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2024年4月16日发(作者：郑州本轮疫情为何难以控制这是)
4
-PointsCongruentSetsforRobustPairwiseSurfaceRegistration
DrorAiger
DepartmentofComputerScience,
BenGurionUniversity
IITDelhi
TUVienna
DanielCohen-Or
SchoolofComputerScience,
TelAvivUniversity
(a)(b)(c)(d)
Figure1:tructionresultsfromnineinputscansofashinnywaterjug.
Neighboringscanshave40%overlaporless,andrequiredanaverageof16secondsforfullyautomaticalignmentstartingfromarbitrary
lpairwisealignmentsareshownin(a)and(b),wherefor
finalalignmentresult,(c)and(d),isobtainedwithoutanydatasmoothing,
outlierremoval,localICPrefinement,globalerrordistribution,oranyassumptionaboutstartingalignment.
Abstract
Weintroduce4PCS,afastandrobustalignmentschemefor3D
pointsetsthatuseswidebases,whichareknowntoberesilientto
orithmallowsregisteringrawnoisydata,
possiblycontaminatedwithoutliers,withoutpre-filteringordenois-
r,themethodsignificantlyreducesthenumber
oftrialsrequiredtoestablishareliableregistrationbetweentheun-
derlyingsurfacesinthepresenceofnoise,withoutanyassumptions
hodisbasedonanoveltech-
niquetoextractallcoplanar4-pointssetsfroma3Dpointsetthat
areapproximatelycongruent,underrigidtransformation,toagiven
tractionprocedurerunsinroughly
O(n
2
+k)time,wherenisthenumberofcandidatepointsand
tice,whennoise
levelislowandthereissufficientoverlap,usinglocaldescriptors
thetimecomplexityreducestoO(n+k).Wealsoproposeanex-
tensiontohandlesimilarityandaffihnique
achievesanorderofmagnitudeasymptoticaccelerationcompared
nstratethe
robustnessofouralgorithmonseveralsetsofmultiplerangescans
withvaryingdegreeofnoise,outliers,andextentofoverlap.
Keywords:computationalgeometry,pairwisesurfaceregistration,
scanalignment,partialshapematching,largestcommonpointset
(LCP)measure,affineinvariantratio
1Introduction
Surfaceregistrationistheprocessofidentifyingandmatchingcor-
respondingregionsacrossmultiplescansgiveninarbitraryinitial
positions,andestimatingthecorrespondingrigidtransformsthat
ntyears,advancesin
geometryscanningtechnologyhaveleadtoagrowinginterestin
surfaceacquisitiontechniqueswheremultiplescansarerequiredto
beregisteredintoacoherentcoordinateframeusingrigidtransfor-
mations[Callierietal.2004,Gelfandetal.2005,LiandGuskov
2005],orusingnon-rigidalignment[Paulyetal.2005,Brownand
Rusinkiewicz2007].Theregistrationproblemisaninstanceof
partialmatchingof3Dpointsets,alargerandmoregeneralfunda-
mentalproblemincomputationalgeometryandcomputervision.
Onepopularphilosophybehindregistrationtechniquesistouse
robustlocalshapedescriptors[LiandGuskov2005]todefinean
approximatetransformation,followedbyanIteratedClosestPoint
(ICP)method[BeslandMcKay1992,ChenandMedioni1992]to
refiransformations,beinglowdimensional
entities,canbeuniquelyrecoveredifthecorrectcorrespondenceis
escriptors,invariant
underrigidtransforms,arecommonlyusedtoextractsuchasmall
rtosuch
asetofpointsasabase.
GiventwopartsPandQinarbitraryinitialposes,matching
pairsofbases,onefromPandonefromQ,generatesasetofcan-
artech-
niquecalledgeometrichashingcanbeusedtopickagoodaligning
transformation[WolfsonandRigoutsos1997]fromsuchacandi-
izedalgorithms,likeRANSAC(RANdomSAm-
pleConsensus)[FischlerandBolles1981],repeatthevotingpro-
cessforanumberofbasecandidatesenoughtimestoensurethatit
finds,withhighprobability,ementsofthis
basicparadigmhavebeenproposedbyChenandco-authors[1999]
withtradeoffbetweenspeedandrobustnesstonoise.
GlobalquantitieslikeobjectcentroidsandPrincipalComponent
Analysis(PCA)areoftenusedtoroughlyalignobjectstotrans-
r,incaseofpartialoverlap,such
Figure2:entwithwide-base(top)ismorestablethanalignmentusingnarrow-base(bottom).Thegray
andthegoldencurvesweregeneratedfromacommoncurve,ustnesswepreferthewidestpossible
base[Goodrichetal.1994],wherethemaximumwidthislimitedbytheextentofoverlapbetweentheshapes.
escriptors[Johnson1997,Li
andGuskov2005],computedfromlocalsurfacegeometryandin-
varianttorigidtransforms,havebeenusedasanefficienttoolfor
ghundernoisyconditionsitispossible
torobustlycomputesuchlocaldescriptors[Pottmannetal.2007],
inpresenceofsignificantnoiseandoutliers,definingareliablelo-
scenarios,
insteadofusinglocaldescriptors,aneffectivealternativeistorely
proachrequiressolving
theLargestCommonPointset(LCP)problem:Giventwopointsets
PandQ,LCPunderδ-congruencesolvesforasubsetP
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