[PDF] Towards Detection of Orthogonal Planes in Monocular Images of

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imagesofindoor environments Abstract - Inthispaper,wedescribethe componentsofa novelalgorithmforthe extractionofdominantorthogonal planarstructuresfrom monocularimagestakeninindoor envi- vanishingpointsandvanishinglinesimposed bythefrequently observed dominanceof threemutually orthogonalvanishing directionsinman-madeworld.Vanishingpointsarefound by an improvedapproach,takingno assumptionson knowninternal or externalcameraparameters.Theproblemofdetecting planarpatchesisattacked using aprobabilisticframework, novelformulationfusing geometricinformationobtainedfrom vanishingpointsandfeatures,suchasrectanglesand partial by animageover-segmentation. largely varyingcharacteristicsconcerningimagequality and scene complexity.Experiments showthat themethod,despite mance comparesfavorablytothestate-of-the-art.

I.INTRODUCTION

Inthelastyearstheinterest in designingmobilerobotsfor domestictaskshasbeenrapidly growingwithintherobotics community.Besidesbeinganimportantfield ofitsown right,buildingscalable andaffordableplatformsinresponse tothediverse applicationscenariostargetedatbyindustry representsatempting goalfor roboticsresearch. Inthiscontext,solutions solely based on visualsensory inputaremovingstillmoreintothe centerofinterest.On onesidethereisthe economicalfactorpushing down prices of robotsbyavoidingexpensivesensors,ontheotherhand, imagesorvideoacquired bycamerasalreadycontainrich informationto harvestfortasks suchas sceneunderstanding, localization,and navigation.Consequently,duringthelast yearsthework on vision-basedsystemshasemergedasa view.Thereisanenormouseffort,partially propelled bythe cognitivevisionresearchfield,to perceive and understanda scenejustfromvisual information. Inthispaper,wedescribe anovelapproach devisedto help arobot to understandthe contentofascene,givenasingle image.To bemorespecific,wepropose amethodfordecom- 1 outduring his stayat theinstitution ofothertwoauthors.

2H.WildenauerandM.Vincze arewiththeAutomationandCon-

trolInstitute,Faculty ofElectricalEngineeringandInformationTech- nology,ViennaUniversity ofTechnology,Austria,{wildenauer, vincze}@acin.tuwien.ac.at. (a) (b) (c) (d) Fig.1.Proposedsequentialchainleadingto detection oforthogonal planesinamonocularimage.(a)Theinput image(844×1126 pixels) with vanishinglinesdepicted.(b)Detectedlinesconsistentwiththree automaticallyestimated orthogonalvanishing points.(c)Detected partial andcompletequadrilateralsutilizingthevanishing pointsandlinespointing tothem.(d)Finalsegmentation ofplanesbased onaMarkovRandomField formulationemploying vanishing points,lines,and quadrilateralsegments. anon-calibratedcamera,into orthogonalplanes,seeFig.1.

Findingtheseplanesintheimage cansignificantlyaida

robot inselflocalization,navigationandfurther recognition designamethodfornon-calibratedacquisitionsettingsto be abletoalso handle casesforwhicheithertheinternalcamera parametersareunknown,orarelikelyto beimprecise.In experimentsit is shownthat themethodisabletoextract asignificantamountofstructural informationfromasingle monocularimage.However,alatermerging ofentireimage sequenceswillgreatlycontributetoastabilization ofthe wholeprocess. ingtosolveitonamoreglobal level than before.Thepaper isinits spiritand goalsmostsimilartotherecentstate-of- the-artwork ofHoiemet.al.[4].They uselearntappearance modelsbased on variousgeometric,color,andtexture cuesto partitionanimageintocoarse3Dsurface entities.Weshow thatevenwithout learningand byapplyinglesscueswe can stillcompetewiththeirmethod.2008 IEEE International Conference on

Robotics and Automation

Pasadena, CA, USA, May 19-23, 2008978-1-4244-1647-9/08/$25.00 ©2008 IEEE.999

Thenovelty ofthepaperistwo-fold.First,anadopted

RANSAC-basedline clusteringstagefordetecting vanishing instability overprevioustechniques.Second,weformulate theproblemofdetecting planesinamonocularimageusing the estimated vanishing pointsinaprobabilisticframework based onsearchingformaximumaposterioriprobability (MAP)ofaMarkovRandomField(MRF).

In ourapproachwepartiallyexploit theso-calledMan-

hattanworldassumption.I.e.,thefrequently observed dom- inanceofthreemutually orthogonalvanishing directionsin man-made environments[5].Motivated byideaspresented in[6],we adoptedaRANSAC-basedline clusteringtech- niquewhichisabletofind dominantvanishing directions imposed bya calibratedcameraintoaccount;however internalcameraparametersdo nothaveto beknowna prioriastheyare estimated duringthe clustering process. Thevanishing pointestimationisfollowed byasearchfor perspectively distortedrectangles-basiclandmarksinman- made environmentsthatarehelpingfurthertoset thepriors forourMRF-based planedetectionmethod.Wepropose howthe estimated vanishing points should beutilizedfor asuitablesetting ofweightsforedgesand verticesofthe graphrepresentingtheMRFwe areoperating on.

Themethodisintent to be applied onmobileplatforms

wherereal-time,orat leastclosetoreal-timeperformance, tothat,sotheycan be efficientlycodedtofulfillsucha requirement. estimation ofvanishing pointsandlinespointingtothem isexplainedinSec.II followed bySec.IIIwithashort description ofthedetection ofquadrilateralstructures.An Explanation ofourMRF-basedapproachforfinal localiza- tion ofplanesinanimageisgiveninSec.IV.Wesummarize the entire algorithminSec.Vandreportexperimentalresults inSec.VI.

II.VANISHINGPOINTDETECTION

Man-made environmentsgenerallyexhibitstrongregular- ityinstructure and oftenmany parallel linesarepresent.In suchsettings,vanishing pointsprovideusefulvisualcuesfor deducinginformationabout the3Dstructureofanimaged scene.Furthermore,iftwo ormorevanishing pointsare found ofwhichtheunderlyingstructure"sorientationsare assumedto beorthogonal,then,takingmildassumptions, internalcameraparameterscan be estimated. processingstagesandtheline errormodel in useisgiven.

A.Linedetection

Initially,connectededgesegmentsarefound utilizinga directionaledgelinking,line candidatesare extracted using Fig.2.Comparison ofthemethod[8]and ourproposedalgorithmon animageofa clutteredscene.Linesetscorrespondingtoeach ofthree detected vanishing points,differentiatebycolor,areshown.Noticethat the orthogonalsetofvanishing points,depicted bymembershipsoflinesto them,wasestimatedincorrectly bythemethod[8],butcorrectly by our algorithm.Whitelinesintheleft image correspondto noisylines,not associatedwithany vanishing point. segmentsarerefined byaTotalLeastSquaresfit tothe edge segmentspixelcoordinatesandshort linesorlineswithlow fitting qualityarerejected[8].

Forimageswithlowresolutionasubstantial increasein

thenumberand quality ofdetectedlinesegmentscan be achieved by up-samplingtheimagebyfactortwo priorto edgedetection[9].

B.RANSAC-basedline clustering

Inthis stagevanishing pointhypothesesarerepeatedly generatedthroughtheintersection oflines.Theintersection pointshavingalarge enoughsetoflinespointingtowards themarelikelyto betruevanishing pointsandarereconsid- eredinfurtherprocessingstages.

1)Linesegmenterror:To quantifythe errorofaline

segmentmeetingavanishing point,anideal linefromthe segment"smidpoint tothevanishing point isconstructed andthenormaldistanceofonesegmentendpoint tothis lineismeasured.Formally,thisdistance can bewrittenas d and¯aiisitsrootpointontheideal line.Thedescribedmodel isbased onthe assumptionthat thereislittlevariationin themidpointofthelinesegment,asit isthemean ofthe involved pixelpositions.Othererrormodelscan befound in[10],[11].

2) IterativeRANSAC:Sincethe actualmixturefraction

oflinesbelongingto differentvanishing pointsisunknown, we adopt the adaptivevariantproposedin[12].Specifically, werunthe algorithmseveral timesoverthedatasetand beforethenext trial.Aftereachtrial,thevanishing point positionisrefined byapplyingKanatani"srenormalization scheme[13]totherespective consensus set.Werejectnewly detected vanishing pointsiftheyliewithintheuncertainty of previously detected onesutilizingtheteststatisticsproposed in[6].Here,however,we adoptedthevanishing pointcovari- ancematricesobtained byrenormalization.Theiterationis stopped,ifnomore consensus setswitha cardinalityabove apredefinedthresholdarefound. onthe complexity ofthescenethedescribedclustering typicallyresultsin numbersofthreeuptoten vanishing point1000 candidates.Fromthis setwe exhaustivelyselectvanishing point triplesandretain onlythosewithapproximately or- theonehavingthelargest totalconsensus set ischosenas

Inthe caseofunknowninternalcameraparameters,the

camera calibration necessaryfortheorthogonalitytestcan be carried out individuallyforeachtripleofvanishing points. Forthiswehave chosenthe composite calibrationmethod describedin[13],assumingsquarepixelsandthe camera"s principlepoint to belocatedinthe centeroftheimage.

Ourexperimentshaveshownthatafurther refinementof

itsposition oftencaused unstable calibrationresults,thuswe did notconsideritfurther.

C.Comparisonto otherknownmethods

In preliminaryexperiments,we compared ourmethodto

provided bythe authors.Wefound ouralgorithmto give

III.QUADRILATERALDETECTION

Humanmade environmentscontainmanyrectangular

structures.These,depending on occlusionsandthe camera"s field ofview,areprojectedascompletequadrilateralsor featuresrepresentstrong visualcuesforthedetection of planarsurfacesandconsequentlyareofaidtothetask of scenereconstructionand understanding.

In ourworkweuse aperspectiverectangledetection

methodrelatedtothe approach of [1],however,applyinga withavanishingline,i.e.,thetwo vanishing pointsgenerat- ingit,aregrouped by principlesofproximityandcontinuity andaprobabilisticinferenceisusedtofind hypotheses forquadrilateral-shapedstructuresinthegraph.On ofthe majoradvantagesofourapproachisthat itdoesnotonly detectperspectively distortedrectangles,butalsosub-parts iftheyare compatiblewiththeinitialplane-hypothesis.For anexampleofthefeaturesfound,seeFig.1.

Asthismethodiscurrently underareviewing process,

furthertechnicaldetailswillbeomitted here.However,it can be easilyreplacedwith othertechniques,suchasthe onepresentedin[2],[15].

IV.MRFBASEDPLANEDETECTION

Having detected vanishing pointsandlinespointingto themwewant toassigntoeach pixel inanimageits3D orientationw.r.t.toa camera coordinatesystem.Aswe assume aManhattanworldstructure,thisisequivalent to assign oneofthreelabels,where eachlabelcorrespondsto oneofthreeorthogonalplanes.

Tosolvetheproblemonaglobal level,i.e.toallow

orientationsandrelationsbetween neighboring pixels simul- taneously,weformulatetheprobleminafully probabilistic objecttwith nodesxtobjectt? edgeswithgtt?(xt,xt?) g t(xt=1)gt(xt=2)g t(xt=3) Fig.3.Anexample3×4 grid graphGfor|X|=3labelswithsymbols explainedinthetext.AlabelingL,i.e.solution,fromEq.(2)is shown by aredthicksubgraph.Imageprovided bycourtesy ofT.Werner [17]. framework;as searchingforamaximumposterior (MAP) configuration oftheMarkovRandomField(MRF) [16].It hasbeenshown[17]that thesolutioncan befoundasa thesocalledlabeling orMax-sumproblemofsecond order -

We assume anMRF,i.e.,agraphG=?T,E?,consisting of

adiscretesetTofobjects(intheliterature alsocalledsites, orlocations)andasetE??|T| 2? ofpairsofthoseobjects.

Each objectt?Tisassignedalabelxt?XwhereXis

label toeach object,represented bya|T|-tuplex?X|T| withcomponentsxt.

AninstanceoftheMax-sumproblemisdenoted bythe

triplet(G,X,g),wherethe elementsgt(xt)andgtt?(xt,xt?) ofgare calledqualities.Thequality ofalabelingxisdefined as

F(x|g)=?

tg t(xt)+? {t,t?}g tt?(xt,xt?).(1)

SolvingtheMax-sumproblem meansfindingthesetof

optimal labellings L

G,X(g)=argmax

x?X|T|F(x|g).(2) Fig.3 depictsthesymbolsandtheprobleminamoreintuitive way onasimplegrid graph.Recently,veryefficientalgo- relaxationanditsLagrangian dual,originally proposed by Schlesingerin 1976[18],hasbeenreviewed[19],[17],[20].

A.Graphentities

toMRFbasedmethodsistoencode allpossiblepriors partitioninganimageinto geometricallyandcolorcoherent regionsasFig.1shows.

Webuildagraph onan over-segmentedimage,i.e.,on

superpixels,seeFig.4,to keeptherunningtimeinreasonable colortogether.Theuseofsuperpixels significantlyreduces1001 information.Simplyreducingtheimagesize and building anMRFon pixelstoavoidthelarge complexityasimple- mentedinmanyapproachesleadstolosing detailsand high

SpanningTreebasedmethod byFelzenszwalb[21],giving

us,byappropriatesetting ofparameters,500-800regionson average.However,any otherover-segmentationcan beused. i.e.thesetE,are established betweeneachtwo neighboring superpixels.Thenumberofnodes(labels)Kis4,that is, weuseonelabelforeach orthogonalplane and onelabel thereisnotenoughinformationto decidewhich planethe superpixelbelongsto. Eachedgegtt?(xt,xt?)andeach objectnodegt(xt)is set accordinglytothesmoothnessand datatermrespectively, thegraph,theMax-sumsolver [17]isrunto obtaina particularlabelxtforeachsuperpixelt.

B.Smoothnessterm

bond ofneighboringsuperpixels.In ourcasewetakeinto account the colordifferencebetweensuperpixelsandthe straightnessofthe common boundary.Thiscan bewritten asfollows g α<0isaparameterpre-set to-10.Werepresentutinthe ofthestandardRGBspace.Ssttt?=P N ilength linei lengthboundaryisasum oflengthsofNlinesfittedtotheshared boundary between A,normalized bythelength oftheboundary.Theparameter βcontrollingtheinfluenceofthesmoothnessterm,was set to 0.5in ourexperiments. superpixelswithsimilarcolorandjagged boundaries.Such jagged boundariesareusually producedaccidentally dueto weak gradients[21]andthereforedo notcorrespondtoreal splitsoftwosuperpixelpatchesinthescene.

C.Dataterm

Thedatatermgt(xt)encodesthequality ofassigning

alabelxfromthesetXtoan object/superpixeltinthe graph.Thequalitymeasureshowthesuperpixel itselfsuits to particularclassmodels,in ourcase,tolieon oneofthe orthogonalplanes.

Foreachsuperpixel4 numbersareneededto beset,

i.e.,howlikelyisthat thesuperpixel ismarked by oneof fourlabels.Thefirst threelabels standforthebeliefthat asuperpixel lieson oneofthethreeorthogonalplanes; the regioncorrespondsto oneobject inthe constructed graph.Right:The smoothnessterm.Boundary-colorencodesthepenaltyset inthegraph betweentheobjectscorrespondingtotwo neighboringsuperpixels.Darker coloring denoteslesspenalization.Note,thatstraightboundarysegments arepenalizedstronger.

The consistency ofasuperpixel toaplaneisexpressed

via adeviation ofgradientorientationsofthepixelsalong theboundary ofthesuperpixel totwo vanishing points correspondingtothatplane.Forcomputation ofthegradient probability ofthepixel lying onanedge,themembership to oneofthethreevanishing points,andtheprobability of being noise.Wetakeintoaccountonlythosepixelshaving aprobability ofbeing onanedge above a certainthreshold.

Then,anormalized histogramht(y)withfourbinsy=

{1,2,3,4}iscomputedfromvanishing pointmemberships fourth binaccumulatespointsclassifiedto beonanedge, however,notconsistentwithany vanishing pointdirection. Finally,the consistency ofthesuperpixelwitheachlabel is setasquotesdbs_dbs35.pdfusesText_40

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