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翻译原文

7.3MultiviewIntegration

Thetechniquesdescribedinthisbookforrecoveringdepthfrommatchedstereo-pairsofim-agesresultinasetofpoints,therangemap,beingacquiredthatcanbetriangulatedtodescribeasingle2.5Dmanifoldin3-space.Inmanypracticalapplicationsof3Dimaging,thereisarequirementtogenerateacompleteandclosed3Dsurfacemanifoldbyfusingtogether,i.e.integrating,multiple2.5Drangemapscorrespondingtomultipleviewscapturedofasingleobject.Inthiscasesufficientviewsoftheobjectmustbecapturedtoensurethataclosed3Dmeshcanbeformed.

CurlessandLevoy[82]stipulatethat,ideally,theaboveprocessshouldmakeuseofalltherangedatacollected,takeintoaccountthequalityorcertaintyofeachlocalrangemeasure-ment,generatethesame3Dmeshirrespectiveoftheorderinwhichrangemapsareprocessedandallowincrementaladditionofrangemaps.Inaddition,theintegrationprocessshouldalsoundertakestepstoamelioratedefectsinthecaptureddata,forexamplebydetectingandre-movingrangemapoutliersorfillingholesintheconstructed3Dmesh（totherebyconstructawatertightmesh）.Finally,theprocessshouldnotberestrictedtoobjectsofanyspecific

topologicalconfigurationandshouldalsobecomputationallyefficient,astensorevenhun-dredsofrangemapsmighthavetobeintegratedinrealapplications.

Averylargebodyofworkonrangesurfaceintegrationhasbeenreportedintheliterature;however,twotechniquesaremostcommonlyadopted,volumetricintegrationanddirectmeshintegration,asdescribedinthefollowingsections.

7.3.1ImplicitSurfacesandMarchingCubes

Thebasicideabehindvolumetricintegration,asdescribedbyCurlessandLevoy[82],involvesdecimatingthe3Dspaceinwhichthecapturedrangesurfacesliebymeansofavoxeldatastructure.RepresentationandintegrationofmultiplerangesurfaceswithinindividualvoxelelementsrelyontheconceptofasigneddistancefunctionD（x）thatrecordsthedistanceinspacefromanimagedsurfacetothecentreofeachvoxel.Thisdistanceisrecordedfromeachvoxelcentretotherangesurface,followingthepathofthesightlinefromtheimagingsensor,forpositivedistances.Negativedistancesoccurwherethesensorsightlinepenetratestherangesurfacepriortoreachingaspecificvoxel.Figure7.2illustratesthisgeometricconfiguration.

Accordingly,thezero-surface,i.e.whenD（x）=0,representseachrangesurfaceand

D（x）isthereforetermedanimplicitfunction.Foreachrangesurfacetobeintegratedthecorrespondingsigneddistancefunctions,di（x）,areconstructedandaccumulatedinvoxelspacetoprovideanewzero-surfacethatineffectaveragestheirrelativedisplacements.This

Figure7.2Signeddistancerangesurfaceencodingofvoxelspace.Figurebasedon[82]

accumulatedzero-surfacecanthenbeextractedandtriangulatedusingatechniquesuchasmarchingcubes[280],describedbrieflyinsection7.3.1.4.

Afurthercomplicationisthatthequalityofthephysicalsensingmechanismisalsotakenintoaccountwhenformingtheimplicitfunctionforeachrangesurface.Whenviewingasurfacefromthereferencecamera（say）ofastereo-pair,assumingfrontoparallelgeometryforsimplicity,thentheoptimumsurfacereconstructionwilltakeplacewhentheobservedsurfacenormaliscollineartothiscamera’ssightline.Acosineangleweightingfunctionwi（x）canthereforebeformedbytakingthedotproductofthe（dominant）camerasightlineunitvectorandtheobservedsurfacenormal.Thisfunctionisusedtoweighteachimplicitfunctionsampled.Itisthenpossibletosumthesampledimplicitfunctionswithineachvoxel（x）fromeachrangeimapbytakingthefirst-ordermomentsasfollows:

i

},wi（x）di（x）

D（x）=

},w（x）.（7.22）

Furthermore,theabovesumcanbeformedincrementallyasfollowstogivethesigneddis-tancefunctionDi（x）andweightfunctionWi（x）accumulatedforthei-thrangemap:

Wi（x）Di（x）+wi+1（x）di+1（x）

Di+1（x）=

Wi（x）

+wi+1

（x）

（7.23）

Wi+1（x）=Wi（x）+wi+1（x）.

Thedistancexinvoxelspaceoverwhichsigneddistancesareformedinfrontofandbehindtherangemaphastoberestrictedtoavoidthesurfacesofself-occludingmanifoldsfrominter-feringwitheachother.Thisplacesalimitontheminimumthicknessofclosedmanifoldthatcanbeconstructedbythismethod.IntheimplementationofCurlessandLevoytheimplicitfunctionisformedforhalfthemaximumuncertaintyintervalintherangemeasurementsinfrontof（andbehind）therangemapsurface.

7.3.1.1RangeMapPre-segmentation

Duetothecharacteristicsofrangemapscapturedbystereo-photogrammetryanumberofpreprocessingstepsareusuallyrequiredtoassistsegmentingacleanlyclosedvolumefrommultiplecapturedrangemapsofanobject.Anotherreasonforsegmentingoutonlysurfacesofinterestisduetothen3memorycostofconstructingavoxelspace,wherenisthesamplesizeofeachdimensionoftheimagedvolume,itisvitaltoreducetheimagedvolumesizetoencompassonlyvaliddata.

Itisnotuncommontoadopt‘bluescreen’coloursegmentationtoisolatetheobjectsurfaceofinterestintheintensityimagesofthestereo-pairsandthenusetheseassegmentationmaskstoisolatethecorrespondingrelevantareaintherangemapsforintegration.Clearlythisimposesthelimitationofcapturingthedesiredobjectinfrontofanappropriatelycolouredbackdrop,typicallyblue,greenororange,thatdoesnotcorrespondtothecolourofthesurfacetobereconstructed.Asthissegmentationprocessmayresultinfragmentationoftherangemap,usuallyanumberofmorphologicaloperationsareappliedtosmooththeresultantbinarysegmentationmask,selectthelargestcontiguousblob（assumedtocorrespondtothesurfaceofinterest）andthenfillanyholesremaininginthisblob.

Whencoloursegmentationisnotpossibleorinappropriate（monochromestereo-pairsmightonlybeavailableoritmightnotbepossibletoconstrainthecaptureconditions）thenitispossibletothresholdtheconfidencemapproducedbythestereomatchingalgorithminordertoidentifycontiguousregionscomprisingviablymatchedsurfaces.

7.3.1.2VolumetricIntegrationAlgorithmOverview

TheprincipalbasicalgorithmicstepssetoutbyCurlessandLevoy[82]areasfollows.

1.Initializethevoxelspacewithzeros.

2.Constructtrianglesonthenearestneighbourelementsoftherangemapssuchthattrianglesarenotformedoversteepdiscontinuitiesbydetectingtriangleswhosesidelengths,whentakenasratiosofeachother,exceedathresholdlimit.Inthismannerthesurfacenormalforeachtrianglecanbeextractedanditsdotproductformedwiththe（dominant）cameralineofsighttoproduceaweightvalueforeachobservedelementofeachrangesurface.

3.Thesigneddistanceforeachvoxelforeachrangemapiscomputedbycastingarayfrom

theprincipalpointinthedominantcamerathrougheachelementintherangemap,andthedistancenotedtoeachvoxelwithinadistanceof±Dmaxvoxelsasdeterminedbytherange

measurementuncertainty.

4.EachvoxelelementisupdatedbyaccumulatingtheweightedsigneddistancesusingEquation（7.24）.

5.IsolateanewisosurfaceforD（x）=0.

7.3.1.3HoleFilling

Whiletheabovealgorithmwillgenerateagoodapproximationtoanisosurface,unseenareascanresultinholeswhenattemptingtotriangulatetheisosurface.Sincethereareoftensitua-tionswherethepresenceofholesinasurfaceisunacceptable,e.g.whenmeasuringvolumechangeduetosurfacedisplacement,acommonclinicalrequirementwhenassessingtheout-comeofcertaintherapiesorsurgeryproceduresonthebodyorface,ameansoffillingholesisrequiredtoproduceawatertightsurfacereconstruction.

Thestandardapproachistolabelthevoxelsaccordingtooneofthefollowingstates:

unseen,emptyorsurface（within±Dmaxoftheaccumulatedsurface）.Figure7.3illustrates

thisapproach,anditcanbeseenthatsurfaceholesariseattheboundaryofemptyandunseenvoxels.Therefore,placingsurfacesattheseboundariesprovidesasimplemeansofgeneratingawatertightsurfacebasedontheminimumofassumptions.

Thepreviouslydescribedalgorithmisnowmodifiedasfollows.

1.Assignallvoxelstoaninitialunseenstate.

2.Computetheweightedsigneddistanceaccumulationonthosevoxelswithin±Dmaxofthe

accumulatedsurfacesasbefore,labellingthesevoxelsassurface.

3.Resetallthevoxelsbetweenthoselabelledassurface,followingthedominantcameraviewingdirection,backtotheboundaryofthevoxelspaceclosesttothiscamerawiththestateempty.

4.OncemoreextracttheisosurfaceforD（x）=0andalsoextractasurfaceattheinterface

betweenthoseregionslabelledunseenandthoseregionslabelledempty.

Unseen

HoleFillIsosurface

SignedDistance±d

Empty

ObservedIsosurface

Sensor

Figure7.3Geometricconfigurationforholefilling.Figurebasedon[82]

Whereholefillingisappliedthensurfacediscontinuitiesarelikelytoarise,therebygen-eratingartefacts.Thisobviouseffectofsuchholefillingcanbereducedbyapplyinglocalfiltering（averagingnearestneighbouringvertices）onlytotheholeregionsthemselves.Inthiswayitispossibletoavoidblurringtheremainderofthemeshwhilesuppressingartefacts.Thesupportregionofthefilterweightsisallowedtotaperbetweenthehole-filledregionandtheobserveddatainordertosmooththeirtransition[82].

7.3.1.4MarchingCubes

Thefinalstepoftheabovevolumetricintegrationmethodrequiresthattheisosurfacefor

D（x）=0isconstructedfromthevoxelscontainingtheac