MRI preprocessing
and
segmentation
Bias References
Segmentation References
Segmentation pipeline
Validation
Clarke, 1995
1. Preprocessing
1.1. Brain extraction
1.2. Removal of field inhomogeneities (bias-field)
1.1. Brain extraction
MRI of head
Intracranial volume
Extracted brain
1.1. Brain extraction
FSL: Initiate a mesh inside the skull and expand-wrap onto brain surface
Huh, 2002 method:
go to mid sagittal, find brain,
copy mask on adjacent slices
correct the copied mask
1.1. Brain extraction
initial mask
adjacent slice j
challenge
mask of slice j
Huh, 2002
1.1. Brain extraction
restoring truncated boundary
Let voxel have a value 1
if its intensity is higher than t
(determine t arbitrarily,
increase when needed)
1.2. Removal of field inhomogeneities
Bias field
Phantom studies:
Typical signal falloff
in SI direction is 20%
intensity
S
20 %
x
I
1.2. Removal of field inhomogeneities
Statistical methods: probabilistic, gaussian and mixture models of bias-field
Polynomial methods: smooth polynomial fit to bias-field
1.2. Removal of field inhomogeneities
Polynomial method example:
Milchenko, 2006
Milchenko, 2006
1.2. Removal of field inhomogeneities
orig
bias
model
result
Shattuck, 2001
2. Feature extraction
Features:
- Intensities in a single MRI: univariate classification
- Feature vector from a single MRI: multi-variate class.
ex: [I(x,y,z) f(N(x,y,z)) g(N(x,y,z))]
where N : neighbourhood around (x,y,z)
f: distribution of I in neighborhood (entropy
g: average I in neighborhood
or
f, g specify edge or boundary information
- Intensities in multiple MRIs with different contrast:
multi-variate (multi-spectral)
3. Segmentation
3 tissue types:
CSF, GM, WM
4 regions:
R1: air, scalp, fat, skull (background, removed)
R2: subarachnoid space (CSF)
R3: parenchyma (GM, WM)
R4: ventricles(CSF)
3. Segmentation
(T1 weighted)
(dual echo:T2, PD or
T1, T2, PD weighted)
Clarke, 1995
3. Segmentation
T1 weighted, single intensity
3.1. Histogram based
thresholding
3.2. Bayesian
dual echo:T2, PD or
T1, T2, PD weighted
or
T1 weighted
with feature vector
Unsupervised
Supervised
Parametric
3.3. Max. Likelihood
Non-parametric
3.4. k-NN
3.6. k-means 3.7. fuzzy
ANN
cmeans
3.5. MLP
3.1. Histogram based thresholding
WM
GM
Lcp crossing point
of tangents
Histogram of extracted, bias corrected brain in T1-weighted MRI
L = g * Lcp (set g manually on 80 images)
if I(x,y,z) < L then GM else WM
Schnack, 2001
3.2. Bayesian segmentation
GM
WM
Population1
Population2
(#of voxels/#ofallvoxels in the brain)
Population3
(intensity)
Hypothetical distributions
3.2. Bayes’ classifier
For each voxel, x,y,z:
Assume K tissue types (for eg. T1, T2, ..., Tk) possible, for 1 observed intensity, I:
setup graphs above
from regional data
P(Tj ! I) =
GM, WM, CSF ratios
from volumetric studies
P(I ! Tj) . P(Tj)
Ξ P(I ! Tk). P(Tk)
k
J,k=1,2,3:
1: CSF, 2: GM, 3:WM
Decide on tissue type m if:
P(Tm ! I) > P(Tj ! I) for all j
Kovacevic, 2002
Methods based on
feature vector or multi-spectral data
Supervised vs unsupervised Methods
Supervised:
- Color indicates known classes
- Separation contour is to be found
during training phase
- Separation contour is used for
classification during recall phase
Unsupervised:
- No color, classes unknown
- Clusters are found during training
phase
- Association with clusters are made
during recall phase
PD weighted
image
intensity
intensity
voxel x,y,z
T2 weighted
Kovacevic, 2001
T2 weighted
image
Suckling, 1999
3.3. Maximum likelihood classifier
- Assume the distribution P(I ! Tj) in Bayes can be obtained by a
mixture of Gaussian or Normal distribution
- Estimate means and co-variance matrix
- For better results use Hidden Markov fields within
neighborhoods
15 classes
Zavaljevski, 2000
3.3. Maximum likelihood classifier
Zavaljevski, 2000
Normal subject
Stroke patient
3.4. K-NN, K-Nearest neighbor classifier
Hypothetical distribution
T2 intensity
T1 intensity
- k is always odd, 1<k<15 (as k increases comput time increases)
- given a point p find k closest samples known from before
- decide on class m where m is the highest number of
classes among these k samples
3.4. K-NN classifier
Uses 5 different contrast MRIs
manual
labels
k=1
k=45
Vrooman, 2007
atlas labels
with linear reg.
atlas labels
with non-lin reg.
3.5. ANN, MLP classifier
for segmentation,
M = 3, 3 classes
:F
MLP
Architecture:
1 layer:
linear contour
>1 layers:
complex contours
countours are
used for class
separation
transfer fcn: sigmoid
feature vector
W1 W3
3.5. ANN, MLP classifier
Results
This page is empty on purpose
3.6. k-means classifier
This classifier is not used much in segmentation,
but explained here as an introduction to fuzzy c-means
Algorithm:
- k is equal to number of classes
- choose k arbitrary initial seed points (*)
- assume seed points are class centroids
1 for each sample point j,
find distance to all k centroids
Let j belong to class m if j is closest
to centroid m
2 for each class k, recalculate centroids
repeat steps 1 and 2 above until
no change in centroids
Note how class assignments change
at each iteration
Minimized measure:
3.7. fuzzy c-means (FCM) classifier
k-means classifier
U: membership
row=each sample x
col=each class
minimized cost
FCM classifier
3.7. fuzzy c-means (FCM) classifier
Initialize U=[uij] matrix, U(0)
initial
At k-step: calculate the centers vectors C(k)=[cj] with U(k)
Update U(k) , U(k+1)
If || U(k+1) - U(k)||<
iteration 8
then STOP; otherwise return to step 2.
iteration 37
3.7. fuzzy c-means classifier
Results
4. Validation
Important issues:
- Partial volume effect, visualization
- Validation in manually segmented image
- Performance comparison with other methods on simulated image:
Ex: Brainweb from Mcgill
4. Validation
Clark, 2006
Partial volume effect
for boundary separation
Shattuck, 2001
segmented
gold std corrrect
WM
misclassified
(colored by subejct number
there are a total of 10 subjects)