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Medical Imaging. Mohammad Dawood Department of Computer Science University of Münster Germany. Recap. Sound wavesPiezoelectric crystalsWave front formation. Inverse Radon transform Filtered back projection. Filtered back projection. - PowerPoint PPT Presentation
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Medical Imaging
Mohammad Dawood
Department of Computer Science
University of MünsterGermany
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Medical Imaging, SS-2011
Mohammad Dawood
Recap
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Medical Imaging, SS-2011
Mohammad Dawood
Sound waves Piezoelectric crystals Wave front formation
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Medical Imaging, SS-2011
Mohammad Dawood
Inverse Radon transform Filtered back projection
Filtered back projection
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Medical Imaging, SS-2011
Mohammad Dawood
Fourier slice theorem Kaczmarz Method (=ART)
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Medical Imaging, SS-2011
Mohammad Dawood
Image Registration
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Medical Imaging, SS-2011
Mohammad Dawood
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
Mohammad Dawood
Registration
Linear Transformations
- Translation
- Rotation
- Scaling
- Affine
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
3D Translation
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
3D Rotation
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
3D Scaling
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Rigid registration
Angles are preserved Parallel lines remain parallel
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Affine registration
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Feature Points
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Feature Points
1. De-mean
2. Compute SVD
3. Calculate the transform
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Medical Imaging, SS-2011
Mohammad Dawood
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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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Feature Points
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Feature Points
Random Sample Consensus Algorithm (RNSAC)
1. Transformation is calculated from hypothetical inliers2. All other data are then tested against the fitted model and, if a point fits well to the model, also considered as a hypothetical inlier3. 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 inliers5. Finally, the model is evaluated by estimating the error of the inliers relative to the model
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Phase Correlation
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Distance Measures
- Sum of Squared Differences (SSD)
- Root Mean Square Difference (RMSD)
- Normalized Cross Correlation (NXCorr)
- Mutual Information (MI)
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Sum of Squared Differences
SSD(f,t) SSD(20f,t)
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Root Mean Squared Differences
RMS(f,t) RMS(20f,t)
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Normalized Cross Correlation
NXCorr(f,t) NXCorr(20f,t)
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Medical Imaging, SS-2011
Mohammad Dawood
Registration
Mutual Information
MI(f,t) MI(20f,t)
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Medical Imaging, SS-2011
Mohammad Dawood
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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Medical Imaging, SS-2011
Mohammad Dawood
Optical flow
Brightness consistency constraint
With Taylor expansion
V : Flow (Motion)
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Medical Imaging, SS-2011
Mohammad Dawood
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Medical Imaging, SS-2011
Mohammad Dawood
Optical flow
Lucas Kanade Algorithm: Assume locally constant flow
=>
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Medical Imaging, SS-2011
Mohammad Dawood
Optical flow
Horn Schunck Algorithm: Assume globally smooth flow
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Medical Imaging, SS-2011
Mohammad Dawood
Optical flow
Bruhn’s Non-linear Algorithm
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Medical Imaging, SS-2011
Mohammad Dawood
Visit
23.05.2011 14:00
EIMITechnologiehof, Mendelstr. 11
48149 Münster
www.uni-muenster.de/eimi
