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Convert keypoint to ellipse


Keypoints in openCV have an orientation and zize, but that's not enough to convert them to an ellipse that describes the region (There are an infinite number of ellipses with the same orientation and size).

I noticed that in the feature2d evaluation file:

they somehow convert a keypoint to an ellipse, but I can't figure out how they uniquely determine the size of the axes.

Can someone please shed some light on this?