Medical Imaging Mohammad Dawood Department of Computer Science University of Münster Germany

2 Medical Imaging, SS-2010 Mohammad Dawood Image Registration

3 Medical Imaging, SS-2010 Mohammad Dawood Registration T : Transformation In this lecture Floating image: The image to be registered Target image: The stationary image

4 Medical Imaging, SS-2010 Mohammad Dawood Registration Linear Transformations - Translation - Rotation - Scaling - Affine

5 Medical Imaging, SS-2010 Mohammad Dawood Registration 3D Translation

6 Medical Imaging, SS-2010 Mohammad Dawood Registration 3D Rotation

7 Medical Imaging, SS-2010 Mohammad Dawood Registration 3D Scaling

8 Medical Imaging, SS-2010 Mohammad Dawood Registration Rigid registration Angles are preserved Parallel lines remain parallel

9 Medical Imaging, SS-2010 Mohammad Dawood Registration Affine registration

10 Medical Imaging, SS-2010 Mohammad Dawood Registration Feature Points

11 Medical Imaging, SS-2010 Mohammad Dawood Registration Feature Points 1. De-mean 2. Compute SVD 3. Calculate the transform

12 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.

13 Medical Imaging, SS-2010 Mohammad Dawood 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

14 Medical Imaging, SS-2010 Mohammad Dawood Registration Phase Correlation

15 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)

16 Medical Imaging, SS-2010 Mohammad Dawood Registration Sum of Squared Differences SSD(f,t)SSD(20f,t)

17 Medical Imaging, SS-2010 Mohammad Dawood Registration Root Mean Squared Differences RMS(f,t)RMS(20f,t)

18 Medical Imaging, SS-2010 Mohammad Dawood Registration Normalized Cross Correlation NXCorr(f,t)NXCorr(20f,t)

19 Medical Imaging, SS-2010 Mohammad Dawood Registration Mutual Information MI(f,t)MI(20f,t)

20 Medical Imaging, SS-2010 Mohammad Dawood Optical Flow

21 Medical Imaging, SS-2010 Mohammad Dawood Optical flow Brightness consistency constraint With Taylor expansion V : Flow(Motion)

22 Medical Imaging, SS-2010 Mohammad Dawood

23 Medical Imaging, SS-2010 Mohammad Dawood Optical flow Lucas Kanade Algorithm: Assume locally constant flow =>

24 Medical Imaging, SS-2010 Mohammad Dawood Optical flow Horn Schunck Algorithm: Assume globally smooth flow

25 Medical Imaging, SS-2010 Mohammad Dawood Optical flow Bruhn’s Non-linear Algorithm