Normalized Cuts Demo
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Transcript of 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
Clustering – How many groups are there?
Out of the various possible partitions, which is the correct one?
Clustering – Why is it hard?
Number of components/clusters?
The structure of the components?
Estimation or optimization problem? Convergence to the globally correct solution?
Clustering – Example 1
Optimal?
How do we arrive at this Clustering?
What does the Affinity Matrix Look Like?
The Eigenvectors and the ClustersStep-Function like behavior preferred!
Makes Clustering Easier.
The Eigenvectors and the Clusters
Clustering – Example 2
Dense Square Cluster
Sparse Square Cluster
Sparse Circle
Cluster
Normalized Cut Result
The Affinity Matrix
The Eigenvectors and the Clusters
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.
K-means Result – Example 1
K-means Result – Example 2
Varying the Number of Clusters
k = 3 k = 4 k = 6
K-
mea
ns
N-C
ut
Varying the Sigma Value
σ = 3 σ = 13 σ = 25
Image Segmentation – Example 1
Affinity/Similarity matrix (W) based on Intervening Contours and Image Intensity
The Eigenvectors
Comparison with K-means
Normalized Cuts K-means Segmentation
How many Segments?
Good Segmentation (k=6,8)
Bad Segmentation (k=5,6)
Missing Edge
Bad Edge
• Choice of # of Segments in Critical.• But Hard to decide without prior knowledge.
Varying Sigma – (σ= Too Large)
Varying Sigma – (σ= Too Small)
• Choice of Sigma is important.• Brute-force search is not Efficient.• The choice is also specific to particular images.
Image Segmentation – Example 2
Image Segmentation – Example 2
Normalized Cuts K-means Segmentation
Image Segmentation – Example 3
Image Segmentation – Example 3
Normalized Cuts K-means Segmentation
Image Segmentation – Example 4
Image Segmentation – Example 4
Normalized Cuts K-means Segmentation
Image Segmentation – Example 5
Image Segmentation – Example 5
Normalized Cuts K-means Segmentation
Image Segmentation – Example 6
Comparison with K-means
Normalized Cuts K-means Segmentation
The End…
The Eigenvectors and the Clusters
Eigenvector #1Eigenvector #2Eigenvector #3Eigenvector #4Eigenvector #5