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1、April1,200511:23WSPC/157-IJCIA00141InternationalJournalofComputationalIntelligenceandApplicationsVol.4,No.4(2004)401416cImperialCollegePressROTATIONALMATCHINGPROBLEMSGREGORYS.CHIRIKJIANDepartmentofMechanicalEngineering,JohnsHopkinsUniversityBaltimore,Maryland21218,USAgregc@jhu.edu.PETERT.KIMDep
2、artmentofMathematicsandStatistics,UniversityofGuelphGuelph,OntarioN1G2W1,Canadapkim@uoguelph.ca.JA-YONGKOODepartmentofStatistics,KoreaUniversitySeoul136-701,Koreajykoo@korea.ac.krCHRISTINEH.LEEDepartmentofPathologyandMolecularMedicine,McMasterUniversityHamilton,50CharltonAveEast,OntarioL8N4A6,Ca
3、nadaclee@mcmaster.caReceived8May2004Accepted13August2004ThispaperaddressestheissueofobtainingtheoptimalrotationtomatchtwofunctionsonthespherebyminimizingthesquarederrornormandtheKullbackLeiblerinfor-mationcriteria.Inaddition,theaccuracyintermsoftheband-limitedapproximationsinbothcasesarealsodisc
4、ussed.Algorithmsforfastandaccuraterotationalmatchingplayasignificantroleinmanyfieldsrangingfromcomputationalbiologytospacecraftattitudeestimation.Inelectronmicroscopy,peaksintheso-calledrotationfunctiondeterminecorrelationsinorientationbetweendensitymapsofmacromolecularstruc-tureswhenthecorrespond
5、encebetweenthecoordinatesofthestructuresisnotknown.InX-raycrystallography,therotationalmatchingofPattersonfunctionsinFourierspaceisanimportantstepinthedeterminationofproteinstructures.Inspacecraftattitudeestimation,astartrackercomparesobservedpatternsofstarswithrotatedversionsofatemplatethatisst
6、oredinitsmemory.Manyalgorithmsforcomputingandsamplingtherotationfunctionhavebeenproposedovertheyears.ThesemethodsusuallyexpandtherotationfunctioninabandlimitedFourierseriesontherotationgroup.Insomecontextsthehighestpeakofthisfunctionisinterpretedastheoptimalrotationofonestructureintotheother,and
7、inothercontextsmultiplepeaksdescribesymmetriesinthefunctionsbeingcompared.Priorworksonrotationalmatchingseektomaximizethecorrelationbetweentwofunctionsonthesphere.WealsoconsidertheuseoftheKullbackLeiblerinformationcriteria.A
