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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
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