Abstract Geometry Images

Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages for many graphics applications. However, current techniques

GeometryImages

XianfengGuHarvardUniversity

StevenJ.GortlerHarvardUniversity

HuguesHoppeMicrosoftResearch

Abstract

Surfacegeometryisoftenmodeledwithirregulartrianglemeshes.Theprocessofremeshingreferstoapproximatingsuchgeometryusingameshwith(semi)-regularconnectivity,whichhasadvan-tagesformanygraphicsapplications.However,currenttechniquesforremeshingarbitrarysurfacescreateonlysemi-regularmeshes.Theoriginalmeshistypicallydecomposedintoasetofdisk-likecharts,ontowhichthegeometryisparametrizedandsampled.Inthispaper,weproposetoremeshanarbitrarysurfaceontoacom-pletelyregularstructurewecallageometryimage.Itcapturesge-ometryasasimple2Darrayofquantizedpoints.Surfacesignalslikenormalsandcolorsarestoredinsimilar2Darraysusingthesameimplicitsurfaceparametrization—texturecoordinatesareab-sent.Tocreateageometryimage,wecutanarbitrarymeshalonganetworkofedgepaths,andparametrizetheresultingsinglechartontoasquare.Geometryimagescanbeencodedusingtraditionalimagecompressionalgorithms,suchaswavelet-basedcoders.Keywords:remeshing,surfaceparametrization.

1INTRODUCTION

Surfacegeometryisoftenmodeledwithirregulartrianglemeshes.Theprocessofremeshingreferstoapproximatingsuchgeometryusingameshwith(semi)-regularconnectivity(e.g.[3,13]).Resamplinggeometryontoaregularstructureoffersanumberofbene http://doc.xuehai.netpressionisimprovedsincetheconnectivityofthesamplesisimplicit.Moreover,remeshingcanreducethenon-uniformityofthegeometricsamplesinthetangentialsurfacedirections,thusreducingoverallentropy[10].Theregularityofsampleneighborhoodshelpsinapplyingsignal-processingoperationsandincreatinghierarchicalrepresentationsformultiresolutionviewingandediting[14,24].

However,currenttechniquesforremeshingarbitrarysurfacescreateonlysemi-regularmeshes.Theoriginalmeshistypicallydecomposedintoasetofdisk-likecharts,ontowhichthegeometryisparametrizedandsampled.Althoughthesamplingoneachchartfollowsregularsubdivision,thechartdomainsformanirregularnetworkoverthesurface.Thisirregulardomainnetworkcomplicatesprocessing,particularlyforoperationsthatrequireaccessingdataacrossneighboringcharts.Incontrast,texturedataistypicallyrepresentedinacompletelyregularfashion,asa(possiblycompressed)2Darrayof[r,g,b]values.Thisdistinction,amongothers,causesgeometryandtexturestobetreatedandrepresentedquitedifferentlybycurrentgraphics

hardware.

Inthispaper,weproposetoremeshanarbitrarysurfaceontoacompletelyregularstructurewecallageometryimage.Itcap-turesgeometryasasimplen×narrayof[x,y,z]values.Othersurfaceattributes,suchasnormalsandcolors,arestoredasaddi-tionalsquareimages,sharingthesamedo-mainasthegeometry.Becausethegeome-tryandattributessharethesameparametriza-Stanfordbunnytion,theparametrizationitselfisimplicit—“texturecoordinates”

areabsent.Moreover,thisparametrizationfullyutilizesthetexturedomain(withnowastedspace).Geometryimagescanbeencodedusingtraditionalimagecompressionalgorithm,suchaswavelet-basedcoders.Also,geometryimagesareideallysuitedforhard-warerendering.Theymaybetransmittedtothegraphicspipelineinacompressedformjustliketextureimages.And,theyeliminateexpensivepointer-basedstructuressuchasindexedvertexlists.Ofcourse,arbitrarysurfacescannotgenerallybemappeddirectlyontoasquareimagedomain,becausetheirtopologycandifferfromthatofadisk.Thebasicideainourapproachistosliceopenthemeshalonganappropriatesetofcutpaths,toallowtheunfoldingofthemeshontoadisk-likesurface.Theverticesandedgesalongthecutpathsarerepresentedredundantly(typicallytwice)alongtheboundaryofthisdisk.Next,weparametrizethiscutsurfaceontothesquaredomainoftheimage,andsamplethegeometryatthe2Dgridsamples.

Representingsurfacesasgeometryimagespresentschallenges: Adisk,cutandmustthatbealsofoundpermitsthataopensgoodparametrizationthemeshintoaoftopologicalthesurfacewithinthisdisk.Wedescribeaneffective,automaticmethodforcuttingarbitrary2-manifoldmeshes(possiblywithboundaries). Thereconstructedimageboundarysurfacematchesmustbeexactlyparametrizedalongthesuchcut,thattoavoidthecracks.Traditionaltexturemappingismoreforgivinginthisrespect,inthatcolordiscontinuitiesatboundariesarelessnoticeable.

Thetheparametrizationsurface,sinceundersamplingmustevenlydistributewouldimageleadtosamplesgeometricoverblurring.Wedonotmakeatechnicalcontributioninthisarea,butsimplyapplythegeometric-stretchparametrizationof[18,17].

Straightforwardintroducetearsalonglossythecompressionsurfacecut.ofWetheallowgeometryfusingimageofthemaycutbyencodingthecuttopologyasasmalldatasideband.Geometryimageshavethefollowinglimitations: Theycannotrepresentnon-manifoldgeometry.

Unwrappingparametrizationsanwithentiregreatermeshdistortionasasingleandlesschartuniformcancreatesam-plingthancanbeachievedwithmultiplelocalcharts,particu-larlyforsurfacesofhighgenus.Inthispaper,wedescribeanautomaticsystemforconvertingarbitrarymeshesintogeometryimagesandassociatedattributemaps(Figure1).Wedemonstratethattheyformapracticalandelegantrepresentationforavarietyofgraphicalmodels(Figure7).

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