Intensity based registration of by chenshu

VIEWS: 5 PAGES: 50

									                                       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
                  Koen Van Leemput   DTU Medical Visionday   May 27, 2009



MRI of the brain

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

        Ideal for studying the
        living human brain
                       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
               Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Overview

   Segmentation basics: modeling and inference
   Modeling MRI bias fields
   Mesh-based brain atlases
   Whole-brain segmentation
               Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Overview

   Segmentation basics: modeling and inference
   Modeling MRI bias fields
   Mesh-based brain atlases
   Whole-brain segmentation
            Koen Van Leemput   DTU Medical Visionday   May 27, 2009



The problem to be solved




MRI image
            Koen Van Leemput   DTU Medical Visionday   May 27, 2009



The problem to be solved




MRI image                           Label image
                     Koen Van Leemput   DTU Medical Visionday   May 27, 2009



    One solution: generative modeling

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




    “labeling                     “imaging
     model”                        model”
                Label image                          MRI image


–   The model depends on some parameters
            Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Segmentation = inverse problem




MRI image                           Label image
                   Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Segmentation = inverse problem




MRI image                                  Label image




Bayesian inference
   –   Start from our statistical model of image formation
   –   Play with the mathematical rules of probability
                    Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Bayesian inference

Practical approximation




Involves two optimizations:
   –   First estimate the optimal model parameters
   –   Then find the optimal segmentation based on those parameter
       estimates
                       Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Example: Gaussian mixture model



    “labeling                       “imaging
     model”                          model”
                  Label image                          MRI image



–    The label in each voxel is drawn independently with a
     probability     for tissue type k
–    Assume a uniform prior            for the labeling model
     parameters
                    Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Example: Gaussian mixture model



“labeling                        “imaging
 model”                           model”
               Label image                          MRI image


–   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
                   Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Example: Gaussian mixture model




                                         three labels

Model parameters                         are unknown

       Mean and variance of           Relative weight of
         each Gaussian                 each Gaussian
                  Koen Van Leemput   DTU Medical Visionday   May 27, 2009



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
                                      – Repeatedly maximize a
                                        lower bound to the objective
                                        function

                                      – Iterative parameter
                                        optimizer using only closed-
                                        form parameter updates!
               current
              estimate
          Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Optimization 1: parameter estimation
          Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Optimization 1: parameter estimation
                     Koen Van Leemput   DTU Medical Visionday   May 27, 2009



 Optimization 2: segmentation




                    white matter

CSF                           Upon completion of the
      gray matter
                              parameter estimation algorithm,
                              assign each voxel to the MAP
                              label
               Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Overview

   Segmentation basics: modeling and inference
   Modeling MRI bias fields
   Mesh-based brain atlases
   Whole-brain segmentation
                    Koen Van Leemput   DTU Medical Visionday   May 27, 2009



MRI bias field artifact
Intensity inhomogeneities across the image area




         MRI data                      after intensity windowing…

Imaging artifact in MRI
   equipment limitations
   patient-induced electrodynamic interactions
                Koen Van Leemput   DTU Medical Visionday   May 27, 2009



MRI bias field artifact

Causes segmentation errors with our segmentation
  procedure so far…
                Koen Van Leemput   DTU Medical Visionday   May 27, 2009



MRI bias field artifact

Causes segmentation errors with our segmentation
  procedure so far…
                 Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Improved imaging model



“labeling                     “imaging
 model”                        model”
            Label image                          MRI image
                 Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Improved imaging model



“labeling                     “imaging
 model”                        model”
            Label image                          MRI image




            old model
                 Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Improved imaging model



“labeling                     “imaging
 model”                        model”
            Label image                          MRI image




                            +
                                    polynomial bias
            old model
                                      field model
                   Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Model parameter estimation

–   Polynomial coefficients are part of the model
    parameters
–   Parameter optimization with a Generalized Expectation
    Maximization (GEM) algorithm
                                       – Repeatedly improve a lower
                                         bound to the objective
                                         function

                                       – Iterative parameter
                                         optimizer using only closed-
                                         form parameter updates!
                current                  [Van Leemput et al., IEEE TMI
               estimate                  1999]
          Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Example




     MRI data                Estimated bias field




          Bias-corrected MRI data
                   Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Example


       MRI data

White matter without
 bias field model

   White matter with
   bias field model


Estimated bias field
                   Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Example


       MRI data

White matter without
 bias field model

   White matter with
   bias field model


Estimated bias field
               Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Overview

   Segmentation basics: modeling and inference
   Modeling MRI bias fields
   Mesh-based brain atlases
   Whole-brain segmentation
                    Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Improving the labeling model



“labeling                        “imaging
 model”                           model”
               Label image                          MRI image


–   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!
          Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Improving the labeling model
                               Koen Van Leemput   DTU Medical Visionday   May 27, 2009



    Improving the labeling model




                               Try to find the underlying
                                probability distribution




Manual segmentations in N
 individuals (training data)
                  Koen Van Leemput   DTU Medical Visionday   May 27, 2009



      Modeling the training data (2-D)




Triangular mesh
 representation
                           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



     Modeling the training data (2-D)




                         “atlas”

Assign label probabilities to each mesh node
    • Flat prior
    • Label probabilities are linearly interpolated over triangle areas
                           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



      Modeling the training data (2-D)




                          “atlas”
 Mesh node positions are sampled
from a topology-preserving Markov
         random field prior

                “knob” that controls the      warped
                                              atlases
              flexibility of the atlas warp
                    Koen Van Leemput   DTU Medical Visionday   May 27, 2009



 Modeling the training data (2-D)




                   atlas


Example segmentations are
 sampled according to the
    deformed atlases                   warped                example
                                       atlases            segmentations
                      Koen Van Leemput   DTU Medical Visionday   May 27, 2009



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
          Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Example atlas




                                         Derived from manual
                                         segmentations of 36
                                        brain substructures in 4
                                               individuals


                                         Has average “shape”
               Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Overview

   Segmentation basics: modeling and inference
   Modeling MRI bias fields
   Mesh-based brain atlases
   Whole-brain segmentation
                      Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Whole-brain segmentation



    “labeling                      “imaging
     model”                         model”
                 Label image                          MRI image


–    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)
                 Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Whole-brain segmentation



“labeling                     “imaging
 model”                        model”
            Label image                          MRI image




                            +
                                    polynomial bias
       Gaussian mixture model
                                      field model
                       Koen Van Leemput     DTU Medical Visionday    May 27, 2009



Whole-brain segmentation

–   Model parameter estimation:
                    Improve the imaging model parameters
                             (Generalized Expectation-Maximization;
                             closed-form expressions)


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

–   Fully automated segmentation procedure
     •   No need for pre-processing (skull stripping, bias field corr., …)
     •   Automatically adapts to different scanners and acquisition
         sequences!
     •   Fast!
           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Examples     (validation under way)
           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Examples     (validation under way)
           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Examples     (validation under way)
           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Examples     (validation under way)
           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Examples     (validation under way)
           Koen Van Leemput   DTU Medical Visionday   May 27, 2009



Examples     (validation under way)
Koen Van Leemput   DTU Medical Visionday   May 27, 2009




      Thanks!

								
To top