A%20Bayesian%20Approach%20for%20Transformation%20Estimation

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A Bayesian Approachfor Transformation Estimation
Landmark Detection in brain MRI
Camille Izard and Bruno Jedynak
Laboratoire Paul Painlevé Université des Sciences
et Technologies de Lille
Center for Imaging Science Johns Hopkins
University
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Image Registration

• Comparing structures
• Time evolution
• Between patients
• Comparing different image modalities
• MRI, CT

• General Approach for registration
• Define the mean image
• Define the norms
• Different types of ?
• Affine transformation
• Diffeomorphisms

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Image Registration

• Use of landmarks
• Characterize the underlying shape
• Rough analysis of the shape (Bookstein, 1991)
• Corresponding point for registration algorithm
• Manual Landmarking

HT
SCC
HoH
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Image Model
Lets denote v 2 I the voxels of an
image Graylevels modeled with a mixture of
Gaussian, Zv the matter at voxel v, unknown
random variable. We define ? R3 ? R3. Matter
in the new coordinate system The template
Generating an image For all u,
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Matter Distribution
Template obtained when ? is a translation,
considering the landmark SCC
CSF
GM
WM
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With a new image
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Unkonwn

• Caracterize the photometry
• Learned for each image by EM algorithm

• Estimating the transformation locating the
  landmarks

• Contains the geometry of the images
• Includes the variation of geometry
• Learned offline on a training set

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Comparison

• Data term
• No needs to define the mean image
• Adjustable weight depending on the law
  distribution
• Use of the matter and not gray level
• Regularity constraints
• Prior on the transformation parameters

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Estimating Photometry distributions

• Mixture of 6 Gaussian distributions
• - Pure Voxels CSF, GM , WM
• Mixed Voxels CSFGM, GMWM
• Outliers
• Use EM to learn the distributions

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Matter Distribution Estimation
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The Template
The Template obtained with ? a translation and
HoH as a landmark
CSF
GM
WM
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Recovering the Transformation
HoH
SCC
Information Map Information contained at each
voxel with ? a translation, left with SCC,
right with HoH.
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Results
? translation, 38 training images, 9 images for
testing
Landmark Error on training set Error on testing set
SCC 1.81 mm (?1.42 mm) 2.46 mm (? 1.92 mm)
HoH 2.75 mm (?1.97 mm) 3.70 mm (? 1.48 mm)
HT 0.26 mm (?0.51 mm) 2.19 mm (?1.11mm)
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Using more complex transformations
If ? has more parameters ?, Gradient descent on
the transformation parameters
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Current extensions

• Affine Transformations
• Able to deal with several landmarks
  simultaneously
• Estimation by gradient descent in the parameter
  space
• Uniqueness issues
• C. Izard, B. Jedynak, Bayesian Registration for
  Landmark detection, ISBI, april 2006
• Splines transformations
• Able to deal with several landmarks at the same
  time,
• Flexibility of the model to various number of
  landmarks,
• Unicity of the transformation
• Estimation by gradient descent in the parameter
  space