PVE for MRI Brain Tissue PVE for MRI Brain Tissue ClassificationClassification

Zeng DongSLST, UESTC

6-9

PVEPVEPartial Volume Effect

ContentsContents

OverviewMethod

Nei. PVE Model

MAPResultDiscussionConclusion

Overview 1-roleOverview 1-role

Roles of Segmentation

in qualitative

in visualization

Overview 2 – difficultyOverview 2 – difficulty

difficulty inhomogeneous

PVE

hard

soft segmentation • Statistic• MAP• MRF

Overview 3 - PVE Overview 3 - PVE

IEE95 NOISE MODELS based Sampling noise Material-dependent NoisePVE

direct

indirect

DirectDirect

Determine PVC directlyIEEE91

nwyK

jjii j

1

multichannel

),()( niii wgwyp

]1,0[,11

jj i

K

ji ww

continuouscontinuous

IEE03

Only tow types

continuouscontinuous

02 Fuzzy Markov

discrete PVC

IndirectIndirect

PV classDetermine PVC based on PV voxels

),()( niii wgwyp

iw

inii dwwgyp ),()(

continuouscontinuous

More TowNot Multi-channalDiscrete PVCBoundary voxelsMore accurate, more efficient

Method-Nei. PVEMethod-Nei. PVE

},,1{ :SetIndex NS

},{ :image Obseved SiyY i

N: numbers of pixels

Assume:

},0;{H : SiyiSetIndexmask i

mask

continuouscontinuous

},,1{ :SetIndex Pure KP K: numbers of pure

j :RV Pure b ),( pj

pjg

Pjpj

pj

p ,,

g(.,.): Gaussian function

continuecontinue

Observed is mixed with its nei.s meanly during sampling

Nei. Size M

M

jii jy

My

1

1

continuecontinue

K

jjji bn

My

1

1

MnK

jj

1

],0[ Mn j

continuecontinue

L kinds of mixed types:Mixed set

Assume

LF ,,1

FlvV l , Pjnv jl , A mixed type

typel)mixed(labe therepresent RV Assume ii yx

SiFxxX ii ,; :Set Label

continuecontinue

),(),( iip

ii gxyp

K

jjji n

M 1

1

K

jjji n

M 1

1

PVE SegmentationPVE SegmentationMAP

)(arg max* YXPXX

Y: observed images

X: segmentation images

prior

likelihood

)()()( XPXYPYXP

Likelihood termLikelihood term

Assume that the intensity at voxel i does not depend on the tissue content of the other voxels.

N

i

pii xypXYP

1

),()(

PriorPrior

Assume X is MRF on nei. System C, and x is a realization RF X

))(exp(1

)( xUZ

xp

Z: Partition function

U(x): Potential energy function

Xx

xUZ ))(exp(

Cc

c xvxU )()(

continuecontinue

SNxxVxU iSi Ni

ii

i

,),()( 2

otherwiseCv

maskivvrxxV

i

ii

x

xxiiii

,

,),(

0

2

2

constant enough large a is C

continuecontinue

)),(exp()(1

2

N

i Niii

i

xxvxp

continuecontinue

)()()( XPXYPYXP

N

i i

ii

i

N

i Niii

y

xxvi

)2

)(exp(

2

1

)),(exp(

2

12

ICMICM

Iterative Constrained Mode

local

combination

continuecontinue

iNiii

K

j

pjj

K

j

pjjiK

j

pjji

xxv

nM

nM

y

nM

U

),(

1

1

2

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2

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1

continuecontinue

jN

kkk

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N 1

)(1

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22 )(1

j

N

kii

jj

j

yyjPN

continuecontinue

1. Init X (beta = 0, M=1)2. Update mixel mean and variance3. ICM4. goto 2

ResultResult

Brain tissue classification

K=3: CSF, GM, WM

N=1,3,7,27

continuecontinue

Generate Mixed types:

for CSF=M:0

for GM=(M-CSF):0 {

WM=M-CSF-GM

…

}

continuecontinue

Example(K=3,M=7)

Reduce: Not tow maximization( 3) CSF !=0 && GM != 0 (18)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

CSF 7 6 6 5 5 5 4 4 4 4 3 3 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0GM 0 1 0 2 1 0 3 1 2 0 4 3 2 1 0 5 4 3 2 1 0 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0WM0 0 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2 3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7

continuecontinue

Ori seg

Ori

Seg with b

Seg without b

continuecontinue

compare

数据 100_23 1_24 11_3 110_3 111_2 112_2 12_3 13_3 15_3* 17_3*CSF 0.3018 0.1089 0.1159 0.3101 0.3418 0.3072 0.1182 0.3097GM 0.8880 0.8460 0.8781 0.8221 0.8195 0.8056 0.9035 0.9022WM 0.8339 0.8170 0.8356 0.7757 0.7956 0.7649 0.8583 0.8529数据 17_3 191_3 202_3 205_3CSF 0.1031 0.1296 0.0891GM 0.642 0.8541 0.8924 0.8781WM 0.782 0.8263 0.8403 0.8433

Mean: csf 20% GM 86% WM :83%

Discussion 4-1Discussion 4-1Mixel of CSF and WM

0:76.614136 297.295471

1:84.838821 316.580113

2:93.063507 335.864755

3:117.737564 393.718680

4:125.962250 413.003322

5:134.186935 432.287964

6:139.243421 377.461605

7:144.299907 322.635246

8:159.469365 158.156170

9:164.525851 103.329811

10:169.582336 48.503452

mix mean and var

0:76.614136 297.295471

1:84.838821 316.580113

2:89.895307 261.753754

3:93.063507 335.864755

4:98.119993 281.038396

5:103.176479 226.212037

6:106.344679 300.323038

7:111.401164 245.496679

8:117.737564 393.718680

9:122.794050 338.892321

10:137.963508 174.413245

11:143.019993 119.586886

12:125.962250 413.003322

13:131.018736 358.176963

14:136.075221 303.350604

15:146.188193 193.697887

16:151.244679 138.871528

17:156.301165 84.045169

18:134.186935 432.287964

19:139.243421 377.461605

20:144.299907 322.635246

21:159.469365 158.156170

22:164.525851 103.329811

23:169.582336 48.503452

continouscontinous

Mixel of CSF and WM

Discussion 4-2Discussion 4-2

Measure Parameter estimation

csf mean : 89.168350

csf var : 836.750610

gm mean : 124.758827

gm var : 385.225983

wm mean : 162.237137

wm var : 186.776108

csf mean : 111.797281

csf var : 273.691200

gm mean : 124.073118

gm var : 359.172593

wm mean : 159.252710

wm var : 212.954779

Result para:Ori para

Csf mean:76.614136

Csf var:297.295471

gm mean:134.186935

gm var:432.287964

wm mean:169.582336

wm var:48.503452

Init para(ML)

Discussion 4-3Discussion 4-3

Prior Parameter estimation

Discussion 4-4Discussion 4-4

Intensity inhomogeneous

ConclusionConclusion

More accurate, more efficientUnify frameworkgeneralization

Thanks