Medical Image Registrationlsiit-miv.u-strasbg.fr/ecoleTIM/download/Cours_Recalage... · 2008-06-02 · Medical Image Registration: ... into the medical decision process To guide the

May 08

Christian BARILLOT, Visages Team, IRISA, Rennes, France 1

Medical Image Registration:Data Fusion in 3D Medical Imaging

Medical Image Registration:Data Fusion in 3D Medical Imaging

Christian BarillotCNRS Director of Research

VisAGeS U746 Unit/Project, INRIA/INSERMIRISA, UMR CNRS 6074Campus de Beaulieu35042 Rennes Cedex, [email protected]://www.irisa.fr/visages

C. Barillot, Visages U746, IRISA, Rennes C. Barillot, Visages U746, IRISA, Rennes

Plan

General ContextIllustration of Data Fusion IssuesPrincipal of Data Fusion in 3D Medical ImagingImage Registration

Basic ConceptsA Focus on Deformable Registration

Local, Global and Hybrid methods

Cooperation between segmentation and registration tasksPerspectives

Deformable registrationSharing heterogeneous and distributed resources

May 08



General Context and Challenges

Context :Expansion of the quantity of data produced and processed in medical imaging (« from the volume to the mass »)

Explosion of the IST and the electronic communication resources

Challenges :To guide the clinician (e.g. a neurologist) within the mass of information to integrate into the medical decision process

To guide the surgeon for the exploitation of the different sensors and effectors (e.g. robots) to use in the interventional theater

70's 80's 90's 2000's 2010's

Molecular Molecular BiologyBiology //

fMRIfMRI3D PET 3D PET SPECTSPECT

3D CT3D CT

DTDT--MRIMRI

3D MRI3D MRI2D CT2D CT0,5 MB

1 GB

►► MS lesionsMS lesions12000 images*/patient/year12000 images*/patient/year

►► Epilepsy surgeryEpilepsy surgery7000 images*/intervention7000 images*/intervention

*: 1 image = 1 2D MRI slice


Coming issuesTo conceive the surgical room of the future

Intra-operative multimodal sensors & effectors (e.g. robots) at macro, micro and nano scalesTo manage the sources of information from observation & knowledge

To better understand the healthy and pathological states of organs at different scales (human physiome)

Imagery of pathologies : from the gross organ to the moleculeModeling healthy and pathological group of individuals from selected image descriptors (computational anatomy and function)

To connect people and medical resources thru high band networks and pooling of information sources for:

Discovering unlikely eventsData mining and knowledge discoveryValidation and certification of new drugs

May 08



Research issuesNeed to interconnect medical information resources (data, programs, medical devices) together:

Data fusion of medical imagesData fusion of medical imagesMerge semantic and computational Grid technologiesDevelopment of new adaptive medical devices (effectors, sensors, …)

Illustration of Data Fusion Issues

May 08



Epilepsy Surgery

Patient selectionSemiology of crisis and relations to anatomy« Static » Exams (search of lesions)« Dynamic » Exams (search of epileptogenicstatus):

Interictal : functional imaging, Electrodes ImplantIctal : Crisis Recordings and labeling

Presurgical PlanningCortectomy (surgery)


Integration of metabolic and functional imaging for presurgical mapping

Temporal Resolution

FDG-PET

Spa

tial R

esol

utio

n (m

m)

8

6

4

2

10

Anatomic MRI

1 ms 1 second 40 seconds static

fMRI

inter-ictalMetabolism of glucose

intra-cerebral Electrodes

Reference

EEG MEG

Inter-ictal Spikes in Epilepsy

SPECT

Cerebral Perfusion

Inter-ictal Ictal

May 08



Magnetic Resonance Imaging (MRI)

Proton Density - NMR

256 x 256 pixels (1mm resolution)

From 20 to 120 slices along three axis


(Sou

rce:

[A. B

irabe

net

al.,

CH

U R

enne

s])

« Static » Exams

May 08



Single Photon Emission Computed Tomography (SPECT)

Distribution of a radio tracer

Typical 64 x 64 à 128 x 128 pixels (resolution 3 to 5mm)

64 to 128 slices per volume


«Dynamic» Metabolic Exams Extended temporal hypo metabolism

(Sou

rce:

[A. B

irabe

net

al.,

CH

U R

enne

s])

May 08



Fusion of “Static” and «Dynamic»Exams

MRI +MRI +interictalinterictal SPECT (HMPAO)SPECT (HMPAO) BrainBrain MRI + MRI + ictalictal SPECTSPECT


Intra cerebral electrodes implant in stereotactic conditions

Registration of 3D referential

3D - 2D Projections

MRI

Angiography

stereotactic referential

May 08



Intra cerebral electrodes recordings


Dynamic Exams and Pre-operative Planning:Functional recording of epileptic region environment

MEG MEG RecordingdRecordingd

ME

G S

igna

ls

May 08



Functional Imaging : MagnetoEncephaloGraphy (MEG)

Measure of the magnetic field issued by the neuronal activity :

Brain : 10-13 TeslaHearth : 10-3 TeslaMRI : 1 to 3++ Tesla

40 to 150+ sensors (SQUID)spontaneous and evoked potentials, e.g.:

motorsomesthesiclanguagevisual


MEG :

Spatio-

temporal

analysis of

interictal

spikes

SpatioSpatio--temporaltemporalMEG MEG analysisanalysis

of of interictalinterictalspikesspikes

ProbabilitProbabilitééss

[Source : D.P. Schwartz, et al., Neuroimage:Functional Mapping of the Human Brain, 7(4):S466, 1998]

May 08



MEG : Spatiotemporal Interictal Analysis Localization

0 ms

100 ms

Left Hemisphere


Epilepsy Surgery :Preoperative Planning

May 08



Talairach Atlas


Functional Mapping of language areas

SilentSilent vsvs Active Word ActivationActive Word Activation

May 08




Preoperative Planning : functional MRI (fMRI)

Acquisition Paradigm

time

intensity

pixel

Detection

mean of activation A-

Mean of rest state R

time

RA

RA

May 08



Epilepsy Surgery:Superposition of graphical data


Image Guided Surgery

May 08



Image-Guided Neurosurgery:Interventional procedure (Neuronavigation)

3D referential system

Patient

3D localizer

Surgical Microscope3D workstation


Surgical resection

Electrodes landmarksElectrodes landmarks ResectionResection

May 08



Evolution in Computer assisted surgery

Integration of new models and observations

Integration of new preoperative images (e.g. DT-MRI)

Fusion between multimodal pre-operative images with intra-operative images to adapt the planning “in real time” for taking into account intra-operative deformations (e.g. brain shift)

IntraIntra--operative Imageryoperative ImageryFusion of observationsFusion of observations

Preoperative ImageryPreoperative Imagery

2.5D Image 3D US ImageryCourtesy I. Corouge, UNC


a priori Knowledge a posteriori Knowledge

Multimodal Multimodal RegistrationRegistration

Segmentation Segmentation Segmented Segmented DataData

ModelingModeling ModeledModeledDataData

Deformable Deformable RegistrationRegistration

InformationInformationModelModel

Cooperative Scheme for Data Fusion

Original Original

Data Data

Registered Registered DataData

May 08



SubjectSubjectData BaseData Base

Anatomical and Functional Imagery Anatomical and Functional Imagery MRI

SPECT MEG

EEG/SEEG2D/3D Angiography

CT

PET

Multimodal RegistrationMultimodal Registration

Anatomical LandmarksInstrumental Referential

Fiducial Markers

Segmentation and LabelingSegmentation and Labeling

ContoursRegions

Deformable Models

Linear Linear TransformationsTransformations Anatomical LabelsAnatomical Labels

3D Visualization/Interaction3D Visualization/Interaction

• Multi-Objects/Volumes Visual.•Graphic/Voxels Visual.•Interactive Labeling

Intra-Individual Data Fusion

fMRI


Deformation ModelDeformation Model

AffineAffine HigherHigher OrderOrder

Inte

r-In

divi

dual

Fus

ion

3D3DNumerical Numerical

ModelModel

SubjectSubject nnData BaseData Base

SubjectSubject iiData BaseData Base

May 08



Data Fusion in medical imaging

What is Data Fusion?Joint Use of Heterogeneous Data

Why?Co-exploitation of multimodal dataRegistration / Matching

Which Context ?Computer assisted image interpretation systems

Image Registration

Basic concepts

May 08



ps1

ps3

ps2

The notion of registration is to: Find a matching between points in one space (an image)and points in another space (also called a referential).

Image Registration : Basic Concepts

Problem: Find a Transformation ΦSuch as Is

Φ Id

Φ = f(R, T, δ(p)): Φ(ps) – pd ≈ 0

DestinationImage Id

SourceImage Is

pd1

pd3

pd2

pd1

pd3

pd2p1

p3

p2p1

p3

p2

pd1

pd3

pd2p1

p3

p2p1

p3

p2p1

p3

p2

≠= ε → Optimization


Image ReferentialImage Referential Instrumental Instrumental ReferentialReferential

Subject ReferentialSubject Referential

p(i,j,k)

p(x,y,z)

p(u,v,w)

Basic Referential

May 08



Class of registration domains

ONE patientONE patient SEVERALSEVERAL patientpatientss

ON

E m

odal

ityO

NE

mod

ality

SEV

ERA

L SE

VER

AL

mod

aliti

esm

odal

ities

Intra-modality registration :Post-operative controlPathology tracking, Treatment probing

Intra-modality registrationModel-based segmentationRegistration/matching with an anatomical atlasSpatial normalization, study of anatomical variability

Inter-modalities registrationComplementarities between sources of imagesComputer assisted therapeutic planningComputer assisted surgeryAnatomy-function correlation

Inter-modalities registrationHuman brain mappingAnatomo-functional normalization


Medical Image Registration :Medical Image Registration :

By generalization, this transformation can be applied to the underlying images Is and It : (It(x1, y1, z1) = Φ[Is(x2, y2, z2)])

For a given optimization method Ψ, the transformation Φθ∈Θ is computed by the optimization of :

where Δ is the similarity measure and (θ∈Θ) the transformation parameters

( )( )tsargmin Ω−ΩΦΔ

ΨΘ∈)(θ

θ

DefinitionDefinition: Let Is and It be two images (source and target) to match, Ωs and Ωt, two homologous structures extracted from these images. The registration procedure consists in finding the transformation Φ : Ωs→ Ωt which registers a landmark ωin Ωs to its correspondent Φ(ω) in Ωt.

Basic ConceptsBasic Concepts

May 08



Registration : The 4 basic stages

Definition of homologous structures (Ω)

Definition of the type of transformation (Φ)

Definition of the cost function (Δ)

Definition of the cost function optimization

algorithm (Ψ)


Types of Homologous Structures (Ω)

Size of the manifold (Dh)0D : point (Ω=Constant)1D : contour (Ω=f(u))2D : surface (Ω=f(u,v))3D : volume (Ω=f(u,v,w))nD : hypersurface (Ω=f(u1,…,un))

Size of the evolution (Euclidian) space (Dw)2D : surface, projection (Ω∈R2)3D : discrete or continuous space (Ω∈R3)nD, nD+t : hypersurface, spatio-temporal (2D+t); (Ω∈Rn)

May 08



Nature of Homologous Structures (Ω)

External Referential :Fiducial markersSurgical frames (e.g. stereotactic)

Anatomical Referential :Anatomical landmarks (reference structures)Image (iconic) features (gray levels, gradients, curvatures, ...)Segmented shape


Which Transformation (Φ) ?

Linear Transforms :

Rigid Transformation (rotation + translation)Affine Transformation (rigid + scale)Projective Transformation (Ωs∈Rn → Ωd∈Rn-i, i>0)

Non-linear Transformation (dense):δ: pd=ps+ δ(ps)

[ ]

11 1 12 13

21 22 2 23

31 32 33 3

0 0 0

x

y

z

r s r r tr r s r tr r r s t

w

⎡ ⎤⎡ ⎤ ⎡ ⎤⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦

May 08



Similarity Function (Δ)

Three big classes of measures:Methods based on the definition of an intrinsic geometry (frame, external landmarks, reference planes, …).Methods based on Euclidian criteria (distances, surfaces, volumes).Methods based on image intensities or their derivatives (correlation in the spatial or frequency domain, entropy, optical flow, …)

Definition: The similarity function defines the objective criteria (cost) used to estimate the quality of the registration between two homologous structures (Ω).


Image registration:Measure from joint histogram

Joint Histogram (HIST[x,y])

Registered Images

(1/2*[X+Φ(X)])

Φ=Ι Φ=Tx

Inte

nsiti

es o

f the

floa

ting

Imag

e Y

=Φ(X

)

Intensities of the reference image X

May 08



Image registration: Relation between the transformation and the joint histogram


Joint Histogram:Linear or Affine Dependencies

( )2

,

,

( , )

( , )x X y Y

x X y Y

SSD X Y x y

SAD X Y x y∈ ∈

∈ ∈

= −

= −

∑

∑

Inte

nsiti

es o

f th

e flo

atin

g Im

age

Y=

Φ(X

)

Optimum SSD/SADy=x

Optimum Corr(x,y)y=αx+β


( , )( , )var( ).var( )Cov X YCorr X Y

X Y=

May 08



Joint Histogram:Examples of Linear or Affine Dependencies


Registered Images

(1/2*[X+Φ(X)])

Φ=Ι Φ=TxIn

tens

ities

of t

he fl

oatin

g Im

age

Y=Φ

(X)



Joint Histogram:Functional Dependencies (e.g. Correlation Ratio)

Intensités de l’image référence

X

YX

Optimum η(Y|X) Y=f(X)

MRIMRI--T2T2 MRIMRI--PDPD


Inte

nsiti

es o

f the

flo

atin

g Im

age

Y=Φ

(X)


( ) ( )[ ])var(

var1

YXYEY

XY−

−=η

May 08



Joint Histogram:Statistical Dependencies (e.g. Mutual Information)

Intensités de l’image référence

X

OptimumMI(X,Y)

X Y

CTCT MRIMRI


Inte

nsiti

es o

f the

flo

atin

g Im

age

Y=Φ

(X)


MI(X,Y) = H(X) + H(Y) - H(X,Y)

NMI(X,Y) = (H(X) + H(Y)) / H(X,Y)


Joint Histogram:Statistical Dependencies (e.g. Mutual Information)

OptimumMI(X,Y)

YX

PETPET MRIMRI

Φ=Ι

Φ=Tx=3mm Φ=Tx=5mm


Inte

nsiti

es o

f the

floa

ting

Imag

e Y

=Φ(X

)


May 08



Optimization Issues (Ψ)

DefinitionDefinition: The optimization method defines how the cost function (Δ) will be minimized (or maximized) with respect to the set of transformation parameters θ∈Θ.

IdeaIdea: the goal is to find the minimal value (i.e. D rather than F) of Δ(θ) from any initialization point (e.g. G)

A

B

C

D

EF

G

Δ

θ

Z

YX

Cos

t Fun

ctio

n Δ

(θ)

Transformation parameters (θ∈Θ)


Optimization Methods (Ψ)

Non Global optimization methods:Quadratic or semi-quadratic approachesMay need the estimation of partial derivatives of Δ(θ).

Assume a quasi-convex energy around the desired solution

Need a hierarchical resolution scheme (multiscale, multi-resolution)

Examples: Least square, ICP, Gradient Descent, Newton-Raphson, Levenberg-Marquardt, Simplex, Powell...

May 08



Optimization Methods (Ψ) (2)

Global optimization methods:More robust approaches (proof of convergence at an infinite state)

Computational cost

Non applicable to high dimensional problems (e.g. iconic registration)

Examples:Dynamic Programming, Simulated Annealing, Genetic Algorithms, Clustering Methods, Branch and Bound, Evolutionary Algorithms, Statistical Methods , ...


Semi-quadratic Optimization using NEWUOA

NEW Unconstrained Optimization Algorithm [Powell 04]

1. Compute a quadratic approximation of the function to optimize by using a set of initial points (parameters), typically (n+1)(n+2)/2 for a problem of dimension n

2. Compute the maximum of the approximation within a “trust region” defined by the initial points

3. Replace the “worst” parameter of the initial set with this newly estimated value and update the trust region

4. Iterate

May 08



Illustration of NEWUOA optimization

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-10 -5 0 5 10

f(x)

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-10 -5 0 5 10

Initial Region

f(x)Function samples

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-10 -5 0 5 10

Trust Region


fit

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-10 -5 0 5 10

Trust Region


fitnext interpolation point

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-10 -5 0 5 10

Trust Region


fit

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-10 -5 0 5 10

Trust Region


fitnext interpolation point

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-10 -5 0 5 10

Trust Region


final fit


Validation and Error Measurement

BrainWeb dataset: T1-w, T2-w, PD-w images in perfect alignment5% additive noise50 random transformations (+/- 5 mm +/- 5 degrees)Warping Index [Thevenaz&Unser00] :

Paired t-tests

May 08



ResultsComparison Table

Mutual information


ResultsAlgorithm Accuracy

May 08



ResultsAlgorithms Run Time


Outcome from this studyMutual Information

Best Similarity Measure for any of the optimizers

NEWUOAFastest Algorithm (compared to Powell or Simplex)Best AccuracyMore Robust

May 08



Recalage Intra-Sujet

Applications:Applications:•• Approche gApproche géénnéérique basrique baséée e ««surfacesurface»»

••Recalage IRM/CT/PETRecalage IRM/CT/PET••Recalage IRM/MEGRecalage IRM/MEG••Recalage Recalage IRMaIRMa/3D/3D--DSADSA

•• Recalage Recalage IRMfIRMf


Multimodal Registration : Surface Matching

Surface Extraction

Registered VolumeRegistered Volume

MultiresolutionProcessing

Distance

Volume

Sx R11 R12 R13 0

R21 Sy R22 R23 0R31 R32 Sz R33 0TX TY TZ 1

Sx R11 R12 R13 0


Sx R11 R12 R13 0

R21 Sy R22 R23 0

R31 R32 Sz R33 0TX TY TZ 1

Sx R11 R12 R13 0


Target Target VolumeVolume

Seg

men

tatio

n

BinaryVolume

Base Base VolumeVolume

P.C.A.

P.C.A

.

Sx R11 R12 R13 0

R21 Sy R22 R23 0

R31 R32 Sz R33 0TX TY TZ 1

May 08



Exemple de recalage multimodal


May 08



Résultats de superpositions SPECT-IRM et PET-IRM


Multimodal Registration: Evaluation

Blinded evaluation of retrospective image registration techniquesNIH Multi-Groups Project (prime: J.M. Fitzpatrick, Univ.. Vanderbilt)Multimodal (CT, MR, PET), 5-7 clinical cases eachVariable resolutions

CT: 512x512x(28-34) slices; 0.65x0.65x4 mmMR: T1, T2, PD; 256x256x(20-26) slices; 1.25x1.25x4 mm

10 brain anatomical structures for reference

May 08



T2PDT1

r

Opt

ic c

hias

m

Who

le h

ead

Left

occi

pita

l hor

n

Rig

ht o

ccip

ital h

orn

0,00

1,00

2,00

3,00

4,00

5,00E

rror i

n m

m

Optic chiasm

Junction of fourth ventricle withaqueductMaximum aperture of fourthventricleWhole head

Apex of left Sylvian fissure

Apex of right Sylvian fissure

Left occipital horn

Left globe

Right globe

Right occipital horn

Junction of central sulcus withmidline(S

ourc

e: [W

est J

. et a

l., JC

AT-

21(4

), 19

97])

Registration Registration ErrorError vs.vs. RegionRegion of of InterestInterest(CT (CT ↔↔ MRI)MRI)




0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10 11

Erro

r in

mm

T1PDT2T1 rectPD rectT2 rect

Point Point SimilSimil. .

VolumetricVolumetricSimilaritiesSimilarities

SurfaceSurface--basedbasedSimilaritiesSimilarities

MeanMean Registration Registration ErrorError CTCT--MR MR (Sou

rce:

[Wes

t J. e

t al.,

JCA

T-21

(4),

1997

])

May 08



Recalage multimodalité : Évaluation

Max Registration Max Registration ErrorError CTCT--MRMR(Source: [West J. et al., JCAT-21(4), 1997])

0

5

1015

20

25

30

1 2 3 4 5 6 7 8 9 10 11

T1

PD

T2

T1 rect

PD rect

T2 rect

>

Erre

ur in

mm

SimilSimil. . PointPoint

SimilaritSimilaritéés s VolumVoluméétriquetrique SimilaritSimilaritéés Surfaciquess Surfaciques


Fin

Recalage Initial

Analyse Multirésolution

Optimisation

Echantillonnage du « Headshape »

Rejet des points aberrants

Recalage IRM-MEG

May 08



Recalage IRM-MEG

Acquisition du Acquisition du «« Head ShapeHead Shape »»

Recalage Recalage «« Head Head ShpeShpe »» vs IRMvs IRM

IRM AnatomiqueIRM Anatomique

Segm

enta

tion

Se

gmen

tati

on

de la

Têt

ede

la T

ête


Recalage MEG-IRM :Evaluation de la précision

Précision théorique sur simulations :erreur moyenne de 3mm

Validation expérimentaleComparaison avec la méthode manuelle (basée sur des amers cutanés)Utilisation CliniqueTransfert technologique

May 08



Recalage MEG-IRM : Résultats


May 08


RecalageAngiographie X 3D / IRM


3D 3D DSADSA

May 08



RecalageAngiographie X 3D / IRM

Segmentation des vaisseaux

Détection des régions sulcales (courbures Lvv)

Minimisation de la distance entre les sillons et les vaisseaux


Résultats

0 à 1mm1 à 2mm2 à 3mm3 à 5mm> 5mm

May 08



Acquisition Paradigme

temps

intensité

pixel

Détection

moyenne activation A-

moyenne repos R

Analyse de donnAnalyse de donnéées es en IRM en IRM

fonctionnelle cfonctionnelle céérréébralebrale

temps

RA

RA


coupes sagittalestemps

TâcheTâche

moyenne reposR

moyenne activationA

coupe sagittale

- =

image différence

A

R

A

RR

A

May 08



moyenne reposR

moyenne activationA

-

image différence

IRMf: Mouvement du sujet


décalage en x

-1

-0,5

0

0,5

1

1,5

1 17 33 49 65 81 97 113


1/10 pixel induit 1 à 7% de variation de signal

May 08



Exemple: Recalage monomodale par flot optique

( ) ( ) ( )[ ]22

,,,; ∑∑

∈∈

−++⋅∇=Crs

rsSs

ts tsftsffU ωωαωω

•• Formulation gFormulation géénnéérale : minimisation de la fonctionnelle de rale : minimisation de la fonctionnelle de conservation de lconservation de l’’intensitintensitéé entre paires dentre paires d’’imagesimages

•• Introduction dIntroduction d’’estimateurs robustesestimateurs robustes

•• Approche multi rApproche multi réésolutionsolution

•• Optimisation alternOptimisation alternéée e [[1)1) estimation des poids estimation des poids δ, βδ, β et et 2)2) estimation estimation des paramdes paramèètres de transformation tres de transformation ωω]]

•• Temps de calcul Temps de calcul < 1s pour des volumes 64< 1s pour des volumes 6433

( ) ( ) ( )[ ]22

,

,,; ∑∑∈∈

−++⋅∇=Crs

rsSs


( ) ( ) ( )( ) ( ) ( )srCrs

rssrsSs

tss tsftsffU βϕωωβαδϕωδβδω 2,

1

22

,,;,, +−+++⋅∇= ∑∑∈∈


Image de différencesans correction

Image de différence avec correction


Activation

May 08


Deformable Registration


Deformable Registration: Not a new topic!Deformable Registration: Not a new topic!

Classical topic in morphometry (e.g. [ D’Arcy Thomson, 1917])

Classical topic for brain imaging (e.g. [Talairach et al., 1967])

Introduction of computer based procedures in the 80’s (R. Bacjsy, C. Broit and coll.; U. Grenander and coll.; F. Bookstein, …)

(Source: J. Talairach, G. Szikla, P. Tournoux, A. Prosalentis, and M. Bornas-Ferrier, Atlas d'Anatomie Stéréotaxique du Télencéphale. Masson, Paris, 1967)

(Source: D’Arcy Thomson, On Growth and Form, Cambridge University Press, 1961)

May 08



Deformable Registration: evolution in a decade*Deformable Registration: evolution in a decade*

In IPMI (oral):[86-88] F. Bookstein (general morphometry, brain, TPS)

[91] F. Bookstein (general morphometry, brain, TPS)D. Lemoine et al. (brain, Talairach Grid System)

[93] F. Bookstein et al. (general morphometry, brain, TPS)K. Shields et al. (carotid plaques in US)

[95] G. Christensen et al. (brain, fluid model)L. Collins et al. (brain, atlas based segmentation)J. Gee et al. (brain, bayesian framework)S. Sandor et al. (brain, atlas based segmentation)

[97] P. Edwards et al. (brain, interventional imaging)T. Schiemann et al. (volume interaction)

[99] A. Caunce et al. (sulci shape model)G. Christensen et al. (brain, homomorphism)H. Chui et al. (brain cortical point)L. Collins et al. (brain, atlas based segmentation)H. Lester et al. (brain, fluid model)D. Rey et al. (brain, growth of pathologies)K. Rohr et al. (TPS)O. Skrinjar et al. (brain, interventional imaging)M. Vaillant et al. (brain cortical surface)

* data collected from IPMI (Information Processing in Medical Imaging)


Deformable registration: When?Deformable registration: When?

ONE patientONE patient SEVERALSEVERAL patientpatientss

ON

E m

odal

ityO

NE

mod

ality

SEV

ERA

L SE

VER

AL

mod

aliti

esm

odal

ities

Registration of temporal sequences :

Temporal deformation of anatomical structures (heart, chest, blood flow)Growth, Pathologiesfollow-up

Model-based segmentationBuilding of digital atlasesRegistration/matching with an anatomical atlasSpatial normalization, study of anatomical variability

Correction of fMRI acquisitionsConstraints to reconstruction /restoration algorithmsComputer Assisted Surgery

registration between pre-and intra-operative images (e.g. MRI and Ultrasound)

Human brain mapping

Anatomo-functional normalization (aid for the study of functional variability)

May 08



Deformable Registration :which transformation?Deformable Registration :which transformation?

Non-linear dense transformation:DefinitionDefinition : The transformation can be represented as a dense

deformation field: a displacement vector δ is associated to each point of the homologous structures Ωs and Ωt :

δ: pt=ps+ δ(ps)

In an energetic framework, the generalformulation becomes:

( )( )( )[ ] [ ]θθ

θδδ EpppEargmin tss ++Δ

ΨΘ∈,

In a Bayesian context: In a Bayesian context: Prior : p(δ)Prior : p(δ)Likelihood : p((ps, pt)|δ)Likelihood : p((ps, pt)|δ)


Continuity of the transformation (E[δθ])Continuity of the transformation (E[δθ])

Piecewise linear (C0 continuity) (e.g. Talairach)

Parametric (C1, C2 continuity) (e.g. Splines, Free-form

deformation, Cosines, RBF)

Physics-inspired Models (e.g. mechanical) :

Linear elasticity models (Navier equations )

Fluid models (Navier-Stokes equations )

May 08



Inversibility of the transformation

The transformation h must be an homeomorphism, that means :

The target volume V is convex (closed and bounded)h must be C1 continuousThe jacobien of h : J(h) > 0 h must be invertible and h-1 continuous

If h is C1 and J(h) > 0, then h is locally injective

In practice to enforce the homeomorphism is difficult people tend to rich the symmetry property only


Symmetry of the transformation

The transformation h is considered as a symmetric transformation between a source S and a target T, when :

h : S(x) T(x); g: T(x) S(x)h(x)°g(x)=h(g(x))=x

Methods iteratively minimize [ ]∑∈

−Vx

xxgh2

))((

May 08



Defomable Registration:Local and Global approachesDefomable Registration:Local and Global approaches

Global, or “photometric”methods (Dh= Dw)

Rely on photometric similarity measures

Provide a dense deformation field

Anatomical coherence of the transformation? _High dimensional optimization problem

Local, or “geometric”methods (Dh< Dw)

Rely on extracted features (point, curves, surfaces)

Interpolation necessary (e.g. thin-plate-spline, RBF, …)

The transformation is mostlyrelevant in the neighborhood of the homologous features

HybridHybrid: use of both homologous structures: use of both homologous structures


Image fusion in neuroimaging using Global, Local and Hybrid methodsImage fusion in neuroimaging using Global, Local and Hybrid methods

Sub

ject

s D

ata

Bas

eS

ubje

cts

Dat

a B

ase

Global RegistrationGlobal Registration

Local RegistrationLocal Registration

Segmented Segmented SulciSulci

Registered Registered SulciSulci

Statistical Statistical Model of Model of SulcusSulcus XX

Probability Probability of of SulcusSulcus XX

Probability of Probability of Activation YActivation Y

Dense Matching Dense Matching to Reference to Reference

BrainBrain

Probability of Probability of SulcusSulcus XX


Hybrid RegistrationHybrid Registration

Hybrid Matching Hybrid Matching to Reference to Reference SulcusSulcus and and

BrainBrain

Probability of Probability of SulcusSulcus XX


+

May 08



Example Example of of InterInter--Individual Individual RegistrationRegistration


Deformable Registration:Local, or “geometric” methodsDeformable Registration:Local, or “geometric” methods

DefinitionDefinition of local of local landmarkslandmarks

DefinitionDefinition of a of a deformationdeformation modelmodel

BeforeBefore registrationregistration

AfterAfter deformabledeformable registrationregistration

AveragingAveraging of 9 of 9 brainsbrains

(Source: F. L. Bookstein, Thin-plate splins and the atlas problem for biomedical images, IPMI, Wye College, UK, 1991)

May 08



(Source: J. Talairach, G. Szikla, P. Tournoux, A. Prosalentis, and M. Bornas-Ferrier, Atlas d'Anatomie Stéréotaxique du Télencéphale, Masson, Paris, 1967)

Talairach Stereotactic Proportional Grid System

Talairach Stereotactic Proportional Grid System


Probabilistic atlas based on local constraintsProbabilistic atlas based on local constraintsProbabilistic atlas based on local constraints

x X b= + Φ

Xm

xii

m=

=∑1

1C T= Φ ΛΦ Λ;

Cm

x x x x Xi iT

i

m

i i= = −=∑1

1

~ ~ ; ~

Statistical Shape AnalysisStatistical Shape Analysis

=⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

λ

λ

1 0

0

L

M O M

L m

Modal Amplitudes

Modes Matrix

SulcusMean

Shape

AnalysisAnalysis

[ ]b1 1 12 2∈ − +λ λ,

x X b= + φ1 1

SynthesisSynthesisx X bi i

i

m

≈ +=

∑ φ1

Sillon moyen

principal Mode of deformation of the right central sulcus

Rec

onst

ruct

ed

Sulc

us

InterInter--subjectssubjects registration registration of of sparse data sparse data (MEG)(MEG)

non-linear local registration non-linear global registration

u u uv v vw w wt t t

i j k

i j k

i j k

x y z

0001

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

uvw

Registration and matchingEx. 29 subjects

local referential

uvw

x0 xi xm

uvw

Modal Analysis

Cortical Sulci

Cons

traint

s on

TPS

Cons

traint

s on

TPS

rU

(r)

zy

xP

Uw

za

ya

xa

az

yx

fn i

ii

=−

++

++

=∑ =

,|))

,,

((|

),

,(

13

21

0

May 08



Extraction of the local featuresExtraction of the local features


Linear Local Registration (LR)Linear Local Registration (LR)

29 subjects

locallocal referentialreferential

uvw

x0 xi xm

uvw

u u uv v vw w wt t t

i j k

i j k

i j k

x y z

0001

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

uvw

May 08



Statistical Shape Model : Principal Component AnalysisStatistical Shape Model : Principal Component Analysis

29 subjects

x X b= + Φ

Xm

xii

m=

=∑1

1C T= Φ ΛΦ Λ;

Cm

x x x x Xi iT

i

m

i i= = −=∑1

1

~ ~ ; ~

=⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

λ

λ

1 0

0

L

M O M

L m

Modal Amplitudes

Modes Matrix

Mean ShapeAnalysisAnalysis

Mean sulcus

[ ]b1 1 12 2∈ − +λ λ,

x X b= + φ1 1

SynthesisSynthesisx X bi i

i

m

≈ +=

∑ φ1

principal Mode of deformation of the right central sulcus

Rec

onst

ruct

ed S

hape


Non-Linear Local Registration (NLL):Use of thin plate splines

Non-Linear Local Registration (NLL):Use of thin plate splines

n target target pointspoints iV

n source source pointspoints iP

f : : interpolation interpolation functionfunction

∑=

−++++=n

iii zyxPUwzayaxaazyxf

13210 |)),,((|),,(

mm bxx Φ+=

Local extension of the Local extension of the deformation fielddeformation field

( )3210 aaaaW

x

Target: mean central sulcus

xSource: left central S. of one subject (x, y, z)

f(x, y, z)

fapplicationapplication

to a dipoleto a dipole

May 08



Somatotopy around the principal mode using the non-linear local method (NLL)SomatotopySomatotopy around the principal mode around the principal mode using the nonusing the non--linear local method (NLL)linear local method (NLL)

Little fingerLittle finger

IndexIndex

ThumbThumb


Deformable Registration:Global, iconic or photometric methodsDeformable Registration:Global, iconic or photometric methods

Find a the transformation between one reference Find a the transformation between one reference (atlas) and one individual (atlas) and one individual

Source Target

Transformed Image

Model 1

Model 2

Deformation Field

May 08



Adaptive Non Rigid Registration:Using optical flow and robust estimators (RoMEO©)

Adaptive Non Rigid Registration:Using optical flow and robust estimators (RoMEO©)

General formulation (optical flow estimation):

Robust estimation of the deformation field :Reduce the sensitivity to noise and preserve the deformation discontinuities:

Adaptative multigrid algorithm:

( ) ( ) ( )[ ]22

,,,; ∑∑

∈∈

−++⋅∇=Crs

rsSs


( ) ( ) ( )( ) ( ) ( )srCrs

rssrsSs

tss tsftsffU βϕωωβαδϕωδβδω 2,

1

22

,,;,, +−+++⋅∇= ∑∑∈∈

Pyramide Pyramide multirmultiréésolutionsolution Minimisation Minimisation multigrillemultigrille

Extensible Extensible to to otherother similaritsimilarityyfunctions (functions (e.g. e.g. fMRIfMRI registrationregistration):):


Deformable Registration: Multiresolution optimizationDeformable Registration: Multiresolution optimization

MultiresolutionMultiresolutionPyramidPyramid

CPU time (CPU time (mnmn))

Inte

nsity

RMS

Inte

nsity

RMS

Grid 4Grid 4

Grid 3Grid 3Grid 2Grid 2

Grid 1Grid 1 Grid 0Grid 0

Init after resolution 1Init after resolution 1

1010 2020 3030 4040 5050 6060 7070

Registration between 2 subjectsRegistration between 2 subjects

May 08



Deformable Registration :Spatial NormalizationDeformable Registration :Spatial Normalization

Aff

ine

RoM

EO©

Targ

et

Averaging of 18 subjects

Tala

irac

h

Hybrid ApproachHybrid Approach

May 08



Hybrid approach:Cooperation between local and global approaches

Hybrid approach:Cooperation between local and global approaches

Global, or “photometric” method:Image registration based on image informationProvides a dense deformation field

Local, or “geometric” method:Rely on landmarks (points, surfaces, …)Use an interpolation function (e.g. TPS)

Cooperative approachCooperative approach, , where geometric and photometric information are combined into the same framework


Creation of a constraints field (ωc) :Use of global constraints (e.g. optical flow) :

Mean without constraints

Mean with constraints

Reference Subject

Hybrid deformable registration :Introduction of sparse constraints (JULIET©)Hybrid deformable registration :Introduction of sparse constraints (JULIET©)

Matching of homologous structures (e.g. sulci )

Taking into account possible interruptions between sulci

May 08



Deformed central sulci (from 18 sujects)Deformed central sulci (from 18 sujects)

Without constraints With constraints

Mean sulci ()


Visualization of the cortical deformation

with constraintswith constraints without constraintswithout constraints

May 08


Cooperation between Segmentation and Registration

Tasks


a priori Knowledge a posteriori Knowledge

Multimodal Multimodal RegistrationRegistration

Segmentation Segmentation Segmented Segmented DataData

ModelingModeling ModeledModeledDataData

Deformable Deformable RegistrationRegistration

InformationInformationModelModel

Cooperative scheme for Data Fusion

Original Original

Data Data

Registered Registered DataData

May 08



Expert SegmentationExpert SegmentationAtlas Based SegmentationAtlas Based Segmentation

(Source: [Collins et al, IPMI’95])

AtlasAtlas

DeformableDeformableRegistrationRegistration

DeformableDeformable Registration Registration + + LevelLevel Sets Sets (simulation) (simulation)

DeformableDeformableRegistrationRegistration

DeformableDeformable Registration Registration + + LevelLevel Sets Sets (real data) (real data)

DeformableRegistration and Segmentation

DeformableRegistration and Segmentation


Model-Guided Segmentation and Labeling:Integration of fuzzy control and level sets*

Objective : Segmentation of brain structures close, with similar intensities and hardly defined contoursMethod :

Statistical analysis of shape and localization of structuresConcurrent evolution of several level sets

Contribution :Integration of fuzzy control to constrain the competitive evolution of level setsUtilization of a statistical shape models to define the fuzzy control variables

*: C. Ciofolo, C. Barillot, IPMI 2005, ECCV 2006

May 08



Deformable Registration:Study of the Anatomical VariabilityDeformable Registration:Study of the Anatomical Variability

Probabilities of cortical labels

(max proba)

Probabilities for Sulci

Occurrence (> 10%)

(Source: MN

I, U. M

cGill, M

ontreal )


Deformable Registration:Labelling from atlasDeformable Registration:Labelling from atlas

Sulci Labeling

(Source: [LeGoulheret al., 2000])

May 08


Application of DeformableRegistration in ClinicalNeuroscience


Before After

Rigid registration of intra-operative 3D free-hand ultrasound with MRI

*: P. Coupe et al.,IEEE-ISBI 2007

Objective: Construct probability maps of hyperechogenic structures from MRI and Ultrasound images for registration.Principal: Find a function frelating the MRI intensity of a voxel X (u(X)) with its probability to be included in the set of hyperechogenic structures:

May 08



Non-rigid registration of intra-operative 3D free-hand ultrasound with MRI

Objective: Compensate for the intra-operative deformations after opening of brain envelopes

Method: Non rigid transformation using a multi-frequential approach (cosines basis defined from their pulsation )

Use the joint probability between hyperechogenic structures and liquid interfaces in MRI

[P. Coupe et al., Patent]

ResultsValidation on a synthetic deformationExperimentation on 5 patients

mean estimated deformation 2.71 +/mean estimated deformation 2.71 +/-- 1.03 mm1.03 mm

mean estimated deformationmean estimated deformation 1.81 +/1.81 +/-- 1.02 mm1.02 mm


Exemplesof MSA

Medical Image Computing in Neurological Diseases:Voxel based morphometry in Parkinsonian disorders*

ObjectiveDifferentiate between Parkinson’s Disease (PD) and MSA (Multiple Systems Atrophy) and PSP (Progressive Supranuclear Palsy) symptoms (current : 66% TP)Early diagnosis from cross-sectional MRI at a single time point at inclusion

ResultOnly 20 patient from each group90% differential diagnosis PD vsMSA/PSPError rate cut by 50%

Normal Mild Severe

*: S. Duchesne et al., SPIE 2007

May 08



Surface based morphometry in Parkinsonian disorders

[D. Tosun et al., Miccai’07]

Objective:Differentiation between Parkinson’s Disorders

Early diagnosis from cross-sectional MRI at a single time point at inclusion

MethodExtraction of GM/WM interface

Computation of cortical indexes

Results:Only 20 patient from each group

Mapping of statistical difference between groups

Cortical Cortical ThicknessThickness

BrainBrainCurvatureCurvature

SulcalSulcal DepthDepth

geodesicgeodesic sulcalsulcal depthdepth

cortical gray cortical gray mattermatter thicknessthickness

Cortical Feature Significant Mean Difference Maps

Cortical Feature Population Average Maps

RedRed//YellowYellow: IPD > MSA, IPD > PSP, MSA> PSP: IPD > MSA, IPD > PSP, MSA> PSPBlueBlue//CyanCyan: : MSA>IPD, PSP>IPD, PSP>MSAMSA>IPD, PSP>IPD, PSP>MSA

Data Fusion of Anatomical and Functional Brain Images

May 08



Deformable Registration forAnatomo-Functional ImagingDeformable Registration forAnatomo-Functional Imaging

Talairach Atlas MEG Localisations


Spatial Normalization for the Analysis of Functional DataSpatial Normalization for the Analysis of Functional Data

Linear RegistrationLinear Registration NonNon--Linear RegistrationLinear Registration

Example of comparison of average activation responsesExample of comparison of average activation responses

Illustrations courtesy from J.C. Gee, GRASP Lab., Univ. of Pennsylvania

May 08



Mapping of the somatotopy using global and hybrid deformable registration methods

MutualMutual Inf. Inf. MethodMethod (M)(M) TalairachTalairach MethodMethod (P)(P)

Romeo Romeo MethodMethod (R)(R)

SPM SPM MethodMethod (S)(S)

Juliet Juliet MethodMethod (H)(H)

Gaussian Ellipsoid at Gaussian Ellipsoid at 33σσ for 15 subjectsfor 15 subjects


Juliet Juliet (hybrid deformable (hybrid deformable registration method)registration method)

NonNon--Linear Local Linear Local deformable deformable

registration methodregistration method

Comparative Somatotopy :local method vs hybrid method

May 08



Deformable Registration : LimitsDeformable Registration : Limits

In GeneralValidation/Generality of methods

Segmentation/LabelingLabeling of highly variable structures (e.g. marginal cortical sulci )

Atlas matching methods using global approaches

Barely efficient on cortical anatomySource dependentNot yet real-time


Deformable Registration: LimitsDeformable Registration: Limits

Line

arN

on L

inea

r

Simulation Real Data(10 Subjects)

(Source: [Collins et al., 1996] )

May 08



Deformable Registration:International project for evaluation of non-rigid registrationDeformable Registration:International project for evaluation of non-rigid registration

Aim of the studyAnatomical and functional validity of the registrationOn the same corpus (18 subjects)

Others Participants:U. McGill (L. Collins), Epidaure Project INRIA, U. Iowa (G. Christensen), SPM, (J. Ashburner)

CriteriaAnatomically meaningfulLocal and global measuresNot related to the similarity used to perform the registration

U. McGillU. McGill EpidaureEpidaureAffineAffine

TalairachTalairach IRISAIRISA TargetTarget

U. IowaU. Iowa

SPMSPM

6 major 6 major sulcisulci per hemisphereper hemisphere


Local Criteria on sulcal matching(highly variable)

MI An

De

PS

RM

Use of cortical sulci (Use of cortical sulci (anatomicalanatomical and and functionalfunctional landmarkslandmarks))Visualization of Visualization of overlappingoverlapping deformeddeformed leftleft central sulci central sulci ((performedperformed alsoalso on on superiorsuperior frontal and on frontal and on laterallateral sulci)sulci)

May 08


Perspectives


Data Fusion and Registration PerspectivesData Fusion and Registration Perspectives

Needs to take into account local and global constraints in the deformable registration process (hybrid registration)More concerns about the clinical practice

pre-surgical mappingintra-operative and real time imagingCope with missing tissues (registration of dissipative material)

Introduction to the statistics of transformations (in a tangent space)

Introduction of statistical information for the guidance of the deformation

Registration of vector and tensor fieldsTighter links between registration and segmentation (e.g. thru active surface formulation)

May 08



Some references :Thesis or Books on data fusion and registration, and on general aspects

1. Barillot, C. (1999). “Fusion de données et imagerie 3D en médecine,” Habilitation àdiriger des recherches, University of Rennes 1, Rennes. ftp://ftp.irisa.fr/techreports/habilitations/barillot.pdf

2. Corouge, I. (2003). “Modélisation statistique de formes en imagerie cérébrale.” PhD, Univ. Rennes I, Rennes. ftp://ftp.irisa.fr/techreports/theses/2003/corouge.pdf

3. Corouge, I., Hellier, P., and Barillot, C. (2005). “From Global to Local Approaches for Non-Rigid Registration.” Medical Imaging Systems Technology: Methods in General Anatomy, vol. 265, C. T. Leondes Ed., Singapore, World Scientific Publishing.

4. Hellier, P. (2000). “Recalage non rigide en imagerie cérébrale: méthodes et validation,”PhdThesis, Université de Rennes1. ftp://ftp.irisa.fr/techreports/theses/2000/hellier.pdf

5. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes in C, 2nd edn, Cambridge University Press, Cambridge. http://www.nr.com/

6. Van Bemmel, J. H., and Musen, M. A. (1997). Handbook of medical informatics, Springer, URL: http://www.mieur.nl/mihandbook .

7. Viola, P. A. (1995). “Alignment by Maximization of Mutual Information,” Ph.D. Thesis, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, MA.


Review Papers1. Barillot, C. (1993). “Basic Principles of Surface and Volume Rendering Techniques to

Display 3D Medical Data.” IEEE Engineering in Medecine and Biology, 12(1), 111-119.

2. Brown, L. F. (1992). “A survey of image registration techniques.” ACM Computing Surveys, 24(4), 325-376.

3. Gee, J. C. (1999). “On matching brain volumes.” Pattern Recognition, 32(1), 99-112.

4. Lester, H., and Arridge, S. R. (1999). “A survey of hierarchical non-linear medical image registration.” Pattern Recognition, 32(1), 129-149.

5. Maintz, J., and Viergever, M. (1998). “A survey of medical image registration.” Medical Image Analysis, 2(1), 1-36.

6. Maurer, C., and Fitzpatrick, J. (1993). “A review of medical image registration.”Interactive image guided neurosurgery, American association of neurological surgeons, pp.17-44.

7. McInerney, T., and Terzopoulos, D. (1996). “Deformable models in medical image analysis: a survey.” Medical Image Analysis, 1(2), 91-108.

8. Zitova, B., and Flusser, J. (2003). “Image registration methods: a survey.” Image and Vision Computing, 21(11), 977-1000.

May 08



Research Papers on deformable registration (1)

1. Ashburner, J., and Friston, K. J. (1999). “Nonlinear Spatial Normalization Using Basis Functions.”Human Brain Mapping, 7(4), 254-266.

2. Bajcsy, R., and Kovacic, S. (1989). “Multiresolution Elastic Matching.” Computer Vision Graphics and Image Processing, 46, 1-21.

3. Bookstein, F. (1989). “Principal Warps: Thin plate splines and the decomposition of deformations.”IEEE Trans. on Pattern Analysis and Machine Intelligence, 11(6), 567-585.

4. Christensen, G., Rabbit, R., and Miller, M. (1996). “Deformable templates using large deformation kinematics.” IEEE trans image processing, 5(10), 1435-1447.

5. Christensen, G. E., and Johnson, H. J. (2001). “Consistent image registration.” IEEE Transactions on Medical Imaging, 20(7), 568 - 582.

6. Collins, L., and Evans, A. (1997). “Animal: validation and applications of nonlinear registration-based segmentation.” International Journal of Pattern Recognition and Artificial Intelligence, 8(11), 1271-1294.

7. Collins, L., Le Goualher, G., Venugopal, R., Caramanos, A., Evans, A., and Barillot, C. (1996). “Cortical constraints for non-linear cortical registration.” Proc. Visu. in Biomed. Computing, LNSC, K. Hohne and R. Kikinis, Eds., Springer, pp.307-316.

8. Corouge, I., Dojat, M., and Barillot, C. (2004). “Statistical shape modeling of low level visual area borders.” Medical Image Analysis, 8(3), 353-360.



1. Corouge, I., Hellier, P., Gibaud, B., and Barillot, C. (2003). “Interindividual functional mapping: a nonlinear local approach.” NeuroImage, 19(4), 1337-1348.

2. Friston, K., Ashburner, J., Frith, C., Poline, J., Heather, J., and Frackowiak, R. (1995). “Spatial registration and normalisation of images.” Human Brain Mapping, 2, 165-189.

3. Gee, J. C., le Bricquer, L., and Barillot, C. (1995). “Probabilistic matching of brain images.”Information Processing in Medical Imaging, Y. Bizais, C. Barillot, and R. di Paola Eds., Dordrecht., Kluwer Academic Publishers, pp.113-125.

4. Hellier, P., Ashburner, J., Corouge, I., Barillot, C., and Friston, K. J. (2002). “Inter subject registration of functional and anatomical data using SPM.” in Lecture Notes in Computer Sciences: Medical Image Computing and Computer-Assisted Intervention - MICCAI 2002, vol. LNCS-2489, R. Kikinis, R. Ellis, and T. Dohi Eds., Tokyo, Springer-Verlag, pp.590-587.

5. Hellier, P., and Barillot, C. (2003). “Coupling dense and landmark-based approaches for non rigid registration.” IEEE Transactions on Medical Imaging, 22(2), 217-227.

6. Hellier, P., Barillot, C., Corouge, I., Gibaud, B., Le Goualher, G., Collins, D. L., Evans, A., Malandain, G., Ayache, N., Christensen, G. E., and Johnson, J. H. (2003). “Retrospective Evaluation of Intersubject Brain Registration.” IEEE Transactions on Medical Imaging, 22(9), 1120-1130.

7. Hellier, P., Barillot, C., Mémin, E., and Pérez, P. (2001). “Hierarchical estimation of a dense deformation field for 3D robust registration.” IEEE Transactions on Medical Imaging, 20(5), 388-402.

8. Le Goualher, G., Argenti, A.-M., Duyme, M., Baaré, W. F. C., Hulshoff Pol, H. E., Boomsma, D. I., Zouaoui, A., Barillot, C., and Evans, A. C. (2000). “Statistical Sulcal Shape Comparisons: Application to the Detection of Genetic Encoding of the Central Sulcus Shape.” Neuroimage, 11(5), 564-574.

May 08




1. Le Goualher, G., Barillot, C., and Bizais, Y. (1997). “Modeling cortical sulci with active ribbons.”International Journal of Pattern Recognition and Artificial Intelligence, 8(11), 1295-1315.

2. Le Goualher, G., Procyk, E., Collins, D. L., Venugopal, R., Barillot, C., and Evans, A. C. (1999). “Automated Extraction and Variability Analysis of Sulcal Neuroanatomy.” IEEE Transactions on Medical Imaging, 18(3), 206-217.

3. Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., and Suetens, P. (1997). “Multimodality image registration by maximisation of mutual information.” IEEE transactions on Medical Imaging, 16(2), 187-198.

4. Miller, M. I., Christensen, G. E., Amit, Y., and Grenander, U. (1993). “Mathematical textbook of deformable neuroanatomies.” Proc Natl Acad Sci U S A, 90(24), 11944-8.

5. Thirion, J.-P. (1998). “Image matching as a diffusion process: an analogy with {Maxwell's} demons.”Medical Image Analysis, 2(3), 243-260.

6. van den Elsen, P. A., Pol, E. J. D., and Viergever, M. A. (1993). “Medical image matching--a review with classification.” IEEE Engineering in Medicine and Biology Magazine, 12(1), 26-39.

7. West, J., Fitzpatrick, J. M., Wang, M. Y., Dawant, B. M., Maurer, C. R., Kessler, R. M., Maciunas, R. J., Barillot, C., Lemoine, D., Collignon, A., Maes, F., Suetens, P., Vandermeulen, D., van den Elsen, P. A., Napel, S., Sumanaweera, T. S., Harkness, B., Hemler, P. F., Hill, D. L. G., Hawkes, D. J., Studholme, C., Maintz, J. B. A., Viergever, M. A., Malandain, G., Pennec, X., Noz, M. E., Maguire, G. Q., Pollack, M., Pellizzari, C. A., Robb, R. A., Hanson, D., and Woods, R. (1997). “Comparison and Evaluation of Retrospective Intermodality Brain Image Registration Techniques.” J. Computer Assisted Tomography, 21(4), 554-566.



Mazziotta, J., Toga, A., Evans, A., Fox, P., and Lancaster, J. (1995). “A probabilistic atlas of the human brain: theory and rationale for its development.” Neuroimage, 2, 89-101.McInerney, T., and Terzopoulos, D. (1996). “Deformable models in medical image analysis: a survey.” Medical Image Analysis, 1(2), 91-108.Miller, M. I., Christensen, G. E., Amit, Y., and Grenander, U. (1993). “Mathematical textbook of deformable neuroanatomies.” Proc Natl Acad Sci U S A, 90(24), 11944-8.Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes in C, 2nd edn, Cambridge University Press, Cambridge.Thirion, J.-P. (1998). “Image matching as a diffusion process: an analogy with {Maxwell's} demons.”Medical Image Analysis, 2(3), 243-260.Van Bemmel, J. H., and Musen, M. A. (1997). Handbook of medical informatics, Springer, URL: http://www.mieur.nl/mihandbook.van den Elsen, P. A., Pol, E. J. D., and Viergever, M. A. (1993). “Medical image matching--a review with classification.” IEEE Engineering in Medicine and Biology Magazine, 12(1), 26-39.Viola, P. A. (1995). “Alignment by Maximization of Mutual Information,” Ph.D. Thesis, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, MA.West, J., Fitzpatrick, J. M., Wang, M. Y., Dawant, B. M., Maurer, C. R., Kessler, R. M., Maciunas, R. J., Barillot, C., Lemoine, D., Collignon, A., Maes, F., Suetens, P., Vandermeulen, D., van den Elsen, P. A., Napel, S., Sumanaweera, T. S., Harkness, B., Hemler, P. F., Hill, D. L. G., Hawkes, D. J., Studholme, C., Maintz, J. B. A., Viergever, M. A., Malandain, G., Pennec, X., Noz, M. E., Maguire, G. Q., Pollack, M., Pellizzari, C. A., Robb, R. A., Hanson, D., and Woods, R. (1997). “Comparison and Evaluation of Retrospective Intermodality Brain Image Registration Techniques.” J. Computer Assisted Tomography, 21(4), 554-566.

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Other related research paper1. Beauchemin, S. S., and Barron, J. L. (1995). “The Computation of Optical Flow.” ACM

Computing Surveys, 27(3), 433-467.

2. Collins, D. L., Zijdenbos, A. P., Kollokian, V., Sled, J. G., Kabani, N. J., Holmes, C. J., and Evans, A. C. (1998). “Design and Construction of a Realistic Digital Brain Phantom.” IEEE Transactions on Medical Imaging, 17(3), 463-468.

3. Cootes, T. F., Taylor, C. J., Cooper, D. H., and Graham, J. (1995). “Active Shape Models - their training and application.” Computer Vision and Image Understanding, 61(1), 38-59.

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