Medical Imaging

Mohammad Dawood

Department of Computer Science

University of MünsterGermany

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Medical Imaging, SS-2010

Mohammad Dawood

Image Registration

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Medical Imaging, SS-2010

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-2010

Mohammad Dawood

Registration

Linear Transformations

- Translation

- Rotation

- Scaling

- Affine

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

3D Translation

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

3D Rotation

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

3D Scaling

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

Rigid registration

Angles are preserved Parallel lines remain parallel

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

Affine registration

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

Feature Points

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

Feature Points

1. De-mean

2. Compute SVD

3. Calculate the transform

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Medical Imaging, SS-2010

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-2010

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-2010

Mohammad Dawood

Registration

Phase Correlation

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Medical Imaging, SS-2010

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-2010

Mohammad Dawood

Registration

Sum of Squared Differences

SSD(f,t) SSD(20f,t)

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

Root Mean Squared Differences

RMS(f,t) RMS(20f,t)

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

Normalized Cross Correlation

NXCorr(f,t) NXCorr(20f,t)

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Medical Imaging, SS-2010

Mohammad Dawood

Registration

Mutual Information

MI(f,t) MI(20f,t)

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Medical Imaging, SS-2010

Mohammad Dawood

Optical Flow

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Medical Imaging, SS-2010

Mohammad Dawood

Optical flow

Brightness consistency constraint

With Taylor expansion

V : Flow (Motion)

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Medical Imaging, SS-2010

Mohammad Dawood

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Medical Imaging, SS-2010

Mohammad Dawood

Optical flow

Lucas Kanade Algorithm: Assume locally constant flow

=>

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Medical Imaging, SS-2010

Mohammad Dawood

Optical flow

Horn Schunck Algorithm: Assume globally smooth flow

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Medical Imaging, SS-2010

Mohammad Dawood

Optical flow

Bruhn’s Non-linear Algorithm