Medical Imaging Dr. 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 Rigid registration Angles are preserved Parallel lines remain parallel Affine registration Parallel lines remain parallel

4 Medical Imaging, SS-2011 Mohammad Dawood Registration Feature Points -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 Imaging, SS-2011 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 Imaging, SS-2011 Mohammad Dawood Image Segmentation

7 Medical Imaging, SS-2011 Mohammad Dawood Segmentation - Locate tumors and other pathologies - Measure tissue volumes - Computer-guided surgery - Diagnosis - Treatment planning - Study of anatomical structure

8 Medical Imaging, SS-2011 Mohammad Dawood Threshold Based Segmentation

9 Medical Imaging, SS-2011 Mohammad Dawood Segmentation Histogram based segmentation

10 Medical Imaging, SS-2011 Mohammad Dawood Segmentation Histogram based segmentation

11 Medical Imaging, SS-2011 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 Imaging, SS-2011 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 Imaging, SS-2011 Mohammad Dawood Segmentation Global Threshold Selection Threshold =

14 Medical Imaging, SS-2011 Mohammad Dawood Segmentation Otsu’s Method Compute histogram For all possible thresholds t Calculate ω i and μ i 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 Imaging, SS-2011 Mohammad Dawood Segmentation Multiple Thresholds (f 180)

16 Medical Imaging, SS-2011 Mohammad Dawood Clustering Methods

17 Medical Imaging, SS-2011 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

18 Medical Imaging, SS-2011 Mohammad Dawood Segmentation K-Means Clustering K-MeansFuzzy K-Means

19 Medical Imaging, SS-2011 Mohammad Dawood Region Growing

20 Medical Imaging, SS-2011 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

21 Medical Imaging, SS-2011 Mohammad Dawood Segmentation Region Growing Threshold 10Threshold 20

22 Medical Imaging, SS-2011 Mohammad Dawood Segmentation Watersheds Image is visualized in 3 dimensions - 2 spatial dimensions - grey levels Three parts: - points belonging to regional minimum - catchment area - dividing lines or watershed lines

23 Medical Imaging, SS-2011 Mohammad Dawood Segmentation Watersheds Label each minimum with a distinct label. Initialize a set S with the labeled nodes Extract from S a node x of minimal altitude F Attribute the label of x to each non labeled node y adjacent to x, and insert y in S Keep the catchment areas separated by dams Repeat until S is empty.

24 Medical Imaging, SS-2011 Mohammad Dawood Segmentation Watersheds

25 Medical Imaging, SS-2011 Mohammad Dawood Thank You!