Recovering estimate of fluid flow from image seque

ComputerVisionandImageUnderstanding80,246–266(2000)doi:10.1006/cviu.2000.0874,availableonlineatfluidflowfromimagesequences.Theapproachcentersaroundamotion-recoveryalgorithmthatisbasedonprinciplesfromfluidmechanics:Thealgorithmisconstrainedsothatrecoveredflowsobserveconservationofmassaswellasphysicallymotivatedboundaryconditions.Empiricalresultsfromapplicationofthealgorithmtotransmittanceimageryoffluidflows,wherethefluidscontainedacontrastmedium,arepresented.Intheseexperiments,thealgorithmrecoveredaccurateandpreciseestimatesoftheflow.Thesignificanceofthisworkistwofold.First,fromatheoreticalpointofviewitisshownhowinformationderivedfromthephysicalbehavioroffluidscanbeusedtomotivateaflow-recoveryalgorithm.Second,fromanapplicationspointofviewthedevelopedalgorithmcanbeusedtoaugmentthetoolsthatareavailableforthemeasurementoffluiddynamics;otherimagedflowsthatobservecompatibleconstraintsmightbenefitinasimilarfashion.c°2000AcademicPress1.INTRODUCTION1.1.MotivationPhysicalmodelingplaysanimportantroleincomputervision.Constraintsderivedfromphysicalconsiderationsareoftenusedtoprovidethebasisforwell-motivatedalgorithms.Thisclosetiebetweenimageinterpretationandphysicalmodelingsuggeststhatmeasure-mentproblemsinthephysicalsciencesmightbeafruitfulsourceofresearchissuesforcomputervision.Aparticulardomainwherethismethodologyislikelytobeofvalueisthemeasurementoffluidflowfromimagesequences.Here,applicablephysicalconstraintscomenaturallyfromfluidmechanics.Forexample,differentialflowconstraintscanarisefromthecontinuityequationsyieldedbyconservationofmassandmomentum.Similarly,realisticboundaryconditionscanbederivedfromphysicalconsiderations.Significantly,1TheresearchthatisdescribedinthispaperwasfundedbyDARPA/ETOunderContractDABT63-95-C-0057.2461077-3142/00$35.00Copyrightc°2000byAcademicPressAllrightsofreproductioninanyformreserved.RECOVERINGESTIMATESOFFLUIDFLOW247itisstandardpracticeinexperimentalfluidmechanicstoseedflowswithtracersforthesakeofvisualization.Thispracticeyieldsimagerywiththepatternedcontrast(i.e.,tex-ture)necessarytodrivestandardcomputervisionmotion-analysisalgorithms.Owingtotheirphysicalunderpinning,algorithmsthatarefoundedontheseprinciplesshouldexhibitgreateraccuracyandprecisionthanthosebasedmoresimplyonthematchingofimageintensitypatterns.Motivatedbytheseobservationsthecurrentpaperpresentsanalgorithm,basedinthephysicsoffluidmechanics,fortherecoveryoffluidflowfromimagesequences.Thealgorithmisparticularlytargetedtotherecoveryoftwo-dimensionallyimagedmotionofthree-dimensionalmedia.Significantly,suchtwo-dimensionalinformationcanbeofimportanceinandofitself,eventhoughtheactualthree-dimensionalmotionisnotmadeexplicit.Asexamples,influidmechanics,two-dimensionalmotionallowscomparisonsbetweenempiricaldataandtheoreticalmodels(Lanzillottoetal.[1]);inmedicalimageanalysis,two-dimensionalmotioncanbeusedtomonitorbloodflowinameaningfulfashion(Amini[2],Nogawaetal.[3]);inmeteorology,two-dimensionalmotioninatmosphericimagesequencescanbeusedtosupportlarge-scalepatternanalysis(CohenandHerlin[4],Larsenetal.[5],MeminandPerez[6]).Theimmediateapplicationofthedevelopedalgorithmistotheexperimentalstudyoffluidicdevices.Moregenerally,however,thedevelopedalgorithmshouldbeapplicabletoavarietyofflow-recoveryproblemswherethekinematicsofimagedmotionisrelatedtothecontinuummechanicsoftheimagedmedia.Inparticular,certaintypesof(i)medicaltransmittanceimaging(e.g.,X-raytimeseriesofbiologicaltissue(Webb[7]))and(ii)visiblereflectanceimaging(e.g.,uncalibratedimagesequencesdepictingdilationand/orangularrotation(DelBimboetal.[8]))mightbewellsuitedtothedescribedalgorithm.1.2.RelatedResearchTherecoveryofopticalflow,i.e.,theapparentmotionofimageintensitypatterns,hasbeenthesubjectofagreatdealofresearch(AggarwalandNandhakumar[9],BeaucheminandBarron[10]).Typically,opticalflowalgorithmsarebasedonthebrightnessconstancyconstraint(Horn[11]).Essentially,thisdictatesthatthealgorithmsestablishamappingbetweentwoimagesbaseddirectlyonthesimilaritiesoftheimageintensities.Variousphenomenologicalextensionstothisconstrainthavebeenproposedtomakeitlessrestrictive(e.g.,CorneliusandKanade[12],NegahdaripourandYu[13]).Otherextensionshavebeenbasedontheanalysisoftheimagingofthree-dimensionalobjectsunderperspectiveprojection(Nagel[14]).Formanyapplications,algorithmsbasedonbrightnessconstancyorthecitedextensionshaveproventobeofvalue.However,theseconstraintsfailtoadequatelycapturethenatureoffluidflowandthereforearelessclearlyapplicabletothatproblemdomain.Forthemattersathand,anaturalconstraintarisesintheflowcontinuityequationasderivedfromtheprincipleofconservationofmass.Thisconstraintdictatestemporalimagetransformationsthatareconsistentwithfluidflowbehavior.Schunck[15]firstappliedtheconservationofmassconstrainttotheanalysisofimagedmotion.Thisworksuggest