Integrating Dynamic Deformations into Interactive Volume(4)

Per-vertexapproachesrelyonatesselationoftheproxygeometrytoprovidethesetofverticestodeform.Iftheproxygeometryistobeviewdependent,itmustbere-tesselatedwhenevertheviewchanges.Thismakesmethodsthatrenderfrommultipleviewpoints(§4)dif cult,particu-larlyifweareconcernedwithusingthesamesamplingsothatmultipleviewscanbeusedseamlessly(asinFigure5).Italsocomplicatestheuseofview-alignedproxygeometry.Suchgeometryisadvantageousasituniformlysamplestheobjectspace,leadingtomoreconsistenttransparentshadingeffects.

Per-vertexmethodsrelyonsubdivisiontoreducethenum-berofdeformationevaluationsthatneedtobeperformed.Sinceweareinterestedindynamicdeformations,thismeansthatchangesinthedeformationwouldrequireanewsub-division,anewtessellation,andnewdeformationevalua-tions.Wecaneliminatethesubdivisionconsiderationifwe

cTheEurographicsAssociation2006.ShaderSine29fps7.1fpsTexture21.7fps5.7fps

Table1:Performancesummary,discussedinsection6.2.Case1representsasimpletransferfunctionandCase2rep-resentsagradientcomputationanddiffuseshading.

ControlTextureSizeSamp/Vox

163264FSTable2:Frameratesinfpsofcontroltexturesizevs.sam-pleplanespervoxel,usingthemousetorsoofFigure1,a256x256x192volume.

assumea xed,uniformsubdivisionisused,whichissensi-bleforevaluationarapidlychanging,unknowndeformation.Wecanalsoeliminatethetesselationconsiderationifweuseobject-orientedgeometry.Undertheseconditions,ourmeth-odsarethemostsimilar.

Ourmethods,therefore,haveadvantagesinprovidingfor exibleproxygeometrythatenablesinteractiontechniquesandavoidsrecomputationwhendeformationschange.Intermsofperformance,ourmethodoffersadifferentsetoftradeoffsaswemovemoreofthecomputationfromtheCPUtothefragmentshaders.Becausefragmentshadersexecuteinparallel,theyaremorelikelytoprovideperformancein-creasesinfuturegenerations.6.2.PerformanceandAccuracy

Weevaluatedtheperformanceofourprototypeimplemen-tationonaPCwitha3GhzIntelPentium4ProcessorandanNVIDIAGeForce6800GTgraphicscard.Whileourim-plementationadjustssamplingratestoprovidefasterperfor-manceattheexpenseofimagequality,we xthesamplingrateatthesizeofthesmallestobject-spacevoxelfortheseperformancemeasurements,exceptwherenotedotherwise.Allmeasurementsarefortheachievedsystemframeratein-cludinganycomputationofthedeformations.

Therenderingratesonarealisticexample(the512x512x106CTHead,Figure5)aresummarizedinTa-ble1.Weevaluatetwoshadingtypesandthreedeformations.Forrenderingcase1,adensityvalueisconvertedtoacolorandalphavaluebasedonatransferfunctiontexturelookup.Forrenderingcase2,weaddouron-the- ygradientcom-putationandadotproductisperformedfordiffuseshading.Thedeformationsweconsiderareatrivialtranslationandasinewave,bothimplementedintheshader,andaHierarchi-calB-Splinethatisevaluatedandstoredina163texture.Thetrivialtranslationdefomationisinterestingbecause

Non-linear geometric deformation (or warping) is a useful tool for working with volumes. Unfortunately, the computational expense of performing the resampling needed to implement volume deformation has precluded its use in interactive applications. In this

Samp/Vox

81632Table3:Frameratesinfpsofcontroltexturesizevs.sampleplanespervoxel,whilechangingtheHBSplinedeformationofthe256x256x192mousetorsoofFigure1.

althoughitadds(almost)nocomputationtotheshadingpro-cess,itdoeseffectperformance.Directlyfeedingthetexturecoordinatetothetexturelookupachieves39fpsincase1.Performingatrivialcomputationonthecoordinate rstre-ducestheperformanceto29.2fps.Thissuggeststhattheun-derlyinggraphicssystemprovidessomeoptimizationfordi-recttexturelookups.Sinceweareunsureifthisoptimizationcouldbeleveragedfordeformations,wereporttheshiftedcaseinthetable.

Thedropinframeratebetweencase1andcase2,whereweaccessanadditionaltexturefourtimes,suggeststhatourperformanceisboundbytextureaccess.Thesetexturelookupsmayhavepoormemorycoherence.Slowdownsinadditiontothisincreasedshadercomplexitycomefromwrit-ingtothedeformationtexture,andfrommemoryband-widthtothegraphicscardtoupdatethedeformationtex-tures.Overall,we ndthattheapplicationsdescribedinsec-tion5areinteractiveifweusethereducednumberofsam-plingplanesduringinteraction.

ToshowtheperformanceimpactofcontroltexturesizeweusethedatasetseeninFigure1.Performanceforasim-pledeformationisshowninTable2.Asexpected,largercon-troltexturesslowrenderingslightly,andthefragmentshaderdeformation,usingnodeformationtexturelookup,isnearlytwiceasfast.

Whentheevaluationsofthedeformationfunctionbecomemoreexpensive,bettersamplingofthedeformationfunc-tionshavemoreofaperformanceimpact.Table3,weshowtheframeratewhilechangingacontrolpoint,solvingforthenewHBSplinedeformation,storingtheevaluationsinthecontroltexture,andrenderingtheimage.

Performanceofourprototypeshowsthatinteractiveview-ingofvolumeswithdynamicdeformationsispracticaloncurrenthardware.Ourmethodsarewell-posedtoleveragetrendsingraphicshardware.Acknowledgments

ThisresearchwassupportedinpartbyNSFgrantsIIS-0416284andCCF-0540653.TBwassupportedbyanNLMCIBMtraininggrant(NLM5T15LM007359).WethankJamieWeichert’slabforprovid-inguswiththemousevolumesseeninFigure1and6.TheCTHeadinFigure5wasobtainedfromOpenQVis.

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