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1、Chapter13.Non-RigidRegistration:Concepts,AlgorithmsandApplicationsDanielRueckertVisualInformationProcessingDepartmentofComputing,ImperialCollege180Queen'sGate,LondonSW72BZ,UK1IntroductionThepreviouschaptersinthisbookhavefocusedonrigidtransformationsforimage-to-image
2、andimage-to-physical-spaceregistration.Inmanyapplicationsarigidtransformationissuf?cienttodescribethespatialrelationshipbetweentwoimages.Forexample,brainimagesofthesamesubjectcanberelatedbyarigidtransformationsincethemotionofthebrainislargelyconstrainedbytheskull.Ho
3、wever,therearemanyotherapplicationswherenon-rigidtransformationsarerequiredtodescribethespatialrelationshipbetweenimagesadequately.Forexample,inintra-subjectregistrationnon-rigidtransformationsarerequiredtoac-commodateanytissuedeformationduetointerventionsorchangeso
4、vertime.Similarly,ininter-subjectregistrationnon-rigidtransformationsareoftenrequiredtoaccommodatethesubstantialanatomicalvari-abilityacrossindividuals.Incontrasttorigidregistrationtechniques,non-rigidregistrationtechniquesarestillthesubjectofsignif-icanton-goingres
5、earchactivity.Thegoalofthischapteristogiveanoverviewofthedifferentnon-rigidregistrationtechniquesandthecurrentstate-of-the-artinthisfastmovingarea.Arecentoverviewofhier-archicalapproachestonon-rigidregistrationcanbefoundin[1].2TechniquesAnynon-rigidregistrationtechn
6、iquecanbedescribedbythreecomponents:Atransformationwhichre-latesthetargetandsourceimages(imagesAandBasde?nedinchapter3),asimilaritymeasurewhichmeasuresthesimilaritybetweentargetandsourceimage,andanoptimisationwhichdeterminestheoptimaltransformationparametersasafunct
7、ionofthesimilaritymeasure.Themaindifferencebetweenrigidandnon-rigidregistrationtechniquesisthenatureofthetransformation.Thegoalofrigidregistrationisto?nd000thesixdegreesoffreedom(3rotationsand3translations)ofatransformationT:(x;y;z)7!(x;y;z)whichmapsanypointinthesou
8、rceimageintothecorrespondingpointinthetargetimage.Anextensionofthismodelistheaf?netransformationmodelwhichhastwelvedegreesoffreedomandallo
