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Given a blob of an image (representing an object), according to Wikipedia, we can compute the co-variance matrix using the image moments.

I understand that the eigenvectors of that matrix can be used to represent the principal axes of an oriented bounding box (OBB), but what are the guarantees for that particular orientation? Is the OBB the one with minimal area? And, are the eigenvectors always orthogonal?

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The eigenvectors will always be orthogonal. There is no guarantee that the eigenvectors will give you the bounding box with minimal area.

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  • $\begingroup$ Thanks for the update. Do you have references/citations on that? Also with the reasons behind that? $\endgroup$ – Domi Dec 6 '13 at 6:02
  • $\begingroup$ Are you working in 2 dimensions? I think the error can actually be quite high in higher dimensions. There are other algorithms that give you an optimal bounding box if that's what you need. $\endgroup$ – Aaron Dec 6 '13 at 7:51
  • $\begingroup$ It's two dimensions - Image processing. What error do you mean? $\endgroup$ – Domi Dec 6 '13 at 7:54
  • $\begingroup$ The error would be the difference between the optimal bounding box and the once you get with PCA $\endgroup$ – Aaron Dec 6 '13 at 16:36
  • $\begingroup$ Ok. Can you give any citations/books/articles/papers or similar on that? $\endgroup$ – Domi Dec 6 '13 at 16:56

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