DTU Medical Visionday May 27, 2009 Generative models for automated brain MRI segmentation Koen Van Leemput Athinoula A. Martinos Center for Biomedical

DTU Medical Visionday May 27, 2009

Generative models for automated brain MRI segmentation

Koen Van Leemput

Athinoula A. Martinos Center for Biomedical Imaging

Department of Radiology, MGH

Harvard Medical School, USA

Computer Science and Artificial Intelligence Laboratory

Massachusetts Institute of Technology, USA

MRI of the brain

Magnetic resonance imaging:– Harmless– Three dimensional (3-D)– High soft tissue contrast– High spatial resolution– Extremely versatile– Possibly multi-spectral

Ideal for studying the living human brain

“voxel”

Koen Van Leemput DTU Medical Visionday May 27, 2009

Segmentation of brain MRI

– Delineating structures of interest in the images

– Segmentation is important: Basic neuroscience Uncovering disease mechanisms Diagnosis, treatment planning,

and follow-up Clinical drug trials …

– Automated computational methods are needed


Overview

Segmentation basics: modeling and inference Modeling MRI bias fields Mesh-based brain atlases Whole-brain segmentation


Overview



MRI image

The problem to be solved


MRI image

The problem to be solved


Label image

One solution: generative modeling

– Formulate a statistical model of how an MRI image is formed

– The model depends on some parameters

“labeling model”

“imaging model”


MRI image Label image

MRI image

Segmentation = inverse problem


Label image

MRI image

Segmentation = inverse problem


Label image

Bayesian inference– Start from our statistical model of image formation– Play with the mathematical rules of probability

Practical approximation

Involves two optimizations:– First estimate the optimal model parameters– Then find the optimal segmentation based on those parameter

estimates

Bayesian inference


Example: Gaussian mixture model

– The label in each voxel is drawn independently with a probability for tissue type k

– Assume a uniform prior for the labeling model parameters


“imaging model”




– The intensity in each voxel is drawn independently from a Gaussian distribution associated with its label

– The imaging model parameters are the mean and variance of each Gaussian:

– Assume a uniform prior


“imaging model”



Model parameters are unknown



Mean and variance of each Gaussian

Relative weight of each Gaussian

three labels

Optimization 1: parameter estimation

– Given an MRI image to be segmented, what is the MAP parameter estimate ?

– Parameter optimization with an Expectation Maximization (EM) algorithm

current estimate

– Repeatedly maximize a lower bound to the objective function

– Iterative parameter optimizer using only closed-form parameter updates!






Optimization 2: segmentation

white matter

gray matterCSF


Upon completion of the parameter estimation algorithm, assign each voxel to the MAP label

Overview



MRI bias field artifact

Intensity inhomogeneities across the image area

Imaging artifact in MRIequipment limitations

patient-induced electrodynamic interactions


MRI data after intensity windowing…


Causes segmentation errors with our segmentation procedure so far…




Causes segmentation errors with our segmentation procedure so far…

Improved imaging model


“imaging model”





“imaging model”

old model





“imaging model”

+

old model polynomial bias field model



Model parameter estimation

– Polynomial coefficients are part of the model parameters

– Parameter optimization with a Generalized Expectation Maximization (GEM) algorithm

current estimate

– Repeatedly improve a lower bound to the objective function

– Iterative parameter optimizer using only closed-form parameter updates! [Van Leemput et al., IEEE TMI 1999]


Example


MRI data Estimated bias field

Bias-corrected MRI data

Example

MRI data

White matter without bias field model

White matter with bias field model

Estimated bias field


Example

MRI data

White matter without bias field model

White matter with bias field model

Estimated bias field


Overview



Improving the labeling model


“imaging model”


– So far our labeling model just expresses the relative frequency of occurrence of different labels

– Too simplistic for segmenting the brain into 30+ subregions

A more realistic labeling model is needed!





Try to find the underlying probability distribution

Manual segmentations in N individuals (training data)


Modeling the training data (2-D)

Triangular mesh representation



Assign label probabilities to each mesh node• Flat prior• Label probabilities are linearly interpolated over triangle areas

“atlas”



Mesh node positions are sampled from a topology-preserving Markov

random field prior

“atlas”

warped atlases


“knob” that controls the flexibility of the atlas warp


Example segmentations are sampled according to the

deformed atlases

atlas

warped atlases

example segmentations


Bayesian inference [Van Leemput, IEEE TMI 2009]

Given a collection of manual segmentations– what is the most probable atlas?– what is the most likely value of the parameter controlling the

flexibility of the deformations?– what is the most likely mesh

representation?

Good models explain regularities in the manual segmentations– Automatically yields sparse representations that explicitly avoid

overfitting to the training data– cf. Minimum Description Length


Example atlas


Derived from manual segmentations of 36

brain substructures in 4 individuals

Has average “shape”

Overview



Whole-brain segmentation

– Tetrahedral mesh-based atlas– The labeling model parameters are the location of the

mesh nodes– The prior is the topology-preserving MRF model

(penalizes deformations)


“imaging model”





“imaging model”

+

Gaussian mixture model polynomial bias field model



– Model parameter estimation:

– Fully automated segmentation procedure• No need for pre-processing (skull stripping, bias field corr., …)• Automatically adapts to different scanners and acquisition sequences!• Fast!


Improve the imaging model parameters (Generalized Expectation-Maximization;

closed-form expressions)

Improve the atlas warp (registration; gradient in analytical form)


Examples (validation under way)












Thanks!


Documents

DTU Medical Visionday May 27, 2009 Generative models for automated brain MRI segmentation Koen Van Leemput Athinoula A. Martinos Center for Biomedical