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

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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

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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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Medical Imaging, SS-2011

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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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Medical Imaging, SS-2011

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Optical Flow

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Medical Imaging, SS-2011

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Optical flow

Brightness consistency constraint

With Taylor expansion

V : Flow (Motion)

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Medical Imaging, SS-2011

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Medical Imaging, SS-2011

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Optical flow

Lucas Kanade Algorithm: Assume locally constant flow

=>

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Medical Imaging, SS-2011

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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

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Visit

23.05.2011 14:00

EIMITechnologiehof, Mendelstr. 11

48149 Münster

www.uni-muenster.de/eimi