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