Improving Arc Detection in Graphics Recognition Philippe Dosch ORIA Universit de Nancy doschloria - Description

fr Grald Masini ORIA C NRS masiniloriafr Karl Tombre ORIA I NPL tombreloriafr Abstract In the context of graphics recognition arc detection con sists in the extraction of circles and arcs from the image of a graphics document or from the segments yie ID: 24336 Download Pdf

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Improving Arc Detection in Graphics Recognition Philippe Dosch ORIA Universit de Nancy doschloria

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fr Grald Masini ORIA C NRS masiniloriafr Karl Tombre ORIA I NPL tombreloriafr Abstract In the context of graphics recognition arc detection con sists in the extraction of circles and arcs from the image of a graphics document or from the segments yie

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Improving Arc Detection in Graphics Recognition Philippe Dosch ORIA Universit de Nancy doschloria






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ImprovingArcDetectioninGraphicsRecognitionPhilippeDoschORIA-UniversitédeNancy2GéraldMasiniORIANRSKarlTombreORIANPLInthecontextofgraphicsrecognition,arcdetectioncon-sistsintheextractionofcirclesandarcsfromtheimageofagraphicsdocumentorfromthesegmentsyieldedbyitsvectorization.Severalmethodshavebeenproposedforthispurpose,andwebrieysurveytheminthispaper.Then,wedescribeanimprovedalgorithminspiredbytwoexistingmethods,andincludingattingstepforabetterprecision.1.IntroductionGraphicsrecognitiontechniquesareslowlymaturing—atleastthelow-levelimageprocessing,segmentationandvectorizationsteps—andemphasishasbeenputonrobuststablemethods,whichcanbeimplementedasasetofstablesoftwarecomponents,reusablefromoneapplicationtotheother[3,7].Acentralaspectingraphicsrecognitionvectorizationi.e.theraster-to-graphicsconversionpro-cess[8].Tobecompleteandusefulforhigher-levelrecog-nitionandanalysisphases,vectorizationshouldnotbelim-itedtotherecognitionofstraightlineprimitives,butshouldatleastincludeareliablecirculararcdetectionprocess.Itmayactuallycoverevenmorethanthat,ashigher-levelpro-cessesoftenneedtoworkonanextendedsetofgraphicalprimitives,suchasdashedlines,cross-hatchedareas,etc.,toprovideusefulresults.Afterhavingdesignedwithgreatcareastableandro-bustvectorizationprocess[8],wethereforeturnedtothetaskofreliablyrecognizingarcs.Aswehavedoneinthepast[7],ouraimwasnotnecessarilytodesignanewand“ashy”method,buttoreuseasoftenaspossiblethebestapproachesfromtheeld.Therefore,westartedourworkbycombiningthebestoftwoapproaches,Rosin&West'sedgesegmentationmethod[6]andDori'svector-basedarcsegmentation[1].However,wefounditnecessarytoaddattingprocesstobetteradjustadetectedarcwiththepixelsofitsskeletonintheimage. Commonaddress:LORIA,B.P.239,54506Vandœuvre-lès-NancyCedex,FranceInthispaper,afterabriefoverviewofthemethodsonwhichwebaseourapproach,andadescriptionoftheirlim-itations(§2),wepresentthemethodwehavedesignedandtheguidelineswefollowed(§3).Weconcludewithsomeresultsandperspectives(§4).2.TheBaseofourApproachAccordingtoDori[1],therearetwomainfamiliesofarcdetectionmethods.ThemethodsoftherstfamilyarebasedontheHoughtransformanddirectlyworkontheoriginalpixelsofthegraphicsimage.Suchatechniqueiswell-knownandprovestobequiterobustinthepresenceofnoise.However,itiscomputationallyexpensiveanddoesnotprovideenoughaccuracyinthelocalizationofthecen-terandendpointsofthedetectedarcs.Thisstemsfromtheverylowlevelatwhichtheinformationisprocessed.Thesecondfamilyofmethodsworksonchainsofpoints,oronsegmentsyieldedbythepolygonalapproximationofsuchchains.Thebasicideaistocomputeanestimationofthecurvatureforthesechains.Thisapproachtypicallyiswhatwearelookingfor,asourvectorizationprocessisbasedonthecomputationofadistanceskeleton.Thepixelsoftheskeletonarethenlinkedtogethertoformchains,andapolygonalapproximationconvertsthechainsintostraightlinesegments.Insteadofdiscardingthechainsafterthat,wehavetakentheoptiontokeepthem,sothattheycanbeusedbythettingprocess.Rosin&West[6]proposeamethodbasedonrecursivesplitting,forsegmentingacurveintoasetofarcsandseg-ments.ItisanextensionofapreviousworkbyLowe[4]tondpointsofmaximumcurvature(Fig.1).Suchapointiscomputedusingaratiobetweenthemaximumdeviationandthelengthoftheapproximatingsegments.WhereasLoweusesthisfeaturetoapproximateachainbyasetofseg-ments,Rosin&Westaddtherecognitionofarcs,whenanarcisabetterapproximationoftheoriginalchain.Asanarcrequiresmoreparametersthanastraightseg-ment,thesimpleratiomeasurementionedaboveisnotenoughtocharacterizeanarc.Therefore,Rosin&Westtakeconnectivity(arcsaresupposedtostartandendatthe (a)Initialarcpassingthroughtheendpointsofa (b)Pointofmaximumdevi- (c)Splittingthechain. (d)Finalarc.Figure1.PrincipleofRosin&West'smethod. CG d(C)=13.0087d(D)=18.8197d(E)=8.15986d(F)=12.0387d(G)=18.2674Figure2.Exampleofinadequatesplittingatamaximumdeviationpoint(D).extremitiesofthesegmentsofthepolygonalapproxima-tion)andgeometry(thecenterofthearcmustbeequidistanttobothextremities,whichstronglyconstrainsitsposition)intoaccount.Inthisway,thepositionofanarccanbecom-putedthroughsimpleleastsquaresminimization.Thismethodisveryinteresting,asitdoesnotrequireanyexplicitthreshold.Weactuallyuseitforourpolyg-onalapproximationbecauseofthisveryreason.More-over,althoughthesignicancemeasure,i.e.theratiodeviation=length,maybeconsideredtobetoosimplis-tic,Rosinhasproposedothersignicancemeasureswhichmayfurtherimprovethemethod[5].Nevertheless,themethodhasalsoitslimitations.Theinitiallistofpointsissplitatthepointofmaximumdevia-tion,andarcdetectionisperformedagainoneachsublist.Insomecases,asillustratedbygure2,themaximumdevi-ationpointisnotthemostrelevantoneandthesubsequent OAB CED OPQ Figure3.Dori'smethodforcomputingthecenterofapotentialarc.P(resp.Q)isthecenterofsub­arcCB(resp.AC).splittingdoesnotleadtoacorrectrecognition.DovDoriandhisteamhavedesignedanothermethod,calledSRAS[1],whichworksiteratively.Asparse-pixelvectorizationofthedocument[2]extractsso-calledbarsthataregroupedtoformpolylines.Thesepolylinesinturnareusedaskeysinthearcrecognitionprocess.Thresholdsareappliedtoselectbarswhicharenottooshortandnottoolong,andwhichformpairswiththerightangularorien-tation.Arstpositionofthecenterofthearccanthenbecomputed.Thispositionisrenedbyusingalltheverticesofthepolylineinvolvedinthearchypothesis.Apotentialarccenterareaisthusdetermined,andeachpixeloftheareaistested,usinganaveragedsquaredistancetooptimizethepositionofthecenter(Fig.3).Afterthevalidationofthisinitialarchypothesis,thealgorithmtriestostepwiseextendthearcatitsextremities,bysearchinginpotentialextensionareasandtestingthearchypothesisagain,intermsofwidth,angularmeasuresandpolylinecontinuity.Foreachpossi-bleextension,thenewcenteriscomputed,accordingtotheprinciplesdescribedpreviously.Themethodyieldsgoodresults,butislimitedbytheuseofacertainnumberofthresholds,inparticulartodeterminethecenterofthearc.Dori'sandRosin&West'smethodsbothshareanotherlimitation:Thearchypothesesandthecomputationoftheerrorarebasedonthepolygonalapprox-imationofthegraphicimage.Althoughtheapproximationisveryusefultondtherighthypothesesinanefcientwayandwithoutlosingtheconnectivity,itleadstouncontrolledlocationerrorswhenreferringbacktotheoriginalimage.Thisexplainsourperceivedneedforattingstep,tomakearchypothesesmatchtheirpixelrepresentations.3.FittingArcHypothesestotheSkeletonThemethodwedesignedisbasicallyinspiredbythatofRosin&West,butweincludedtwoideasfromDori'smethod:Thewaytocomputethecenterofthearc,andtheuseofpolylinesinsteadofsimplesegments.Wealsoaddedsomeimprovements.Themostimportantofthemconcernsthecomputationoftheerrorassociatedwithanarchypoth- StepwiseRecoveryArcSegmentationAlgorithm. esis:Itisnolongerperformedwithrespecttothepolyg-onalapproximation,butwithrespecttotheoriginalchainofskeletonpixels.Infact,eachsetofsegmentsdeliveredbythepolygonalapproximationstepofourvectorizationprocessisassociatedwiththepixelchainthatthesegmentsapproximate.Segmentsaregroupedintopolylines,eachpolylinebeingtheapproximationofacompletechain.Theoriginallinkedchaincorrespondingtoapolylinecanthenberetrievedusingasimpleindex.Ourarcdetectionalgorithmworksintwophases:Archypothesesgenerationandvalidationofthehypotheses.Thehypothesesarebuiltfromthepolygonalapproxima-tion.Let;:::;Sbeachainofconnectedsegments,describedbytheirextremities;:::;P,suchthat:Itcontainsatleastfourpoints(asthereisalwaysapos-siblearcpassingthroughthreepoints),thesuccessiveanglesarequitethesame.Suchachainisretainedasanhypothesistobeexaminedbythearcdetectionprocess.Ifthechainasawholecan-notbeconsideredasrepresentinganarc,asegmentisre-movedatoneoftheextremitiesofthechain,andthechainistestedagain,untilavalidarcisfoundoruntiltherearetoofewpointsforapertinenthypothesis.ThetestphaseisperformedusingRosin&West'sleastsquaresminimiza-tionapproach.Theerrorisnotestimatedusingthesegmentsofthepolygonalapproximation,butusingthesubchainsofpoints,whichcanberetrievedthankstoourindexingstruc-ture,aspreviouslymentioned.Themethodalsodetectsfullcircles.Whenworkingonaclosedloopofsuccessivesegments,oneofthesegmentsiseliminatedbeforeapplyingarcdetection.Ifauniquearc,includingallthesegments,isdetected,thepresenceofacircleistestedbycheckingthevalidityofthelastsegment.4.ResultsandConclusionInthefallofSeptember,themethodparticipatedintheThirdIAPRGraphicsRecognitioncontest,wherecompletevectorizationmethodsarerunonground-trutheddata.Atthetimeofwritingthispaper,wearestillawaitingtheper-formanceevaluationresultsonthesedata.Figure4illustratesresultsobtainedfromarathersimplearchitecturaldrawing.WithRosin&West'srawmethod,falsearcsaredetectedduetochainsofshortsegmentspro-videdbythevectorization,inparticulararoundjunctionpoints(Fig.4b).Thesearcsdisappearwhenusingourimprovedmethod,andfullcirclesarecorrectlyextracted(Fig.4c).Arclocationisalsomoreaccurate(Fig.4d),al-thoughitisnotplainlyemphasizedbythegure(drawingsshouldbedisplayedatalargerscale).Therearestillseveralpossibleimprovementstothemethod.Oneofthemistotestarchypothesesonmorethanonepolyline,astheskeletonlinkingalgorithmstartsnewchainsateachjunction.Thiswouldleadtothepossibilityofrecognizingasinglearc,evenwhenitiscrossedbyanotherline,ortorecognizetwofullarcswhenevertheyshareshortsegmentslikethosepointedbydottedarrowsongure4d.Themaindifcultyheredoesnotconcernthemethod,butthecomputationalcomplexityoftheimplementation.Wealsostillhavethresholdsinthemethod,especiallyforthesimilaritybetweentwoangularmeasures.ApossibleimprovementwouldbetoextendRosin&West'sworktodenerelevantsignicancemeasuresforarcs.AcknowledgmentsWewouldliketothankWissamDagher,NicolasLieber,AntoineSorbaandSéverinVoisin,whoparticipatedintheimplementationworkforalargepart.References[1]D.DoriandW.Liu.Stepwiserecoveryofarcsegmentationincomplexlineenvironments.InternationalJournalonDoc-umentAnalysisandRecognition,1(1):62–71,Feb.1998.[2]D.DoriandW.Liu.SparsePixelVectorization:AnAlgo-rithmandItsPerformanceEvaluation.IEEETransactionsonPAMI,21(3):202–215,Mar.1999.[3]P.Dosch,C.Ah-Soon,G.Masini,G.Sánchez,andK.Tombre.DesignofanIntegratedEnvironmentfortheAu-tomatedAnalysisofArchitecturalDrawings.InS.-W.LeeandY.Nakano,editors,DocumentAnalysisSystems:The-oryandPractice.SelectedpapersfromThirdIAPRWorkshop,DAS'98,Nagano,Japan,November4–6,1998,inrevisedver-,LectureNotesinComputerScience1655,pages295–309.Springer-Verlag,Berlin,1999.[4]D.Lowe.Three-DimensionalObjectRecognitionfromSin-gleTwo-DimensionalImages.ArticialIntelligence,31:355–395,1987.[5]P.L.Rosin.TechniquesforAssessingPolygonalApproxima-tionofCurves.IEEETransactionsonPAMI,19(6):659–666,June1997.[6]P.L.RosinandG.A.West.SegmentationofEdgesintoLinesandArcs.ImageandVisionComputing,7(2):109–114,May[7]K.Tombre,C.Ah-Soon,P.Dosch,A.Habed,andG.Masini.Stable,RobustandOff-the-ShelfMethodsforGraphicsRecognition.InProceedingsofthe14thInternationalCon-ferenceonPatternRecognition,Brisbane(Australia),pages406–408,Aug.1998.[8]K.Tombre,C.Ah-Soon,P.Dosch,G.Masini,andS.Tab-bone.StableandRobustVectorization:HowtoMaketheRightChoices.InProceedingsof3rdInternationalWorkshoponGraphicsRecognition,Jaipur(India),pages3–16,Sept.1999.RevisedversiontoappearinaforthcomingLNCSvol- (a)Originalimage.(b)ArcdetectionusingRosin&West'srawmethod. (c)Arcdetectionusingourmethod.(d)Superpositionofbothresults.Figure4.Resultsofarcdetection.