# Normalized Cuts Demo

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14-Jan-2016Category

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### Transcript of Normalized Cuts Demo

Normalized Cuts DemoOriginal Implementation from: Jianbo ShiJitendra Malik

Presented by:Joseph Djugash

OutlineClustering PointThe EigenvectorsThe Affinity MatrixComparison with K-meansSegmentation of ImagesThe EigenvectorsComparison 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 1Optimal?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

Normalized Cut Result

The Affinity Matrix

The Eigenvectors and the Clusters

K-means Why not?InputEigenvectorsAffinity MatrixEigenvector ProjectionNCut OutputK-means OutputK-means Clustering?Possible but not Investigated Here.

K-means Result Example 1

K-means Result Example 2

Varying the Number of Clustersk = 3k = 4k = 6K-meansN-Cut

Varying the Sigma Value = 3 = 13 = 25

Image Segmentation Example 1Affinity/Similarity matrix (W) based on Intervening Contours and Image Intensity

The Eigenvectors

Comparison with K-meansNormalized CutsK-means Segmentation

How many Segments?

Good Segmentation (k=6,8)

Bad Segmentation (k=5,6) Choice of # of Segments in Critical. But Hard to decide without prior knowledge.

Varying Sigma (= Too Large)

Varying Sigma (= 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 2Normalized CutsK-means Segmentation

Image Segmentation Example 3

Image Segmentation Example 3Normalized CutsK-means Segmentation

Image Segmentation Example 4

Image Segmentation Example 4Normalized CutsK-means Segmentation

Image Segmentation Example 5

Image Segmentation Example 5Normalized CutsK-means Segmentation

Image Segmentation Example 6

Comparison with K-meansNormalized CutsK-means Segmentation

The End

The Eigenvectors and the ClustersEigenvector #1Eigenvector #2Eigenvector #3Eigenvector #4Eigenvector #5

Boundary cues are incorporated by looking for the presence of an intervening contour, a large gradient along a straight line connecting two pixels.

Boundary cues are incorporated by looking for the presence of an intervening contour, a large gradient along a straight line connecting two pixels.

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