Normalized Cuts Demo

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Normalized Cuts Demo

• Original Implementation from
• Jianbo Shi
• Jitendra Malik
• Presented by
• Joseph Djugash

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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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Clustering How many groups are there?
Out of the various possible partitions, which is
the correct one?
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Clustering Why is it hard?

• Number of components/clusters?
• The structure of the components?
• Estimation or optimization problem?
• Convergence to the globally correct solution?

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Clustering Example 1
Optimal?
How do we arrive at this Clustering?
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What does the Affinity Matrix Look Like?
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The Eigenvectors and the Clusters
Step-Function like behavior preferred! Makes
Clustering Easier.
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The Eigenvectors and the Clusters
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Clustering Example 2
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Normalized Cut Result
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The Affinity Matrix
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The Eigenvectors and the Clusters
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K-means Why not?
Affinity Matrix
NCut Output
Input
Eigenvectors
K-means Clustering?
Possible but not Investigated Here.
K-means Output
Eigenvector Projection
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K-means Result Example 1
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K-means Result Example 2
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Varying the Number of Clusters
N-Cut
K-means
k 3
k 4
k 6
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Varying the Sigma Value
s 3
s 13
s 25
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Image Segmentation Example 1
Affinity/Similarity matrix (W) based on
Intervening Contours and Image Intensity
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The Eigenvectors
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Comparison with K-means
Normalized Cuts
K-means Segmentation
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How many Segments?
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Good Segmentation (k6,8)
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Bad Segmentation (k5,6)

• Choice of of Segments in Critical.
• But Hard to decide without prior knowledge.

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Varying Sigma (s Too Large)
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Varying Sigma (s Too Small)

• Choice of Sigma is important.
• Brute-force search is not Efficient.
• The choice is also specific to particular
  images.

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Image Segmentation Example 2
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Image Segmentation Example 2
Normalized Cuts
K-means Segmentation
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Image Segmentation Example 3
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Image Segmentation Example 3
Normalized Cuts
K-means Segmentation
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Image Segmentation Example 4
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Image Segmentation Example 4
Normalized Cuts
K-means Segmentation
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Image Segmentation Example 5
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Image Segmentation Example 5
Normalized Cuts
K-means Segmentation
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Image Segmentation Example 6
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Comparison with K-means
Normalized Cuts
K-means Segmentation
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The End
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The Eigenvectors and the Clusters
Eigenvector 2
Eigenvector 3
Eigenvector 4
Eigenvector 5
Eigenvector 1