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DTU Compute
Introduction to Medical Image AnalysisRasmus R. PaulsenDTU
Compute
[email protected]
http://www.compute.dtu.dk/courses/02511http://www.compute.dtu.dk/courses/02512
mailto:[email protected]://www.compute.dtu.dk/courses/02511http://www.compute.dtu.dk/courses/02512
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Lecture 10 Registration
9.00 Lecture
12.00 13.00 Lunch break13.00 Exercises
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What can you do after today? Describe the clinical use of image
registration Describe the different types of landmarks Annotate a
set of image using anatomical landmarks Describe the objective
function used for landmark based
registration Compute the objective function when the
transformation
is given Compute the optimal translation between two sets of
landmarks Use the rigid body transformation for image
registration Use the similarity transformation for image
registration
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Image Registration The act of adjusting something to match a
standard Align images
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Image registration Monitoring of change in the individual Fusion
of information from different sources in a
clinically meaningful way Comparison of one subject with others
Comparison of groups with others Comparing with an atlas
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Data fusion
MR CT
Same patient two scans
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Change detection Patient image before and after operation What
has changed? Images need to be aligned before comparison
Before operation After operation
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Reference and template image The reference image R Template
image T Transform the template so it
fits the reference
transformed
T
T
R
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The transformations
Translation
Rotation
Scaling
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Similarity measures The aim is to transform the template so it
looks like
the reference Looks like = Similarity measure Image
similarity
Subtract the two images and see what is left Landmark
similarity
Landmarks from the two images should be close together
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Landmark Based Registration Landmarks placed on both reference
and template image The landmark should have correspondence
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Point correspondence Landmarks are numbered Each landmark should
be placed the same place on both images
12
3
12
3
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Landmark types Anatomical landmark
a mark assigned by an expert that corresponds between objects in
a biologically meaningful way
Mathematical landmark a mark that is located on a
curve according to some mathematical or geometrical property
Pseudo landmark a mark that is constructed on a
curve based on anatomical or mathematical landmarks
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Landmarks
Reference image Template image TR
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The aim of registration Find a transformation that maps the
coordinates of
the reference to the coordinates of the template Why not the
template to the reference?
Sampling of template image:
Backward mapping -> inverse transform
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The Transformation Transforms point p Into point p T is for
example a
Translation Rotation Rigid body transform Similarity
transform
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The Transformation Transforms points
from the reference
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The parameters The parameters is a vector
with p elements The type of transformation
determines the number of parameters
Translation p = 2 Rotation p = 1 Scaling p = 1
parameters
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Rigid body transformHow many parameters?
A) 1B) 2C) 3D) 4E) 5 0 0 0 0 0
A B C D E
Chart1
0
0
0
0
0
Sheet1
A0
B0
C0
D0
E0
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Similarity transformHow many parameters?
A) 1B) 2C) 3D) 4E) 5
0 0 0 0 0
A B C D E
Chart1
0
0
0
0
0
Sheet1
A0
B0
C0
D0
E0
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Objective function The objective function
measures how well two point sets match
Points from the template image
Transformed points from the reference image
= =1
, 2
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Objective function The objective function
measures how well two point sets match
Distance between points
DT(a5)
b5
= =1
, 2
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Objective function
D3T(a3)
b3D2
T(a2)
b2D1
T(a1)
b1Template
Transformed reference
= =1
3
, 2 = 12 + 22 + 32
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Minimization / Optimization Find the set of
parameters that minimizes the objective function
= =1
, 2
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Minimization pure translation
D3T(a3)
b3D2
T(a2)
b2D1
T(a1)
b1Template
Transformed reference
F = D 21 + D 22 + D 23
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Minimization pure translation
D3T(a3)
b3D2T(a2)
b2D1
T(a1)
b1Template
Transformed reference
F = D 21 + D 22 + D 23 Decreased!
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Minimization pure translation
D3T(a3)
b3D2T(a2)
b2D1
T(a1)
b1Template
Transformed reference
F = D 21 + D 22 + D 23 Decreased!
Overall minimum lengths!
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ObjectivefunctionA) 600B) 50C) 100D) 900E) 300
0 0 0 0 0
A B C D E
Chart1
0
0
0
0
0
Sheet1
A0
B0
C0
D0
E0
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Translation Simple shift of coordinates
parameters
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Translation Simple shift of coordinates
parameters
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Objective function for translation
Objective function
Translation
Objective function for translation
= =1
, 2
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Optimal function value
= =1
, 2
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Optimal translation
Objective function
Parameters
Optimal translation
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Optimal translation
Original landmarks Reference points translated
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Decrease in F
A) 1B) 2C) 3D) 4E) 5
0 0 0 0 0
A B C D E
Chart1
0
0
0
0
0
Sheet1
A0
B0
C0
D0
E0
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Rigid body transformation Translation and rotation Rigid body =
stift legeme Angles and distances are kept
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Rigid body transformation objective function
Transformation
Rotation matrix
Objective function
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Optimal rigid body transformation The minimum of the objective
function can be found
in several ways Always start by matching the centre of masses
The rotation can be found by singular value
decomposition In 2D it can also be found in simpler ways
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Rigid body transformation Comparing images of the same
patient
Images taken with the same scanner Compensate for different
positioning in the scanner
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Similarity transformation Translation, rotation, and isotropic
scaling Angles are kept
Solution found using SVD
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Similarity transform Same patient different scanners
Different pixel/voxel sizes Same patient over time
Growing Different patients Atlas to patient
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Image transformation The found transformation maps the
coordinates of
the reference to the coordinates of the template We want to
transform the template? Backward image mapping!
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Backward mapping Run through all the pixel in the output image
Use the inverse transformation to find the position in
the input image Use bilinear interpolation to calculate the
value Put the value in the output image
Here output image = transformed template image Input image =
template image Inverse transform = the computed transform
From reference to template
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Hvad er forkert
A) 1B) 2C) 3D) 4E) 5
0 0 0 0 0
A B C D E
Chart1
0
0
0
0
0
Sheet1
A0
B0
C0
D0
E0
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What can you do after today? Describe the clinical use of image
registration Describe the different types of landmarks Annotate a
set of image using anatomical landmarks Describe the objective
function used for landmark based
registration Compute the objective function when the
transformation
is given Compute the optimal translation between two sets of
landmarks Use the rigid body transformation for image
registration Use the similarity transformation for image
registration
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Exercise Registration
Matching of hands using landmarks Cancer treatment follow up in
a brain
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Next week Hough Transformation and Path Tracing
Hough transform
-50 0 50
-400
-200
0
200
400
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Exercises
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Introduction to Medical Image AnalysisLecture 10
RegistrationWhat can you do after today?Image RegistrationImage
registrationData fusionChange detectionReference and template
imageThe transformationsSimilarity measuresLandmark Based
RegistrationPoint correspondenceLandmark typesLandmarksThe aim of
registrationThe TransformationThe TransformationThe parametersRigid
body transformHow many parameters?Similarity transformHow many
parameters?Objective functionObjective functionObjective
functionMinimization / OptimizationMinimization pure
translationMinimization pure translationMinimization pure
translationObjectivefunctionTranslationTranslationObjective
function for translationOptimal function valueOptimal
translationOptimal translationDecrease in FRigid body
transformationRigid body transformation objective functionOptimal
rigid body transformationRigid body transformationSimilarity
transformationSimilarity transformImage transformationBackward
mappingHvad er forkertWhat can you do after today?ExerciseNext
weekExercises
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