1. Normalized Cuts Demo Original Implementation from: Jianbo Shi Jitendra Malik Presented by: Joseph Djugash

2. Outline Clustering Point  The Eigenvectors  The Affinity Matrix  Comparison with K-means Segmentation of Images  The Eigenvectors  Comparison with K-means

3. Clustering – How many groups are there? Out of the various possible partitions, which is the correct one?

4. Clustering – Why is it hard? Number of components/clusters? The structure of the components? Estimation or optimization problem?  Convergence to the globally correct solution?

5. Clustering – Example 1 Optimal? How do we arrive at this Clustering?

6. What does the Affinity Matrix Look Like?

7. The Eigenvectors and the Clusters Step-Function like behavior preferred! Makes Clustering Easier.

8. The Eigenvectors and the Clusters

9. Clustering – Example 2 Dense Square Cluster Sparse Square Cluster Sparse Circle Cluster

10. Normalized Cut Result

11. The Affinity Matrix

12. The Eigenvectors and the Clusters

13. K-means – Why not? e1 e2 Input Eigenvectors Affinity Matrix Eigenvector Projection NCut Output K-means Output K-means Clustering? Possible but not Investigated Here.

14. K-means Result – Example 1

15. K-means Result – Example 2

16. Varying the Number of Clusters k = 3k = 4k = 6 K-means N-Cut

17. Varying the Sigma Value σ = 3σ = 13σ = 25

18. Image Segmentation – Example 1 Affinity/Similarity matrix (W) based on Intervening Contours and Image Intensity

19. The Eigenvectors

20. Comparison with K-means Normalized Cuts K-means Segmentation

21. How many Segments?

22. Good Segmentation (k=6,8)

23. Bad Segmentation (k=5,6) Missing Edge Bad Edge Choice of # of Segments in Critical. But Hard to decide without prior knowledge.

24. Varying Sigma – (σ= Too Large)

25. Varying Sigma – (σ= Too Small) Choice of Sigma is important. Brute-force search is not Efficient. The choice is also specific to particular images.

26. Image Segmentation – Example 2

27. Normalized Cuts K-means Segmentation

28. Image Segmentation – Example 3

29. Normalized Cuts K-means Segmentation

30. Image Segmentation – Example 4

31. Normalized Cuts K-means Segmentation

32. Image Segmentation – Example 5

33. Normalized Cuts K-means Segmentation

34. Image Segmentation – Example 6

35. Comparison with K-means Normalized Cuts K-means Segmentation

36. The End…

37. The Eigenvectors and the Clusters Eigenvector #1 Eigenvector #2Eigenvector #3Eigenvector #4Eigenvector #5