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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. - PowerPoint PPT Presentation

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.