Calculating the eigenvalues of simple shapes

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John Bach
John Bach 2023-3-13
编辑： John Bach 2023-3-25
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.
Thank you in advance,
  1 个评论
the cyclist
the cyclist 2023-3-13
编辑：the cyclist 2023-3-13
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?

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采纳的回答

Walter Roberson
Walter Roberson 2023-3-13
Ran in:
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 = 
  1 个评论
Bjorn Gustavsson
Bjorn Gustavsson 2023-3-15
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.

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更多回答（1 个）

Bjorn Gustavsson
Bjorn Gustavsson 2023-3-13
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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