MRI preprocessing and segmentation. Bias References.

MRI preprocessing and

segmentation

Bias References

Segmentation References

Segmentation pipeline

Clarke, 1995

Validation

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 slicescorrect the copied mask

1.1. Brain extraction

initial mask adjacent slice j mask of slice j

challengeHuh, 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%

S

I20 %

x

intensity

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 inhomogeneitiesPolynomial method example:

Milchenko, 2006

Milchenko, 2006

1.2. Removal of field inhomogeneities

Shattuck, 2001

orig model

bias result

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

4 regions:R1: air, scalp, fat, skull (background, removed)R2: subarachnoid space (CSF)R3: parenchyma (GM, WM)R4: ventricles(CSF)

3 tissue types:CSF, GM, WM

3. Segmentation

Clarke, 1995

(T1 weighted)(dual echo:T2, PD or T1, T2, PD weighted)

3. Segmentation

T1 weighted, single intensity dual echo:T2, PD or T1, T2, PD weighted

or T1 weighted

with feature vector3.1. Histogram based

thresholding

Unsupervised

3.6. k-means 3.7. fuzzy cmeans

Supervised

Parametric Non-parametric ANN

3.3. Max. Likelihood 3.4. k-NN 3.5. MLP

3.2. Bayesian

3.1. Histogram based thresholding

Schnack, 2001

WM

GM

Histogram of extracted, bias corrected brain in T1-weighted MRI

Lcp crossing point of tangents

L = g * Lcp (set g manually on 80 images)if I(x,y,z) < L then GM else WM

Population1

Population2

Population3

3.2. Bayesian segmentation

WMGM

Hypothetical distributions

(intensity)

(#of voxels/#ofallvoxels in the brain)

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:

P(Tj ! I) = P(I ! Tj) . P(Tj)

Ξ P(I ! Tk). P(Tk) k

GM, WM, CSF ratiosfrom volumetric studies

setup graphs above from regional data

Decide on tissue type m if: P(Tm ! I) > P(Tj ! I) for all j

Kovacevic, 2002

J,k=1,2,3:1: CSF, 2: GM, 3:WM

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

Kovacevic, 2001

T2 weightedvoxel x,y,z

PD weightedimage

T2 weightedimage

intensity

intensity

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

Zavaljevski, 2000

15 classes

3.3. Maximum likelihood classifier

Zavaljevski, 2000

Normal subject Stroke patient

3.4. K-NN, K-Nearest neighbor classifier

T1 intensity

T2 intensity

Hypothetical distribution

- 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

k=1 k=45

manual atlas labels atlas labels labels with linear reg. with non-lin reg.

Vrooman, 2007

Uses 5 different contrast MRIs

MLPArchitecture:1 layer: linear contour

>1 layers: complex contours

countours areused for classseparation

transfer fcn: sigmoid

W1 W3

:F

3.5. ANN, MLP classifier

for segmentation,M = 3, 3 classes

feature vector

3.5. ANN, MLP classifier

Results

This page is empty on purpose

3.6. k-means classifier

Algorithm:- k is equal to number of classes- choose k arbitrary initial seed points (*)- assume seed points are class centroids1 for each sample point j, find distance to all k centroids Let j belong to class m if j is closest to centroid m2 for each class k, recalculate centroids

repeat steps 1 and 2 above until no change in centroids

Note how class assignments changeat each iteration

Minimized measure:

This classifier is not used much in segmentation, but explained here as an introduction to fuzzy c-means

3.7. fuzzy c-means (FCM) classifier

k-means classifier FCM classifier

U: membership row=each sample xcol=each class

minimized cost

3.7. fuzzy c-means (FCM) classifier

initial

iteration 8

iteration 37

Initialize U=[uij] matrix, U(0)

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)||< then STOP; otherwise return to step 2.

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

Partial volume effectfor boundary separationShattuck, 2001

corrrect WM misclassified(colored by subejct number

there are a total of 10 subjects)

segmentedgold std

Clark, 2006