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

Figure7:Aftertheseconditerationofconvergence,themodelisshownsuperimposedontheoriginalimage.

onlyasmallsubsetofthepredictedimageedges.However,duetotheoverconstrainednatureoftheproblem,inwhichfarmoremeasurementsareavailablethanunknownparameters,the nalresultcanbereliableandaccurate.

7Conclusionsandfuturedirections

Thispaperhaspresentedgeneralmethodsfor ttingmodelswitharbitrarycurvedsurfacesandanynumberofinternalparameterstomatchedimagefeatures.Considerableattentionhasbeengiventoissuesofrobustnessandef ciency,andthesetechniquesshouldserveasapracticalbasisformodel ttinginmostapplicationsofmodel-basedvision.

Thereareanumberofdirectionsinwhichthesemethodscouldbefurtherimproved.Oneisindealingwithobjectsthathaveverylargenumbersofvariableparameters.Sincethecomplex-

inthenumberofvariables,itwouldlikelybemoreityofsolvingalinearsystemrisesas

ef cienttopartitionproblemswithverylargenumbersofparametersintosmallersubsets.Thesimultaneoussolutionmethodwouldbeusedforallparameterswithlargerangesofuncertainty,buttheremainingoneswouldbesolvedforonthebasisoflocalindependentoptimization.Thiswouldbecomeparticularlyimportantifgenericclassesofobjectsaremodeled,aswasdonein

19