Information Sciences) degrees from NUS in 1993 and 1987 respectively. For his postgraduate
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VarianceInvariantAdaptiveTemporalSupersamplingforMotionBlurring
DanielNeilsonandYee-HongYang
ComputerGraphicsResearchGroup
DepartmentofComputingScience
UniversityofAlberta
dneilson,yang@cs.ualberta.ca
Abstract
Adaptivetemporalsampling,usedtocreatemotionblur
indistributedraytracing,generatesmoresamplepointsin
regionswithmotionblurthaninregionswithoutmotion
blur.Whenthenumberofsamplepointsusedonstation-
aryobjectsinregionswithmotionblurexceedsthenumber
ofsamplepointsusedinotherregionsoftheimage,thevari-
anceinthecolouroftheobjectcandifferbetweenthetwo
regions.Thispaperidentifiesthecauseofthisvariancedis-
crepancy,andproposesamodificationtoexistingadaptive
temporalsamplingalgorithmswhicheliminatesit.Ourre-
sultsdemonstratethatthevarianceofstationaryobjectsre-
mainsapproximatelythesamethroughouttheentireimage
andthattheproposedmodificationiscapableofimproving
therunningtimeofexistingadaptivetemporalsamplingal-
gorithms.
1.Introduction
Motionblurringisgenerallyconsideredtobeimportant
whensynthesizinghighqualityimageswhichcontainmov-
ingcomponents.Infilmordigitalphotography,motion
blurariseswhenacomponentofthesceneismovingata
highvelocitywithrespecttotheshutterspeedofthecam-
era.Thismotionwhiletheshutterisopencausesablurring
effectwhichimagesynthesisalgorithms,strivingforphoto-
realism,mustduplicate.
Thedistributedraytracingalgorithm[1]isableto
achievemotionblurbydistributingthesamplepointsin
timeaswellasinspace.However,simplysamplingthe
entireimage-spaceinthetemporaldomainisinefficient
whenonlyaportionoftheimageisaffectedbymotionblur.
Thisinefficiencygaverisetoanadaptivetemporalsampling
techniquetosamplearayinthetemporaldomainonlywhen
itpassesthroughthepathofmotionofanobject.
Thisadaptivetemporalsamplingtechniquecausesmore
samplepointstobeusedinthetemporallysampledregionsoftheimagethaninthenon-temporallysampledregionsof
theimage.Whenanobjectismovingatahighervelocity
withrespecttotheframeexposuredelay,apotentiallylarge
percentageofthetemporalsampleswillstrikethestation-
aryobjectsbehindthemovingobjects.Thus,thenumberof
pointsamplestakeninregionsoftheimagethathavebeen
supersampledinthetemporaldomaincouldbesubstantially
largerthanthenumberofpointsamplestakeninotherre-
gions.Thismeansthattherenderingequationwillbeeval-
uatedtoahigheraccuracyforstationaryobjectsinregions
withmotionblurthaninregionsoftheimagewhicharenot
motionblurred.
Theobjectiveofthispaperistobringthisdisparityto
theattentionofthecomputergraphicscommunity,andto
proposeasolutiontothedisparity.Theproposedsolutionis
amodificationoftheadaptivetemporalsamplingtechnique
whichpreventstherenderingequationonstationaryobjects,
intemporallysupersampledregionsoftheimage,frombe-
ingevaluatedmoreaccuratelythaninthenon-temporally
supersampledportionsoftheimage.Itisshownthatthe
proposedmodificationisequivalenttotheadaptivetempo-
ralsamplingtechniqueinblurredregionswherenostation-
aryobjectsareintersected,andoutperformstheadaptive
techniqueinblurredregionswhereastationaryobjectisin-
tersected.
2.Background
Inthissection,wereviewamodificationtothedis-
tributedraytracingalgorithm,proposedbyKajiya[2],com-
monlyknownaspathtracing.Thepathtracingalgorithm
isusedinplaceofthedistributedraytracingalgorithmin
theremainderofthispapertodemonstratetheoversampling
problemandtheproposedsolution.Wealsoreviewanadap-
tivetemporalsamplingmodificationtoKajiya’spathtracing
algorithm.
Thebasicpathtracingalgorithmwithsupportformotion
blurringgeneratesacolourforeachpixelintherendered
imagebyaveragingthelightcolourofapotentiallylargenumberoflightraysthroughthepixel.Eachindividualray
isassignedarandomtime,withinthedefinedframeexpo-
sureinterval,andthentracedthroughthesceneforanumber
ofreflections,accumulatinglightasitgoes.Pseudo-code
forthealgorithmispresentedinappendixB;thealgorithm
onlyshowsdiffuserayreflections,thoughthealgorithmcan
easilyaccommodaterefractionandmirrorreflections.
Fewchangesarerequiredtomodifythebasicpathtrac-
ingalgorithmtoadaptivelysamplethetemporaldomain
onlyinregionswithmotionblur.Asinthebasicpathtrac-
ingalgorithm,wedeterminethecolourofapixelbyaver-
agingthelightcolourofanumber,,oflightraysthrough
thepixel.However,theraysarenotassignedarandom
time;rather,theyarenotassignedatimeatall.Whiletrac-
ingaraythroughthescene,wetestwhethertheraypasses
throughthepathofanymovingobjectspriortointersecting
theneareststationaryobject.Whentheraypassesthrough
thepathofamovingobject,wegeneratetemporalsam-
plesfortherayandcalculatetheshadeoftherayastheaver-
ageoftheshadeateachofthetemporalsamples.Also,
whileperforminglightingcalculationsforasamplepoint,
whichisnotatemporalsample,wedetermineiftheline
segmentbetweenthepointandthelightsourceintersects
thepathofamovingobject.Ifitdoesintersectamoving
object,weperformthelightingcalculationoftemporal