Fast Shapebased Road Sign Detection for a Driver Assistance System Gareth Loy Computer - PDF document

Fig.1.Votinglinesassociatedwithagradientelementwhensearchingfordifferentshapes.threshold1,aresettozeroandtheremainingelementsnormalised.Eachremainingnon-zerogradientelementvotesforapotentialcirclecentreadistanceraway(whereristheradiusofthecirclebeingtargeted)alongthelineofthegradientvector.Thevoteisplacedattheclosestpixeltothispoint.Thepointsvotedforarecalledaffectedpixelsandaredenedby:pve(p)=pround(rg(p));whereg(p)istheunitgradientatpointp.Thereareposi-tivep+veandnegativep�veaffectedpixelscorrespondingtopointsthatthegradientpointstowardsandawayfromrespectively.Sincewedonotknowaprioriwhetherasignwillbelighterordarkerthanthebackgroundweusebothpositivelyandnegativelyaffectedpixelsconcurrently.However,ifsuchinformationisknownitcanbeused.Toextendthisvotingschemetoregularpolygonswedenethe`radius'ofapolygonastheperpendiculardistancefromanedgetothecentroid.Further,ratherthangradientelementsvotingforasinglepoint,alineofvotesiscastdescribingpossibleshapecentroidpositionsthatwouldaccountfortheobservedgradientelement.Figure1showsdifferentvotescastbyagradientelementg(p)whensearchingfordifferentshapesatagivenradius(onlythevotesassociatedwiththepositivelyaffectedpixelareshown).Whereasinthecaseofacircleasinglevoteiscastpergradientelement,alineofvotesiscastwhensearchingforstraight-sidedshapes.Thewhitebarsindicatepotentialcentroidlocationsthatreceiveapositivevote,andthedarkbarsindicatelocationsthatreceiveanegativevote.Thenegativevotingisintroducedtoattenuatetheresponsegeneratedbystraightlinestoolongtocorrespondtoshapeedgesatthetargetradius.ThelengthofthelineofpixelsvotedforisdenedbywasshowninFigure2.Thewidthparameterwischosensothateverypointonashapeedgewillcastavoteforthecorrectshapecentroid,andisgivenby:w=roundrtan n;whereristheradiusandnthenumberofsidesofthepolygonbeingtargeted.Thelineonwhichtheaffectedpixelsliecanbeapprox-imatedby:L(p;m)=pve(p)+round(mg(p));1Athresholdequalto5%ofthemaximumpossiblegradientmagnitudewasusedforourexperiments. Fig.2.Lineofpixelsvotedforbyagradientelement Fig.3.Exampleofn-anglegradientprojectedfromapointpwhereg(p)isaunitvectorperpendiculartog(p).Thepixelsreceivingapositivevotearethengivenby:L(p;m)jm2[�w;w];andthosereceivinganegativevoteby:L(p;m)jm2[�2w;�w�1][[w+1;2w]:Whethertargetingcirclesorregularpolygons,allvotesareaccumulatedintoavoteimageOr.Figure4(b)showsanexamplevoteimageforanoctagonaltarget.Regularpolygonsareequiangulari.e.,theirsidesareseparatedbyaregularangularspacing;forann-sidedpolygonthisis360=ndegrees.Toimproveourdetectionoftheseshapesweintroducearotationallyinvariantmeasureofhowwellasetofedgestsaparticularangularspacing.Dene (x;y)=n(x;y)where=6 gisthegradientangle,andnisthenumberofsidesofthetargetpolygon.Letvbetheunitvectoreldsuchthat6 v(x;y)= (x;y).Foragivensetofedgepointspi,themagnitudeofthevectorsumPiv(pi)indicateshowwellthesetofedgesg(pi)tstheangularspacingdenedbyn.ConsidertheexampleinFigure5.Threeedgepointspiaresampledfromthesidesofanequilateraltriangle.Theunitgradientvectorsandtheirassociatedanglesareshownin(a).Bymultiplyingthegradientanglesbyn(n=3foratriangle)theresultingvectorssharethesamedirectionif,andonlyif,theiroriginalorientationswerespaced360=ndegreesapart.Thusthemagnitudeofthevectorsumofthesen-anglevectorsismaximaliftheedgepointsoccuratthetargetedangularspacing.Toutilisethisresultweconstructavectoreldofprojectedn-anglegradientsbyconsideringeachnon-zeroelementofgandprojectingitsassociatedn-anglevectorv(p)ontoitsvotingspaceasshowninFigure3(notethesignisreversedwhenprojectingontonegativelyvotedpixels).Vectorsprojectedontothesamepixelaresummed.TheresultisavectoreldBr,whosemagnitudeindicateshowwellthegradientelementsvotingoneachpointmatchthetargetangularspacing.Figure4(c)showsanexampleofsuchamagnitudeimageforanoctagonaltarget.Forincreasingnthen-anglerepresentationislimitedbytheaccuracyofthegradientorientationestimate.However,itisperfectlyadequateforn=8(e.g.Figure4(c))whichisthemaximumrequiredforroadsigndetection. Fig.8.Resultsforsearchingfortriangles(toprow)withr2f8;10;::;18g,andsquares(middlerow)andoctagons(bottomrow)withr2f10;12;14;17;20;25g.Alltargetedsignsarecorrectlydetected. 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