m. pokric, p.a. bromiley, n.a. thacker, m.l.j. scott, and a. jackson university of manchester...
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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
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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
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Data Modelling
Pure tissues - Gaussian distribution (blue lines).Mixtures of tissues - Triangular distribution convolved with Gaussian (red lines).The resulting distribution (green lines).
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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
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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
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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
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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
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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
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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)
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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
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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
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Probability Maps
Bone and air Fat Soft tissue
CSFCSF GM WM
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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
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AcknowledgmentsAn Integrated Environment for the Rehearsal
and Planning of Surgical Interventions
IERAPSI
European Commission Project IST-1999-12175
http://www.tina-vision.net