2317-abstract.pdf

Image-SpaceHorizon-BasedAmbientOcclusion

LouisBavoil MiguelSainz RouslanDimitrov

NVIDIACorporation

Figure1:Ambientocclusionwithoutanyshading.(left)67MPixels/swithourhorizon-basedalgorithm.(right)15MPixels/swithray

marchingand4raysperdirection.ImagesrenderedwithN d =8andN s =8onGeForce8800GTXUltra.

1Introduction

Ambientocclusionisalightingmodelthatapproximatesthe

amountoflightreachingapointonadiffusesurfacebasedon

itsdirectlyvisibleoccluders. Itgivesperceptualcluesofcurva-

tureandspatialproximity.Like[Mittring2007]and[Shanmugam

andArikan2007],weproposeareal-timeambientocclusioncom-

putationasapostprocessingpassmainlybasedonadepthimage

fromtheeye’spointofview.Thisapproachrequiresnoscene-

dependentprecomputationsandisapplicabletodynamicscenes.

Ourproposedmethoddoesnothavetheoverocclusionissuefrom

[ShanmugamandArikan2007]andsamplesinsidetheradiusof

inﬂuence,unlike[Mittring2007].

WeusethefollowingformoftheambientocclusionilluminationA

atagivensurfacepoint P

(a)

(b)

(c)

Figure2:(a)Theazimuthalangleqaroundtheviewvector ~ V.The

tangentanglet(q)isthesignedelevationangleofthesurfacetan-

gentvector.(b)Thehorizonangleh(q)isthemaximumelevation

a>=t(q)forwhich ~ wisoccludedforalla<h(q)(c)Example

ofsamplelocationsfor4directionsandastepsizeof2texels.

A=1− 1

directionsinimagespaceandsteppingontheheightﬁeldstoredin

thedepthimage.WepickN d directionsqinimagespacearound

thecurrentpixelwhichcorrespondtodirectionsaroundtheZaxisin

eyespace( ~ VonFigure2a).Foreachangleq,wecomputethehori-

zonangleh(q)bysamplingthedepthimagealongalinesegment

inimagespace.Theeye-spaceradiusofinﬂuenceRisprojectedon

theimageplaneandissubdividedintoN s stepsofequallengths.

Forﬁndingthehorizonangleindirectionq,westartbycomputing

thetangentanglet(q)andintersectaviewraywiththetangent

planedeﬁnedby P andthesurfacenormal~n.Wethenstepinthe

depthimageindirectionqandcomputeD=S i −P,whereS i is

thereconstructedeye-spacepositionofagivensampleS i .Based

ontheelevationanglesa(S i )=atan(−D.z/||D.xy||),thehorizon

angleh(q)ismax(t(q),a(S i ),i=1..N s )whereN s isthenumber

ofstepsperdirection.Weignoresamplesforwhich||S i −P||>R.

BecauseD.zmustbetheexactdepthassociatedwiththeoffsetD.xy,

wemakesuretoalwayssampleattexelcenters.Todoso,wesnap

thetexturecoordinatesofthesamplesalongeachdirectiontothe

nearesttexelcenters(seeFigure2c).

Totradebandingartifactsfornoise,werandomlyjitterthestepsize

perpixelandrandomlyrotatetheN d uniformdirectionsperpixel.

Althoughusingasingledepthlayertypicallyproducesplausible

results(seeFigure1),itcouldbeextendedbyusingmultiplelayers

suchasthefrontandbackfaces.

V( ~ w)W( ~ w)dw (1)

whereVisthevisibilityfunctionoverthenormal-orientedunit

hemisphere W ,whichreturns1ifaraystartingfrom P indirec-

tion ~ wintersectsanoccluderand0otherwise,andWisalinear

attenuationfunction.

2Horizon-BasedAmbientOcclusion

Weuseasphericalcoordinatesystemwiththezenithaxisaligned

intheviewdirection ~ V,azimuthangleqandelevationanglea(see

Figure2a).Similarlytohorizonmapping[Max1986],wesplitthe

unitspherebyahorizonlinedeﬁnedbythesignedhorizonangle

h(q)(seeFigure2b).Assumingthattheneighborhoodof P isa

continuousheightﬁeld,raysthatwouldnormallybetracedbelow

thehorizonareknowntointersectanoccludersotheintersection

testfortheserayscanbeomitted.Underthecontinuousheightﬁeld

assumption,Equation1canberewrittenas:

Z p

Z h(q)

a=t(q) W(~w)cos(a)dadq (2)

A=1− 1

q=−p

WeusethelinearattenuationfunctionW(q)=max(0,1−r(q)/R)

wherer(q)isthedistancebetween P andthehorizonpointindi-

rection~wandRistheradiusofinﬂuence.Inthiscase,

References

M AX ,N.L.1986.Horizonmapping:Shadowsforbump-mappedsurfaces.InPro-

ceedingsofComputerGraphicsTokyo’86onAdvancedComputerGraphics.

M ITTRING ,M. 2007.Findingnextgen:Cryengine2. InSIGGRAPH’07:ACM

SIGGRAPH2007courses.

S HANMUGAM ,P., AND A RIKAN ,O.2007.Hardwareacceleratedambientocclusion

techniquesongpus.InI3D’07:Proceedingsofthe2007symposiumonInteractive

3Dgraphicsandgames.

Z p

A=1− 1

(sin(h(q))−sin(t(q)))W(q)dq (3)

q=−p

3Image-SpaceIntegration

Ouralgorithmtakesasinputper-pixellineardepthsandeye-space

normals.Foreverypixel,wecomputeitseye-spaceposition P and

weintegrateEquation3usingaMonteCarloapproachbysampling

SIGGRAPH 2008, Los Angeles, California, August 11–15, 2008.

ISBN 978-1-60558-466-9/08/0008

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