Medical Image Registration - MIV

May 08

Medical Image Registration: Data Fusion in 3D Medical Imaging

Christian Barillot CNRS Director of Research VisAGeS U746 Unit/Project, INRIA/INSERM IRISA, UMR CNRS 6074 Campus de Beaulieu 35042 Rennes Cedex, FRANCE [email protected] http://www.irisa.fr/visages

Plan

General Context Illustration of Data Fusion Issues Principal of Data Fusion in 3D Medical Imaging Image Registration

Basic Concepts A Focus on Deformable Registration

Local, Global and Hybrid methods

Cooperation between segmentation and registration tasks Perspectives

Deformable registration Sharing heterogeneous and distributed resources C. Barillot, Visages U746, IRISA, Rennes

Christian BARILLOT, Visages Team, IRISA, Rennes, France

1

May 08

General Context and Challenges

1 GB

Context :

Molecular Biology /

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 :

DTDT-MRI

0,5 MB

2D CT

3D CT

70's

3D PET SPECT

fMRI

3D MRI

80's

90's

2000's

2010's

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

► MS lesions 12000 images*/patient/year

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

► Epilepsy surgery 7000 images*/intervention *: 1 image = 1 2D MRI slice

C. Barillot, Visages U746, IRISA, Rennes

Coming issues

To conceive the surgical room of the future

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

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

Imagery of pathologies : from the gross organ to the molecule Modeling 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 events Data mining and knowledge discovery Validation and certification of new drugs



2

May 08

Research issues

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

Data fusion of medical images Merge semantic and computational Grid technologies Development of new adaptive medical devices (effectors, sensors, …) C. Barillot, Visages U746, IRISA, Rennes

Illustration of Data Fusion Issues


3

May 08

Epilepsy Surgery Patient selection Semiology of crisis and relations to anatomy « Static » Exams (search of lesions) « Dynamic » Exams (search of epileptogenic status): ¾ ¾

Interictal : functional imaging, Electrodes Implant Ictal : Crisis Recordings and labeling

Presurgical Planning Cortectomy (surgery) C. Barillot, Visages U746, IRISA, Rennes

Integration of metabolic and functional imaging for presurgical mapping EEG

MEG

SPECT Inter-ictal

Ictal

Spatial Resolution (mm)

10 Inter-ictal Spikes in Epilepsy

8

Cerebral Perfusion

FDG-PET

6 4 2

inter-ictal Metabolism of glucose

Reference

intra-cerebral Electrodes

1 ms

Anatomic MRI

fMRI

1 second

40 seconds

static

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


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May 08

Magnetic Resonance Imaging (MRI) Proton Density - NMR ¾ 256

x 256 pixels (1mm resolution)

¾ From

20 to 120 slices along three

axis


» Exams

(Source: [A. Biraben et al., CHU Rennes])

« Static



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May 08

Single Photon Emission Computed Tomography (SPECT) Distribution of a radio tracer ¾ Typical

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

¾ 64

to 128 slices per volume


«Dynamic» Metabolic Exams

(Source: [A. Biraben et al., CHU Rennes])

Extended temporal hypo metabolism



6

May 08

Fusion of “Static” and «Dynamic» Exams MRI +interictal +interictal SPECT (HMPAO)

Brain MRI + ictal SPECT


Intra cerebral electrodes implant in stereotactic conditions MRI

Angiography 3D - 2D Projections

Registration of 3D referential stereotactic referential



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May 08

Intra cerebral electrodes recordings


Dynamic Exams and Pre-operative Planning:

MEG Signals

Functional recording of epileptic region environment

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


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May 08

Functional Imaging :

MagnetoEncephaloGraphy (MEG) Measure of the magnetic field issued by the neuronal activity : : 10-13 Tesla : 10-3 Tesla ¾ MRI : 1 to 3++ Tesla ¾ Brain

¾ Hearth

40 to 150+ sensors (SQUID) spontaneous and evoked potentials, e.g.: ¾ motor ¾ somesthesic ¾ language ¾ visual


MEG : Spatiotemporal

Probabilité Probabilités

analysis of Spatio-temporal MEG analysis of interictal spikes

interictal spikes

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



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May 08

MEG : Spatiotemporal Interictal Analysis Localization

100 ms

0 ms

Left Hemisphere


Epilepsy Surgery : Preoperative Planning



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May 08

Talairach Atlas


Functional Mapping of language areas

Silent vs Active Word Activation



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May 08


Preoperative Planning :

functional MRI (fMRI)

Paradigm

Acquisition

A

A R

R time

mean of activation A Mean of rest state R intensity

Detection

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


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May 08

Epilepsy Surgery:

Superposition of graphical data


Image Guided Surgery



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May 08

Image-Guided Neurosurgery:

Interventional procedure (Neuronavigation) 3D referential system

3D workstation

Surgical Microscope 3D localizer

Patient


Surgical resection

Electrodes landmarks

Resection C. Barillot, Visages U746, IRISA, Rennes


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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)

2.5D Image

3D US Imagery

Courtesy I. Corouge, UNC

Preoperative Imagery

IntraIntra-operative Imagery

Fusion of observations C. Barillot, Visages U746, IRISA, Rennes

Cooperative Scheme for Data Fusion Multimodal Registration

Original

Registered Data

Segmentation

Data

Segmented Data

Modeling

Modeled Data

Deformable Registration

a priori Knowledge

Information Model

a posteriori Knowledge



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May 08

Intra-Individual Data Fusion MRI

2D/3D Angiography

EEG/SEEG

Anatomical and Functional Imagery SPECT

CT

PET

MEG

fMRI

Segmentation and Labeling

Multimodal Registration Anatomical Landmarks Instrumental Referential Fiducial Markers

Contours Regions Deformable Models

Linear Transformations

Anatomical Labels

3D Visualization/Interaction Subject Data Base

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

Inter-Individual Fusion


Subject i

Subject n

Data Base

Data Base

Deformation Model

Affine

Higher Order

3D Numerical Model



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May 08

Data Fusion in medical imaging What is Data Fusion? Joint Use of Heterogeneous Data

Why? Co-exploitation of multimodal data Registration / Matching

Which Context ? Computer assisted image interpretation systems


Image Registration Basic concepts


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May 08

Image Registration : Basic Concepts Source Image Is

ps2 p2

ps1 p1 p1 p1 p p1 p2 p2 p2 ppdd2 22

ps3 p3

p3 p3

p3

Destination pp pd11d1 Image Id

pd3 p3 p 3 d

¾ 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). Problem: Find a Transformation Φ Such as Is Φ Id Φ = f(R, T, δ(p)): Φ(ps) – pd≠=≈ε 0→ Optimization C. Barillot, Visages U746, IRISA, Rennes

Basic Referential Image Referential

Instrumental Referential

Subject Referential

p(u,v,w) p(x,y,z) p(i,j,k)



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May 08

Class of registration domains ONE patient ONE modality

Intra-modality registration : Post-operative control Pathology tracking, Treatment probing

SEVERAL modalities

Inter-modalities registration Complementarities between sources of images Computer assisted therapeutic planning Computer assisted surgery Anatomy-function correlation

SEVERAL patients patients Intra-modality registration Model-based segmentation Registration/matching with an anatomical atlas Spatial normalization, study of anatomical variability

Inter-modalities registration Human brain mapping Anatomo-functional normalization


Medical Image Registration : Basic Concepts Definition: Definition 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 ω in Ωs to its correspondent Φ(ω) in Ωt.

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 :

argmin Δ (Φ θ ( Ω s)− Ω t ) (θ ∈Θ Ψ )

where Δ is the similarity measure and (θ∈Θ) the transformation parameters C. Barillot, Visages U746, IRISA, Rennes


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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 1D 2D 3D nD

: : : : :

point (Ω=Constant) contour (Ω=f(u)) surface (Ω=f(u,v)) volume (Ω=f(u,v,w)) 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) C. Barillot, Visages U746, IRISA, Rennes


20

May 08

Nature of Homologous Structures (Ω)

External Referential :

Fiducial markers Surgical frames (e.g. stereotactic)

Anatomical Referential :

Anatomical landmarks (reference structures) Image (iconic) features (gray levels, gradients, curvatures, ...) Segmented shape C. Barillot, Visages U746, IRISA, Rennes

Which Transformation (Φ) ?

Linear Transforms :

⎡ ⎡r11s1 r12 r13 ⎤ ⎢⎢ ⎥ r r s r 22 2 23 ⎥ ⎢ ⎢ 21 ⎢ ⎢⎣ r31 r32 r33 s3 ⎥⎦ ⎢ 0 0 ] ⎢⎣[ 0

⎡t x ⎤ ⎤ ⎢t ⎥ ⎥ ⎢ y ⎥⎥ ⎢⎣tz ⎥⎦ ⎥ ⎥ w ⎥⎦

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) C. Barillot, Visages U746, IRISA, Rennes


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May 08

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

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

Intensities of the floating Image Y=Φ(X)

Image registration: Measure from joint histogram Joint Histogram (HIST[x,y])

Intensities of the reference image X

Registered Images (1/2*[X+Φ(X)])

Φ=Ι

Φ=Tx



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May 08

Image registration:

Relation between the transformation and the joint histogram


Joint Histogram: Linear or Affine Dependencies Optimum Corr(x,y) y=αx+β

Corr ( X , Y ) =

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


Optimum SSD/SAD y=x SSD( X , Y ) = ∑ ( x − y ) 2

x∈ X , y∈Y

SAD( X , Y ) =

∑

x− y

x∈ X , y∈Y




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May 08

Joint Histogram:


Examples of Linear or Affine Dependencies

Joint Histogram (HIST[x,y])


Registered Images (1/2*[X+Φ(X)])

Φ=Ι

Φ=Tx


Joint Histogram:

Functional Dependencies (e.g. Correlation Ratio)



Optimum η(Y|X) Y=f(X) Intensités de l’image référence

X

MRIMRI-T2

MRIMRI-PD

Intensities of the reference image X η (Y X ) = 1 −

var[Y − E (Y X )] var(Y )

X

Y



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May 08

Joint Histogram:

Statistical Dependencies (e.g. Mutual Information)


Joint Histogram (HIST[x,y]) Optimum

MI(X,Y)

Intensités de l’image référence

X

CT

MRI


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

X

Y


Joint Histogram: Intensities of the floating Image Y=Φ(X)

Statistical Dependencies (e.g. Mutual Information) Optimum

MI(X,Y)

Φ=Ι



Φ=Tx=3mm

Φ=Tx=5mm

PET

X

MRI

Y



25

May 08

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

Δ

Cost Function Δ(θ)

A

G

C E

B D

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

Z X

F

Transformation parameters (θ∈Θ)

Y

θ C. Barillot, Visages U746, IRISA, Rennes

Optimization Methods (Ψ)

Non Global optimization methods:

Quadratic or semi-quadratic approaches

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


26

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

Semi-quadratic Optimization using NEWUOA

NEW Unconstrained Optimization Algorithm [Powell 04] 1.

2.

3.

4.

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 Compute the maximum of the approximation within a “trust region” defined by the initial points Replace the “worst” parameter of the initial set with this newly estimated value and update the trust region Iterate C. Barillot, Visages U746, IRISA, Rennes


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May 08

Illustration of NEWUOA optimization 1.4 1.4

f(x) f(x) Function samples final fit next interpolation point

1.2 1.2

11

Initial Region

Region Trust Trust Region

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

00

-0.2 -0.2

-0.4 -0.4 -10 -10

-5 -5

00

55

10 10


Validation and Error Measurement

BrainWeb dataset: T1-w, T2-w, PD-w images in perfect alignment 5% additive noise 50 random transformations (+/- 5 mm +/- 5 degrees) Warping Index [Thevenaz&Unser00] :

Paired t-tests



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May 08

Results Comparison Table

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

Results Algorithm Accuracy



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May 08

Results Algorithms Run Time


Outcome from this study

Mutual Information

Best Similarity Measure for any of the optimizers

NEWUOA

Fastest Algorithm (compared to Powell or Simplex) Best Accuracy More Robust C. Barillot, Visages U746, IRISA, Rennes


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May 08

Recalage Intra-Sujet Applications: • Approche générique basée «surface» •Recalage IRM/CT/PET •Recalage IRM/MEG •Recalage IRMa/3D-DSA • Recalage IRMf


Multimodal Registration : Surface Matching Sx R11 R21

R13

0

Sy R22 R23

R12

0

R32 Sz R33 TY TZ

Surface Extraction

0 1

Binary Volume

.A .

P.C.A. P. C

Target Volume

Segmentation

R31 TX

Distance Volume Base Volume

Registered Volume

R12

R13

0

R21

Sy R22

R23

0

R31 TX

R32 TY

Sz R33 TZ

0 1

Sx R11

R12

R13

R21

Sy R22

R23

R31 TX

R21 R31 TX

R12

R13

Sy R22 R23 R32 Sz R33 TY TZ

0 0

R32 Sz R33 TY TZ

0 1

Sx R11

R12

R13

0

R21

Sy R22

R23

0

R31 TX

Sx R11

Multiresolution Processing

Sx R11

R32 Sz R33 TY TZ

0 1

0 0 0 1



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May 08

Exemple de recalage multimodal




32

May 08

Résultats de superpositions SPECT-IRM et PET-IRM


Multimodal Registration: Evaluation

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

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

10 brain anatomical structures for reference C. Barillot, Visages U746, IRISA, Rennes


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May 08

Multimodal Registration: Evaluation Optic chiasm

(Source: [West J. et al., JCAT-21(4), 1997])

Junction of fourth ventricle with aqueduct Maximum aperture of fourth ventricle Whole head

4,00 3,00

Apex of left Sylvian fissure

T2 Optic chiasm

T1r

PD

0,00

Apex of right Sylvian fissure

Right occipital horn

1,00

Left occipital horn

2,00

Whole head

Error in mm

5,00

Left occipital horn Left globe Right globe Right occipital horn Junction of central sulcus with midline

Registration Error vs. Region of Interest (CT ↔ MRI)


Multimodal Registration: Evaluation Volumetric Similarities

Point Simil. Simil.

SurfaceSurface-based Similarities

Error in mm

(Source: [West J. et al., JCAT-21(4), 1997])

10

T1 PD T2 T1 rect

8 6 4

PD rect T2 rect

2 0 1

2

3

4

5

6

7

8

9

10

11

Mean Registration Error CT-MR C. Barillot, Visages U746, IRISA, Rennes


34

May 08

Recalage multimodalité : Évaluation Similarité Similarités Volumé Volumétrique

Similarité Similarités Surfaciques

Simil. Simil. Point

> 30 Erreur in mm

25

T1

20

PD

15

T2 T1 rect

10

PD rect

5 0

T2 rect

1

2

3

4

5

6

7

8

9

10

11

Max Registration Error CT-MR (Source: [West J. et al., JCAT-21(4), 1997])


Recalage IRM-MEG

Analyse Multirésolution Recalage Initial

Echantillonnage du « Headshape » Optimisation Rejet des points aberrants

Fin C. Barillot, Visages U746, IRISA, Rennes


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May 08

Recalage IRM-MEG IRM Anatomique

Segmentation de la Tête

Acquisition du « Head Shape »

Recalage « Head Shpe » vs IRM


Recalage MEG-IRM : Evaluation de la précision

Précision théorique sur simulations :

erreur moyenne de 3mm

Validation expérimentale

Comparaison avec la méthode manuelle (basée sur des amers cutanés) Utilisation Clinique Transfert technologique C. Barillot, Visages U746, IRISA, Rennes


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May 08

Recalage MEG-IRM : Résultats




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May 08

Recalage Angiographie X 3D / IRM

3D DSA



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May 08

Recalage Angiographie 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 1mm 1 à 2mm 2 à 3mm 3 à 5mm > 5mm



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May 08

Acquisition

Paradigme A

A R

R temps

Analyse de données en IRM fonctionnelle cérébrale Détection

moyenne activation A moyenne repos R

intensité

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

A

Tâche

R A R

A R temps

coupes sagittales

moyenne activation A

coupe sagittale

= moyenne repos R

image différence



40

May 08

IRMf: Mouvement du sujet -

moyenne repos R

moyenne activation A

image différence


IRMf: Mouvement du sujet 1,5

décalage en x

1 0,5 0 -0,5

1 17 33 49 65 81 97 113

-1 1/10 pixel induit 1 à 7% de variation de signal C. Barillot, Visages U746, IRISA, Rennes


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May 08

Exemple: Recalage monomodale par flot optique • Formulation gé générale : minimisation de la fonctionnelle de conservation de l’l’intensité intensité entre paires d’ d’images U (ω ; f ) = ∑ [∇f (s, t ) ⋅ ω s + f t (s, t )] + α 2

s∈S

∑ω

s , r ∈C

s

− ωr

2

• Introduction d’ d’estimateurs robustes

U (ω ; f ) = ∑ [∇f (s, t ) ⋅ ω s + f t (s, t )] + α ∑ ω s − ω2r s∈S U (ω , δ , β ; f ) = ∑ δ s (∇f (s, t )⋅ω s + s,fr t∈(Cs, t )) + ϕ1 (δ s ) + α 2

2

s∈S

∑β

s , r ∈C

sr

ωs − ωr

2

+ ϕ 2 (β sr )

• Approche multi ré résolution • Optimisation alterné alternée [1) estimation des poids δ, β et 2) estimation des paramè paramètres de transformation ω]

• Temps de calcul < 1s pour des volumes 643 C. Barillot, Visages U746, IRISA, Rennes

IRMf: Mouvement du sujet Activation

Image de différence sans correction

Image de différence avec correction



42

May 08


Deformable Registration: Not a new topic!

Classical topic in morphometry (e.g. [ D’Arcy Thomson, 1917]) (Source: D’Arcy Thomson, On Growth and Form, Cambridge University Press, 1961)

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

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

Introduction of computer based procedures in the 80’s (R. Bacjsy, C. Broit and coll.; U. Grenander and coll.; F. Bookstein, …) C. Barillot, Visages U746, IRISA, Rennes


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May 08

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) C. Barillot, Visages U746, IRISA, Rennes

Deformable registration: When? ONE modality

ONE patient Registration of temporal sequences : Temporal deformation of anatomical structures (heart, chest, blood flow)

Growth, Pathologies follow-up

SEVERAL modalities

Correction of fMRI acquisitions Constraints to reconstruction / restoration algorithms Computer Assisted Surgery registration between preand intra-operative images

SEVERAL patients patients Model-based segmentation Building of digital atlases Registration/matching with an anatomical atlas Spatial normalization, study of anatomical variability Human brain mapping Anatomo-functional normalization (aid for the study of functional variability)

(e.g. MRI and Ultrasound) C. Barillot, Visages U746, IRISA, Rennes


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May 08

Deformable Registration : which transformation?

Non-linear dense transformation: Definition : 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 general formulation becomes:

argmin

(θ ∈ Θ Ψ )

In a Bayesian context:

E [Δ ( p s + δ θ ( p s ), p t )]+ E [δ θ ] Likelihood : p((p (pss, pptt)|)|δ)

Prior : p(δ)


Continuity of the transformation (E[δθθ])

Piecewise linear (C0 continuity)

Parametric (C1, C2 continuity)

(e.g. Talairach)

(e.g. Splines, Free-form

deformation, Cosines, RBF)

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

Linear elasticity models (Navier equations )

Fluid models (Navier-Stokes equations )



45

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 continuous The 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 Î people tend to rich the symmetry property only C. Barillot, Visages U746, IRISA, Rennes

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)ÆT(x); g: T(x) Æ S(x) h(x)°g(x)=h(g(x))=x Methods iteratively minimize

∑ [h( g ( x)) − x]

2

x∈V



46

May 08

Defomable Registration: Local and Global approaches

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

Local, or “geometric” methods (Dh< Dw)

Rely on photometric similarity measures Provide a dense deformation field Anatomical coherence of the transformation? _ High dimensional optimization problem

Rely on extracted features (point, curves, surfaces)

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

The transformation is mostly relevant in the neighborhood of the homologous features

¾ Hybrid: Hybrid: use of both homologous structures C. Barillot, Visages U746, IRISA, Rennes

Image fusion in neuroimaging using Global, Local and Hybrid methods

Subjects Data Base

Probability of Activation Y Statistical Model of Sulcus X

Segmented Sulci

Registered Sulci

Probability of Sulcus X

Local Registration Hybrid Matching to Reference Sulcus and Brain

Probability of Sulcus X

+

Probability of Activation Y

Hybrid Registration Probability of Sulcus X

Dense Matching to Reference Brain

Probability of Activation Y

Global Registration



47

May 08

Example of Inter-Individual Registration


Deformable Registration: Local, or “geometric” methods Definition of local landmarks

Before registration

Averaging of 9 brains

Definition of a deformation model

After deformable registration

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



48

May 08

Talairach Stereotactic Proportional Grid System

(Source: J. Talairach, G. Szikla, P. Tournoux, A. Prosalentis, and M. Bornas-Ferrier, Atlas d'Anatomie Stéréotaxique du Télencéphale, Masson, Paris, 1967) C. Barillot, Visages U746, IRISA, Rennes

Probabilistic atlas based on local constraints Cortical Sulci

InterInter-subjects registration of sparse data (MEG) local referential non-linear local registration non-linear global registration

x0

xi

xm wu v

Statistical Shape Analysis X = Sillon moyen

m

∑ xi i =1

C=

∑ φi bi

⎡ ui ⎢v ⎢ i ⎢wi ⎢ ⎢⎣ t x

m

1 ∑ ~xi ~xi T ; ~xi = xi − X m i =1

C = Φ ΛΦ ; Λ T

Analysis

x = X + Φb m

x≈ X +

1 m

Sulcus Mean Shape

Reconstructed Sulcus

n

i=1

Constraints on TPS

f (x , y , z ) = a 0 + a 1x + a 2 y + a 3z + ∑ w iU (| Pi − (x , y , z ) |) , U(r) = r

wu v

⎡ λ1 = ⎢⎢ M ⎢⎣ 0

uj

uk

vj wj

vk wk

ty

tz

0⎤ 0⎥⎥ 0⎥ ⎥ 1⎥⎦

wv

u

0 ⎤ O M ⎥⎥ L λm ⎦⎥ L

Modal Amplitudes Modes Matrix

Modal Analysis

Synthesis

i =1

x = X + φ 1b1

[

b1 ∈ − 2 λ1 , + 2 λ1

]

principal Mode of deformation of the right central sulcus

Ex. 29 subjects

Registration and matching



49

May 08

Extraction of the local features


Linear Local Registration (LR) local referential

x0

xi

xm wu v

wu v

⎡ ui ⎢ ⎢ vi ⎢ wi ⎢ ⎢⎣ t x

uj vj wj ty

uk vk wk tz

0⎤ 0 ⎥⎥ 0⎥ ⎥ 1 ⎥⎦

w v u

29 subjects



50

May 08

Statistical Shape Model :

Principal Component Analysis 1 m X = ∑ xi m i =1

Reconstructed Shape

Mean sulcus

29 subjects

Mean Shape

m

∑ ~xi ~xi T ; ~xi = xi − X

1 m

i =1

⎡ λ1

C = Φ Λ Φ T ; Λ = ⎢⎢ M ⎢0 Analysis ⎣

x = X + Φb

L O L

0 ⎤ M ⎥⎥

λm ⎥⎦

Modal Amplitudes Modes Matrix

Synthesis

m

x≈ X +

C=

∑ φi bi i =1

x = X + φ 1b1

[

b1 ∈ − 2 λ1 ,+ 2 λ1

]

principal Mode of deformation of the right central sulcus


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

f : interpolation n source points Pi

n target points Vi

x Source: left central S. of one subject

function

(W a

0

a1

a2

a3 )

i =1

x = x + Φ mbm application

x Target: mean central sulcus

n

f ( x, y, z ) = a0 + a1 x + a2 y + a3 z + ∑ wiU (| Pi − ( x, y, z ) |)

(x, y, z)

f

to a dipole Local extension of the deformation field

f(x, y, z)



51

May 08

Somatotopy around the principal mode using the non -linear local method (NLL) non-linear Little finger

Index

Thumb


Deformable Registration: Global, iconic or photometric methods Find a the transformation between one reference (atlas) and one individual Model 1 Source

Target

Transformed Deformation Image Field

Model 2 C. Barillot, Visages U746, IRISA, Rennes


52

May 08

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

General formulation (optical flow estimation): U (ω ; f ) = ∑ [∇f (s, t ) ⋅ ω s + f t (s, t )] + α 2

s∈S

Robust estimation of the deformation field :

Ö

Reduce the sensitivity to noise and preserve the deformation discontinuities: U (ω , δ , β ; f ) = ∑ δ (∇f (s, t )⋅ ω + f (s, t )) + ϕ (δ ) + α ∑ β ω − ω

s

Adaptative multigrid algorithm:

s

t

1

s

s , r ∈C

Pyramide multiré multirésolution

sr

s

s , r ∈C

2

2

s∈S

∑ω

r

s

− ωr

2

+ ϕ 2 (β sr )

Minimisation multigrille

Ö Extensible to other similarity similarity

functions (e.g. (e.g. fMRI registration): registration):


Registration between 2 subjects

Deformable Registration: Multiresolution optimization

Intensity RMS

Init after resolution 1

Grid 4 Grid 3 Grid 2

10

20

30

40

Grid 1 Grid 0 50

60

70

CPU time (mn (mn))

Multiresolution Pyramid



53

May 08

RoMEO ©

Talairach

Affine

Deformable Registration : Spatial Normalization

Target

Averaging of 18 subjects


Hybrid Approach


54

May 08

Hybrid approach:

Cooperation between local and global approaches

Global, or “photometric” method:

Image registration based on image information Provides a dense deformation field

Local, or “geometric” method:

Rely on landmarks (points, surfaces, …) Use an interpolation function (e.g. TPS) Cooperative approach, where geometric and photometric information are combined into the same framework


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

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

Matching

of homologous structures (e.g. sulci )

Mean without constraints

Taking

into account possible interruptions between sulci Mean with constraints

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


55

May 08

Deformed central sulci (from 18 sujects) Without constraints

With constraints

Mean sulci ()


Visualization of the cortical deformation with constraints

without constraints



56

May 08

Cooperation between Segmentation and Registration Tasks

Cooperative scheme for Data Fusion Multimodal Registration

Original

Registered Data

Segmentation

Data

Segmented Data

Modeling

Modeled Data


a priori Knowledge

Information Model

a posteriori Knowledge



57

May 08

Deformable Registration and Segmentation

Atlas Based Segmentation

Expert Segmentation

Atlas (Source: [Collins et al, IPMI’95])


Deformable Registration + Level Sets (simulation)


Deformable Registration + Level Sets (real data)


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

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

Statistical analysis of shape and localization of structures Concurrent evolution of several level sets

Contribution :

Integration of fuzzy control to constrain the competitive evolution of level sets Utilization of a statistical shape models to define the fuzzy control variables *: C. Ciofolo, C. Barillot, IPMIC.2005, 2006IRISA, Rennes Barillot,ECCV Visages U746,


58

May 08

Deformable Registration:

Study of the Anatomical Variability

(Source: MNI, U. McGill, Montreal )

Probabilities of cortical labels (max proba)

Probabilities for Sulci Occurrence (> 10%) C. Barillot, Visages U746, IRISA, Rennes

Deformable Registration: Labelling from atlas Sulci Labeling

(Source: [LeGoulher et al., 2000] )



59

May 08

Application of Deformable Registration in Clinical Neuroscience

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

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

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


After


60

May 08

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

Objective: Compensate for the intraoperative deformations after opening of brain envelopes

Results

Validation on a synthetic deformation

Experimentation on 5 patients

Method:

Non rigid transformation using a multi-frequential approach (cosines basis defined from their pulsation ) mean estimated deformation 2.71 +/+/- 1.03 mm

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

mean estimated deformation 1.81 +/+/- 1.02 mm

[P. Coupe et al., Patent]


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

Objective

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

Result

Only 20 patient from each group 90% differential diagnosis PD vs MSA/PSP Error rate cut by 50%

Exemples of MSA Normal

*: S. Duchesne et al., SPIE 2007


Mild

Severe


61

May 08

Surface based morphometry in Parkinsonian disorders Cortical Feature Population Average Maps

Objective:

Differentiation between Parkinson’s Disorders Early diagnosis from crosssectional MRI at a single time point at inclusion

Method

Extraction of GM/WM interface

Computation of cortical indexes cortical gray matter thickness

Results:

Sulcal each Depth group Only 20 patient from

Brain

Mapping of statistical difference between groups

Curvature

Cortical Thickness

geodesic sulcal depth

Cortical Feature Significant Mean Difference Maps Red/ Red/Yellow: Yellow: IPD > MSA, IPD > PSP, MSA> PSP Blue/ Blue/Cyan: Cyan: MSA>IPD, PSP>IPD, PSP>MSA

[D. Tosun et al., Miccai’07]


Data Fusion of Anatomical and Functional Brain Images


62

May 08

Deformable Registration for Anatomo-Functional Imaging Talairach Atlas

MEG Localisations


Spatial Normalization for the Analysis of Functional Data Example of comparison of average activation responses Linear Registration

NonNon-Linear Registration

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



63

May 08

Mapping of the somatotopy using global and hybrid deformable registration methods

Mutual Inf. Method (M)

Romeo Method (R)

SPM Method (S)

Talairach Method (P)

Juliet Method (H)

Gaussian Ellipsoid at 3σ for 15 subjects C. Barillot, Visages U746, IRISA, Rennes

Comparative Somatotopy : local method vs hybrid method Juliet (hybrid deformable registration method)

NonNon-Linear Local deformable registration method



64

May 08

Deformable Registration : Limits

In General

Segmentation/Labeling

Validation/Generality of methods Labeling of highly variable structures (e.g. marginal cortical sulci )

Atlas matching methods using global approaches

Barely efficient on cortical anatomy Source dependent Not yet real-time


Non Linear

Linear

Deformable Registration: Limits

Simulation

Real Data

(10 Subjects)

(Source: [Collins et al., 1996] ) C. Barillot, Visages U746, IRISA, Rennes


65

May 08

Deformable Registration:

International project for evaluation of non-rigid registration

Affine

U. McGill

Talairach

SPM

Target

Anatomical and functional validity of the registration On the same corpus (18 subjects)

Others Participants:

U. Iowa

Aim of the study

IRISA

Epidaure

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

Criteria

Anatomically meaningful Local and global measures Not related to the similarity used to perform the registration C. Barillot, Visages U746, IRISA, Rennes

6 major sulci per hemisphere

Local Criteria on sulcal matching (highly variable) Use of cortical sulci (anatomical (anatomical and functional landmarks) landmarks) Visualization of overlapping deformed left central sulci

(performed also on superior frontal and on lateral sulci)

MI

An

PS

De

RM



66

May 08

Perspectives

Data 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 mapping intra-operative and real time imaging Cope 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 fields Tighter links between registration and segmentation (e.g. thru active surface formulation) C. Barillot, Visages U746, IRISA, Rennes


67

May 08

Some references : Thesis or Books on data fusion and registration, and on general aspects 1.

2.

3.

4.

5.

6.

7.

Barillot, C. (1999). “Fusion de données et imagerie 3D en médecine,” Habilitation à diriger des recherches, University of Rennes 1, Rennes. ftp://ftp.irisa.fr/techreports/habilitations/barillot.pdf Corouge, I. (2003). “Modélisation statistique de formes en imagerie cérébrale.” PhD, Univ. Rennes I, Rennes. ftp://ftp.irisa.fr/techreports/theses/2003/corouge.pdf 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. 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 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/ Van Bemmel, J. H., and Musen, M. A. (1997). Handbook of medical informatics, Springer, URL: http://www.mieur.nl/mihandbook . Viola, P. A. (1995). “Alignment by Maximization of Mutual Information,” Ph.D. Thesis, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, MA. C. Barillot, Visages U746, IRISA, Rennes

Review Papers 1.

2.

3. 4.

5.

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. Brown, L. F. (1992). “A survey of image registration techniques.” ACM Computing Surveys, 24(4), 325-376. Gee, J. C. (1999). “On matching brain volumes.” Pattern Recognition, 32(1), 99-112. Lester, H., and Arridge, S. R. (1999). “A survey of hierarchical non-linear medical image registration.” Pattern Recognition, 32(1), 129-149. Maintz, J., and Viergever, M. (1998). “A survey of medical image registration.” Medical

Image Analysis, 2(1), 1-36. 6.

7.

8.

Maurer, C., and Fitzpatrick, J. (1993). “A review of medical image registration.” Interactive image guided neurosurgery, American association of neurological surgeons, pp.17-44. McInerney, T., and Terzopoulos, D. (1996). “Deformable models in medical image analysis: a survey.” Medical Image Analysis, 1(2), 91-108. Zitova, B., and Flusser, J. (2003). “Image registration methods: a survey.” Image and Vision Computing, 21(11), 977-1000. C. Barillot, Visages U746, IRISA, Rennes


68

May 08

Research Papers on deformable registration (1) 1.

2.

3.

4.

5.

6.

7.

8.

Ashburner, J., and Friston, K. J. (1999). “Nonlinear Spatial Normalization Using Basis Functions.” Human Brain Mapping, 7(4), 254-266. Bajcsy, R., and Kovacic, S. (1989). “Multiresolution Elastic Matching.” Computer Vision Graphics and Image Processing, 46, 1-21. 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. Christensen, G., Rabbit, R., and Miller, M. (1996). “Deformable templates using large deformation kinematics.” IEEE trans image processing, 5(10), 1435-1447. Christensen, G. E., and Johnson, H. J. (2001). “Consistent image registration.” IEEE Transactions on Medical Imaging, 20(7), 568 - 582. 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), 12711294. 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. Corouge, I., Dojat, M., and Barillot, C. (2004). “Statistical shape modeling of low level visual area borders.” Medical Image Analysis, 8(3), 353-360. C. Barillot, Visages U746, IRISA, Rennes


2.

3.

4.

5.

6.

7.

8.

Corouge, I., Hellier, P., Gibaud, B., and Barillot, C. (2003). “Interindividual functional mapping: a nonlinear local approach.” NeuroImage, 19(4), 1337-1348. 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. 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. 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. 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. 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. 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. 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. C. Barillot, Visages U746, IRISA, Rennes


69

May 08


2.

3.

4.

5.

6.

7.

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. 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. 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. 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. Thirion, J.-P. (1998). “Image matching as a diffusion process: an analogy with {Maxwell's} demons.” Medical Image Analysis, 2(3), 243-260. 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. 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. C. Barillot, Visages U746, IRISA, Rennes

Research Papers on deformable registration (4)

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. C. Barillot, Visages U746, IRISA, Rennes


70

May 08

Other related research paper 1.

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

Computing Surveys, 27(3), 433-467. 2.

3.

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. 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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Medical Image Registration - MIV

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