M. Pokric, P.A. Bromiley, N.A. Thacker, M.L.J. Scott, and A. Jackson

University of Manchester

Imaging Science and Biomedical Engineering

Probabilistic Multi-modality Image Segmentation with

Partial Voluming

ISMRM 2002

Problem Definition Segment the medical images to derive accurate and

meaningful representation of all tissues present. The model is to be used in simulation and for visualisation (e.g. pre-operative planning, surgical rehearsal and training).

Multi-dimensional image segmentation which models effect of mixtures of tissues present in a single voxel (i.e. partial volume effect).

Bayes theory used to obtain tissue probability maps to estimate the most likely tissue volume fraction present within each voxel.

ISMRM 2002

Data Modelling

Pure tissues - Gaussian distribution (blue lines).Mixtures of tissues - Triangular distribution convolved with Gaussian (red lines).The resulting distribution (green lines).

Data Modelling

Mt - mean tissue vector

Ct - inverse of covariance matrix

At - a constant which gives unit normalisation

A Multi-dimensional Gaussian Distribution for data g for each tissue t

)(C)(eA)(d

ttT

ttt

MgMgg

2

1

ISMRM 2002

Bts

- constant which gives unit normalisation

h - fractional distance g along the line between two centres of distribution, h[0,1]

N(g) – normal distance of g from the line between the two centres of distribution

Tts(h) - partial volume distribution

Ch - inverse covariance matrix: Ch= h Ct + (1-h) C

A Multi-dimensional Partial Volume Distribution Modelled along the line between two pure tissues means, Mt and Ms

)N(C)N((h)eTB)(d h

T

tststsgg

g 21

ISMRM 2002

Data Optimisation by Expectation Maximisation Expectation step - calculation of conditional

probability of the model given the data using pure tissue and mixture of tissues distributions.

t t stststt0

nn)f(d)f(df

)f(d)|P(n

ggg

g

ISMRM 2002

Data Optimisation by Expectation Maximisation

Maximisation step - update of model parameters.

T

tv

V

vtvvV

11't

v

V

vvV

1't

V

vvv2

1'st

'ts

V

vv

't

)|P(tC

)|P(t

)|P(st)|P(tsff

)|P(tf

MgMgg

ggM

gg

g

MR Image Sequences

VE (PD)

5500/20

(TR/TE)

TSE8

VE (T2)

5500/100

(TR/TE)

TSE8

FLAIR

6000/100/2200

(TR/TE/TI)

TSE19

IRTSE

6850/18/300

(TR/TE/TI)

TSE9

Scatter Plots

Scatter plots for IRTSE and VE(PD) images for:(a) original data

(b) density models with initial parameters (c) density models after 10 iterations of EM algorithm

(a) (b)

(c)

Histogram Plots

Histogram plots for original data (red), sum of pure tissue models (green), sum of partial volume models (pink); sum of all models

(blue)(i)initial parameters (ii) parameters after 10 iterations

Histogram Plots

Histogram plots for original data (red), sum of pure tissue models (green), sum of partial volume models (pink); sum of all models

(blue)(i)initial parameters (ii) parameters after 10 iterations

Probability Maps

Bone and air Fat Soft tissue

CSFCSF GM WM

Conclusions Half of the data we observed is due to partial

voluming (mainly due to slice thickness, 3.5mm)

Multi-dimensional segmentation with partial voluming enables more accurate segmentation of medical images of different modalities

Better visual appearance of segmented tissues - important factors for simulation and visualisation

This method can be applied to any sequence of images for which the linearity assumption holds

ISMRM 2002

AcknowledgmentsAn Integrated Environment for the Rehearsal

and Planning of Surgical Interventions

IERAPSI

European Commission Project IST-1999-12175

http://www.tina-vision.net