Transcript Folie 1 - uni

Medical Imaging
Mohammad Dawood
Department of Computer Science
University of Münster
Germany
Medical Imaging, SS-2011
Recap
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Medical Imaging, SS-2011
Sound waves
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Piezoelectric crystals
Wave front formation
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Inverse Radon transform
Filtered back projection
Filtered back projection
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Fourier slice theorem
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Kaczmarz Method (=ART)
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Medical Imaging, SS-2011
Image Registration
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Registration
T
: Transformation
In this lecture
Floating image
: The image to be registered
Target image
: The stationary image
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Medical Imaging, SS-2011
Registration
Linear Transformations
- Translation
- Rotation
- Scaling
- Affine
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Registration
3D Translation
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Medical Imaging, SS-2011
Registration
3D Rotation
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Medical Imaging, SS-2011
Registration
3D Scaling
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Registration
Rigid registration
Angles are preserved
Parallel lines remain parallel
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Registration
Affine registration
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Registration
Feature Points
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Registration
Feature Points
1. De-mean
2. Compute SVD
3. Calculate the transform
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Medical Imaging, SS-2011
Registration
Feature Points
Iterative Closest Points Algorithm (ICP)
1. Associate points by the nearest neighbor criteria.
2. Estimate transformation parameters using a mean square cost
function.
3. Apply registration and update parameters.
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Registration
Feature Points
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Medical Imaging, SS-2011
Registration
Feature Points
Random Sample Consensus Algorithm (RNSAC)
1. Transformation is calculated from hypothetical inliers
2. All other data are then tested against the fitted model and, if a point fits well to
the model, also considered as a hypothetical inlier
3. The estimated model is reasonably good if sufficiently many points have been
classified as hypothetical inliers.
4. The model is re-estimated from all assumed inliers
5. Finally, the model is evaluated by estimating the error of the inliers relative to
the model
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Registration
Phase Correlation
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Registration
Distance Measures
- Sum of Squared Differences (SSD)
- Root Mean Square Difference (RMSD)
- Normalized Cross Correlation (NXCorr)
- Mutual Information (MI)
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Registration
Sum of Squared Differences
SSD(f,t)
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SSD(20f,t)
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Registration
Root Mean Squared Differences
RMS(f,t)
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RMS(20f,t)
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Registration
Normalized Cross Correlation
NXCorr(f,t)
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NXCorr(20f,t)
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Registration
Mutual Information
MI(f,t)
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MI(20f,t)
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Entropy for Image Registration
Define a joint probability distribution:
– Generate a 2-D histogram where each axis is the number of possible
greyscale values in each image
– each histogram cell is incremented each time a pair (I1(x,y), I2(x,y))
occurs in the pair of images
• If the images are perfectly aligned then the histogram is highly
focused. As the images mis-align the dispersion grows
• recall Entropy is a measure of histogram dispersion
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Optical Flow
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Optical flow
Brightness consistency constraint
With Taylor expansion
V
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: Flow
(Motion)
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Optical flow
Lucas Kanade Algorithm: Assume locally constant flow
=>
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Optical flow
Horn Schunck Algorithm: Assume globally smooth flow
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Optical flow
Bruhn’s Non-linear Algorithm
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Medical Imaging, SS-2011
Visit
23.05.2011 14:00
EIMI
Technologiehof, Mendelstr. 11
48149 Münster
www.uni-muenster.de/eimi
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