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

2 Medical Imaging, SS-2011 Mohammad Dawood Recap

3 Medical Imaging, SS-2011 Mohammad Dawood Sound wavesPiezoelectric crystalsWave front formation

4 Medical Imaging, SS-2011 Mohammad Dawood Inverse Radon transformFiltered back projection Filtered back projection

5 Medical Imaging, SS-2011 Mohammad Dawood Fourier slice theoremKaczmarz Method (=ART)

6 Medical Imaging, SS-2011 Mohammad Dawood Image Registration

7 Medical Imaging, SS-2011 Mohammad Dawood Registration T : Transformation In this lecture Floating image: The image to be registered Target image: The stationary image

8 Medical Imaging, SS-2011 Mohammad Dawood Registration Linear Transformations - Translation - Rotation - Scaling - Affine

9 Medical Imaging, SS-2011 Mohammad Dawood Registration 3D Translation

10 Medical Imaging, SS-2011 Mohammad Dawood Registration 3D Rotation

11 Medical Imaging, SS-2011 Mohammad Dawood Registration 3D Scaling

12 Medical Imaging, SS-2011 Mohammad Dawood Registration Rigid registration Angles are preserved Parallel lines remain parallel

13 Medical Imaging, SS-2011 Mohammad Dawood Registration Affine registration

14 Medical Imaging, SS-2011 Mohammad Dawood Registration Feature Points

15 Medical Imaging, SS-2011 Mohammad Dawood Registration Feature Points 1. De-mean 2. Compute SVD 3. Calculate the transform

16 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.

17 Medical Imaging, SS-2011 Mohammad Dawood Registration Feature Points

18 Medical Imaging, SS-2011 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

19 Medical Imaging, SS-2011 Mohammad Dawood Registration Phase Correlation

20 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)

21 Medical Imaging, SS-2011 Mohammad Dawood Registration Sum of Squared Differences SSD(f,t)SSD(20f,t)

22 Medical Imaging, SS-2011 Mohammad Dawood Registration Root Mean Squared Differences RMS(f,t)RMS(20f,t)

23 Medical Imaging, SS-2011 Mohammad Dawood Registration Normalized Cross Correlation NXCorr(f,t)NXCorr(20f,t)

24 Medical Imaging, SS-2011 Mohammad Dawood Registration Mutual Information MI(f,t)MI(20f,t)

25 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 (I 1 (x,y), I 2 (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

26 Medical Imaging, SS-2011 Mohammad Dawood Optical Flow

27 Medical Imaging, SS-2011 Mohammad Dawood Optical flow Brightness consistency constraint With Taylor expansion V : Flow(Motion)

28 Medical Imaging, SS-2011 Mohammad Dawood

29 Medical Imaging, SS-2011 Mohammad Dawood Optical flow Lucas Kanade Algorithm: Assume locally constant flow =>

30 Medical Imaging, SS-2011 Mohammad Dawood Optical flow Horn Schunck Algorithm: Assume globally smooth flow

31 Medical Imaging, SS-2011 Mohammad Dawood Optical flow Bruhn’s Non-linear Algorithm

32 Medical Imaging, SS-2011 Mohammad Dawood Visit :00 EIMI Technologiehof, Mendelstr Münster