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

Camera-centered

stretching subpart

Figure1:Modelpoints(incircles)arerepresentedasleavesinatreeofrotationortranslationtransformations.Thepositionandpartialderivativesofeachpointincamera-centeredcoordi-natesisdeterminedbythetransformationsalongthepathbacktotheroot.

The eldthathasmostthoroughlyexaminedtheproblemofrepresentingthevisualappear-anceofarbitraryobjectsiscomputergraphics.Thelessonsfromdevelopmentsinthat eldarequiteclear:complexanalyticrepresentationshavegivenwaytosimplelocalapproximationsasthemostcost-effectivesolution.Themostcommonformsoflocalapproximationnowusedformodelrepresentationpriortorenderingarepolygonalsurfacepatches,withtheappropriateinterpolationinthevariousparametersofinterestfordisplay.Sinceanarbitraryfunctioncanbeapproximatedtoanydesireddegreeofaccuracybyusingenoughsimplelocalapproximations,theonlyimportantissueatthislevelofrepresentationisoneofef ciency.Experienceincom-putergraphicshastendedtoshowthattheincreasednumberofapproximatingpatchesrequiredforsimplelinearapproximationsismorethancompensatedforbythespeedwithwhichtheycanbemanipulated.Ofcourse,morecomplexsplinesandvolumetricprimitivesmaystillbeusedformodelinputorotherhigher-levelreasoning.

Aswithcomputergraphics,visionisbasedupontheartofapproximation.Ofcourse,itisimportanttoapproximatetheappropriatemeasurements,asotherwiseanapproximationinonequantitymayintroduceunwantederrorsinitsderivativesorotherfunctionsthatdependuponit.Inmodel-basedvision,weareconcernedwithcorrectlyapproximatingthosefunctionsthatwillbematchedwithimagemeasurements.Inthecaseofedge-basedmatching,thiswill

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