Medical Image Analysis Dr. Mohammad Dawood Department of Computer Science University of Münster Germany

2 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Recap

3 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Rigid registration Angles are preserved Parallel lines remain parallel Affine registration Parallel lines remain parallel

4 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Registration Feature Points - PCA - SVD - Iterative Closest Points Algorithm (ICP) - Random Sample Consensus Algorithm (RNSAC) Distance Measures - Sum of Squared Differences (SSD) - Root Mean Square Difference (RMSD) - Normalized Cross Correlation (NXCorr) - Mutual Information (MI)

5 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Registration Optical flow methods - Brightness consistency constraint: Lucas Kanade Algorithm: Assume locally constant flow Horn Schunck Algorithm: Assume globally smooth flow Bruhn’s Non-linear Algorithm

6 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Image Segmentation

7 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation - Locate tumors and other pathologies - Measure tissue volumes - Computer-guided surgery - Diagnosis - Treatment planning - Study of anatomical structure

8 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Threshold Based Segmentation

9 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Histogram based segmentation

10 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Histogram based segmentation

11 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Zack Method A line is constructed between the maximum of the histogram at brightness bmax and the lowest value bmin The distance d between the line and the histogram h[b] is computed for all values of b from b = bmin to b = bmax The brightness value bo where the distance between h[bo] and the line is maximal is the threshold value.

12 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Global Threshold Selection -Select an initial threshold (T) -Segment into object and background 1.G 1 = {f >= T} 2.G 2 = {f < T} -The average of each set is m 1 = average value of G 1 m 2 = average value of G 2 -New threshold is average of m 1 and m 2 T’ = (m 1 + m 2 )/2. - Repeat until convergence

13 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Global Threshold Selection Threshold =

14 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Otsu’s Method Compute histogram For all possible thresholds t Calculate ω i (weight) and μ i (mean) of the classes Compute variance: ω 1 (t) *ω 2 (t) [μ 1 (t)- μ 2 (t)] Desired threshold corresponds to the maximum Threshold for the Head Image: 153.0

15 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation K-Means Clustering - Pick K cluster centers - Assign each pixel in the image to the nearest cluster center - Re-compute the cluster centers by averaging all pixels in the cluster - Repeat until convergence

16 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood k1k1 k2k2 k3k3

17 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood k1k1 k2k2 k3k3

18 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood k1k1 k2k2 k3k3

19 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood k1k1 k2k2 k3k3

20 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood k1k1 k2k2 k3k3

21 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood k1k1 k2k2 k3k3

22 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Region Growing

23 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Region Growing - Select seeding points - Starting from seeds, look at the neighbors if neighbor similar, add to region else proceed with next unclassified neighbor - Repeat until all pixels are classified

24 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Region Growing Threshold 10Threshold 20

25 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Watersheds Image is visualized in 3 dimensions - 2 spatial dimensions - grey levels

26 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Segmentation Watersheds Three parts: - points belonging to regional minimum - catchment area - dividing lines or watershed lines Flooding: e.g. by morphological dilation

27 Medical Image Analysis, SS-2015 Dr. Mohammad Dawood Thank You!