Modeling, Calibration, and Rendition of Color Logarithmic CMOS Image Sensors

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IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT,VOL.52,NO.5,OCTOBER20031581Modeling,Calibration,andRenditionofColorLogarithmicCMOSImageSensors

DileepanJoseph,Member,IEEE,andSteveCollinsAbstract—LogarithmicCMOSimagesensorsencodeahighdynamicrangesceneinamannerthatroughlyapproximateshumanperceptionwhereaslinearsensorswithequivalentquan-tizationsufferfromsaturationorlossofdetail.Moreover,thecontinuousresponseoflogarithmicpixelspermithighframeratesandrandomaccess,featuresthatareusefulinmotiondetection.Thispaperdescribeshowtomodel,calibrate,andrenderpixelresponsesfromacolorlogarithmicsensorintoastandardcolorspace.Theworkunifiescolortheoryinconventionallinearsensorsandfixedpatternnoisetheoryinmonochromaticlogarithmicsensors.ExperimentswithaFuga15RGBsensordemonstratecalibrationandrenditionusingaMacbethchartandneutraldensityfilters.Colorrenditionofthesensorwithanempiricalmodel,testedoverthreedecadesofdynamicrange,competeswithconventionaldigitalcameras,testedover1.5decades.Photo-diodeleakagecurrentscomplicatemodelingandcalibrationanddegraderenditionindimlighting.

IndexTerms—Colorrendition,fixedpatternnoise,logarithmicpixels.

I.INTRODUCTION

CMOSIMAGESENSORSaredisplacingCCDsensors

forseveralreasons,suchastheintegrationofsignalprocessingwithimagesensingononedieandtheeconomiesofscaleavailableintheCMOSindustry[1].ResearchonCMOSimagingincludesthedevelopmentofsensorstocapturehighdynamicrangescenes,whereilluminancesandreflectancesspanseveraldecades,withoutsaturationorlossofperceptibledetail[2].Forreasonsofhighdynamicrangeandhighframerate,togetherwithrandomaccessibilityofpixels,theautomotiveindustryfindslogarithmicimagingtobeusefulintheautoma-tionoftrafficsupervisionandtheimprovementofroadsafety[3].HumanperceptionroughlyapproximatesWeber’slaw,whichstatesthatthethresholdtosenseadifferencebetweentheilluminanceofafixationpointanditssurroundingsisafraction,about1–10%,ofthesurroundingilluminance[4].Whenilluminancesareencodedbyalogarithmicsensor,suchalawmakesthethresholdforsensitivityconstant,idealforquantization.Moreover,insteadofintegratingphoto-generatedchargeoveradiscreteperiodoftime,asinalinearpixel,alogarithmicpixelconvertsphotonfluxcontinuouslyintoa

ManuscriptreceivedMay26,2002;revisedMay20,2003.ThisworkwassupportedinpartbytheNaturalSciencesandEngineeringResearchCouncil(Canada)andinpartbytheEngineeringandPhysicalSciencesResearchCouncil(U.K.).TheauthorsarewiththeDepartmentofEngineeringScience,Uni-versityofOxford,Oxford,U.K.(e-mail:dileepan@robots.ox.ac.uk;collins@robots.ox.ac.uk).DigitalObjectIdentifier10.1109/TIM.2003.818551

current,whichmeansthatanimageisavailableatvirtuallyanymoment.Studieswithpulsedlasershaveshownapixelbandwidthof100kHz,atnormallightlevels,thatincreaseswithillumination[5].Inpractice,thespeedofthereadoutcircuitlimitstheframerate.Scenesobservedbythehumaneyespanovereightdecadesofilluminance,rangingfromluxinstarlightto1582IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT,VOL.52,NO.5,OCTOBER2003aboutcolorrenditioninlinearsensorsbutlittlehasbeenwrittenonrenditionincolorlogarithmicsensors,thesubjectofthispaper.SectionIIunitescolortheoryinlinearsensorswithmonochromatictheoryinlogarithmicsensorstomodelcolorsensationinlogarithmicsensors.SectionIIIdescribesaproce-duretocalibratethismodelandSectionIVoutlinesamethodtorendertheresponseofacalibratedsensorintoastandardcolorspace.SectionVdemonstratescalibrationandrenditionwithaFuga15RGBlogarithmicsensor,acolorversionoftheFuga15ddevelopedatIMEC[9],andcomparescolorrenditionofthesensortothatofconventionaldigitalcameras.

II.MODELLING

Acolorimagesensorismadebyinsertingcolorfiltersinthepathoflightraysbeforetheyformanimageonamonochro-maticsensor[10].Correspondingtohumancolorvision,threefiltersareneeded,selectivetothered(R),green(G),andblue(B)regionsofthespectrum.Multisensorimagersuseprismswithspecialcoatingstosplitandfilteranimageintothreeim-ages,whicharecapturedbyseparatesensorsandcombinedtoproduceasingleimage.Single-sensorimagershaveapatternofred,green,andbluefiltersoverlaiduponpixels.Thougheachpixelisselectivetoonecolor,itsneighborsareselectivetotheothers.Byinterpolatingpixelresponses,ared,green,andblueresponsemaybeestimatedforeachpixelatalossofspatialres-olution.Asmultisensorimagersobeyasimilartheory,therestofthispaperdiscussesonlysingle-sensorimagers.Acolorfilteronapixelmodifiesthespectralcompositionofincidentlightpriortoabsorptionbythephotodiodeinthepixel.Thephotodiodeabsorbsthefilteredlighttovaryingde-greesasafunctionofwavelength