Computational Anatomy:
VBM and Alternatives
Overview
* Volumetric differences
* Serial Scans
* Jacobian Determinants
*
*
*
*
Voxel-based Morphometry
Multivariate Approaches
Difference Measures
Another approach
Deformation Field
Original
Warped
Deformation field
Template
Jacobians
Jacobian Matrix (or just “Jacobian”)
Jacobian Determinant (or just “Jacobian”) - relative volumes
Serial Scans
Early
Late
Difference
Data from the
Dementia Research
Group, Queen Square.
Regions of expansion and contraction
* Relative
volumes
encoded in
Jacobian
determinants.
Late
Warped early
Early
Difference
Late CSF
Relative volumes
Early CSF
CSF “modulated” by
relative volumes
Late CSF - modulated CSF
Late CSF - Early CSF
Smoothed
Smoothing
Smoothing is done by convolution.
Each voxel after smoothing effectively
becomes the result of applying a weighted
region of interest (ROI).
Before convolution
Convolved with a circle
Convolved with a Gaussian
Overview
* Volumetric differences
* Voxel-based Morphometry
* Method
* Interpretation Issues
* Multivariate Approaches
* Difference Measures
* Another approach
Voxel-Based Morphometry
* Produce a map of statistically significant differences
among populations of subjects.
* e.g. compare a patient group with a control group.
* or identify correlations with age, test-score etc.
* The data are pre-processed to sensitise the tests to
regional tissue volumes.
* Usually grey or white matter.
* Can be done with SPM package, or e.g.
* HAMMER and FSL
http://oasis.rad.upenn.edu/sbia/
http://www.fmrib.ox.ac.uk/fsl/
Pre-processing for Voxel-Based
Morphometry (VBM)
SPM5 Segmentation includes Warping
Tissue probability
maps are deformed
to match the image
to segment
g
a0
a
Ca
c1
y1
m
c2
y2
s2
c3
y3
b
cI
yI
Cb
b0
SPM5b Pre-processed data for four subjects
Warped, Modulated Grey Matter
12mm FWHM Smoothed Version
Validity of the statistical tests in SPM
* Residuals are not normally distributed.
* Little impact on uncorrected statistics for
experiments comparing groups.
* Invalidates experiments that compare one subject
with a group.
* Corrections for multiple comparisons.
* Mostly valid for corrections based on peak heights.
* Not valid for corrections based on cluster extents.
* SPM makes the inappropriate assumption that the
smoothness of the residuals is stationary.
* Bigger blobs expected in smoother regions.
Interpretation Problem
* What do the blobs really mean?
* Unfortunate interaction between the algorithm's spatial
normalization and voxelwise comparison steps.
* Bookstein FL. "Voxel-Based Morphometry" Should Not Be
Used with Imperfectly Registered Images. NeuroImage
14:1454-1462 (2001).
* W.R. Crum, L.D. Griffin, D.L.G. Hill & D.J. Hawkes. Zen
and the art of medical image registration: correspondence,
homology, and quality. NeuroImage 20:1425-1437 (2003).
* N.A. Thacker. Tutorial: A Critical Analysis of Voxel-Based
Morphometry. http://www.tina-vision.net/docs/memos/2003011.pdf
Some Explanations of the Differences
Mis-classify
Mis-register
Folding
Thickening
Thinning
Mis-register
Mis-classify
Overview
* Volumetric differences
* Voxel-based Morphometry
* Multivariate Approaches
* Scan Classification
* Difference Measures
* Another approach
“Globals” for VBM
* Shape is multivariate
* Dependencies among
volumes in different
regions
* SPM is mass univariate
* “globals” used as a
compromise
* Can be either ANCOVA or
proportional scaling
Where should any
difference between the two
“brains” on the left and that
on the right appear?
Training and Classifying
?
?
Patient
Training Data
Control
Training Data
?
?
Classifying
?
?
Patients
Controls
?
?
y=f(wTx+w0)
Support Vector Classifier (SVC)
Support Vector Classifier (SVC)
Support
Vector
Support
Vector
Support
Vector
w is a weighted linear
combination of the
support vectors
Nonlinear SVC
Regression (e.g. against age)
Overview
*
*
*
*
Volumetric differences
Voxel-based Morphometry
Multivariate Approaches
Difference Measures
* Derived from Deformations
* Derived from Deformations + Residuals
* Another approach
Distance Measures
* Classifiers such as SVC use measures of distance
between data points (scans).
* I.e. measure of how different each scan is from each other
scan.
* Distance measures can be derived from
deformations.
Deformation Distance Summary
•Deformations can be considered within a small or
large deformation setting.
•Small deformation setting is a linear approximation.
•Large deformation setting accounts for the nonlinear nature of
deformations.
• Miller, Trouvé, Younes “On the Metrics and Euler-Lagrange
Equations of Computational Anatomy”. Annual Review of
Biomedical Engineering, 4:375-405 (2003) plus supplement
• Beg, Miller, Trouvé, L. Younes. “Computing Large Deformation
Metric Mappings via Geodesic Flows of Diffeomorphisms”. Int.
J. Comp. Vision, 61:1573-1405 (2005)
Computing the geodesic: problem statement
I0: Template I1:Target

Problem Statement: Given I0 and I1 , compute v such that
1


arg min   Lv ( y , t ), Lv( y , t ) dydt   I0 ( ( y,1))  I1 dy
v
0
1
2

 1
where
( y , t )  ty 1 ( y, t )v( y, t )
t
Slide from Tilak Ratnanather
One-to-One Mappings
* One-to-one mappings
between individuals
break down beyond a
certain scale
* The concept of a
single “best” mapping
may become
meaningless at higher
resolution
Pictures taken from
http://www.messybeast.com/freak-face.htm
Overview
*
*
*
*
*
Volumetric differences
Voxel-based Morphometry
Multivariate Approaches
Difference Measures
Another approach
Anatomist/BrainVISA Framework
* Free software available from:
http://brainvisa.info/
* Automated identification and labelling of sulci etc.
* These could be used to help spatial normalisation etc.
* Can do morphometry on sulcal areas, etc
* J.-F. Mangin, D. Rivière, A. Cachia, E. Duchesnay, Y. Cointepas, D.
Papadopoulos-Orfanos, D. L. Collins, A. C. Evans, and J. Régis. ObjectBased Morphometry of the Cerebral Cortex. IEEE Trans. Medical Imaging
23(8):968-982 (2004)
Design of an artificial neuroanatomist
Elementary
folds
3D
retina
Fields of
view of
neural nets
Bottom-up
flow
Sulci
Correlates of handedness
14 subjects
128 subjects
Central sulcus
surface is larger
in dominant hemisphere
Some of the potentially interesting
posters
* (#728 T-PM ) A Matlab-based toolbox to facilitate multi-voxel pattern
classification of fMRI data.
* (#699 T-AM ) Pattern classification of hippocampal shape analysis in a
study of Alzheimer's Disease
* (#697 M-AM ) Metric distances between hippocampal shapes predict
different rates of shape changes in dementia of Alzheimer type and
nondemented subjects: a validation study
* (#721 M-PM ) Unbiased Diffeomorphic Shape and Intensity Template
Creation: Application to Canine Brain
* (#171 T-AM ) A Population-Average, Landmark- and Surface-based
(PALS) Atlas of Human Cerebral Cortex
* (#70 M-PM ) Cortical Folding Hypotheses: What can be inferred from
shape?
* (#714 T-AM ) Shape Analysis of Neuroanatomical Structures Based on
Spherical Wavelets