MIDAG@UNCMIDAG@UNC

Medical Image Synthesis Medical Image Synthesis via Monte Carlo Simulationvia Monte Carlo SimulationMedical Image Synthesis Medical Image Synthesis

via Monte Carlo Simulationvia Monte Carlo SimulationAn Application of Statistics in GeometryAn Application of Statistics in Geometry

&&Building a Geometric Model with CorrespondenceBuilding a Geometric Model with Correspondence

James Z. Chen, Stephen M. Pizer, James Z. Chen, Stephen M. Pizer,

Edward L. Chaney, Sarang Joshi, Joshua StoughEdward L. Chaney, Sarang Joshi, Joshua Stough

Presented by: Joshua StoughPresented by: Joshua StoughMedical Image Display & Analysis Group, UNCMedical Image Display & Analysis Group, UNC

midag.cs.unc.edumidag.cs.unc.edu

An Application of Statistics in GeometryAn Application of Statistics in Geometry&&

Building a Geometric Model with CorrespondenceBuilding a Geometric Model with Correspondence

James Z. Chen, Stephen M. Pizer, James Z. Chen, Stephen M. Pizer,

Edward L. Chaney, Sarang Joshi, Joshua StoughEdward L. Chaney, Sarang Joshi, Joshua Stough

Presented by: Joshua StoughPresented by: Joshua StoughMedical Image Display & Analysis Group, UNCMedical Image Display & Analysis Group, UNC

midag.cs.unc.edumidag.cs.unc.edu

MIDAG@UNCMIDAG@UNC

Population Simulation Requires Statistical Population Simulation Requires Statistical Profiling of ShapeProfiling of Shape

Population Simulation Requires Statistical Population Simulation Requires Statistical Profiling of ShapeProfiling of Shape

Goal: Develop a methodology for generating realistic synthetic medical images AND the attendant “ground truth” segmentations for objects of interest.

Why: Segmentation method evaluation.

How: Build and sample probability distribution of shape.

Goal: Develop a methodology for generating realistic synthetic medical images AND the attendant “ground truth” segmentations for objects of interest.

Why: Segmentation method evaluation.

How: Build and sample probability distribution of shape.

MIDAG@UNCMIDAG@UNC

Basic IdeaBasic IdeaBasic IdeaBasic Idea

New images via New images via deformation of template deformation of template geometry and image.geometry and image.

CharacteristicsCharacteristics Legal images represent Legal images represent

statistical variation of statistical variation of shape over a training set.shape over a training set.

Image quality as in a Image quality as in a clinical setting.clinical setting.

New images via New images via deformation of template deformation of template geometry and image.geometry and image.

CharacteristicsCharacteristics Legal images represent Legal images represent

statistical variation of statistical variation of shape over a training set.shape over a training set.

Image quality as in a Image quality as in a clinical setting.clinical setting.

Ht

MIDAG@UNCMIDAG@UNC

The ProcessThe ProcessThe ProcessThe Process

James Chen

MIDAG@UNCMIDAG@UNC

RegistrationRegistrationRegistrationRegistration

Registration – Composition of Two TransformationsRegistration – Composition of Two Transformations Linear – MIRIT, Frederik MaesLinear – MIRIT, Frederik Maes

Affine transformation, 12 dofAffine transformation, 12 dof Non-linear–Deformation Diffeomorphism, JoshiNon-linear–Deformation Diffeomorphism, Joshi

For all For all IItt , , IItt H Htt((II00) and ) and SStt H Htt((SS00))

Registration – Composition of Two TransformationsRegistration – Composition of Two Transformations Linear – MIRIT, Frederik MaesLinear – MIRIT, Frederik Maes

Affine transformation, 12 dofAffine transformation, 12 dof Non-linear–Deformation Diffeomorphism, JoshiNon-linear–Deformation Diffeomorphism, Joshi

For all For all IItt , , IItt H Htt((II00) and ) and SStt H Htt((SS00))

MIDAG@UNCMIDAG@UNC

Consequence of an Erroneous HConsequence of an Erroneous HttConsequence of an Erroneous HConsequence of an Erroneous Htt

James Chen

MIDAG@UNCMIDAG@UNC

Generating the Statistics of HGenerating the Statistics of HttGenerating the Statistics of HGenerating the Statistics of Htt

James Chen

MIDAG@UNCMIDAG@UNC

Fiducial Point ModelFiducial Point ModelFiducial Point ModelFiducial Point Model

HHtt isis locally correlated locally correlated

Fiducial point choice via Fiducial point choice via greedy iterative algorithmgreedy iterative algorithm

HHtt'' determined by Joshi determined by Joshi

Landmark Deformation Landmark Deformation Diffeomorphism Diffeomorphism

The Idea: Decrease The Idea: Decrease

HHtt isis locally correlated locally correlated

Fiducial point choice via Fiducial point choice via greedy iterative algorithmgreedy iterative algorithm

HHtt'' determined by Joshi determined by Joshi

Landmark Deformation Landmark Deformation Diffeomorphism Diffeomorphism

The Idea: Decrease The Idea: Decrease

MIDAG@UNCMIDAG@UNC

FPM Generation AlgorithmFPM Generation AlgorithmFPM Generation AlgorithmFPM Generation Algorithm

1. Initialize {Fm} with a few geometrically salient points on S0;

2. Apply the training warp function Ht on {Fm} to get the warped

fiducial points: Fm,t = Ht(Fm);

3. Reconstruct the diffeomorphic warp field H't for the entire image

volume based on the displacements {Fm,t – Fm};

4. For each training case t, locate the point pt on the surface of S0

that yields the largest discrepancy between Ht and H't;

5. Find most discrepant point p over the point set {pt} established

from all training cases. Add p to the fiducial point set;

6. Return to step 2 until a pre-defined optimization criterion has been reached.

MIDAG@UNCMIDAG@UNC

A locally accurate warp via FPM landmarksA locally accurate warp via FPM landmarksA locally accurate warp via FPM landmarksA locally accurate warp via FPM landmarks

Volume overlapVolume overlap optimizationoptimization criterion trackscriterion tracks mean warpmean warp discrepancydiscrepancy

Under 100 fiducialUnder 100 fiducial points, ofpoints, of thousands onthousands on surfacesurface

Volume overlapVolume overlap optimizationoptimization criterion trackscriterion tracks mean warpmean warp discrepancydiscrepancy

Under 100 fiducialUnder 100 fiducial points, ofpoints, of thousands onthousands on surfacesurface

ATLASATLAS WARPWARP TRAININGTRAINING

MIDAG@UNCMIDAG@UNC

Human Kidney ExampleHuman Kidney ExampleHuman Kidney ExampleHuman Kidney Example

36 clinical CT 36 clinical CT images in the images in the training settraining set

Monotonic Monotonic OptimizationOptimization

88 fiducial points 88 fiducial points sufficiently mimick sufficiently mimick inter-human rater inter-human rater results (94% volume results (94% volume overlap)overlap)

36 clinical CT 36 clinical CT images in the images in the training settraining set

Monotonic Monotonic OptimizationOptimization

88 fiducial points 88 fiducial points sufficiently mimick sufficiently mimick inter-human rater inter-human rater results (94% volume results (94% volume overlap)overlap)

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

32 42 52 62 72 82 92

Fiducial Points

Dis

tanc

es (i

n vo

xel u

nits

)

91.0

91.5

92.0

92.5

93.0

93.5

94.0

94.5

95.0

Volu

me

Ove

rlap

(%)

<Closest Surface Distance>

<Ht-H't Surface Distance>

<Volume Overlap>

MIDAG@UNCMIDAG@UNC

Fiducial Point Model Is an Object Representation Fiducial Point Model Is an Object Representation with Positional Correspondencewith Positional Correspondence

Fiducial Point Model Is an Object Representation Fiducial Point Model Is an Object Representation with Positional Correspondencewith Positional Correspondence

Positional Positional correspondence is via correspondence is via the Hthe H'' interpolated from interpolated from the displacements at the the displacements at the fiducial pointsfiducial points

The correspondence The correspondence makes this makes this representation suitable representation suitable for statistical analysisfor statistical analysis

Positional Positional correspondence is via correspondence is via the Hthe H'' interpolated from interpolated from the displacements at the the displacements at the fiducial pointsfiducial points

The correspondence The correspondence makes this makes this representation suitable representation suitable for statistical analysisfor statistical analysis

MIDAG@UNCMIDAG@UNC

Statistical Analysis of the Geometry RepresentationStatistical Analysis of the Geometry RepresentationStatistical Analysis of the Geometry RepresentationStatistical Analysis of the Geometry Representation

James Chen

MIDAG@UNCMIDAG@UNC

Principal Components Analysis of the FPM Principal Components Analysis of the FPM DisplacementsDisplacements

Principal Components Analysis of the FPM Principal Components Analysis of the FPM DisplacementsDisplacements

Points in 3M-d spacePoints in 3M-d space Analyze deviation from meanAnalyze deviation from mean

Example: Example: first seven modes of FPM cover 88% of the total variation.

Points in 3M-d spacePoints in 3M-d space Analyze deviation from meanAnalyze deviation from mean

Example: Example: first seven modes of FPM cover 88% of the total variation.

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7

Modes

Varia

tion

Cove

rage

(%)

Component Coverage

Accumulative Coverage

MIDAG@UNCMIDAG@UNC

Modes of Variation – Human KidneyModes of Variation – Human KidneyModes of Variation – Human KidneyModes of Variation – Human Kidney

-2-2 +2+2-1-1 +1+1

II

IIII

IIIIII

ATLASATLAS

MEANMEAN

MIDAG@UNCMIDAG@UNC

Generating Samples of Image Intensity PatternsGenerating Samples of Image Intensity PatternsGenerating Samples of Image Intensity PatternsGenerating Samples of Image Intensity Patterns

James Chen

MIDAG@UNCMIDAG@UNC

ResultsResultsResultsResults

James Chen

MIDAG@UNCMIDAG@UNC

ResultsResultsResultsResults

MIDAG@UNCMIDAG@UNC

MiscellaneousMiscellaneousMiscellaneousMiscellaneous

National Cancer Institute Grant P01 CA47982National Cancer Institute Grant P01 CA47982 National Cancer Institute Grant P01 CA47982National Cancer Institute Grant P01 CA47982ReferencesGerig, G., M. Jomier, M. Chakos (2001). “Valmet: A new validation tool for assessing and improving 3D object

segmentation.” Proc. MICCAI 2001, Springer LNCS 2208: 516-523.

Cootes, T. F., A. Hill, C.J. Taylor, J. Haslam (1994). “The Use of Active Shape Models for Locating Structures in Medical Images.” Image and Vision Computing 12(6): 355-366.

Rueckert, D., A.F. Frangi, and J.A. Schnabel (2001). “Automatic Construction of 3D Statistical Deformation Models Using Non-rigid Registration.” MICCAI 2001, Springer LNCS 2208: 77-84.

Christensen, G. E., S.C. Joshi and M.I. Miller (1997). “Volumetric Transformation of Brain Anatomy.” IEEE Transactions on Medical Imaging 16: 864-877.

Joshi, S., M.I. Miller (2000). “Landmark Matching Via Large Deformation Diffeomorphisms.” IEEETransactions on Image Processing.

Maes, F., A. Collignon, D. Vandermeulen, G. Marchal, P. Suetens (1997). “Multi-Modality Image Registration by Maximization of Mutual Information.” IEEE-TMI 16: 187-198.

Pizer, S.M., J.Z. Chen, T. Fletcher, Y. Fridman, D.S. Fritsch, G. Gash, J. Glotzer, S. Joshi, A. Thall, G. Tracton, P. Yushkevich, and E. Chaney (2001). “Deformable M-Reps for 3D Medical Image Segmentation.” IJCV, submitted.