Correspondence Transfer for the Registration of Multimodal Images(9)

Gene expression data provide information on the location where certain genes are active; in order for this to be useful, such a location must be registered to an anatomical atlas. Because gene expression maps are considerably different from each other – t

tothe rstvariation.Inthecombinedmodel,wehavef(x,w(x))= δΦMIδΦgeom

δw δw

=

=1|A|G LI1,I2

σ w

I(I1(w(x)),I2(x)) I1(w(x))·1·P(x∈B2) α (φ1(w(x)) φ2(x)) φ1(w(x))·

·(1 P(x∈B2)).(16)Thedeformationu(x)=x w(x)issuccessivelyaccu-mulatedthrough

u

t

=v (v· )u.(17)

Thisextensionisratherstraightforward,theonlysigni cantchangebeingtheexpressionoftheweightP(x∈B2).Sincemutualinformationbetweentwoim-agesisrelatedtopixellocationsthroughintensitydistri-butions,weneedtonotonlyconsidertheintensitygra-dients,butalsothespatialgradientsofintensitydistribu-tions.Adirectextensionoftheargumentfor(5)leadstomultiplyingthetargetintensitygradientsbythespatialgradientofaParzenwindow-basedjointdensityestima-torfromthesamplehistogramsofthetwoimages,i.e.,P(x ∈B2)=| normI· 2(x)|·

LI1,I2 Gσ w I(I1(w(x)),I2(x)) .(18)

2

norm

4.Experiments

Inthissectionwereportasubsetoftheexperimentswehaveconductedtovalidatethemodelproposed.AsdiscussedinSect.2.1,ground-truthcannotbeestab-lishedforcorrespondencetransfersincethereisnocor-respondenceforunilateralregions,sovalidationisper-formedsubjectivelybydomainexperts,andultimateperformancewillhingeonhowourapproachisinte-gratedwithshapepriorsandotherhigh-levelinforma-tion.

Fig.2showstheresultsofapplyingourapproachtothesimplesyntheticphantomsshowninFig.1.Itispatentthatourapproachhasthedesirablepropertyofnotmakingtheunilateralregionsdisappear,andatthesametimeofproperlydeformingbilateralregions.

InFig.3weillustrateourapproachonrealdata.Inordertodoso,wemustuseamoreelaboratediscrep-ancymeasure,asdiscussedinSect.3.Inthetoprowweshowtheresultsobtainedusingonlyanintensitytermwherediscrepancyismeasuredusingmutualinforma-tion.Asitcanbeseen,thedeformationgridis

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