Problem in kmeans, image segmentation algorithm.

In K-means clustering using tutorial

http://www.mathworks.in/products/image/examples.html?file=/products/demos/shipping/images/ipexhistology.html

images we get after clustering are random as cluster centers are randomly selected. I am using this code to land use and land cover analysis where regions such as green/forest area, water area, soil area road area, built up area etc etc are clustered out as an output. Now, I want to use only green/forest area for further coding and since that clustered image, sometimes comes under cluster 1; sometimes under cluster 5/4/3/2; it is impossible to code further.

Can anybody help me in how to avoid random selection of cluster centers in kmeans.

Answer 1

[Matt Tearle]

You can do

... = kmeans(...,'start',M);

where M is a matrix of the initial locations of the centers (each row of M is a vector representing the location of one cluster center).

The other alternative would be to post-process -- look at the centroids returned and pick the one that is the most "green".

[Sadashiv pradhan]

Matt thank you so much for your help. I tried code using the first method 'M' matrix. In code http://www.mathworks.in/products/image/examples.html?file=/products/demos/shipping/images/ipexhistology.html

I made following changes. M=[0 0;115 0;227 145]; [cluster_idx cluster_center] = kmeans(ab,nColors,'distance','sqEuclidean', ... 'Replicates',3,'start',M); and now I am getting this error- The third dimension of the 'Start' array must match the 'replicates' parameter value.

can you please tell me where exactly I am going wrong? Thanks

[Matt Tearle]

The M you're providing tells kmeans to look for 3 clusters in a 2-D space; the centroids of the 3 clusters are (0,0), (115,0), and (227,145).

The 'Replicates' option essentially runs kmeans multiple times (you've specified 3 in this case). But this only makes sense if you have different starting centroids for each run. Otherwise, you're just doing the exact same thing 3 times. So with the Replicates option given, you need to provide 3 sets of starting centroids. Each one of those sets is a matrix like M. Hence, you need a 3-by-2-by-3 array for M (or turn off Replicates). That's (number of clusters)-by-(dimension)-by-(number of replicates).

[Sadashiv pradhan]

Matt, Thank you so so much... You have been great help to me...!! Thanks once again.

[Sadashiv pradhan]

and can you please elaborate on alternative option that you mentioned in first comment? lets take a same example http://www.mathworks.in/products/image/examples.html?file=/products/demos/shipping/images/ipexhistology.html

in output I am getting following centroids

M=[ 179.0785   82.9036
  161.5292   82.0460
  142.2662  107.5307];

and I am getting output clusters in sequence pink,purple,white and lets say I want white cluster. so when you say, "The other alternative would be to post-process -- look at the centroids returned and pick the one that is the most 'white'" what do you exactly mean and how should I proceed?

[Matt Tearle]

I'm not an image processing expert, so I don't know exactly, but it seems like your 2-D space is this "a*b* space" (which, according to the link, is red/green vs blue/yellow). But whatever the actual coordinates are, "green" things must live in a cluster somewhere in that space, whereas "white" things would be in a different region. In fact, given that it's 2-D, you could actually plot your data points and the centroids to see what the segmentation looks like:

scatter(ab(:,1),ab(:,2),10,cluster_idx)
hold on
plot(cluster_center(:,1),cluster_center(:,2),'kx','linewidth',3,'markersize',10)
xlabel('red-green'), ylabel('blue-yellow')

(Using the variables created in the demo you linked to.) Now you can see how kmeans is doing the segmentation in a*-b* space.

"White" or "green" or whatever is therefore associated with some region in this space, so whichever centroid is closest to some "canonical" value of "white" is the cluster I would take to be the white group.

For example, if you were working in RGB (rather than a*-b*), I'd take the centroid that was closest to [1,1,1] to be the white cluster, and the one that was closest to [0,1,0] to be green, and so on.

Bottom line: if you have a reasonable idea of the colors that will be selected and, therefore, roughly where the centroids will be, you should be able to map the groups to colors according to the group centroid locations.

EDIT TO ADD: I just reread the link more carefully -- this is basically what they're doing in Step 6. They just say "The blue cluster has the smallest cluster_center value (determined experimentally)" -- so that's the criterion they're using to determine with cluster is "blue".