Medical Image Analysis

1
Medical Image Analysis

• Image Registration

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
2
Image Registration

• Atlas
• Study the variability of anatomical and
  functional structures among the subjects
• Structural computerized atlas (SCA) CT or
  conventional MRI.
• A model for image segmentation and extraction of
  a structural volume of interest (VOI)

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
3
Image Registration

• Functional computerized atlas (FCA) SPECT, PET,
  or fMRI.
• Understanding the metabolism of functional
  activity in a specific structural VOI
• Image registration methods and algorithms
• Transformation of a source image space to the
  target image space

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
4
Figure 9.1. A schematic diagram of multi-modality
MR-PET image analysis using computerized atlases.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
5
Figure 9.2. Image registration through
transformation.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
6
Image Registration

• External markers and stereotactic frames based
  landmark registration
• External markers
• Coordinate transformation (rotation, translation
  and scaling) and interpolation computed from
  visible markers
• Optimizing the mean squared error
• Stereotactic frames are usually uncomfortable for
  the patient

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
7
Image Registration

• Rigid-body transformation based global
  registration
• Principal axes transformation
• PET-PET, MR-MR, MR-PET
• Image feature-based registration
• Boundary and surface matching based registration
• Edges, boundary and surface information
• A geometric transformation is obtained by
  minimizing a predefined error function between
  the surfaces

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Image Registration

• Image landmarks and features based registration
• Utilize pre-defined anatomical landmarks or
  features
• Bayesian model based probabilistic methods
• Neuroanatomical atlases for elastic matching of
  brain images
• Landmark-based elastic matching algorithm
• Maximum likelihood estimation

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
9
Rigid-Body Transformation

• Rigid transformation
• rotation matrix
• translation vector
• Translation along -axis by

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Rigid-Body Transformation

• Translation along -axis by
• Translation along -axis by

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Rigid-Body Transformation

• Rotation about -axis by
• Rotation about -axis by

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Rigid-Body Transformation

• Rotation about -axis by

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Figure 9.3. The translation and rotation
operations of a 3-D rigid transformation.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
14
Rigid-Body Transformation

• The rotation matrix for the
  rotational order

Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
15
Affine Transformation

• Affine matrix including the translation, rotation
  and scaling transformation

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Principal Axes Registration

• Principal axes registration (PAR)
• Global matching of two binary volumes
• a binary segmented volume
• centroid of

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Principal Axes Registration
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Principal Axes Registration

• The principal axes of are the
  eigenvectors of the inertia matrix

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Principal Axes Registration
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Principal Axes Registration

• Resolve 6 degrees of freedom
• Three rotations and three translations
• Equate the normalized eigenvector matrix to the
  rotation matrix

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Principal Axes Registration
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Principal Axes Registration

• PAR for two volumes and
• 1. Translate the centroid of to the origin
• 2. Rotate the principal axes of to
  coincide with the , and axes
• 3. Rotate the , and axes to
  coincide with the principal axes of
• 4. Translate the origin to the centroid of
• is scaled to match the volume using the
  scaling factor

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Principal Axes Registration

• Probabilistic models
• Counting the occurrence of a particular binary
  subvolume that is extracted from the registered
  volumes corresponding to various images

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Figure 9.4. A 3-D model of brain ventricles
obtained from registering 22 MR brain images
using the PAR method.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
25
Figure 9.5. Rotated views of the 3-D brain
ventricle model shown in Figure 9.3.
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
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Iterative Principal Axes Registration

• Iterative principal axes registration (IPAR)
• Developed by Dhawan et al.
• Register MR and PET brain images
• Used with partial volumes

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(a)
Figure 9.6. Three successive iterations of the
IPAR algorithms for registration of vol 1 and vol
2 The results of the first iteration (a), the
second iteration (b) and the final iteration (c).
Vol 1 represents the MR data while the PET image
with limited filed of view (FOV) is represented
by vol 2.
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(b)
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
29
(c)
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
30
(a)
Figures 9.7 a, b and c Sequential slices of MR
(middle rows) and PET (bottom rows) and the
registered MR-PET brain images (top row) of the
corresponding slices using the IPAR method.
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(b)
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
32
(c)
Figures come from the textbook Medical Image
Analysis, by Atam P. Dhawan, IEEE Press, 2003.
33
Image Landmarks and Features Based Registration

• Image landmarks and features based registration
• Rigid and non-rigid transformations
• Image landmarks (points) and features

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Similarity Transformation for Point-Based
Registration

• A non-rigid transformation
• ratation
• scaling
• translation
• the total number of landmarks

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Similarity Transformation for Point-Based
Registration

• Algorithm
• 1.
• 2. Find

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Similarity Transformation for Point-Based
Registration

• Singular value decomposition
• 3. Compute the scaling factor
• 4. Compute

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Weighted Features Based Registration

• , 1, 2, 3,, a set of
  corresponding data shapes in and spaces

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Elastic Deformation Based Registration

• Elastic deformation
• Mimic a manual registration
• Map the elastic volume to the reference volume
• The elastic volume is deformed by applying
  external forces such that it matches the
  reference model
• Constraints
• Smoothness
• incompressibility

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Elastic Deformation Based Registration

• Motion of a deformable body in Lagrangian form
• the force acting on a particle
• the position
• time
• the mass
• the damping constant
• the internal energy of deformation

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Elastic Deformation Based Registration

• Find the displacement vector that maximizes
  the similarity measure
• metric tensor
• curvature tensor

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Figure 9.8. Block diagram for the MR image
registration procedure.
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Figure 9.9. Results of the elastic deformation
based registration of 3-D MR brain images The
left column shows three images of the reference
volume, the middle column shows the respective
images of the brain volume to be registered and
the right column shows the respective images of
the registered brain volume.