Spectral Clustering, Image Segmentation and Eigenvectors

Question

Based on the book Computer Vision a Modern Approach page 425, I attempted to use eigenvectors for image segmentation.

http://dl.dropbox.com/u/1570604/tmp/comp-vis-moder

Answer 1

I've just tried the algorithm in Mathematica, it works fine on your image, so there must be a subtle bug in your code.

This part:

V,D = np.linalg.eig(A)
V = np.real(V)
res = n_max(V,1) # take largest 
idx = res[0][1][0] 
a = np.real(D[idx]) # look at corresp eigv

looks strange: all linear algebra packages I know return the eigenvalues/eigenvectors sorted, so you'd just take the first eigenvector in the list. That's the one that corresponds to the highest eigenvalue. Try plotting the eigenvalues list to confirm that.

Also, where did you get the fixed threshold from? Have you tried normalizing the image to display it?

For what it's worth, the results I'm getting for the first 3 eigenvectors are:

This is the Mathematica code I use:

pixels = Flatten[image];
weights = Table[N[Exp[-(pixels[[i]] - pixels[[j]])^2]], {i, 1, 900}, {j, 1, 900}];
eigenVectors = Eigenvectors[weights];
ImageAdjust[Image[Partition[eigenVectors[[1]], 30]]]