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 Clusters Step-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 = 3k = 4k = 6 K-means N-Cut

Varying the Sigma Value σ = 3σ = 13σ = 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

Normalized Cuts K-means Segmentation

Image Segmentation – Example 3

Normalized Cuts K-means Segmentation

Image Segmentation – Example 4

Normalized Cuts K-means Segmentation

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 #1 Eigenvector #2Eigenvector #3Eigenvector #4Eigenvector #5