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  M t - mean tissue vector  C t - inverse of covariance matrix  A t - a constant which gives unit normalisation A Multi-dimensional Gaussian Distribution for data g for each tissue t ISMRM 2002

 B ts - 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  T ts (h) - partial volume distribution  C h - inverse covariance matrix: C h = h C t + (1-h) C A Multi-dimensional Partial Volume Distribution Modelled along the line between two pure tissues means, M t and M s 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. ISMRM 2002

Data Optimisation by Expectation Maximisation  Maximisation step - update of model parameters.

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 6850/18/30 0 (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 CSF 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

Acknowledgments An Integrated Environment for the Rehearsal and Planning of Surgical Interventions IERAPSI European Commission Project IST