionswiththe pro-posedmethodareshowninthethirdcolumnofthistable.Inorder toclarifytheinfluenceonOD detectionofthe twomain crite-ria(entropyandintensity)whicharecombinedintheproposed methodology,wehaveappliedeachcriterionseparately,andwe haveconsideredasODpositiontheimagelocationwherethe max-imumvaluefor thecriterionis achieved.Thetwo lastcolumns ofthetablecontainthenumberof successfuldetectionswhere theOD location was associated withthe position of the abso-lutemaximumofentropy(fourthcolumn)andwiththeabsolute

maximumofintensity(fifthcolumn).Fromtheanalysisofthe val-uesinTable1,wecanconcludethatbothentropyandintensity areusefulfeaturesfor ODlocation; however,thesefeaturesare sensitivetoimagequalityand totheoccurrenceofpathological conditions,whichhaveasignificantinfluenceontheperformance of discdetection.Nevertheless, thecombination of information frombothfeaturesimprovestherobustnessofODlocalization,as clearlydemonstratedbytheresultsobtainedusingtheproposed methodology.

Table2detailstheresultsofthecombinationofentropyand intensity,byindicatingthenumberofimageswheretheODhas beensuccessfullylocatedineachphaseofthealgorithm.Besides thetotalnumberofcorrectlydetectedODpositions,ineachroware presentedthenumberofimageswherethefinalODlocation corre-spondstotheinitialestimation,andthecorrectODlocationsthat wereaccomplishedinthevalidationphase,eitherbythemaximum

Table1

Resultsoftheproposedmethodcomparedwiththestand-alonedetectionbasedonthemaximumofentropyandthemaximumofintensity.

Database Numberof

images

Number(percentage)of successfulODlocations

Absolutemaximumof entropy(reduced resolutionimages)

Absolute maximumof intensity

DRIVE 40 40(100%) 39 37

STARE 81 80(98.8%) 63 58

MESSIDOR 1200 1197(99.8%) 1192 1155

INSPIRE-AVR 40 40(100%) 40 38

Table2

CriteriaforODlocalization.

Database Numberof

successfulOD locations

Initial estimation

Validation

Maximumofentropyin intensitycandidates(reduced resolutionimages)

Maximumofentropyin intensitycandidates

Maximumofintensityin largestareasegment

DRIVE 40 40 0 0

STARE 80 74 1 5

MESSIDOR 1197 1193 3 1

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Fig.6.Sixoriginalimageswiththeinitialestimationafterthefirstphaseofthealgorithm(whitecross)andthefinalODlocation(blackcross).Imagesonthetoproware fromDRIVEdatabasewhilethebottomrowshowsimagesfromtheINSPIRE-AVRdatabase.

valueofentropycalculatedontheoriginalimages(followingthe detectionofseverallocalmaximaofentropy)orbythemaximum valueofintensityinthelargestsegment(whentheentropyvalues werenotreliable).

Table3comparestheresultsofourmethodwiththe perfor-manceofothersolutionsreportedintheliteratureforthesame datasets.

Fig.6showssomeresultsfortheDRIVE(toprow)and INSPIRE-AVR(bottomrow)images.Inthetoprow,wecanobserveontheleft thesinglecasewheretheabsolutemaximumofentropywasnot associatedwiththeODlocation,whileinthecenterispresented thesingleimagewheretheintensitymaximumdidnotbelongto theOD;inbothcases,theproposedmethodwasabletoachievea

correctsolution.Finally,intherightmostimagetheabsolute max-imumofentropyiscoincidentwiththefinalODlocation.Thetwo leftmostimagesinthebottomrowofFig.6aretheINSPIRE-AVR imageswherethehighestintensitypixelsdonotcoincidewiththe disc.Inalltheseimagestheblackdotmarksthepositionofthe absolutemaximumofentropy,andthewhiteandblackcrossesare theinitialandfinalODpositions,respectively.

Fig.7presentstheresultsofODlocalizationinsixSTAREimages. Thetop-leftimageistheonlyimagewherethealgorithmfailedOD localization.Fig.7(b)and(c)showtwoimageswheretheinitial esti-mation(firstphase)gotawrongsolution,butacorrectpositionwas achievedinthesecondphasewherethefinalODpositionis asso-ciatedwithtothecentroidofthelargestsegmentintheintensity

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Fig.8.OriginalMESSIDORimageswiththefinalODlocation(blackcross),theinitialestimationafterthefirstphaseofthealgorithm(whitecross),theresultafterthesecond phase(graycross),whenapplicable,andtheabsolutemaximumofentropy(blackdot).ThetoprowcontainsthethreeimageswherethemethodfailedtodetecttheOD location,whilethebottomrowshowssuccessfulresults.

Table3

PerformanceofmethodsforODlocalization.

Method Database Percentageof

correctOD locations

Proposedmethod DRIVE 100%

STARE 98.8%

MESSIDOR 99.8%

Hoover[11] STARE 89.0%

Foracchia[12] STARE 97.5%

Haar[13] STARE 93.8%

Perez-Rovira[16] STARE 91.4%

Youssif[14] DRIVE 100%

STARE 98.8%

Lu[6] STARE 98.8%

MESSIDOR 99.8%

segmentedimage.AsuccessfulestimationofODpositionusinglow resolutionimageswasobtainedforeachoneofthethreeimagesin thebottomrowofFig.7.

ThethreeimagesoftheMESSIDORdatabasewheretheproposed algorithmfailedatlocalizingtheODaredepictedinthetoprowof

Fig.8.Fortheimagesontheleftandcenter,theabsolutemaximum ofentropyisinsidethedisc,butthediscareawasnotincludedin theintensityimage;thelargestareacandidatewasselectedinthe leftmostimage,whileintheimageshowninthecentertheinitial ODposition(whitecross)wasrefinedbutcouldnotreachthedisc. Inthethirdimage,afinalpositionneartheborderoftheODwas finallyselected.

4. Conclusions

AmethodologyforautomatingthelocalizationoftheODincolor imagesoftheretinawasdescribed,basedonthecombinationof vascularandintensityinformation.Thenewmeasureofentropyof vasculardirectionsprovedtobeagoodsolutionforassessingvessel

convergence,whichisonemajorfeatureoftheopticdiscregionin aretinalimage.Althoughformostnormalandpathologicalimages thesimpledetectionoftheabsolutemaximumofentropyis suffi-cientforcorrectlylocalizingtheOD,therobustnessofthemethod wasincreasedbyincludingadditionalintensityconstraints.

Theperformanceofthemethodhereindescribedwasgreatly improvedbythedeterminationofaninitialODpositionusinga lowresolutionentropymap,andfurtherbytheinclusionofa sub-sequentvalidationphasewhereanalternativesolutionissearched forifthecalculatedentropyvaluesarenotconsideredreliable.A significantreductionincomputationtime,andtheattainmentofa usefulODlocalizationeveninimageswhereeitherthedisc inten-sitycontrastorthequalityofthesegmentedvasculatureislow, arethemostrelevantimprovements.Theinclusionofarefinement phasealsoallowedafinalpositionthatingeneralisnearertothe idealODcenter.

Themethodwasevaluatedusingimagesfromfourdatabases withverypromisingresults,outperformingmostofthe previously-knownsolutions.TheODlocationobtainedwiththisautomatic approachwillbeusedasaninitialstepforthecomplete segmen-tationofthediscarea.

Acknowledgment

Wewanttothanktheauthorsofthefourpublicdatabasesfor makingtheirimagesavailableThisworkwassupportedbyFEDER fundsthroughtheProgramaOperacionalFactoresde Competitivi-dade-COMPETEandbyPortuguesefundsthroughFCT-Fundac¸ão paraaCiênciaeaTecnologiaintheframeworkoftheproject PEst-C/SAU/LA0002/2011.

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AnaMariaMendonc¸areceivedthePh.D.degreeinElectricalEngineeringfromthe FacultyofEngineering,UniversityofPorto(FEUP)in1994.Currently,sheisAssociate ProfessorattheDepartmentofElectricalandComputerEngineeringattheFacultyof Engineering,UniversityofPorto,Portugal.ShejoinedINEB–InstituteforBiomedical Engineering–in1989,whereshehasbeenaresearcheroftheBioimagingGroup. Herresearchinterestsincludeimageprocessingandanalysis,and,morespecifically, medicalimageanalysis.

AntónioV.SousareceivedthePh.D.degreeinEngineeringSciencesfromtheFaculty ofEngineering,UniversityofPorto(FEUP)in2008.Presently,heisAdjoinedProfessor attheDepartmentofMathematicsofISEP,PolytechnicInstituteofPorto,Portugal. HeisaresearcheroftheBioimagingGroupofINEB.Hisresearchinterestsinclude imageprocessingandclassification.

LuísMendonc¸aisaboardcertifiedophthalmologistfromtheHospitaldeBraga (Braga,Portugal).HereceivedhisMDdegree(1999–2005)fromtheFacultyof MedicineoftheUniversityofPortoandcompletedhisophthalmologyresidency (2007–2010)attheDepartmentofOphthalmologyofHospitalSãoJoão(Porto, Portugal).HeattendedaRetinalResearchFellowship(2010–2011)atLuEstherT. MertzRetinalResearchCentre/VitreousRetinaMaculaConsultantsofNewYork (NewYork,NY,USA)andhasclinicalandresearchinterestinretinalandchoroidal disorderssuchasdiabeticretinopathy,age-relatedmaculardegenerationandretinal vascularocclusions.