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Normalized Cuts Demo

Normalized Cuts Demo. Original Implementation from: Jianbo Shi Jitendra Malik Presented by: Joseph Djugash. Outline. Clustering Point The Eigenvectors The Affinity Matrix Comparison with K-means Segmentation of Images The Eigenvectors Comparison with K-means.

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Normalized Cuts Demo

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

  10. Normalized Cut Result

  11. The Affinity Matrix

  12. The Eigenvectors and the Clusters

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

  14. K-means Result – Example 1

  15. K-means Result – Example 2

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

  17. Varying the Sigma Value σ = 3 σ = 13 σ = 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 Edge Missing Edge Bad Segmentation (k=5,6) • 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. Image Segmentation – Example 2 Normalized Cuts K-means Segmentation

  28. Image Segmentation – Example 3

  29. Image Segmentation – Example 3 Normalized Cuts K-means Segmentation

  30. Image Segmentation – Example 4

  31. Image Segmentation – Example 4 Normalized Cuts K-means Segmentation

  32. Image Segmentation – Example 5

  33. Image Segmentation – Example 5 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 #2 Eigenvector #3 Eigenvector #5 Eigenvector #4 Eigenvector #1

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