112008 4-Points Congruent Sets for Robust-Linux大棚

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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)

-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

+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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