# Calculating the eigenvalues of simple shapes

3 views (last 30 days)
John Bach on 13 Mar 2023
Edited: John Bach on 25 Mar 2023
Hi there,
I've used the strel function to create a range of shapes and I would like to now calculate the eigenvalues of each shape although I am struggling to do this and would really appreciate any help regarding this.
the cyclist on 13 Mar 2023
Edited: the cyclist on 13 Mar 2023
Do you have a reference for what the eigenvalue of a binary shape is? I did some googling of keywords, but didn't find something definite. (Maybe this is well known in image processing, but that is not my specialty.)
Are you stuck on the math of it, or the MATLAB coding? Have you written any code?

Walter Roberson on 13 Mar 2023
M = double(strel('disk',5).Neighborhood)
M = 9×9
0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0
E = simplify(eig(sym(M)))
E =
vpa(E)
ans =
(the imaginary component is due to round-off error)
M2 = double(strel('octagon',12).Neighborhood)
M2 = 25×25
0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
E2 = simplify(eig(sym(M2)))
E2 =
vpa(imag(E2))
ans =
vpa(E2)
ans =
Bjorn Gustavsson on 15 Mar 2023
The/One benefit of using svd instead of eig is that one get real singular values - which is not a guarantee with eig. Appart from that the soutions should be comparable/similar/identical.

Bjorn Gustavsson on 13 Mar 2023
If you have a binary image then why not just run through the svd and see what you get:
I = zeros(256);
I(64:(64+128),64:(64+128)) = 1;
[U,S,V] = svd(I);
figure
subplot(1,2,1)
plot(diag(S))
subplot(1,2,2)
imagesc(U(:,1)*S(1,1)*V(:,1)')
% Or for a funnier example:
I = numgrid('B',258);
I = I(2:end-1,2:end-1);
[U,S,V] = svd(I);
subplot(2,2,1)
plot(diag(S))
subplot(2,2,2)
imagesc(U(:,1)*S(1,1)*V(:,1)')
subplot(2,2,2)
imagesc(U(:,1:4)*S(1:4,1:4)*V(:,1:4)')
subplot(2,2,2)
imagesc(U(:,1:16)*S(1:16,1:16)*V(:,1:16)')
You can also look at the individual eigen-images by something like:
imagesc(U(:,7)*V(:,7)')
HTH

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