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![Page 1: Images for del Mo Deformation esian y Ba A - Departmentsbcaffo/statimaging/files/sining.pdf · Statistics in Imaging W orkshop July 8, 2004 A Ba y esian Deformation Mo del for Images](https://reader034.fdocuments.in/reader034/viewer/2022051718/5a71130e7f8b9a93538c9f42/html5/thumbnails/1.jpg)
StatisticsinImagingWorkshop
July8,2004
ABayesianDeformationModel
forImages
SiningChen
PostdoctoralFellow
BiostatisticsDivision,Dept.ofOncology,SchoolofMedicine
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Outline
1.Introducingtheproblem
2.Modeldescription
3.Applicationtomousebrainsegmentation
4.Inter-subjectregistrationofhumanbrains
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ProblemstoSolve
•Identifyingabnormaltissuefromaseriesofgatedcardiac
images
•Markingaregionofinterestinalargenumberofhumanbrain
MRIs
•Repeatingthesameoperationonsimilarimages
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ImageRegistration
Tobringtwosimilarimagesintospatialalignment,suchthat
“correspondingpointsoftheimagedsceneappearinthesame
positionontheregisteredimages”.
Alsoreferredtoas”spatialnormalization”incertaincontexts.
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RegistrationMethods
•Curvedtransformationsusingbasisfunctions(Ashburnerand
Friston1999HumanBrainMapping),implementedinthe
softwarepackageSPM.
•Modelsderivedfromthephysicsofelasticobjects(Bajcsyand
Kovacic1989Comp.Vision,Graphics&ImageProcessing)
•Spatialmodelingindeformabletemplates...
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Facets–generalizedlandmarks
Deformationmodelmechanism:placelargenumberoffacetsinthe
volumeoftemplateimage.Thenlocateeachinthetargetimage.
templatetarget
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ModelHeuristic
Abalancebetween
•“preservingspatialrelationships”–expressedintheprior
•“matchingimagefeatures”–expressedinthelikelihood
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Notation
TemplateTarget
facetlocationµx
facetfeatureφf
Thefeatureofafacetisafunctionoftheimageevaluatedatthat
location:canbeintensity(brightness),gradience(edgeness),
laplacian(medialness),etc.
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(a)(b)
(c)(d)
(e)(f)
Figure1:a)Originalimage;b)localrankofintensity;
c)d)directionalderivatives;e)gradientmagnitude;f)
Laplacian
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Prior–presevingspatialrelationship
Markovrandomfieldpriorspecifiedonafirst-degreeneighborhood
system.
Thespatialrelationshipamongianditsneighbors∂iinthetarget
imageremainssimilarbeforeandafterdeformation.
ij
PSfragreplacements
γij
µ1
µ2
µ3
µ4
µ5
x1
x2
µ3|x∂3
x4
x5
PSfragreplacements
γij
µ1
µ2µ3µ4
µ5
x1
x2µ3|x∂3
x4
x5
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Prior–continued
p(x)=1
Z(γ)exp{−
1
2
∑
〈i,j〉
γij((xi−µi)−(xj−µj))a}
Fullconditional(leta=2):
p(xi|.)∝exp{−1
2
∑
j∈∂i
γij((xi−µi)−(xj−µj))2}
∝exp{−1
2(∑
j∈∂i
γij)(xi−µi−
∑
j∈∂iγij(xj−µj)∑
j∈∂iγij
)2}
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Likelihood–matchingfeatures
Foreachfaceti,featureafterdeformationfishouldbesimilarto
templatefeatureφi
p(xi|T,φi)=1
Ci(T,φi)exp{sim(fi,φi)}
where
fi=QT(xi)
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MeasureofFeatureSimilarity
sim(fi,φi)=b(ri·ρi)α·cos(ui−νi),α>0
ri,ρi:quantilesofgradientmagnitude,
ui,νi:directionsofgradients.
PSfragreplacements(u,r)
(u,r)
(ν,ρ)(ν,ρ)
θ
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MeasureofFeatureSimilarity–continued
Advantages:
•robustunderweakassumptionsonintensity
•abilitytodistinguishbetween“meaningful”and“meaningless”
features
•accomodates“no-match”situations
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PosteriorInference
MAP(maximumaposteriori)estimatecanbeobtainedbyICM
(iterativeconditionalmodes,Besag1986).
Toobtainestimatethatisclosertoglobalmaximum,webuilda
hierarchyoffacetsinscale-space.
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FacetTreeinScale-Space
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AugmentedFull-Conditional
Spatialpartonly
p(xi|xs,s∈∂i,xp)∝exp{−γp((xi−µi)−(xp−µp))2
+∑
s∈∂i
γis((xi−µi)−(xs−µs))2}
Faceti,
facettargetlocationxi,
facettemplatelocationµi,
i’ssiblingss∈∂i,
i’sparentp,
pre-selectedparametersγpandγis
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AutomatedSegmentationofMouseBrainImages
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ManualSegmentationofMouseHippocampus
Goal:toinvestigatetherelationshipofAlzheimer’sdiseaseto
changesinthevolumeofthehippocampus.
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AutomaticsegmentationofanothermouseMRI
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TemplateImage
5010
015
020
025
0
50 100
150
200
250
Figure2:Threeregionsofinterestaremarkedonthetemplateimage
withrectangles.
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12
01
40
16
01
80
12
0
13
0
14
0
15
0
16
0
17
0
18
0
12
01
40
16
01
80
12
0
13
0
14
0
15
0
16
0
17
0
18
0
80
100
120
140
60
70
80
90
100
110
80
100
120
140
60
70
80
90
100
110
160
180
200
30
40
50
60
70
80
150
160
170
180
190
200
30
40
50
60
70
80
Figure3:Facetsbeforeandafterdeformation.
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QuantitativeAssessmentofAuto-segmentation
PSfragreplacementsmi
ticiI
tI
logm(k)i=logti+ε
(k)i,ε∼N(0,∆
2)
logc(k)iI=logtI+(logm
(k)i−logti)+e
(k)iI,e∼N(0,δ
2)
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00.010.020.030.040.050.060.070
2000
4000
6000
8000
10000
12000
00.010.020.030.040.050.060.070
2000
4000
6000
8000
10000
12000
Figure4:a)∆2,b)δ
2
Inourdataset,theinconsistencyofauto-segmentationis
approximatelythesameashumansegmentation.
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Inter-subjectRegistrationofHumanBrainMRIs
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Areallbrainsalike?
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Issuesinevaluatinginter-subjectregistration
Problematicduetolackofinformationongroundtruth.
Whatwasdone:
•Qualitativeassessment:visualinspection,mosaic,facet
movement;
•Quantitativeevaluation:segmentationbased,cross-correlation;
•DoneincomparisontotheindustrialstandardSPM.
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Mosaic
beforeregistrationafterfacetreg.afterSPMreg.
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Facetmovement
Figure5:Locatingfacetsonsubject3
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HumanbrainMRIsegmentation
originalMRIwhitemattergraymatter(a)(b)(b)
(a)(b)(c)
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Overlap,misclassification
Figure6:Comparisonofgraymattersegmentationof“warpedtem-
plate”andmanuallysegmentedtarget
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Segmentationbasedevaluation
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misclassify(%)facetSPM
subject117.420.7
subject224.424.4
subject316.515.8
Table1:Percentmisclassifiedforwhitematter
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overlap(%)facetSPM
subject187.881.0
subject279.070.1
subject379.773.0
Table2:Percentageoverlapforwhitematter
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misclassify(%)facetSPM
subject116.223.3
subject237.054.0
subject326.947.3
Table3:Percentmisclassifiedforgraymatter
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overlap(%)facetSPM
subject272.767.8
subject565.960.2
subject666.262.7
Table4:Percentageoverlapforgraymatter
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NormalizedCross-covarianceMap
C(f,g)=n·
∑
Afij·gij−∑
Afij·∑
Agij
n√
(∑
Af2+n−2n
2(∑
Af)2)(∑
Ag2+n−2n
2(∑
Ag)2)
(1)
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facetSPM
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Conclusion
•UsedMarkovrandomfieldtomodelpriorbeliefoffacet
locations;
•proposedanew,robustmeasureofsimilarity;
•successfullyperformedauto-segmentationofmousebrain
hippocampigivenasegmentedtemplate;
•registeredbrainMRIofdifferentindividuals;
•quantitativeevaluatedperformanceofregistration;
•themodelperformsmarginallybetterthanSPM.
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Thankyou!