title: Covariance Matrix of an Ellipse
body: <p>I've been trying to solve a problem. I'm surprised I haven't been able to find anything really useful on the net.</p>
  
  <p>I know that from the eigenvalues of the covariance matrix of the ellipse, the major and the minor axis of the ellipse can be computed. As the following: </p>
  
  <pre><code>a1 = 2*sqrt(e1)
  a2 = 2*sqrt(e2)
  </code></pre>
  
  <p>where <code>a1</code> and <code>a2</code> are the major and minor axis, <code>e1</code> and <code>e2</code> are the eigenvalues of covariance matrix.</p>
  
  <p>My question is:  given an edge points <code>(xi,yi)</code> of the image ellipse, how it possible to find the 2×2 covariance matrix of that ellipse?</p>