AlbertJ.Ahumada,Jr.
NASAAmesResearchCenter,HumanandSystemsTechnologiesBranch
MoffettField,California,94035-1000
BettinaL.Beard
UniversityofCalifornia,SchoolofOptometry
Berkeley,California,94720-2020
Abstract
Observersviewedasimulatedairportrunwaylandingscenewithanobstructingaircraftontherunwayandratedthevisibilityoftheobstructingobjectinvaryinglevelsofwhitefixed-patternnoise.Theeffectofthenoisewascomparedwiththepredictionsofsingleandmultiplechanneldiscriminationmodels.Withoutacontrastmaskingcorrection,bothmodelspredictalmostnoeffectofthefixed-patternnoise.Aglobalcontrastmaskingcorrectionimprovesbothmodels’predictions,butthepredictionsarebestwhenthemaskingcorrectionisbasedonlyonthenoisecontrast(doesnotincludethebackgroundimagecontrast).Keywords:imagequality,targetdetection,noise,visionmodels,contrastsensitivity
1.Introduction
Objectdetectiontypicallyinvolvessearchandpatternrecognitioninarangeofbackgrounds.Visualobjectdetectionisfundamentallylimitedbybackground-inducedcontrastmasking.Whentheobjectispresentorabsentinaconstantbackground,contrastmaskingcanbemeasuredasthediscriminabilitybetweentwoimages.Weareevaluatingtheabilityofimagediscriminationmodelstopredictobjectvisibilitywithafixedbackgroundimage.Ifthemodelsaresuccessful,theypredicttheupperlimitofobserverperformanceinanobjectdetectiontask.
Ahumada,Rohaly,andWatson(SPIE1995)1applieddiscriminationmodelstoobjectdetectioninnaturalbackgrounds.Wereportedthatthedetectabilityoftanktargetswasbetterpredictedbyamultiplechannelmodelthanbyasinglechannelmodel.Wethenaddedasimplecorrectionformaskingbasedonvisiblecontrastenergy.Itimprovedthepredictionsforbothmodelsandequalizedtheirperformance.2,3,4
*PublishedinB.RogowitzandJ.Allebach,eds.,HumanVision,VisualProcessing,andDigitalDisplayVII,SPIEProceedingsVolume2657,SPIE,Bellingham,WA,Paper23.
AhumadaandBeardObjectDetectioninaNoisyScene-2-
Someobjectdetectionsituationsinvolvenoisydisplays.Herewemeasureobjectdetectabilityinacompleximagemaskedbyfixed-patternnoise.Wecomparethese
measurementswithdiscriminationmodelpredictions.Withoutthemaskingcorrection,thesinglechannelmodelpredictsnoeffectofnoiseandthemultiplechannelmodelpredicts
maskingonlybythenoiseinthechannelsaffectedbytheobject.So,neithermodelcorrectlypredictstheeffectofthefixed-patternnoise.Withthemaskingcorrection,bothmodels’predictionsareimproved.Thepredictionsareevenbetterwhenthemaskingcorrectionisbasedonlyonthenoisecontrastanddoesnotincludethebackgroundimagecontrast.
2.Experiment
2.1Methods
2.1.1Stimuli.Twodigitalimagesofasimulatedairportsceneweregenerated.ImageI1,shownatthetopofFigure1,hasanobstructingaircraftontherunway.ImageI0,showninthemiddleofFigure1,isthesameimagewithouttheobstructingaircraft.Weusedasinglefixed-patternwhitenoisemaskNwithuniformlydistributedpixelvalues.Imagesfortheexperimentwereconstructedfromtheseimagesbyaddingthebackgroundimage,afractionpofthedifferencebetweenthebackgroundandtheobjectimages,andafractionqofthenoiseimage,
.Ip,q=I0+p(I1−I0)+qN+(1−q)N
(1)
isthemeanofthenoiseimage.AfractionofNisaddedtokeepthemeanluminanceN
constant.Imagesweregeneratedforthesixpvalues0,0.05,0.10,0.20,0.40,and1,andfortheqvalues0,0.25,0.50,and1.0.TheimageatthebottomofFigure1illustratesthecaseofp=1andq=0.5.The128×128pixelgray-scaleimageswerepresentedona15inchSonycolormonitorwhoseluminanceincd/m2wascloselyapproximatedby
L=0.05+(0.024d)2.4,
(2)
wheredisthedigitalimagepixelvalue.Themeanluminanceoftheimagesandsurroundingscreenregionwasabout10cd/m2.Theviewingdistanceof127.5cmandtheimagesizeof6.0cmgiveaviewingresolutionof47.5pixelsperdegreeofvisualangle.Theplane/runwayscenethussubtended2.7degvisualangle,theplanealonefitinarectangle0.78degby0.17degofvisualangle(37horizontaland8verticalpixels).Itaffectedatotalof96pixels.Whenanimagewasnotpresent,thescreenwasfilledwithrandom,uniformlydistributed,grayscalepixels.Becausethedisplayhadonly32differentlevelsofgrayscale(IBM-PCcompatibleVGAdisplaymode)theno-noiseconditionwasrunattwicethedigitalimagecontrasttoallowmoredynamicrange.Theimagedurationwas1.0second.
2.1.2Observers.Fourfemaleobservers,aged18to37years,withcorrectedacuityof20/20orbetterweretested.
2.1.3Procedure.Theobserverswereaskedtorateeachimageona4pointratingscaleaccordingtothefollowinginterpretation:1-Definitelydidnothaveaplane.2-Probablydidnothaveaplane.3-Probablydidhaveaplane.
AhumadaandBeardObjectDetectioninaNoisyScene-3-
4-Definitelydidhaveaplane.Inaddition,theobserverswereaskedtotrytousethe4responsecategorieswithroughlyequalfrequency.
Withinablockof60trials,themasknoiselevelqwasheldconstant,whilethefourobject/backgroundplevelsoccurredrandomly(withprobability0.25).Table1showsthefourvaluesofpusedateachqvalue(thecoefficientdeterminingthenoiselevel).
Table1-Signallevelvaluespusedateachnoiselevelvalueqqp’s00.050.10.2000.050.10.20.250.500.10.20.4100.20.41.0Groupsoffourrepetitionsofthefournoiselevelswereindependentlysequencedusing4×4
Latinsquares.Observers1and2completed16repetitionsofeachnoiselevel,Observer3completed8repetitions,andObserver4completed10repetitionsin5×5Latinsquares,includingano-noiseconditionatthesamecontrastasthenoiseconditions.
2.2Dataanalysis
2.2.1Method.Foragivennoiselevel,thedistanced′indiscriminabilityunitsfromeachobjectimagetoitsnon-objectimagewasmeasuredinthecontextofaone-dimensionalThurstonescalingmodel.5Thescalingmodelhasthefollowingassumptions:
1.Thepresentationofanimagegeneratesaninternalvaluethatisasamplefromanormaldistributionwithunitvariance.
2a.ThemeanofthedistributiongeneratedbyabackgroundimageI0iszero.2b.ThemeanofthedistributiongeneratedbyanoriginalobjectimageI1isd′.2c.ThemeanofthedistributiongeneratedbyanimageIpispd′.
3.Theobserverhas3fixedcriteriathatareusedtocategorizeaninternalvaluetooneofthe4responses.
Thescalingmodelforthisexperimenthas4d′parametersand3categoryboundariesforeachobserver.Parameterswereestimatedbythemethodofmaximumlikelihoodseparatelyforeachblock.
2.2.2Experimentalresults.Mediand′estimatesforeachobserverandforthe4noiselevelsaregiveninTable2.
AhumadaandBeardObjectDetectioninaNoisyScene-4-
Table2-Medianexperimentaldiscriminabilityindicesd′noiselevelq00.250.5118.511.96.63.3Observer111.68.84.1Observer224.9
Observer39.58.85.824.4Observer428.415.49.05.224.8Geometricmean11.98.24.5
Thestandarddeviationofanindividualscoreindecibels(dB=20×thelogofthescore)is
estimatedtobe1.3dB,basedontheobserverbynoiselevelinteraction,whichhas9degreesoffreedom.Thisleadsto95%confidenceintervalsof±1.4dBforthemeansforeachnoiselevel.Figure2plotsthedataofTable2withtheconfidenceintervalsaboutthemeans.Observer4hadamediand′of18.4fortheno-noiseconditionatthesamecontrastasthenoiseconditions,onlyslightlyhigherthanherd′valueof15.4fortheq=0.25condition.Thelargedifferencefromtheq=0andtheq=0.25conditionsisseentobemainlyaneffectofthelowersignallevelinthenoiseconditions.
3.Models
3.1Algorithms
3.1.1Multiplechannelmodel.ThemultiplechannelmodelisbasedontheCortextransformofWatson.6Itissimilarinspirittohisoriginalmultiplechannelmodel,7andissimilarindetailtoothersbasedontheCortextransform.8,9,10
Themultiplechannelmodelcalculationforapairofimages(I0andI1)hasthe
followingsteps.TheimagesI1andI0areconvertedtoluminanceimagesbythecalibrationfunctionofEquation(2).Theimagesareconvertedtoluminancecontrastbysubtractingand
0,thendividingbythebackgroundimagemeanluminanceL
0)/L0.Ij←(Ij−L
Theoperationsontheimageindicatetheoperationappliedseparatelytoeachpixel.A
contrastsensitivityfunction(CSF)filterSisthenappliedtothetwocontrastimages.
Ij←F−1[SF[Ij]],
(4)
whereFandF−1aretheforwardandinverseFouriertransforms.NexttheCortextransformisappliedtotheimagesresultingincoefficientsCj,k,wheretheindexkrangesoverspatialfrequency,orientation,andspatiallocation.Thedetectabilitydkcontributedbythekthspatialfrequency,orientation,andpositionisthencomputedastheabsolutevalueofthedifferenceintheCortextransformcoefficients,maskedbythebackgroundcoefficientifitisabovethreshold.
dk=C1,k−C0,k,
ifC0,k≤1.0,
0.7,
(3)
dk=C1,k−C0,k/C0,kifC0,k>1.0.
(5)
Finally,d′isgivenbyaMinkowskisumoftheindividualcontributionswithsummation
AhumadaandBeardObjectDetectioninaNoisyScene-5-
exponentβ,
d′=(Σdkβ)1/β.
k
(6)
Forthecasethatβ=∞,theresultisthelargestofthedk.
3.1.2Singlechannelmodel.Forthesinglechannelmodel,thestepsarethesamethroughtheimagefiltering,thenthefilteredimagevaluesareusedtocompute
dk=I1,k−I0,k,
(7)
wheretheindexknowreferstoimagepixels.Equation(6)isthenusedtoobtaind′.
3.1.3Contrastnormalization.Withoutthecorrectionfactor,thesinglechannelmodelpredictsnocontrastmaskingatallandthemultiplechannelmodelonlypredictsmaskingwithinthechannelsaffectedbythesignal.Recentworkdemonstratesmaskingbycontrastenergyinchannelsnotcontainingthesignal.11Newversionsofthemultiplechannelmodelsincorporatinglateralinteractionsamongcorticalunitchannelstoaccountforbetween-channelmaskinghavebeendeveloped.12−15AmodelsimilartotheirswouldresultbyreplacingEquation(5)with
c0
dk=C1,k−C0,k,(8)a0a1/a(c0+Σck,k′C0,k′k,k′)0
k′
wherec0anda0areconstants,ck,k′representstheweightofthemaskingofchannelk′onchannelk,andak,k′representsthegrowthofthatmaskingwiththeactivityinchannelk′.Ifwemakethesimplifyingassumptionsthattheck,k′areallequalandsumtounity,thattheak,k′=2,anda0=2,theresultisthatthefactormultiplyingthedifferencetermisnolongerafunctionofkandcanbefactoredoutoftheMinkowskimetricEquation(6).Also,theCortextransformhasthepropertythatthesumofsquaresofthecoefficientsequalsthesumofsquaresoftheimagevalues,sothesimplificationassumptionsresultinthed′predictionformula,
c0d′=d′unmasked,(9)
220+c√cwhered′unmaskediscomputedfromtheunmaskeddifferences,cistheRMSbackgroundimage
contrastpassedbytheCSFfilter,andc0isaparameterrepresentingthecontrastlevelatwhichthemaskingbecomeseffective.Tocomputec,theCSFisnormalizedtounityatitspeakvalue.InsteadofdealingwiththeadditionalcomputationalcomplexityandparameterestimationproblemsofEquation(8),wewillsimplyuseEquation(9)tocorrectthepredictionsofthesingleandmultiplechannelmodels.
3.2Modelparameters
Themodelparametersusedarethosethatprovedtobebestinpreviousstudies.1−4TheCSFfilterswerecalibratedtoagreewiththeCSFformuladevelopedbyBarten.16ThefiltershaveadifferenceofGaussianform,
AhumadaandBeardObjectDetectioninaNoisyScene
−(f/fc)2
−(f/fs)2
-6-
S(f)=acexp−asexp
,(10)
whereacandasarethecenterandsurroundamplitudeparametersandfcandfsarethe
centerandsurroundfrequencycutoffparameters.Table3givestheCSFandβparametersforthemultiplechannelandthesinglechannelmodels.TheamplitudeparametershavethedimensionsofJND’sperunitcontrastandthecutoffparametershavethedimensionsofcyclesperdegreeofvisualangle.
Table3-Modelparameterschannelsβafcas/acfc/fsc20.80.775.6multiple415.5single418.516.40.687.93.3Modelpredictionsandresults
3.3.1Predictionswithoutacontrastmaskingcorrection.Themodelpredictionsford′withoutacontrastmaskingcorrectiongiveninTable4foreachofthefournoiselevels.
Table4-Modeld′’swithoutacontrastmaskingcorrection
noiselevelq00.250.514.02.32.21.9multiplechannelsinglechannel11.511.511.824.5Figure3showsthepredictionsofTable4plottedwiththemeanobserverresults.Both
modelscorrectlypredictthedifferencebetweenq=0andq=0.25causedbyscalingthedowntheaircraftimagetomakeroomforthenoise.Thesinglechannelmodelpredictsnomaskingbythenoise.Themultiplechannelmodelpredictsverylittlemaskingbythenoise.Table5showsthesensitivityscalefactorsneededtoequalizetheaveragelogpredictionsofthe
modelsandtheobservers.ItalsoshowstheaverageerrorofpredictionindecibelsusingthescalefactorandanFstatisticrepresentingthestatisticalgoodness-of-fitoftheerror.Themultiplechannelmodelaveragesafactorof4tooinsensitive,whilethesinglechannelaveragesensitivityiswithintherangeofthatoftheobservers.Theunderpredictionofthemaskingeffectscausestheerrorstobelarge.BothF’sarehighlysignificant,sincethe99.9percentileoftheFdistributionwith3and9degreesoffreedomis13.9.
Table5-Modelfitswithoutcontrastmaskingcorrectionscalefactormodelerror,dBF4.13.530.5multiplechannelsinglechannel0.724.038.53.3.2Withcontrastmaskingcorrection.RMScontrastvaluesfornormalizingthed′
valuesareshowninTable6foreachofthe4noiseplusbackgroundimages,filteredbytheCSFforeachmodel.
AhumadaandBeardObjectDetectioninaNoisyScene-7-
Table6-RMSimagecontrastnoiselevelq00.250.510.0760.0980.158multiplechannel0.136
singlechannel0.0790.0930.1360.150
Figure4showsthepredictionsofFigure3correctedwithac0of0.04andtheRMScontrast
valuesofTable6.Nowbothmodelspredicttheeffectofthenoisebetterwhenthenoiseispresent,buttheypredicttoomuchmaskingofthetargetbytheimagealone.Table7showsthegoodness-of-fitmeasuresasinTable5.Thescalefactorsshowthatnowbothmodelspredicttoomuchmasking.
Table7-Modelfitswithcontrastmaskingcorrectionscalefactormodelerror,dBF12.23.325.3multiplechannelsinglechannel2.13.834.73.3.3Contrastmaskingcorrectionbasedonnoisealone.Thepoorfitaboveiswhat
onemightexpectfromusinganimage-wideestimateforimagemaskingwhiletherunwayregionhaslittlecontrastvariation.ThevaluesofTable6canbedecomposedtoshowthattheRMSvisiblecontrastfromthefull(q=1)noisealoneis0.144forthemultiplechannelmodeland0.114forthesinglechannelmodel.Figure5showsthepredictionsofFigure3correctedwithac0of0.04andthenoisecomponentoftheRMSvisiblecontrast.Nowbothmodelsfitwell,withaslighterrorinthedirectionthatwouldresultfromasmallimage
maskingeffect.Table8showsthegoodness-of-fitmeasuresasinTable5.Nowbothmodelshavescalefactorsclosetounityandthesinglechannelmodelfitsthenoiseeffectquitewell.ThemultiplechannelFnowbarelyexceedsthe99thpercentileoftheFdistribution(6.99),andthesinglechannelFisjustabovethe90thpercentile(2.81).
Table8-Modelfitsusingonlynoiseinthecontrastmaskingcorrectionmodelscalefactorerror,dBFmultiplechannel1.301.77.02singlechannel1.161.12.844.Discussion
Theimprovementinthemodelpredictionsresultingfromlimitingthecontrastmaskingcorrectiontothenoise,suggeststhatthecontrastmaskingcorrectionshouldbebasedonthecontrastinasmallerregioncontainingthetargetobject.Wehadsuccessbefore2−4withthecorrectionbasedonthesamesizedimage,andexperimentsmeasuringcontrasteffectsonperceivedcontrastindicateconsiderablespatialspread.19−22Currentmodels12−15extendthemaskinginteractionsonlytochannelsdifferinginorientationatthesamelocationandspatialfrequency.Alsorecentattemptstomeasurecontrastmaskingbyasurroundmaskerfoundnone.23,24Wecurrentlyrecommendthatthecontrastmaskingcorrectionbebasedonanestimateoftheimagecontrastintheimmediateregionofthetargetobject.
AhumadaandBeardObjectDetectioninaNoisyScene-8-
Theresultsdemonstratethatthesinglechannelmodelwithanappropriatecontrast
maskingcorrectioncanoutperformthemultiplechannelmodelwithorwithoutageneralgaincontrol.Althoughamultiplechannelmodelwithinter-channelinteractionsmightdobetterinthissituation,itprobablywouldrequiremorestronglyorientedsignalsandmaskerstoobtainabenefitfortheextracalculations.Oneproblemwiththecontrastmaskingcorrectionandthemultiplechannelmodelisthatcontrastinthesignalchannelscontributestomaskingtwice.Themultiplechannelmodelmightbethebetterofthetwowiththecorrectionif,forexample,thewithin-channelmaskingexponentandthecorrectionexponentwerebothlowered.Theresultshereshowthateventhoughthesinglechannelmodeldoesnotpredictthedetailsoforientedcontrastmasking,suchastheresultsofFoley,11itcanbeausefulalternativetomorecomplicatedmodels.
5.Acknowledgments
Ren-ShengHorngwrotetheexperimentaldisplayandresponsecollectionprogram.AndrewWatsonwrotethebasicMathematicaroutinesthatgeneratedthemodelandmetricpredictionsandmadehelpfulsuggestions.WearealsogratefulforthehelpofAnnMarieRohaly,CynthiaNull,JeffreyMulligan,andRobertEriksson.ThisworkwassupportedinpartbyNASAGrant199-06-39toAndrewWatsonandNASAAeronauticsRTOP#505--53.
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Figure 1. (Top) Airport scene with an obstacle aircraft on the runway.
(Middle) The same scene without the aircraft.
(Bottom) The aircraft scene (p=1) masked by the noise at q=0.5.
Figure 2. Object detectability data from 4 observers for 4 noise levels.
3020
individualsgeometric mean
d’10
30.0
0.25
0.5
0.75
1.0
Noise proportion
Figure 3. Predictions of scaled models without contrast masking correction.
3020
multiple channelsingle channelobservers’ mean
d’10
30.0
0.25
0.5
0.75
1.0
Noise proportion
Figure 4. Predictions of scaled models with the contrast masking correction.
3020
multiple channelsingle channelobservers’ mean
d’10
30.0
0.25
0.5
0.75
1.0
Noise proportion
Figure 5. Predictions of scaled models with the contrast masking correction based only on the noise.
3020
multiple channelsingle channelobservers’ mean
d’10
30.0
0.25
0.5
0.75
1.0
Noise proportion
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