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Fast Cost-Volume Filtering for Visual Correspondence and Beyond

FastCost-VolumeFilteringforVisualCorrespondenceandBeyond

ChristophRhemann1,AsmaaHosni1,MichaelBleyer1,CarstenRother2,MargritGelautz1

1

ViennaUniversityofTechnology,Vienna,Austria

2

MicrosoftResearchCambridge,Cambridge,UK

Abstract

Manycomputervisiontaskscanbeformulatedasla-belingproblems.Thedesiredsolutionisoftenaspatiallysmoothlabelingwherelabeltransitionsarealignedwithcoloredgesoftheinputimage.Weshowthatsuchsolutionscanbeef cientlyachievedbysmoothingthelabelcostswithaveryfastedgepreserving lter.Inthispaperweproposeagenericandsimpleframeworkcomprisingthreesteps:(i)constructingacostvolume(ii)fastcostvolume lteringand(iii)winner-take-alllabelselection.Ourmaincontributionistoshowthatwithsuchasimpleframeworkstate-of-the-artresultscanbeachievedforseveralcomputervisionap-plications.Inparticular,weachieve(i)disparitymapsinreal-time,whosequalityexceedsthoseofallotherfast(lo-cal)approachesontheMiddleburystereobenchmark,and(ii)optical ow eldswithvery nestructuresaswellaslargedisplacements.Todemonstraterobustness,thefewpa-rametersofourframeworkaresettonearlyidenticalvaluesforbothapplications.Also,competitiveresultsforinterac-tiveimagesegmentationarepresented.Withthiswork,wehopetoinspireotherresearcherstoleveragethisframeworktootherapplicationareas.

1.Introduction

Discretelabel-basedapproacheshavebeensuccess-fullyappliedtomanycomputervisionproblemssuchasstereo,optical ow,interactiveimagesegmentationorob-jectrecognition.Inatypicallabelingapproach,theinputdataisusedtoconstructathree-dimensionalcostvolume,whichstoresthecostsforchoosingalabell(i.e.disparitiesinstereo)atimagecoordinatesxandy.Forstereo,thesecostsaregivenbypixel-wisecorrelation(e.g.absolutedif-ferencesoftheintensities)betweencorrespondingpixels.Thenthegoalisto ndasolutionwhich(i)obeysthelabelcosts,(ii)isspatiallysmooth;and(iii)labelchangesarealignedwithedgesintheimage.Tothisend,apopularapproachistoutilizeaConditional(Markov)RandomFieldmodel(CRF).Thismeansthatanenergyfunctionisformu-lated,wherethelabelcostsareencodedinadatatermandthespatiallysmoothedge-alignedsolutionisenforcedbyane.g.pairwisesmoothnessterm.Thiscostfunctioncanthen

ThisworkwassupportedinpartbytheViennaScienceandTechnol-ogyFund(WWTF)underprojectICT08-019.

beminimizedusingglobalenergyminimizationapproachessuchasgraphcutorbeliefpropagation.Adrawbackisthatsuchglobalmethodsareoftenrelativelyslowanddonotscalewelltohigh-resolutionimagesorlargelabelspaces.Fastapproximations(e.g.[26])usuallycomeatthepriceoflossinquality,duetoless-globaloptimizationschema.Continuouscounterpartstodiscretelabelingmethodsarebasedonconvexenergyfunctionalswhichcanbeef cientlyoptimizedontheGPU,e.g.[17,13,10].Adrawbackisthatmanyoftheseapproacheshavearestrictedformofthedataandsmoothnessterm.Forinstance,thebrightnessconstancyassumptioninoptical owisusuallylinearizedandthusonlyvalidforsmalldisplacements.Toovercomethisproblem,acoarse-to- neframeworkiscommonlyusedwhichhowever,stillcannothandleobjectswhosescaleismuchsmallerthantheirmotion.Anotherproblemisposedbytheconvexityofthesmoothnessterm,whichmightover-smooththesolution.Thismaybethereasonwhyconvexmodelshavenotreportedstate-of-the-artstereoresultsyet.Aninterestingalternativetoanenergy-basedapproachistoapplyalocal lteringmethod.The lteringoperationachievesaformofspatially-localsmoothingofthelabelspace,incontrasttoapotentialspatially-globalsmoothingofaCRF.Despitethisconceptualdrawback,anobserva-tionofthisandpreviouswork[31]isthat“localsmooth-ing”isabletoachievehighqualityresults.Webelievethatthereasonisthedominanceofthedatatermwithrespecttothesmoothnessterm.1Animportantobservationisthatthedatatermwillplayanevenmoredominantroleinthefuture,sincebothvideoandstill-picturecamerasarecon-sistentlygrowingintermsofframe-resolutionandalsody-namicrange.Note,adetailedcomparisonbetweenenergy-basedand ltering-basedmethodsisbeyondthescopeofthispaper,andwewillonlybrie ydiscusstheminsec.6.Ingeneral,relativelylittleworkhasbeendoneinthedo-mainof lter-basedmethodsfordiscretelabelingproblems[31,19,8].Aboveall,thereisno lter-basedapproachforgeneralmulti-labelingproblemswhichisbothfast(real-time)andachieveshighqualityresults.Thekeycontribu-tionofthispaperistopresentsuchaframework.

someapplicationsitmaybepossibletoshowthatthesmoothness

termofalearnedenergypropagatesinformationonlylocally.Notethatforsomeapplicationsglobalconstraintsexistsuchastheocclusioncon-straintinstereomatchingandoptical ow.Inourapproachwemodeltheocclusionconstraintwithafastadditionaloperation.

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