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

Figure4:Animagefromamotionsequenceofapersonusingahanddrill.

oftheprojectedsegmentswerechosenformatching.ThemodelparameterswerechangedtoproducethestartingparameterestimatesshowninFigure3(b).Inthis gure,theperpendicularerrorsbeingminimizedaredisplayedasgraybarsbetweentheprojectedmodelsegmentsandthematchingimagesegments.Figures3(c)and3(d)showtheoutputfollowingthe rsttwoiter-ationsofthestabilizedalgorithmpresentedabove.Thisfastrateofconvergencewithinacoupleofiterationsistypicaloverawiderangeofinitialparametervalues(uptoatleast60degreeer-rorsinrotationparameters).SeeWorrall,Baker&Sullivan[34]forasystematicexplorationofconvergenceoverawiderangeoferrors,evenpriortotheadditionofthestabilizationandLevenberg-Marquardtmethods.Infact,divergenceisrelativelyrare,soitisuncommonfortheLevenberg-Marquardtmethodtotakeeffect;however,itscomputationalcostisalsolow,soitisprobablyofpracticalvalue.

6.1Applicationtomotiontracking

Oneinitialapplicationofthesemethodshasbeentotheproblemofmodel-basedmotiontrack-ing.ADatacubeimageprocessorwasusedtoimplementMarr-Hildreth[25]edgedetectioninrealtimeon512by485pixelimages.Theimagecontainingtheseedgepointsistransferredto

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