# Purpose of eigenspace of covariance matrix of a blob?

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?

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

• Thanks for the update. Do you have references/citations on that? Also with the reasons behind that?
– Domi
Commented Dec 6, 2013 at 6:02
• 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. Commented Dec 6, 2013 at 7:51
• It's two dimensions - Image processing. What error do you mean?
– Domi
Commented Dec 6, 2013 at 7:54
• The error would be the difference between the optimal bounding box and the once you get with PCA Commented Dec 6, 2013 at 16:36
• Ok. Can you give any citations/books/articles/papers or similar on that?
– Domi
Commented Dec 6, 2013 at 16:56