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HSfM:HybridStructur e-from-Motion

HainanCui

1,XiangGao 1,2,ShuhanShen 1,2,andZhan yiHu1,2,3

1 NLPR,Instituteof Automation,ChineseAcademy ofSciences,Beijing ,China

2UniversityofChineseAcademyofSciences,Beijing, China

3CASCenterfor ExcellenceinBrain ScienceandIntelligence Technology, Beijing,China

{hncui,xiang.gao, shshen,huzy}@nlpr.ia.ac.cn

Abstract

categorizedasincrementalor globalaccording totheir waystoestimate initialcamera poses.Whileincr emental systemhasadvanced inrob ustnessandaccur acy,the ef- ficiencyremains itskeychalleng e.T osolvethisproblem, globalreconstruction systemsimultaneouslyestimatesal- lcamera posesfromtheepipolarg eometrygraph, butit isusuallysensitive tooutliers. Inthiswork, wepropose anew hybridSfMmethodtotackle theissuesof efficien- cy,accuracyandr obustnessinaunifiedfr amework.Mor e specifically,weproposean adaptivecommunity-basedr o- tationavera gingmethodfirsttoestimatecamerar otations inaglobal manner.Then, basedonthese estimatedcamera rotations,cameracenters arecomputedinanincr emental way.Extensiveexperimentsshow thatourhybrid method performssimilarlyor betterthanmany ofthestate-of-the- artglobalSfM approaches, intermsof computationaleffi- ciency,whileachieves similarreconstruction accuracyand robustnesswithtwootherstate-of-the-artincremental SfM approaches.

1.Introduction

Structure-from-Motion(SfM)technique istoestimate

the3Dscene structureandcamera posesfroma collection ofimages[ 2,38 ].Itusuallyconsistsofthreemodules:fea- turesextraction andmatching,initialcameraposesestima- tion,andb undleadjustment.According tothedifferenceof initialcameraposes estimationmanner, SfMcanbe broadly dividedintotwoclasses: incrementalandglobal.

ForincrementalSfMapproaches,one way[ 34,38 ]is

tostartfrom selectingafe wseedimages forinitialre- construction,thenrepeatedly addnew images.Another

way[21,41 ]istoclustertheimagesintoatomicmodels first,thenreconstruct eachatomicmodel andincrementallymergethemafter.Arguably,incremental manneristhemostpopularstrategy for3Dreconstruction[22, 39].Ho wever ,itissensiti veto theinitialseedmodelreconstructionandthemannerof modelgrowing. Inaddition,the reconstruc-tionerroris accumulatedwiththe iterationsgoingon. Forlarge-scalescenereconstruction,thereconstructed structuremaysuffer fromscenedrift[24]. Furthermore,thetime- consumingbundle adjustment(BA)[42] isrepeatedlyper -formed,whichdramatically decreasesthesystem scalabili-tyandef ficiency. Totackletheseweaknesses,globalSfMapproachesbecomepopular inthepast fewyears.

ForglobalSfMapproaches[31 ,13], initialcamerapos-

esareestimated simultaneouslyfromthe epipolargeometry graph(EG),whose verticescorrespond toimagesand edges linkmatchedimage pairs,andthe bundleadjustment isper- formedonlyonce, whichbringsa betterpotentialin system efficiencyandscalability.Thegenericpipeline forglobal cameraposesestimation consistsoftw osteps:rotation av- eragingandtranslation averaging. Forthe rotationaverag- ing,itsaccurac ymainlydepends ontwofactors:the struc- tureofEG andtheaccurac yofpairwise epipolargeome- tries[43 ].Currentlymanyliteratures[5,17 ]onlyminimize theresidualson theepipolaredges. Asaresult, whenthe camerasarenot welldistributed, forexample theInternet data[44 ],thosemethodssometimesperformpoorly.For the translationav eraging,sinceepipolargeometryonlyencodes thedirectionof pairwisetranslation,it isdifficult todeter- minecamerapositions. Moreover ,thetranslation estima- tionismore sensitive tofeaturematch outliers.Incompar- ison,incrementalSfM approachesbenefitfrom RANSAC techniquetodiscard badepipolargeometries. Thus,itis desirabletotak etheadv antagesofbothincrementaland globalmanners.

Contribution:(1)wepropose anew hybridSfMapproach

totacklethe issuesofef ficiency, robustnessand accuracyin aunifiedframe work;(2) acommunity-basedrotationaver- 1212

Figure1.Result ofQuad[ 7]with 5061imagesre gisteredoutof 5520images,where thecalibrationtime-cost ofourh ybridmethodisabout55 minsandthe mediancalibrationaccurac yis1.03m. agingmethodis proposedina globalmanner, whichcon-sidersboththe structureofEG andtheaccurac yofpairwise geometries;(3)based ontheestimated camerarotations,cameracentersare estimatedinan incrementalway .For eachcameraaddition, bothcamerarotations andintrinsicparametersarek eptasconstant, whilethecameracentersandscenestructure arerefinedby amodifiedb undleadjust-

ment.

Inourh ybridSfM,global rotationaveragingdecreases

theriskof scenedrift,and incrementalcentersestimation increasesrobustness tothenoisydata.With knowncamera rotations,cameracenters registrationonly needstwo scene points,thusthe RANSACtechnique makesour methodbe- comemorerob usttooutliers andmorecamerascouldbe calibratedateach cameraaddingstep. Additionally,since onlythescene structureandcamera centersarerefined in eachcameraaddition, thebundle adjustmentinour hybrid workismuchfaster thanthecon ventionalone [38,39].

Inthee xperiments,wee valuateourhybridSfM system

onbothsequential andunorderedimage data.Ourmethod outperformsmany recentstate-of-the-artglobalSfMmeth- ods[11 ,31,40,44],interms ofthenumberofreconstruct- edcameras,indicating thatourmethod ismorerob ustto outliers.Interms ofreconstructionef ficiency, ourmethod performssimilarlyor betterthanthe globalSfMmethods, whileitis upto13 timesfaster thanaparallelized version ofBundler[ 38],and 5timesfasterthantheparallelizedver - sionofTheia [39]. Fig.1illustrates areconstructionresult onthepublic datasetQuad[ 7],where morethan5K images arecalibratedby ourhybrid SfMsystem.W ithacompara- blecalibrationaccurac y,the speedofourhybridmethodis

50timesf asterthanBundler [38],and7times fasterthan

DISCO[7 ].

2.RelatedW ork

IncrementalSfMmethodsOneway toreconstructthe

scenestartsfrom twoor three“seed"vie ws,thenincre-mentallyaddne wviews intosystemtoinitializethefinal BA[2,16 ,28,34,35,38, 45,48].Suchapproaches aresensitivetotheseedselectioncriteria,and accumulateder- rormaycause scenedrift.T odecreasethe accumulatederrors,bothVSFM [45]and COLMAP[34 ]proposedtore-triangulatetracksin theimageadding process.Anoth-erway [20,21,41 ]istocreateatomic3Dmodelsfirst,and thenmerge differentmodels.Suchhierarchicalmethods aresensitivetotheatomicmodelselectionand modelgrow- ingscheme.F orlarge imagecollections,alltheincrementalmethodssufferfromscenedriftandheavycomputationloadduetothe repeatedactiv ationofb undleadjustment.GlobalSfMmethods GlobalSfMapproaches [3, 7,10 ,11,

23,29,31, 33,40,44] simultaneouslyestimateallthecam-

eraposesand performbundle adjustmentonlyonce. The cameraposesestimation processmainlycontains twoparts: rotationav eragingandtranslationaveraging. RotationAv eragingRotationav eragingestimatesallthe camerarotationsfrom pairwiserelativ erotationssimul- taneously,whichhasbeenwell studiedinman ylitera- tures[5 ,14,17,27,43]. Martinecetal.[27 ]proposedto proposedtotransform therotationa veragingproblem in- toaLie-algebraic averaging. Basedon[ 14],betterresult isachiev edbycombiningwithrobustL1optimization[ 5]. Recently,Wilsonetal.[43 ]foundtwofactorsimpactingthe rotationestimationaccurac y,one istheEGstructureandthe otheristhe epipolargeometryaccurac y,and recommend- edtocluster camerasfirstwhen theydistrib utedunev enly.

However,theydidnotdescribehowtogroupand mergeim-

ageseffecti velybasedonthistheory.Inspiredbythistheo- reticalanalysis,we proposeacommunity-based rotationav- eragingmethodto automaticallydeterminewhen andhow tocluster, andfollowedbyagreedy mergingstep.

TranslationAveragingManylinearmethods[3 ,23, 33]

proposedtosolv ethecamera positionsbymatrixdecom- position.Whileef ficient,suchapproaches aresensitiveto epipolargeometryoutliers. Hence,many globalSfMap- proaches[15 ,46,47]carefullyfilteredtheerroneous edges first.Zachetal.[47 ]proposedtofilteredgesbyloopcon- sistencycheck,andWilson etal.[44 ]presentedahashing- likemethod,called1DSfM.Ho wever ,thismethod [44] re- quiresabundant pairwiseassociations(O(n2)).Insteadof filtering,somemethods refinedtheepipolar relationsbylo- calbundle adjustment[11]ormulti-vie wtrackconsisten- cy[40].Other methods[7,11,37,25] solvedthe scene pointsandcamera centerstogether. Inthisw ay,not only thecollinearmotion problemissolv ed,but allthecameras arefusedinto aconnectedparallel-rigid graph[31 ].Be- sides,methods[ 4,8 ,9,32,37]fusedauxiliary imagingin- formationtoobtain thecameracenters. Whileefficient and scalable,they areheavilyrelyingonthe auxiliaryinforma- tion. 1213

Epipolar

Geometry

GraphCommunity

Detection Rotation

AveragingSeed Selection

and

ReconstructionAdd Cameras

and

TriangulationRefine Centers

and

Scene Structure

Incremental Centers EstimationGlobal Rotations Estimation

Final Bundle

Adjustment

Figure2.Pipeline ofourh ybridSfMsystem.

3.Over viewofHybridSfM

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