Shape analysis to assess
neurodevelopment and
neurodegeneration
Guido Gerig, UNC Chapel Hill
IPAM June, 2004
Acknowledgements:
Martin Styner, Sarang Joshi, Stephen
Pizer, Tom Fletcher, Tim Terriberry
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
•
•
•
•
•
Motivation
(Neuroimaging)
Driving Clinical Questions
Shape/Manifolds
Applications of Shape Analysis:
♦ Hippocampal morphology in SZ
♦ Twin study:
• Shape similarity vs. genetic similarity
• Identical twins discordant for SZ
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Neuroimaging
• Multidisciplinary
♦
♦
♦
♦
♦
♦
♦
♦
Radiology, Imaging Research
Psychiatry, Psychology, Neurology
Computer Science
Mathematics, Applied Math
(Bio)Statistics
Biomedical Engineering
Biology
….
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
The ethics of brain science
Open your mind
May 23rd 2002
From The Economist print edition
Genetics may yet threaten privacy, kill autonomy,
make society homogeneous and gut the concept of
human nature. But neuroscience could do all of
these things first
Courtesy of Bruce Rosen, A.A. Martinos Center, Boston
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Neuromaging
• Sampling of anatomy: Aperture /
Scale
• Measurement of physical properties
• Multimodal Imaging
• Longitudinal follow-up
• Link from in-vivo imaging to ex-vivo
tissue analysis
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
“Conventional” Imaging
Dual-Echo Spin-Echo
1x1x3mm3
Tradeoff
Tissue Contrast / Spatial Resolution
T1 Gradient Echo
1x1x1.5mm3
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
3Tesla Siemens UNC W. Lin
2D FSE 1x1x1mm3 (T2w, PDw), T1 MPRage 1x1x1mm3
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
3D T2w FSE 1x1x1mm3
John Mugler, Radiology 2000
1.5T GE, T2w 1x1x1mm3, single 9.4minute 3D acquisition
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Henri M. Duvernoy, The Human Hippocampus:
An Atlas of Applied Anatomy, Springer-Verlag, New York, 1988, Fig. 2., p. 15
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Hippocampus seen by different
pulse sequences
3T, T1 PRage and T2w FSE, 1mm3
1.5T, T2w, 1.5mm3
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Visible Human 1.0 (180um)
Peter Ratiu, BWH (NLM Project)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Neonatal scans: 3T MRI
T1 3D MPRage
1x1x1 mm3
FSE T2w
1x1x2 mm3
FSE PDw
1x1x2 mm3
3T Siemens Allegra, UNC Weili Lin:
Scan Time: Structural MRI (T1, SpinEcho): 8min, DTI: 4min -> 12 Min tot
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
a
b
c
d
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Longitudinal Analysis in
Schizophrenia Study
baseline
6 months
growth
18 months
shrinking
Difference 6mt - baseline
Difference 18mt - 6mt
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Fluid Deformation Baseline to 6mt
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Validation: Duke Quality Control
WM/GM/CSF volumes for atlas based segmentation
600
Volume ccm
• Dataset: Same subject
scanned 2-times (24 hour
window) at 5 different sites
(4 GE, 1 Philips) within 60
days
• Automatic brain tissue
segmentation using threechannel (T1, T2w, PDw) MRI
• Results show excellent
reliability and stability of
multi-site scanning and brain
tissue segmentation
450
300
150
0
GE1 GE1 GE2 GE2 GE3 GE3 GE4 GE4 PH
PH
GM 558 557 538 535 552 558 571 578 571 564
WM 158 155 148 148 151 152 155 162 160 158
CSF 369 379 359 364 377 372 379 367 370 363
M. Styner, C. Charles, J. Park, G. Gerig, Multisite validation of image analysis methods
- Assessing intra and inter site variability, Proc. SPIE MedIm ‘02, 09/2002
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Atlas-based EM Segmentation of
multi-modal MRI
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Reliability of Segmentation
QC control series (Cecil Charles, Duke University), EM-Segmentation UNC
(Same subject, four GE 1.5T scanners with 2 replications, several months)
case1
Tot. icc
csf
gm
wm
case2
case3
case4
case5
case6
case7
case8
ave
stdev
1085701
1083892
1098832
1097972
1080694
1078151
1099079
1101917
1090779.75
99.53%
99.37%
100.74%
100.66%
99.08%
98.84%
100.76%
101.02%
100.00%
135359
138407
138734
137304
134278
133389
135322
135156
135993.63
99.53%
101.77%
102.02%
100.96%
98.74%
98.08%
99.51%
99.38%
100.00%
554315
551559
562860
560928
553880
554499
562317
565207
558195.63
99.30%
98.81%
100.84%
100.49%
99.23%
99.34%
100.74%
101.26%
100.00%
396027
393926
397238
399740
392536
390263
401440
401554
396590.50
99.86%
99.33%
100.16%
100.79%
98.98%
98.40%
101.22%
101.25%
100.00%
coefvar
9591.11
0.88%
1939.59
1.43%
5165.28
0.93%
4181.35
1.05%
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
E
scans
FS
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ho
1
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CNR
10.00
9.00
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7.00
6.00
5.00
4.00
3.00
2.00
1.00
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Evaluation of MRI Acquisition
protocols
CNR cortical gray/white
CNR csf/cortical gray
6.00
5.00
4.00
3.00
2.00
1.00
0.00
scans
Contrast to Noise Ratio as a function of field strength, spatial
resolution, and pulse sequence
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Summary Imaging
• Multimodal: better tissue contrast
• Spatial resolution: Scale at which we do the
measurements
• Noninvasive, in-vivo imaging: Longitudinal
Follow-up
• Todo: Validation, cross-comparison
• Open issues:
♦ Technology change: compatibility
♦ Different sequences: Do we measure the same
properties?
♦ Scale, resolution, level of details
♦ Inter-site calibration, standardization
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clinical Neuroimaging
Research Projects at UNC
• Schizophrenia Research
♦
♦
♦
♦
♦
•
•
•
•
•
•
•
Neonatal Study: Infants at Risk
Prodromal (subjects at risk)
First Episode FE
Schizo-affected adolescents(TAPS)
Treatment Studies (CHOR, CATIE)
Autism / Fragile-X (w. Stanford)
Twin Study / Sibling Study
Neurodevelopment Research Center NDRC
Surgical Planning: Tumor & Vascularity
Neonatal screening by 3D ultrasound/ 3D MRI
Neonatal twin study (heritability)
….
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Representative Clinical Study:
Neuropathology of Schizophrenia
• When does it develop ?
• Fixed or Progressive ?
• Neurodevelopmental or
Neurodegenerative ?
• Neurobiological Correlations ?
• Clinical Correlations ?
• Treatment Effects ?
Noninvasive neuroimaging studies using MRI/fMRI to
study morphology and function
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Natural History of Schizophrenia
Stages of Illness
Premorbid Prodromal/Onset/Deterioration
Healthy


Worsening
Severity of
Signs and
Symptoms
Chronic/Residual
Deterioration
Schizophrenia is a genetic
neurodevelopmental disorder
with environmental interactions
that begins to manifest its
symptoms predominantly in the
second and third decades and
runs a progressive course.
Gestation/Birth
10 Puberty 20
30
Years
40
50
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Shape Modeling
Shape Representation:
♦ High dimensional warping
Miller,Christensen,Joshi /
Thompson,Toga / Ayache, Thirion
♦ Boundary / Surface
Bookstein /
Cootes, Taylor / Duncan,Staib /
Szekely, Gerig / Leventon, Grimson
/ Davatzikos
♦ Skeleton / Medial model Pizer /
Goland / Bouix,Siddiqui / Kimia /
Styner, Gerig
♦ Issues: Correspondence,
Invariance Properties, Scale
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Criteria for shape models
•
•
•
•
•
•
•
•
generality
stability
specificity
intuitiveness
compactness
shape and intensity
time-efficient analysis
conversion between different
modeling schemes
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Shape in Mathematics
•Kendall, Dryden and Mardia,
Bookstein, Small:
•Efficient representation of
data,transformations, shape
distributions
•Shape is all the geometrical
information that remains when
location, scale and rotational effects
are filtered out from an object.
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Data Primitives of Object
Representation
• A voxel with its intensity
value(s): (x, I)
• A landmark: x
• A boundary atom: b =
(x,n)
• A medial atom: m =
(x,F,r,q)
b
q q
x
n
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
3D Shape Representations I
Template
Raw 3D voxel model
Coarse Registration Target
Manifold
Transformation
Fluid Transformation
SNAP/IRIS tool: UNC
Miller, Joshi, Christensen, Csernansky:
Shape decoded in deformation field
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3D Shape Representations II
SPHARM
PDM
Skeleton
M-rep
Boundary, fine
scale, parametric
Boundary, fine
scale, sampled
Medial, fine
scale,
continuous,
implied surface
Medial, coarse
scale, sampled,
implied surface

r (q ,  )  
k
c
k 0 m   k
Y (q ,  )
m m
k k
m  x, r, F ,q 
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
3D Shape Representations III:
“Manifolds” for DTI tracts?
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Modeling fiber tracts: Model
curve and sweeping trajectory
Right cortico-spinal tract:
Reconstruction
Callosal tract:
Isabelle Corouge, UNC, ribbon bunles, MICCAI 2004
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I. Parametrized 3D surface models
Raw 3D voxel model
Smoothed object
Parametrized surface
Ch. Brechbuehler, G. Gerig and O. Kuebler,
Parametrization of closed surfaces for 3-D shape description,
CVIU, Vol. 61, No. 2, pp. 154-170, March 1995
A. Kelemen, G. Székely, and G. Gerig,
Three-dimensional Model-based Segmentation,
IEEE TMI, 18(10):828-839, Oct. 1999
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Surface Parametrization
Mapping single faces to spherical quadrilaterals
Latitude and longitude from diffusion
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Initial Parametrization
a) Spherical parameter space with surface net, b)
cylindrical projection, c) object with coordinate grid.
Problem: Distortion / Inhomogeneous distribution
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Parametrization after
Optimization
a) Spherical parameter space with surface net, b)
cylindrical projection, c) object with coordinate grid.
After optimization: Equal parameter area of elementary
surface facets, reduced distortion.
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Nonlinear Optimization with
Constraints
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Shape Representation by
Spherical Harmonics (SPHARM)
 x(q ,  ) 


r (q ,  )   y (q ,  ) 
 z (q ,  ) 


K
r (q ,  )  
k
m m
c
 k Yk (q ,  )
k 0 m   k
 c xkm 
 m
m
c k   c yk 
 cm 
 zk 
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Calculation of SPHARM
coefficients
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Reconstruction from
coefficients
Global shape description by expansion into spherical harmonics:
Reconstruction of the partial spherical harmonic series, using
coefficients up to degree 1 (a), to degree 3 (b) and 7 (c).
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Importance of uniform
parametrization
non-uniform
uniform
non-uniform
uniform
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Parametrization with spherical
harmonics
3
1
7
12
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Correspondence through
Normalization
Normalization using first order ellipsoid:
• Spatial alignment to major axes
• Rotation of parameter space.
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3D Natural Shape Variability:
Left Hippocampus of 90 Subjects
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Computing the statistical
model: PCA
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Major Eigenmodes of
Deformation by PCA
• PCA of parametric
shapes  Average
Shape, Major
Eigenmodes
• Major Eigenmodes
of Deformation
define shape space
 expected
variability.
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Set of Statistical Anatomical Models
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Medial Representation
•Shape Representation:
♦ High dimensional warping
Miller,Christensen,Joshi /
Thompson,Toga / Ayache, Thirion
♦ Boundary / Surface
Bookstein /
Cootes, Taylor / Duncan,Staib /
Szekely, Gerig / Leventon, Grimson
/ Davatzikos
♦ Skeleton / Medial model Pizer /
Goland / Bouix,Siddiqui / Kimia /
Styner, Gerig
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
3D Skeleton / Medial Manifold
• Generation in 3D extremly
difficult, approaches:
♦ Voronoi Diagram and pruning
(Naef & Szekely, Attali &
Montanari, Styner & Gerig)
♦ Shocks of level set evolution
(Siddiqi, Kimia)
• 3D skeleton to graph
description not yet presented
• Martin Styner: Pruning 3D VD
• Pizer et al.: Deformation of
medial template
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Model Building
VSkelTool
Medial
representation for
shape population
Styner, Gerig et al. ,
MMBIA’00 / IPMI 2001 /
MICCAI 2001 / CVPR
2001/ MEDIA 2002 / IJCV
2003 /
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Modeling of Caudate Shape
PDM
M-rep
Surface Parametrization
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
3b. Minimal sampling of
medial sheet
• Find minimal sampling given a predefined approximation error
3x6
2x6
3x12
3x7
4x12
norm. MAD error vs sampling
0.16
0.14
0.14
MAD / AVG(radius)
0.12
0.1
0.08
0.08
0.075
0.053
0.06
0.048
0.04
0.02
0
2x6
3x6
3x7
4x12
The UNIVERSITY
of NORTH CAROLINA at CHAPEL HILL
3x12
Medial models of
subcortical structures
Shapes with common m-rep model and implied boundaries
of putamen, hippocampus, and lateral ventricles.
Each structure has a single-sheet branching topology.
Medial representations calculated automatically.
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Shape Statistics and
Analysis
Guido Gerig
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Overview
• HDLSS: High Dimension and Low Sample
Size
• Correspondence:
♦ Model Quality: Specificity, Compactness,
Sensitivity
• Shape Space and Dimensionality
Reduction:
♦ Principal Component Analysis PCA
♦ Fisher Linear Discriminant
• M-rep:
♦ Principal Geodesic Analysis PGA
• Metric for shape difference/distance
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation
• Statistical models of anatomical
shape
♦ Average shape
♦ Variability of shape
• Useful for
♦ Medical image segmentation
♦ Diagnosis of disease
♦ Disease type and locality
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
I: HDLSS: High Dimension
and Low Sample Size
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
High Dimension and Low Sample Size
(HDLSS)
Complex shape represented in a very high dimensional space:
Example:
12
 x1,1 
 x1,n 




  ,  ,   
x 
x 
 d ,1 
 d ,n 
•3D Hippocampus characterized by 169x3 (n=507) dimensional
feature vector (SPHARM order 12)
•Sample size: 15 controls + 15 schizophrenics (n=30)
Common problem n << d
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Classical Multivariate Analysis
•Assume multivariate data Gaussian distributed.
 
X ~ N , 
Critical Assumption:
 invertible
•Fails for HDLSS
•Estimates of  are “sensitive”
Solution: Use lower dimensional projections
•Principal component Analysis(PCA) or “Eigen Shapes”
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Eigen Shapes (Hippocampus)
Outward
+1.5mm
Top View
-1.5mm
Inward
Mean Difference between Schiz and controls Mapped on Composite Control
First 3 Eigenshapes Shapes of the Hippocampus
•PCA - Captures the modes of
most variation in the Ensemble.
•Fisher Linear discrimination Powerful for discrimination
between populations under
common covariance different mean
assumption.
Sarang Joshi, John G. Csernansky, Lei Wang, J. Philip Miller, Mohktar Gado, Daniel Kido, John Haller, Michael I. Miller
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Object Alignment / Surface
Homology
MZ pair
DZ pair
Surface Correspondence
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Shape change relative to
anatomical coordinates
Morphing of
amygdala/hippocampal complex
between mean shapes
of NCL versus SZ
(Shenton/McCarley,
BWH Boston)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Object Alignment prior to
Shape Analysis
1stelli TR, no scal
1stelli TR, vol scal
Procrustes TRS
side
top
top
side
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Correspondence through
parameter space rotation
Parameters rotated to
first order ellipsoids
Normalization using first order ellipsoid:
•Rotation of parameter space to align major axis
•Spatial alignment to major axes
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Correspondence ctd.
Rhodri Davies and
Chris Taylor
♦ MDL criterion applied
to shape population
♦ Refinement of
correspondence to
yield minimal
description
♦ 83 left and right
hippocampal surfaces
♦ Initial correspondence
via SPHARM
normalization
♦ IEEE TMI August 2002
Homologous points before (blue)
and after MDL refinement (red).
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Correspondence ctd.
Homologous points before (blue)
and after MDL refinement (red).
MSE of reconstructed vs. original
shapes using n Eigenmodes (leave
one out). SPHARM vs. MDL
correspondence.
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Evaluation of Correspondence
• Generalization
♦ Ability to describe instances outside of
the training set
• Compactness
♦ Ability to use a minimal set of parameters
• Specificity
♦ Ability to represent only valid instances of
the object
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
SPHARM vs. MDL
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Model Compactness
• Little variance as possible
• Compactness: Cumulative variance
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Model Generalization
• Capability to represent unseen
instances of object class
• Measurement: Leave-one-out
reconstruction of objects
♦ Model with all-but-one member
♦ Fit of excluded example
♦ Approximation error between fit and
original (MAD)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Model Specificity
• Only generate instances of object
class that are similar to training
set objects
♦ Random generation of population of
instances using the model
♦ Average distance to nearest member of
training class
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Comparison of three
Correspondence Schemes
(M. Styner, MICCAI’03)
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
IV: M-rep Statistics PGA
Acknowledgement:
Tom Fletcher
Sarang Joshi
Steve Pizer
Relevant Literature: CVPR’03, IPMI’03, Fletcher et al.
Principal Geodesic Analysis for the Study ofNonlinear Statistics of
Shape, P. Thomas Fletcher, Conglin Lu, Stephen M. Pizer, and Sarang
Joshi, to appear IEEE TMI
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Modeling Anatomy
• M-rep models based on medial axis
(skeleton)
• Advantages
♦ Intuitive shape changes (bending, widening)
♦ Models interior as well as boundary
♦ Coarse-to-fine
• Tom Fletcher: PGA
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Statistics of M-reps
• M-rep parameters are not
linear
♦ Rotations
♦ Scalings
• High-dimensional, curved
space (Lie group)
• Standard linear statistics
do not apply
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Principal Geodesic Analysis
PGA
Linear Statistics (PCA)
Curved Statistics (PGA)
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Example: PGA of Hippocampus
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Example: PGA of Hippocampus
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Example: PGA of Hippocampus
Fletcher et al., TMI’04, to appear
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
V: Shape Distance Metric
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Boundary Analysis:
Shape Distance Metrics
• Pairwise MSD between
surfaces at
corresponding points
• PDM: Signed or
unsigned distance to
template at
corresponding points
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Boundary Shape Difference
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Shape Distance Metrics using
Medial Representation
radius
deformation
Local width differences (MA_rad): Growth, Dilation
Positional differences (MA_dist): Bending, Deformation
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Example: M-rep:
Local Width Difference
A
B
A minus B: Left Ventricles
-0.3
A
B
A minus B: Right Ventricles
+1.5
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Summary
Key Criteria Statistical Shape Analysis:
• Choice of shape representation:
SPHARM, PDM, M-rep, etc.
• Definition of correspondence
• Compact representation of shape
space: HDLSS problem
• Non-Euclidean framework for medial
primitives
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clinical Study: Hippocampal
Shape in Schizophrenia
• IRIS: Tool for interactive
image segmentation.
• Manual contouring in all
orthogonal sections.
• 2D graphical overlay and
3D reconstruction.
• Hippocampus
segmentation protocol
(following Duvernoy).
• Hippocampus: reliability
>0.95 intra-, >0.85 interrater)
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Hippocampal Volume Analysis
Absolute Hippocampal Volumes

4.5

4.0
3.5
3.0

2.5
2.0
Left smaller than
right
SZ smaller than
CNTRL, both left
and right
Variability SZ
larger than CNTL
1.5
1.0
Patient Left
Control Left
Patient Right
Control Right
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Example: Hippocampal
Morphometry in Schizophrenia
•Left
hippocampus
of 90 subjects
•30 Controls
•60 Schizophr.
CTRL
SZ
? Biological
variability
? Metric for
measuring
subtle
differences
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Hippocampal Shape Analysis
left
right
Left and right
hippocampus: Comparison
of mean shapes CNTL-SZ
(signed distance
magnitude relative to SZ
template)
Left
in
out
Movie: Flat tail: SZ, curved tail: CNTL
Right
Movie: Flat tail: SZ, curved tail: CNTL
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Statistical Analysis of M-rep
Shape including patient variables
• *Work in progress Keith
Muller, Emily Kistner, M.
Styner, J. Lieberman, G.
Gerig, UNC Chapel Hill
• Systematic embedding of
interaction of age, duration
of illness and drug type into
statistical shape analysis
• Correction for multiple tests
*Repeated measures ANOVA, cast as a General Linear
Multivariate Model, as in Muller, LaVange, Ramey, and
Ramey (1992, JASA). Exploratory analysis included
considering both the "UNIREP" Geisser-Greenhouse test
and the "MULTIREP" Wilks test.
Difference in hippocampus shape
between SZ and CNTRL as
measured by M-rep deformation
M-rep 3x8 mesh
Tail
Head
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Model: Row x Col x Drug (y/n)
x Age: p = 0.0097
Patient-CNTL Deformation
Difference at Age 30
AGE
Deformation at mesh nodes (mm)
Patient-CNTL Deformation
Difference at Age 40
Patient-CNTL Deformation
Difference at Age 20
Tail
Head
Difference in hippocampus shape between
patients and controls: Located mostly in the
tail of the hippocampus, becomes more
pronounced over time.
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Comparison to CNTLs
Deformation at mesh nodes (mm)
Change in hippocampus
shape over ten years for
controls
Tail
Head
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How do different shape
representations compare?
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Surface Based Analysis
Not corrected for multiple comparisons
0.001
Corrected for multiple comparisons
0.05
Posterior (L)
Lateral (L)
Posterior (R)
Lateral (R)
Significance maps of left (L) and right (R) hippocampus of
schizophrenic patients vs. healthy controls
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Boundary Analysis:
Shape Distance Metrics
• Pairwise MSD between
surfaces at
corresponding points
• PDM: Signed or
unsigned distance to
template at
corresponding points
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Medial Representation M-rep
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Comparison Surface-Medial
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Medial Shape Analysis
0.001
Not corrected for multiple comparisons
Corrected for multiple comparisons
0.05
Posterior (L)
Lateral (L)
Posterior (R)
Lateral (R)
Significance maps of left (L) and right (R) hippocampus of
schizophrenic patients vs. healthy controls
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Application: Ventricle Shape in
Twin Study
Twin Pairs:
• Monozygotic (MZ):
Identical twins
• Dizygotic (DZ): Nonidentical
twins
• MZ-Discordant (MZ-DS)
for Schizophrenia: Identical
twins: one affected, co-twin at
risk
• Nonrelated (NR):
age/gender matched
• Ventricle size and shape
• Data: D. Weinberger,
NIMH
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Application: Twin Study
Collection of ventricular shapes of 4 twin pairs (unsorted)
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Visual Comparison: Shape
similarity
MZ
DZ
Size
Normalization
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Clinical Study:
MZ twin pairs discordant for SZ
10 identical twin
pairs, ventricles
marker for SZ?
left: co-twin at
risk
right:
schizophrenics
co-twin
Data: D.
Weinberger, NIMH
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Twin Study: Volume Analysis
30000
25000
20000
15000
10000
5000
0
MZ
Total Ventricle Vol. MZ vs. DZ (mm3)
DZ
25000
20000
Twin A
Twin B
15000
Tw in B
volume (mm3)
Ventricle Volumes Twin Pairs
(MZ 1-5, DZ 6-10)
MZ
10000
DZ
Linear (MZ)
5000
1 2 3 4 5
Linear (DZ)
6 7 8 9 10
Twin Pairs
0
0
10000
20000
30000
-5000
Tw in A
• Large variability of volumes overall (CV 63%) (All healthy)
• Considerable volume differences between twin pairs
• Correlation between twin pairs: MZ: 0.93 / DZ: 0.95
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Pairwise tests among co-twins
Trend MZ < DZ < NR:
Volume similarity
correlates with
genetic difference
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Group Tests of Ventricular
Volumes
All tests
nonsignificant
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SPHARM Parametrization
T1AL / T1BL
T1BR / T1AR
T2AL / T2BL
T2BR / T2AR
Monozygotic
twin pairs
Dizygotic
twin pairs
T10AL / T10BL
T10BR / T10AR
T8AL / T8BL
T8BR / T8AR
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Global Shape Distance Metrics
• Pairwise MSD
between surfaces
• PDM: Signed or
unsigned distance
to template at
corresponding
points
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Pairwise tests among co-twins
Trend MZ < DZ < NR:
Volume similarity
correlates with
genetic difference
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Pairwise MSD shape differences
between co-twin ventricles
Shape similarity as pairwise cotwin difference: MZ < DZ < NR
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Co-twin pairwise ventricle shape
difference
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Group Tests
• Both subgroups of
the MZ discordant
twins (affected and
at risk) compared
to healthy.
• Ventricular shape:
Marker for disease
and possibly for
vulnerability (?)
Healthy All
Affected
At Risk
MZ discordant
Pairwise tests
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Group Tests of Ventricular Volumes
All tests
nonsignificant
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Group Tests: Shape Difference to Healthy
CNT
Affected AtRisk
CNT
Affected AtRisk
Mean difference from CNTL
• Both subgroups of MZ discordant for SZ (affected and at risk) differ.
• Ventricular shape seems to be marker for disease/ vulnerability (?)
• Submitted to PNAS (Dec. 2003)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Shape Analysis of
ventricles via M-reps
Timothy B. Terriberry
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Pair-based Analysis
• M-rep compared to that of twin.
• Mean difference compared between
MZ, DS, DZ, and NR groups.
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Statistics of M-reps
• M-rep parameters are not
linear
♦ Rotations
♦ Scalings
• High-dimensional, curved
space (Lie group)
• Standard linear statistics
do not apply
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Pair-based Results: Global
M-rep shape diff. ΔSL
PDM shape diff. ΔSL (Styner 2004)
200
150
100
50
0
1
2
3
4
P-values for group difference tests (results significant at 5% level in bold)
MZ vs. NR
MZ vs. DZ
MZ vs. DS
DS vs. NR
DS vs. DZ
DZ vs. NR
Position
L
R
0.0000
0.0003
0.0000
0.0137
0.1354
0.3368
0.1330
0.0018
0.1396
0.0787
0.0461
0.0136
Orientation
L
R
0.2332
0.2627
0.1356
0.0483
0.1806
0.1839
0.5981
0.5677
0.5011
0.2696
0.6335
0.7810
Radius
L
R
0.0010
0.0770
0.0003
0.0232
0.1545
0.3932
0.1798
0.1656
0.1225
0.0977
0.6019
0.6017
M-reps
Object Angle
L
R
0.6345
0.0608
0.1815
0.0236
0.1467
0.1834
0.9106
0.2097
0.4753
0.1545
0.8873
0.4947
Total
L
0.0001
0.0000
0.1611
0.0439
0.3264
0.0490
R
0.0001
0.0112
0.2337
0.0045
0.1894
0.0086
PDMs (Styner 2004)
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Conclusions
• Neuroimaging/-analysis: Strong multi-disciplinary
effort essential
• Excellent opportunities and challenges for research
• Shape represents changes not reflected by volume
analysis
• Several clinical studies: Shape discriminates better
than volume
• Open issues:
♦ Correspondence, homology
♦ Shape representations, invariants
♦ Variability/standardization of image data
• Clinical studies:
♦ Often exploratory analysis, need replication
♦ Exchange of methods and test data (ITK, BIRN)
• UNC Hippocampal Dataset: SPHARM, PDM, Def.Maps
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