Post on 22-Dec-2015
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Segmentation Isolating a region/regions of interest in an
image Useful for:
Collect more meaningful data from an image Easier analysis Locate objects Locate boundaries
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K-means clustering Unsupervised clustering algorithm
Classifies input data points into K classes based on their inherent distance to each other
Points are clustered around centroids/means
Which are obtained by minimizing:
Where there are K clusters and is the centroid of all points
Ref: http://www.ics.uci.edu/~dramanan/teaching/ics273a_winter08/projects/avim_report.pdf
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Example – 1 Channel Given a gray scale image, use K-means to
segment the image. Choose K = 2 (Cluster A and Cluster B)
1 5 3
2 6 2
5 5 1
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2.) Initialize centroids Randomly initialize centroids
0 1 2 3 4 5 60
0.51
1.52
2.53
3.5
Intensity
Fre-quency
𝜇𝐴 𝜇𝐵
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3) Cluster intensities based on distance
1 2 3 5 6
Distance with 0 1 4 16 25
Distance with 4 1 0 4 9
A A B B B
Note: Points with intensity 2 can be classified as either, but our algorithm chooses the first cluster.
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4.) Recalculate centroids New centroids
0 1 2 3 4 5 60
0.51
1.52
2.53
3.5
Intensity
Fre-quency
𝜇𝐴2 𝜇𝐵 2
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5.) Recluster intensities using new centroids
1 2 3 5 6
Distance with 0.25 0.25 2.25 12.25 20.25
Distance with 14.44 7.84 3.24 0.04 1.44
A A A B BWe have a new clustering!
Recalculate the centroid.
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Recalculate the means and we find:
This means we can stop and we have our final clusters
1 2 3 5 6
Distance with 0.64 0.04 1.44 10.24 17.64
Distance with 18.063 10.56 5.063 0.63 0.56
A A A B B
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Final Clustering/Segmentation
A B A
A B A
B B A
This answer would change if we chose K = 3. Also, the number of iterations would change depending on the starting centroids.
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What about colour segmentation? Different regions of interest may have the
same intensity but different colours Can use the colour information of an image to
improve segmentation Let’s focus only on the colour and remove the
intensity by converting to a different colour space: HSI (Hue Saturation Intensity) YCbCr (Luma, Blue difference, Red difference) L*a*b* (Lightness, a* - colour that falls on the red-
green axis, b* - colour that falls on the blue-yellow axis)
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Using L*a*b* space Our K-means problem becomes a 2D problem Our centroid will now have two variables, one
defining the intensity of the a* channel and one defining the b* channel
http://www.mathworks.com/help/releases/R2013b/stats/kmeans.gif