Fitting Parameterized Three-dimensional Models to Images(2)

Model-based recognition and motion tracking depends upon the ability to solve for projection and model parameters that will best fit a 3-D model to matching 2-D image features. This paper extends current methods of parameter solving to handle objects with

1Introduction

Model-basedvisionallowspriorknowledgeoftheshapeandappearanceofspeci cobjectstobeusedduringtheprocessofvisualinterpretation.Reliableidenti cationscanbemadebyidentifyingconsistentpartialmatchesbetweenthemodelsandfeaturesextractedfromtheimage,therebyallowingthesystemtomakeinferencesaboutthescenethatgobeyondwhatisexplicitlyavailablefromtheimage.Byprovidingthislinkbetweenperceptionandpriorknowledgeofthecomponentsofthescene,model-basedrecognitionisanessentialcomponentofmostpotentialapplicationsofvision.

Oneimportantcomponentofmodel-basedvisionistheabilitytosolveforthevaluesofallviewpointandmodelparametersthatwillbest tamodeltosomematchingimagefeatures.Thisisimportantbecauseitallowssometentativeinitialmatchestoconstrainthelocationsofotherfeaturesofthemodel,andtherebygeneratenewmatchesthatcanbeusedtoverifyorrejecttheinitialinterpretation.Thereliabilityofthisprocessandthe nalinterpretationcanbegreatlyimprovedbytakingaccountofallavailablequantitativeinformationtoconstraintheunknownparametersduringthematchingprocess.Inaddition,parameterdeterminationisnecessaryforidentifyingobjectsub-categories,forinterpretingimagesofarticulatedor exibleobjects,andforroboticinteractionwiththeobjects.

Inmostcases,itispossibletosolveforallunknownparametersfora3-Dmodelfrommatchestoasingle2-Dimage.However,insomecircumstances—suchaswhenboththesizeanddistanceofthemodelisunknown—theaccuracyofparameterdeterminationcanbesub-stantiallyimprovedbysimultaneously ttingthemodeltoimagestakenfrommorethanoneviewpoint.Themethodspresentedherecanbeusedineithersituation.

Thelocationsofprojectedmodelfeaturesinanimageareanon-linearfunctionoftheview-pointandmodelparameters.Therefore,thesolutionisbasedonNewton’smethodoflineariza-tionanditerationtoperformaleast-squaresminimization.Thisisaugmentedbyastabilizationmethodthatincorporatesapriormodeloftherangeofuncertaintyineachparameterandesti-matesofthestandarddeviationofeachimagemeasurement.Thisallowsusefulapproximateso-lutionstobeobtainedforproblemsthatwouldotherwisebeunderdeterminedorill-conditioned.Inaddition,theLevenberg-Marquardtmethodisusedtoalwaysforceconvergenceofthesolu-tiontoalocalminimum.Thesetechniqueshaveallbeenimplementedandtestedaspartofasystemformodel-basedmotiontracking,andtheyhavebeenfoundtobereliableandef cient.2Previousapproaches

AttemptstosolveforviewpointandmodelparametersdatebacktotheworkofRoberts[30].Althoughhissolutionmethodswerespecializedtocertainclassesofobjects,suchasrectangularblocks,Robertsclearlyunderstoodthevalueofquantitativeparameterdeterminationformakingvisionrobustagainstmissingandnoisydata.Unfortunately,therewerefewattemptstobuilduponthisworkformanyyearsfollowingitsinitialpublication.

In1980,theauthor[19]presentedageneraltechniqueforsolvingforviewpointandmodel

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