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