title: Fit Quadrilateral (Tetragon) to a blob
body: <p>After applying different filtering and segmentation techniques, I end up with an image like this:</p>
  
  <p><a href="https://i.stack.imgur.com/XwzWQ.png" rel="noreferrer"><img src="https://i.stack.imgur.com/XwzWQ.png" alt="enter image description here"></a></p>
  
  <p>I have access to some contours detection functions that return a list of points on the edge of that object, or returns a fitted polygon (with many edges though, much more than 4).
  I want a way to fit a quadrilateral to that shape as I know it is a front face of a shoebox that is supposed to be a quadrilateral. Due to the perspective view, the parallelity is not conserved so I have no constraints for now and just need four line segments encompassing this box.</p>
  
  <p>What I could find until now was only rectangle fitting, which doesn't really returns the result I need as it forces the fitted quadrilateral to be rectangular.</p>
  
  <p>If I had access to the relative angle of the camera to that shoebox and knew the distance of the shoebox from my camera, I could generate a Homography matrix and warp the image such that the shoebox appears rectangular again, but for now I have no access to such information and want to do it based purely vision.</p>
  
  <p>Any known approaches for solving such a problem?</p>